# TRM Instruments: Processing And Calculations Instrument Guide

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www.wallstreetsystems.com Wall Street Systems – Empowering Treasury Trade and Settlement Wallstreet Suite Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations Version 7.3.14 Information in this document is subject to change without notice and does not represent a commitment on the part of Wall Street Systems. The software and documentation, which includes information contained in any databases, described in this document is furnished under a license agreement or nondisclosure agreement and may only be used or copied in accordance with the terms of the agreement. It is against the law to copy the software or documentation except as specially allowed in the license or nondisclosure agreement. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of Wall Street Systems. Although Wall Street Systems has tested the software and reviewed the documentation, Wall Street Systems makes herein no warranty or representation, either expressed or implied, with respect to software or documentation, its quality, performance, marketability, or fitness for a particular purpose. As a result, this software is provided "as is", and in no event will Wall Street Systems be liable for direct, indirect, special, incidental, or consequential damages from any defect in the software or by virtue of providing this documentation, even if advised of the possibility of such damages. The documentation may contain technical inaccuracies and omissions. The mention of an activity or instrument in this publication does not imply that all matters relating to that activity or instrument are supported by Wallstreet Suite, nor does it imply that processing of or by that activity or instrument is carried out in any particular way, even if such processing is customary in some or all parts of the industry. The windows and screen images shown herein were obtained from prototypes during software development. The actual windows and screen images in the software may differ. © Copyright 2011 Wall Street Systems IPH AB. All rights reserved. Second Edition (May 2011) This edition applies to Wallstreet Suite version 7.3.14 and to all later releases and versions until indicated in new editions or Wall Street Systems communications. Make sure you are using the latest edition for the release level of the Wall Street Systems product. Wall Street Systems, WSS, WALLSTREET, WALLSTREET SUITE and the Wall Street Systems logos are trademarks of Wall Street Systems Delaware, Inc. Finance KIT, Trema and Trema logo are trademarks of Wall Street Systems Sweden AB. Microsoft and Windows are either registered trademarks or trademarks of Microsoft Corporation in the United States and/or other countries. Adobe, Acrobat, and Acrobat Reader are either registered trademarks or trademarks of Adobe Systems Incorporated in the United States and/or other countries. All other products mentioned in this book may be trademarks or service marks of their respective companies or organizations. Company names, people names, and data used in examples are fictitious unless otherwise noted. 2 Contents Preface ...........................................................................................................................19 Intended audience ........................................................................................................................ 19 Associated documents ................................................................................................................ 19 Change history ............................................................................................................................. 20 1 Concepts ....................................................................................................................21 1.1 Instruments ............................................................................................................................ 21 1.2 Classes and types ................................................................................................................. 21 1.2.1 Creating types ................................................................................................................. 22 1.2.2 Customizing types ........................................................................................................... 22 1.3 Instrument templates ............................................................................................................ 23 1.4 Groups ................................................................................................................................... 23 1.5 Features ................................................................................................................................. 24 1.5.1 Primary and trading features ........................................................................................... 25 1.5.2 Action features ................................................................................................................ 25 1.5.3 Valuation approach and valuation setup features ........................................................... 25 1.6 Schedules .............................................................................................................................. 25 1.7 Deal capture ........................................................................................................................... 27 1.7.1 Input data ........................................................................................................................ 27 1.7.2 Generated data ............................................................................................................... 27 1.8 Processing ............................................................................................................................. 28 1.8.1 Setup ............................................................................................................................... 28 1.8.2 Execution ........................................................................................................................ 29 1.8.3 Cancellation .................................................................................................................... 29 1.9 Valuation and results ............................................................................................................ 29 1.9.1 Market value ................................................................................................................... 29 1.9.2 Profits and results ........................................................................................................... 29 1.9.3 Valuation modes ............................................................................................................. 30 2 Market standards and calculations .........................................................................33 2.1 Market standards .................................................................................................................. 33 2.1.1 Date basis ....................................................................................................................... 33 2.1.2 Interest types .................................................................................................................. 37 2.1.3 Price types ...................................................................................................................... 38 2.1.4 Yield/price conversions ................................................................................................... 38 2.1.5 Discount Margin .............................................................................................................. 66 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 3 2.1.6 Calculation methods ....................................................................................................... 67 2.2 Yield curves ........................................................................................................................... 81 2.2.1 Yield curve ...................................................................................................................... 81 2.2.2 Basis swaps .................................................................................................................... 91 2.2.3 Yield Curve interpolation ................................................................................................. 98 2.2.4 FX rate interpolation ...................................................................................................... 110 2.3 Key-figures .......................................................................................................................... 112 2.3.1 Valuation ....................................................................................................................... 112 2.3.2 Profit and Loss .............................................................................................................. 113 2.3.3 Option figures ................................................................................................................ 115 2.3.4 Risk ............................................................................................................................... 119 2.3.5 Dual currency ................................................................................................................ 147 2.4 Performance calculations .................................................................................................. 149 2.4.1 Actual basis and all cash basis ..................................................................................... 150 2.4.2 Trade date and value date based performance ............................................................ 150 2.4.3 Time-weighted rate of return (TWR) ............................................................................. 151 2.4.4 Money-weighted return ................................................................................................. 154 2.4.5 Instrument market values for third currency .................................................................. 155 2.4.6 Instrument market values and cashflows ...................................................................... 160 2.4.7 Example portfolio .......................................................................................................... 163 2.4.8 Risk-adjusted returns .................................................................................................... 166 2.4.9 Risk-adjusted return measures ..................................................................................... 175 2.4.10 Performance attribution ............................................................................................... 180 2.4.11 Performance measurement key-figures ...................................................................... 189 2.5 Value-at-Risk calculations .................................................................................................. 200 2.5.1 TRM approach to VaR calculations .............................................................................. 201 2.5.2 RiskMetrics data ........................................................................................................... 201 2.5.3 Market variables ............................................................................................................ 202 2.5.4 Transforming RiskMetrics data ..................................................................................... 204 2.5.5 VaR calculations ........................................................................................................... 207 2.5.6 Incremental VaR ........................................................................................................... 212 3 Debt instruments .....................................................................................................215 3.1 Bond ..................................................................................................................................... 215 3.1.1 Fixed-rate bond ............................................................................................................. 215 3.1.2 Floating rate note .......................................................................................................... 228 3.1.3 Australian floating rate note .......................................................................................... 236 3.1.4 Zero-coupon bond ......................................................................................................... 239 3.1.5 Amortizing bond ............................................................................................................ 241 3.1.6 Step-up bond ................................................................................................................ 243 3.2 Structured bonds ................................................................................................................ 244 3.2.1 Callable bond ................................................................................................................ 244 3.2.2 Dual-currency bond ....................................................................................................... 246 3.2.3 Credit step-up bond ...................................................................................................... 249 3.3 Schuldscheindarlehen ........................................................................................................ 250 3.3.1 Instrument setup ........................................................................................................... 250 4 © Wall Street Systems IPH AB - Confidential 3.3.2 Deal capture .................................................................................................................. 251 3.3.3 Processing .................................................................................................................... 251 3.3.4 Position monitoring ....................................................................................................... 251 3.4 Denominated bond .............................................................................................................. 254 3.4.1 Instrument setup ........................................................................................................... 254 3.4.2 Deal capture .................................................................................................................. 255 3.4.3 Processing .................................................................................................................... 256 3.4.4 Position monitoring ....................................................................................................... 256 3.5 Convertible bond ................................................................................................................. 258 3.5.1 Instrument setup ........................................................................................................... 258 3.5.2 Deal capture .................................................................................................................. 259 3.5.3 Processing .................................................................................................................... 259 3.6 Index-linked bond ............................................................................................................... 260 3.6.1 Instrument setup ........................................................................................................... 260 3.6.2 Deal capture .................................................................................................................. 262 3.6.3 Processing .................................................................................................................... 262 3.6.4 Australian index-linked annuity bond ............................................................................ 263 3.6.5 Australian index-linked bond ......................................................................................... 267 3.6.6 Brazilian (LFT) selic-linked security .............................................................................. 270 3.6.7 Brazilian FX-linked NBC-E/NTN-D ................................................................................ 271 3.6.8 Brazilian inflation-linked NTN ........................................................................................ 272 3.6.9 Canadian real return bond ............................................................................................ 273 3.6.10 French OAT€i .............................................................................................................. 274 3.6.11 Greek index-linked bond ............................................................................................. 277 3.6.12 Israeli index-linked bond ............................................................................................. 279 3.6.13 Italian BTP €i ............................................................................................................... 281 3.6.14 Japanese index-linked bond ....................................................................................... 282 3.6.15 Swedish index-linked bond ......................................................................................... 283 3.6.16 UK index-linked gilt ..................................................................................................... 287 3.6.17 US Tips ....................................................................................................................... 292 3.7 Asset backed security ........................................................................................................ 297 3.7.1 Instrument setup ........................................................................................................... 297 3.7.2 Deal capture .................................................................................................................. 299 3.7.3 Processing .................................................................................................................... 300 3.7.4 Position monitoring ....................................................................................................... 302 3.7.5 Australian MBS ............................................................................................................. 302 3.8 Short term loan .................................................................................................................... 305 3.8.1 Instrument setup ........................................................................................................... 306 3.8.2 Deal capture .................................................................................................................. 307 3.8.3 Processing .................................................................................................................... 308 3.8.4 Position monitoring ....................................................................................................... 311 3.9 Discount paper .................................................................................................................... 316 3.9.1 Instrument setup ........................................................................................................... 316 3.9.2 Deal capture .................................................................................................................. 317 3.9.3 Processing .................................................................................................................... 319 3.9.4 Position monitoring ....................................................................................................... 320 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 5 3.10 Loan .................................................................................................................................... 326 3.10.1 Fixed-rate loan ............................................................................................................ 326 3.10.2 Floating-rate loan ........................................................................................................ 337 3.10.3 Other loan structures .................................................................................................. 340 4 Equities ....................................................................................................................345 4.1 Equity ................................................................................................................................... 345 4.1.1 Instrument setup ........................................................................................................... 345 4.1.2 Deal capture .................................................................................................................. 346 4.1.3 Processing .................................................................................................................... 347 4.1.4 Position monitoring ....................................................................................................... 352 5 Security lending ......................................................................................................355 5.1 Repurchase agreement ...................................................................................................... 355 5.1.1 Repo (classic) ............................................................................................................... 355 5.1.2 Buy/sell back and sell/buy back .................................................................................... 362 5.1.3 Floating Repo ................................................................................................................ 363 5.1.4 Collateral ....................................................................................................................... 365 5.1.5 Substitution ................................................................................................................... 366 5.1.6 Margin movement ......................................................................................................... 370 5.1.7 Cash Collateral ............................................................................................................. 376 5.2 Security loan ........................................................................................................................ 380 5.2.1 Instrument setup ........................................................................................................... 380 5.2.2 Deal capture .................................................................................................................. 380 5.2.3 Processing .................................................................................................................... 381 6 Forex ........................................................................................................................383 6.1 FX spot and FX forward ...................................................................................................... 383 6.1.1 Instrument setup ........................................................................................................... 383 6.1.2 Market information ........................................................................................................ 384 6.1.3 Deal capture .................................................................................................................. 384 6.1.4 Processing .................................................................................................................... 387 6.1.5 Position monitoring ....................................................................................................... 393 6.2 Average FX rate forward ..................................................................................................... 406 6.2.1 Instrument setup ........................................................................................................... 406 6.2.2 Deal capture .................................................................................................................. 406 6.2.3 Processing .................................................................................................................... 408 6.2.4 Position monitoring ....................................................................................................... 409 6.3 Open Window FX Forward (FX Time Option) ................................................................... 409 6.3.1 Instrument setup ........................................................................................................... 410 6.3.2 Deal capture .................................................................................................................. 410 6.3.3 Processing .................................................................................................................... 411 6.3.4 Position monitoring ....................................................................................................... 411 6.4 FX swap ................................................................................................................................ 416 6.4.1 Instrument setup ........................................................................................................... 416 6 © Wall Street Systems IPH AB - Confidential 6.4.2 Market information ........................................................................................................ 418 6.4.3 Deal capture .................................................................................................................. 418 6.4.4 Processing .................................................................................................................... 420 6.4.5 Position monitoring ....................................................................................................... 422 6.5 Cost-of-funding FX swap .................................................................................................... 422 6.5.1 Instrument setup ........................................................................................................... 423 6.5.2 Deal capture .................................................................................................................. 423 6.5.3 Processing .................................................................................................................... 424 6.5.4 Position monitoring ....................................................................................................... 424 7 Index .........................................................................................................................425 7.1 Index types .......................................................................................................................... 425 7.2 Instrument setup ................................................................................................................. 426 7.2.1 Simple Index ................................................................................................................. 426 7.2.2 Composite Index ........................................................................................................... 427 7.2.3 Derived Index ................................................................................................................ 430 7.2.4 Performance averaging index ....................................................................................... 433 7.2.5 Performance totaling index ........................................................................................... 436 7.3 Market information .............................................................................................................. 440 7.4 Processing ........................................................................................................................... 440 7.4.1 Revision ........................................................................................................................ 440 7.4.2 Freezing Index Values .................................................................................................. 440 7.4.3 Updating Factors and Cash .......................................................................................... 441 7.4.4 Rebalancing .................................................................................................................. 441 8 Cash .........................................................................................................................443 8.1 Bank account ....................................................................................................................... 443 8.1.1 Instrument setup ........................................................................................................... 443 8.1.2 Deal capture .................................................................................................................. 444 8.1.3 Processing .................................................................................................................... 445 8.2 Call account ......................................................................................................................... 446 8.2.1 Instrument setup ........................................................................................................... 446 8.2.2 Deal capture .................................................................................................................. 447 8.2.3 Processing .................................................................................................................... 447 8.3 Call money ........................................................................................................................... 450 8.3.1 Instrument setup ........................................................................................................... 450 8.3.2 Deal capture .................................................................................................................. 451 8.3.3 Processing .................................................................................................................... 451 8.3.4 Position monitoring ....................................................................................................... 454 8.4 Cash ..................................................................................................................................... 454 8.4.1 Payment ........................................................................................................................ 454 8.4.2 Transfer ......................................................................................................................... 455 8.4.3 Complex payment ......................................................................................................... 457 8.5 Forecast ............................................................................................................................... 459 8.5.1 Instrument setup ........................................................................................................... 459 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 7 8.5.2 Deal capture .................................................................................................................. 459 8.5.3 Processing .................................................................................................................... 459 8.6 Cost-of-carry ........................................................................................................................ 460 8.6.1 Instrument setup ........................................................................................................... 461 8.6.2 Deal capture .................................................................................................................. 462 8.6.3 Processing .................................................................................................................... 462 9 Futures .....................................................................................................................465 9.1 Forward rate agreement ..................................................................................................... 465 9.1.1 FRA deposit and FRA discount ..................................................................................... 465 9.1.2 Australian FRA .............................................................................................................. 476 9.1.3 Swedish FRA ................................................................................................................ 477 9.2 Bond forward ....................................................................................................................... 479 9.2.1 Bond forward ................................................................................................................. 479 9.2.2 Swedish Bond forward .................................................................................................. 482 9.3 Money market future ........................................................................................................... 485 9.3.1 Money market future (single contract) .......................................................................... 485 9.3.2 Money market future chain ........................................................................................... 503 9.4 Bond future .......................................................................................................................... 506 9.4.1 Bond future ................................................................................................................... 506 9.4.2 CTD future .................................................................................................................... 509 9.4.3 Australian bond future ................................................................................................... 518 9.5 Equity future ........................................................................................................................ 519 9.5.1 Instrument setup ........................................................................................................... 519 9.5.2 Deal capture .................................................................................................................. 521 9.5.3 Processing .................................................................................................................... 521 9.6 FX future .............................................................................................................................. 523 9.6.1 Instrument setup ........................................................................................................... 523 9.6.2 Deal capture .................................................................................................................. 525 9.6.3 Processing .................................................................................................................... 525 9.6.4 Position monitoring ....................................................................................................... 527 9.7 Index future .......................................................................................................................... 529 9.7.1 Instrument setup ........................................................................................................... 530 9.7.2 Deal capture .................................................................................................................. 531 9.7.3 Processing .................................................................................................................... 531 10 Options ...................................................................................................................533 10.1 Cap/floor/collar .................................................................................................................. 533 10.1.1 Vanilla cap/floor/collar ................................................................................................. 533 10.1.2 Exotic cap/floor/collar .................................................................................................. 544 10.2 Swaption ............................................................................................................................ 546 10.2.1 Instrument setup ......................................................................................................... 547 10.2.2 Deal capture ................................................................................................................ 548 10.2.3 Processing .................................................................................................................. 549 10.2.4 Position monitoring ..................................................................................................... 550 8 © Wall Street Systems IPH AB - Confidential 10.3 Option on MM future ......................................................................................................... 559 10.3.1 Instrument setup ......................................................................................................... 560 10.3.2 Market information ...................................................................................................... 562 10.3.3 Deal capture ................................................................................................................ 562 10.3.4 Processing .................................................................................................................. 563 10.3.5 Position monitoring ..................................................................................................... 564 10.3.6 Australian MM Future option ....................................................................................... 568 10.4 Bond option ....................................................................................................................... 569 10.4.1 Instrument setup ......................................................................................................... 570 10.4.2 Deal capture ................................................................................................................ 572 10.4.3 Processing .................................................................................................................. 573 10.5 Bond Future Option .......................................................................................................... 574 10.5.1 Instrument setup ......................................................................................................... 574 10.5.2 Australian Bond Future Option .................................................................................... 574 10.6 Equity option ..................................................................................................................... 575 10.6.1 Instrument setup ......................................................................................................... 576 10.6.2 Deal capture ................................................................................................................ 577 10.6.3 Processing .................................................................................................................. 578 10.6.4 Position monitoring ..................................................................................................... 579 10.7 Index option ....................................................................................................................... 582 10.7.1 Instrument setup ......................................................................................................... 582 10.7.2 Deal capture ................................................................................................................ 583 10.7.3 Processing .................................................................................................................. 584 10.8 FX option ............................................................................................................................ 585 10.8.1 Vanilla FX option ......................................................................................................... 585 10.8.2 Digital FX option .......................................................................................................... 593 10.8.3 Barrier FX option ......................................................................................................... 596 10.8.4 Compound FX option .................................................................................................. 601 10.8.5 Average FX rate option ............................................................................................... 605 10.8.6 Position monitoring ..................................................................................................... 610 10.9 Exchange traded FX option .............................................................................................. 628 11 Swaps .....................................................................................................................629 11.1 Interest rate swap .............................................................................................................. 629 11.1.1 Single-currency IR swap ............................................................................................. 629 11.1.2 Asset swap .................................................................................................................. 656 11.1.3 Cross-currency swap .................................................................................................. 656 11.1.4 Brazilian IDxUSD Swap .............................................................................................. 677 11.1.5 Overnight index swap ................................................................................................. 677 11.1.6 Other swap structures ................................................................................................. 682 11.2 Total return swap .............................................................................................................. 682 11.2.1 Instrument setup ......................................................................................................... 683 11.2.2 Deal capture ................................................................................................................ 684 11.2.3 Processing .................................................................................................................. 685 11.3 Credit default swap ........................................................................................................... 688 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 9 11.3.1 11.3.2 11.3.3 11.3.4 11.3.5 Instrument setup ......................................................................................................... 688 Market information ...................................................................................................... 690 Deal capture ................................................................................................................ 690 Processing .................................................................................................................. 692 Position monitoring ..................................................................................................... 694 12 Commodities .........................................................................................................699 12.1 Gold .................................................................................................................................... 699 12.1.1 Gold deposit ................................................................................................................ 699 12.1.2 Gold IR swap .............................................................................................................. 702 12.2 Setting up commodities as currencies ........................................................................... 702 12.3 Commodity futures ........................................................................................................... 703 12.3.1 Setting up instruments ................................................................................................ 703 12.4 Commodity swaps and forwards ..................................................................................... 703 12.4.1 Schedule structure ...................................................................................................... 703 12.4.2 Setting up instruments ................................................................................................ 704 12.4.3 Deal capture ................................................................................................................ 705 13 Funds .....................................................................................................................707 13.1 Fund shares ....................................................................................................................... 707 13.1.1 Instrument setup ......................................................................................................... 707 13.1.2 Deal capture ................................................................................................................ 708 13.2 Fund fees ........................................................................................................................... 708 13.2.1 Instrument setup ......................................................................................................... 708 13.2.2 Deal capture ................................................................................................................ 710 13.2.3 Processing .................................................................................................................. 710 Appendix A: Features ............................................................................................................713 A.1 Categories of features ........................................................................................................ 713 A.2 List of features .................................................................................................................... 713 A.2.1 ABS - Asset Backed Security ....................................................................................... 713 A.2.2 ABS Valuation .............................................................................................................. 714 A.2.3 Accrual Yield Setup ...................................................................................................... 714 A.2.4 Allow Ad-Hoc Instructions ............................................................................................. 715 A.2.5 Allow Ad-Hoc Clients/Instructions ................................................................................. 715 A.2.6 Allow Forcing Type to Spot ........................................................................................... 715 A.2.7 Allow FX Currency Pair Shift ........................................................................................ 716 A.2.8 Allow Manual Classification .......................................................................................... 716 A.2.9 Allow Roll Over ............................................................................................................. 716 A.2.10 Allow Roll Over (Dual Currency) ................................................................................. 717 A.2.11 Allow Roll Over (FX) ................................................................................................... 717 A.2.12 Allow Roll Over (FX - Margin Result) .......................................................................... 718 A.2.13 Allow Roll Over (repo) ................................................................................................ 719 A.2.14 Allow Roll Over (Short Loan) ...................................................................................... 719 A.2.15 Allow Roll Over (Short Loan - Margin Result) ............................................................. 719 10 © Wall Street Systems IPH AB - Confidential A.2.16 A.2.17 A.2.18 A.2.19 A.2.20 A.2.21 A.2.22 A.2.23 A.2.24 A.2.25 A.2.26 A.2.27 A.2.28 A.2.29 A.2.30 A.2.31 A.2.32 A.2.33 A.2.34 A.2.35 A.2.36 A.2.37 A.2.38 A.2.39 A.2.40 A.2.41 A.2.42 A.2.43 A.2.44 A.2.45 A.2.46 A.2.47 A.2.48 A.2.49 A.2.50 A.2.51 A.2.52 A.2.53 A.2.54 A.2.55 A.2.56 A.2.57 A.2.58 A.2.59 A.2.60 A.2.61 A.2.62 A.2.63 Allow Roll Over (FX - Swap Style) .............................................................................. 720 Allow Roll Over (FX - Swap Style - Margin Result) .................................................... 720 Allow Roll Over (Guarantee) ....................................................................................... 720 Allow Security Loan .................................................................................................... 721 Allow Sight Account Transfer ..................................................................................... 721 Allow Signature Date .................................................................................................. 721 Allow Spread Curves .................................................................................................. 721 Allow Swap ................................................................................................................. 722 Allow Transaction Transfer ......................................................................................... 722 Allow Weight Difference ............................................................................................. 722 Allow Valuation Curves ............................................................................................... 723 Alternative Repayment Estimates .............................................................................. 723 Australian Bond Future Option ................................................................................... 724 Australian CIB ............................................................................................................. 724 Australian FRN ........................................................................................................... 724 Australian FRN Method .............................................................................................. 725 Australian IAB ............................................................................................................. 725 Australian IAB Valuation ............................................................................................. 725 Australian IAB (Round to 3) ........................................................................................ 725 Australian IAB Valuation (Round to 3) ........................................................................ 726 Australian IAB Par Curve Valuation ............................................................................ 726 Australian IAB Par Curve Valuation (Round to 3) ....................................................... 727 Australian Index-Linked Bond Valuation ..................................................................... 727 Australian MBS ........................................................................................................... 727 Australian MBS Valuation ........................................................................................... 728 Average FX Rate Forward .......................................................................................... 728 Average FX Rate Valuation ........................................................................................ 728 Average FX Rate Option ............................................................................................ 729 Average FX Rate Option Valuation ............................................................................ 729 Bank Account Balance ............................................................................................... 729 Bank Account Interest ................................................................................................ 730 Bank Account Valuation ............................................................................................. 732 Base IR Exposure Setup ............................................................................................ 732 Base IR Setup ............................................................................................................ 733 Base Valuation Setup ................................................................................................. 734 Bond ........................................................................................................................... 734 Bond - Brazilian LFT ................................................................................................... 737 Bond - Brazilian LFT Valuation ................................................................................... 737 Bond - Brazilian FX-Linked NBC ................................................................................ 737 Bond - Brazilian FX-Linked NBC Valuation ................................................................ 737 Bond - Brazilian Inflation-Linked NTN ........................................................................ 738 Bond - Brazilian Inflation-Linked NTN Valuation ........................................................ 738 Bond - Canadian RRB ................................................................................................ 738 Bond - Canadian Index-Linked Bond Valuation .......................................................... 738 Bond Denominations Setup ........................................................................................ 739 Bond Forward ............................................................................................................. 739 Bond Forward (Swedish) ............................................................................................ 740 Bond Forward Dates ................................................................................................... 741 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 11 A.2.64 Bond Forward Valuation ............................................................................................. 741 A.2.65 Bond - French OAT€i .................................................................................................. 741 A.2.66 Bond - French Index-Linked Bond Valuation .............................................................. 742 A.2.67 Bond Future ................................................................................................................ 742 A.2.68 Bond Future - Australian ............................................................................................. 743 A.2.69 Bond Future Valuation ................................................................................................ 743 A.2.70 Bond Future Option Valuation .................................................................................... 743 A.2.71 Bond - Greek Index-Linked Bond ............................................................................... 744 A.2.72 Bond - Greek Index-linked Bond Valuation ................................................................ 744 A.2.73 Bond - Israeli Index-Linked Bond ............................................................................... 744 A.2.74 Bond - Israeli Index-Linked Bond Valuation ............................................................... 745 A.2.75 Bond - Italian BTP€i .................................................................................................... 745 A.2.76 Bond - Italian Index-Linked Bond Valuation ............................................................... 745 A.2.77 Bond Option ................................................................................................................ 745 A.2.78 Bond Option Valuation ................................................................................................ 746 A.2.79 Bond Pricing ............................................................................................................... 746 A.2.80 Branch Codes ............................................................................................................. 747 A.2.81 Bootstrap Instrument .................................................................................................. 747 A.2.82 Call Account ............................................................................................................... 747 A.2.83 Call Account Valuation ............................................................................................... 749 A.2.84 Call Money .................................................................................................................. 750 A.2.85 Call Money Valuation .................................................................................................. 750 A.2.86 Cancel Provisional Settlements .................................................................................. 750 A.2.87 Cap/Floor/Collar ......................................................................................................... 751 A.2.88 Cap/Floor/Collar Valuation ......................................................................................... 751 A.2.89 Cashflow Charges ...................................................................................................... 751 A.2.90 Cash Collateral Account ............................................................................................. 752 A.2.91 Cash Payment ............................................................................................................ 754 A.2.92 Choose Coupon .......................................................................................................... 755 A.2.93 Collateral .................................................................................................................... 755 A.2.94 Collateral Delivery ...................................................................................................... 755 A.2.95 Collateral Setup .......................................................................................................... 756 A.2.96 Collateral Transfer ...................................................................................................... 756 A.2.97 Collateral Valuation .................................................................................................... 756 A.2.98 Competitive Premiums ............................................................................................... 756 A.2.99 Competitive Prices ...................................................................................................... 757 A.2.100 Competitive Rates .................................................................................................... 757 A.2.101 Competitive Rates (FX Swap) .................................................................................. 757 A.2.102 Complex Payment (cash) ......................................................................................... 757 A.2.103 Convertible Bond ...................................................................................................... 759 A.2.104 Convertible Bond Valuation ...................................................................................... 759 A.2.105 Convertible Bond Setup ............................................................................................ 759 A.2.106 Cost of Carry Balance .............................................................................................. 760 A.2.107 Cost of Carry Interest ............................................................................................... 760 A.2.108 Cost of Carry Valuation ............................................................................................ 761 A.2.109 Credit Client Setup ................................................................................................... 761 A.2.110 Credit Default Swap .................................................................................................. 762 A.2.111 Credit Default Swap Valuation .................................................................................. 763 12 © Wall Street Systems IPH AB - Confidential A.2.112 A.2.113 A.2.114 A.2.115 A.2.116 A.2.117 A.2.118 A.2.119 A.2.120 A.2.121 A.2.122 A.2.123 A.2.124 A.2.125 A.2.126 A.2.127 A.2.128 A.2.129 A.2.130 A.2.131 A.2.132 A.2.133 A.2.134 A.2.135 A.2.136 A.2.137 A.2.138 A.2.139 A.2.140 A.2.141 A.2.142 A.2.143 A.2.144 A.2.145 A.2.146 A.2.147 A.2.148 A.2.149 A.2.150 A.2.151 A.2.152 A.2.153 A.2.154 A.2.155 A.2.156 A.2.157 A.2.158 A.2.159 CreditManager position template .............................................................................. 764 Credit Rating ............................................................................................................. 764 Credit Default Swap Curve Setup ............................................................................. 764 Credit-Step-Up .......................................................................................................... 765 CTD Future ............................................................................................................... 765 Currency Conversion ................................................................................................ 767 Debt Flows Valuation (payment amount extraction) ................................................. 767 Delivery ..................................................................................................................... 767 Denominated Bond ................................................................................................... 767 Discount Paper ......................................................................................................... 768 Discount Paper OTC ................................................................................................ 770 Discount Valuation .................................................................................................... 770 Dividend Estimate ..................................................................................................... 771 Dual Currency ........................................................................................................... 771 Dual Currency Forecast ............................................................................................ 772 Equity ........................................................................................................................ 772 Equity Cash Dividend ............................................................................................... 773 Equity Conversion .................................................................................................... 773 Equity Detachment ................................................................................................... 774 Equity Future ............................................................................................................ 775 Equity Info ................................................................................................................. 776 Equity Option ............................................................................................................ 776 Equity Option Pricing ................................................................................................ 777 Equity Option Setup .................................................................................................. 777 Equity Option Valuation ............................................................................................ 778 Equity Return of Capital ............................................................................................ 778 Equity Split ................................................................................................................ 779 Estimation Curve Setup ............................................................................................ 780 Exotic Structure (Option) .......................................................................................... 780 Expiry Date Setup ..................................................................................................... 781 External Valuation .................................................................................................... 781 Fed Fund Future Chain ............................................................................................ 781 Fed Fund Future Dates ............................................................................................ 782 Fed Fund Future Par Valuation ................................................................................ 782 Fed Fund Future Valuation ....................................................................................... 783 Filtered Valuation ...................................................................................................... 783 Fixed Bond Valuation ............................................................................................... 783 Fixed IR Quote Valuation ......................................................................................... 783 Fixed IR Valuation .................................................................................................... 784 Fixed Quoted Valuation ............................................................................................ 784 Force Trade Date Performance ................................................................................ 784 Forecast .................................................................................................................... 784 Forecast Valuation .................................................................................................... 785 Forward Price Setup ................................................................................................. 785 FRA Dates ................................................................................................................ 785 Forward Rate Agreement (Deposit) .......................................................................... 786 Forward Rate Agreement (Discount) ........................................................................ 787 Forward Rate Agreement (Swedish) ........................................................................ 788 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 13 A.2.160 A.2.161 A.2.162 A.2.163 A.2.164 A.2.165 A.2.166 A.2.167 A.2.168 A.2.169 A.2.170 A.2.171 A.2.172 A.2.173 A.2.174 A.2.175 A.2.176 A.2.177 A.2.178 A.2.179 A.2.180 A.2.181 A.2.182 A.2.183 A.2.184 A.2.185 A.2.186 A.2.187 A.2.188 A.2.189 A.2.190 A.2.191 A.2.192 A.2.193 A.2.194 A.2.195 A.2.196 A.2.197 A.2.198 A.2.199 A.2.200 A.2.201 A.2.202 A.2.203 A.2.204 A.2.205 A.2.206 A.2.207 14 FRA Valuation .......................................................................................................... 789 FRA Option ............................................................................................................... 790 FRA Option Valuation ............................................................................................... 790 FRA Periods ............................................................................................................. 790 FRN Valuation .......................................................................................................... 791 Fund ......................................................................................................................... 791 Fund Fee Accrual and Realization .......................................................................... 792 Fund Fee Valuation .................................................................................................. 794 Future Dates ............................................................................................................. 795 Future Valuation ....................................................................................................... 795 FX ............................................................................................................................. 795 FX Cross Method ...................................................................................................... 796 FX Estimate (Forward) ............................................................................................. 797 FX Estimate (IR Difference) ...................................................................................... 797 FX Fixing .................................................................................................................. 797 FX Forward ............................................................................................................... 797 FX Future .................................................................................................................. 798 FX Future Netting ..................................................................................................... 798 FX Future Valuation .................................................................................................. 799 FX - Lagged FX Function ......................................................................................... 799 FX Margin Result ...................................................................................................... 800 FX Valuation ............................................................................................................. 800 FX Option ................................................................................................................. 800 FX Option Compound ............................................................................................... 801 FX Option Digital ...................................................................................................... 801 FX Option Listed ....................................................................................................... 802 FX Option Premium .................................................................................................. 803 FX Option Pricing ..................................................................................................... 803 FX Option Setup ....................................................................................................... 804 FX Option Valuation ................................................................................................. 805 FX Pricer (Forward) .................................................................................................. 805 FX Pricer (Option) ..................................................................................................... 806 FX Setup ................................................................................................................... 806 FX Swap ................................................................................................................... 807 FX Swap Cost-of-Funding ........................................................................................ 807 FX Swap Margin Result ............................................................................................ 808 FX Swap Quote Default ............................................................................................ 808 FX Swap Split ........................................................................................................... 810 FX Time Option ........................................................................................................ 810 FX Time Option Valuation ........................................................................................ 811 FX Trading Platform ................................................................................................. 811 Generic IR Valuation ................................................................................................ 811 Generic Loan ............................................................................................................ 812 Index ......................................................................................................................... 813 Index Averaging ........................................................................................................ 813 Index Composite ....................................................................................................... 814 Index Derived ........................................................................................................... 816 Index Estimate .......................................................................................................... 817 © Wall Street Systems IPH AB - Confidential A.2.208 A.2.209 A.2.210 A.2.211 A.2.212 A.2.213 A.2.214 A.2.215 A.2.216 A.2.217 A.2.218 A.2.219 A.2.220 A.2.221 A.2.222 A.2.223 A.2.224 A.2.225 A.2.226 A.2.227 A.2.228 A.2.229 A.2.230 A.2.231 A.2.232 A.2.233 A.2.234 A.2.235 A.2.236 A.2.237 A.2.238 A.2.239 A.2.240 A.2.241 A.2.242 A.2.243 A.2.244 A.2.245 A.2.246 A.2.247 A.2.248 A.2.249 A.2.250 A.2.251 A.2.252 A.2.253 A.2.254 A.2.255 Index Future ............................................................................................................. 818 Index - Lagged Index Function ................................................................................. 818 Index-Linked Bond .................................................................................................... 818 Index Option ............................................................................................................. 818 Index Option Setup ................................................................................................... 819 Index Option Valuation ............................................................................................. 820 Index Rebase (Index-Linked Bond) .......................................................................... 820 Index Totaling ........................................................................................................... 821 Index - UK Index Function ........................................................................................ 822 Index Valuation ......................................................................................................... 822 Instrument Quote Estimate ....................................................................................... 822 Internal Deal Mirroring .............................................................................................. 823 IR Derivative Valuation ............................................................................................. 823 IR Derivative Valuation Setup ................................................................................... 823 IR Pricer (Swap) ....................................................................................................... 824 IR Pricer (Swaption) ................................................................................................. 824 Issue ......................................................................................................................... 825 Japanese JGBi ......................................................................................................... 825 Japanese Index-Linked Bond Valuation ................................................................... 826 Loan Structure .......................................................................................................... 826 Manual Charges ....................................................................................................... 826 Margin Movement ..................................................................................................... 827 Maturity Date Setup .................................................................................................. 827 MM Future ................................................................................................................ 827 MM Future - Australian Bank Bill Future ................................................................... 828 MM Future - Australian 90-Day Bank Bill Future Chain ............................................ 829 MM Future - Money Market Future Chain ................................................................ 830 MM Future - Money Market 1M Future Chain .......................................................... 831 MM Future - Money Market 3M Future Chain .......................................................... 831 MM Future Method - Australian ................................................................................ 832 MM Future Dates ...................................................................................................... 832 MM Future Option ..................................................................................................... 833 MM Future Option - Australian Bank Bill Future Option ........................................... 834 MM Future Option Valuation ..................................................................................... 834 Money Market Future Par Valuation ......................................................................... 834 Money Market Future Valuation ............................................................................... 834 Mode Specific Method .............................................................................................. 835 Mode/Transaction Specific Method .......................................................................... 836 MtoM Instrument Setup ............................................................................................ 836 Netted Instrument ..................................................................................................... 837 Non Deliverable Forward FX Instrument .................................................................. 837 NumeriX Asset Swap Setup ..................................................................................... 838 NumeriX Setup ......................................................................................................... 839 NumeriX Single-Swap Valuation .............................................................................. 840 NumeriX Swap Valuation .......................................................................................... 841 NumeriX Valuation .................................................................................................... 841 Option Dates ............................................................................................................. 841 Option Premium ........................................................................................................ 842 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 15 A.2.256 A.2.257 A.2.258 A.2.259 A.2.260 A.2.261 A.2.262 A.2.263 A.2.264 A.2.265 A.2.266 A.2.267 A.2.268 A.2.269 A.2.270 A.2.271 A.2.272 A.2.273 A.2.274 A.2.275 A.2.276 A.2.277 A.2.278 A.2.279 A.2.280 A.2.281 A.2.282 A.2.283 A.2.284 A.2.285 A.2.286 A.2.287 A.2.288 A.2.289 A.2.290 A.2.291 A.2.292 A.2.293 A.2.294 A.2.295 A.2.296 A.2.297 A.2.298 A.2.299 A.2.300 A.2.301 A.2.302 A.2.303 16 Option Template Setup ............................................................................................. 842 Payment Agent ......................................................................................................... 842 Performance, Cash In/Out ........................................................................................ 843 Performance, FX Hedge ........................................................................................... 843 Performance, Index .................................................................................................. 843 Per-Leg Cashflow Valuation ..................................................................................... 844 Premium ................................................................................................................... 844 Premium Date Setup ................................................................................................ 844 Price Exposure Setup ............................................................................................... 845 Price Valuation ......................................................................................................... 845 Quote Default ........................................................................................................... 845 Quote Default (Australian FRN) ................................................................................ 846 Quote Default (Australian MBS) ............................................................................... 846 Quote Default (Chain) ............................................................................................... 847 Quote Default (Collateral) ......................................................................................... 847 Quote Default (Discount Paper OTC) ....................................................................... 847 Quote Default (FX) ................................................................................................... 848 Quote Default (Short Loan) ...................................................................................... 849 Quoted ...................................................................................................................... 849 Quoted Chain ........................................................................................................... 851 Range Accrual .......................................................................................................... 852 Repo Cash Delivery .................................................................................................. 853 Repo Cash Delivery (Floating) ................................................................................. 853 Repo Cash Delivery (Substitution) ........................................................................... 853 Repo Rounding ......................................................................................................... 854 Repo Valuation ......................................................................................................... 854 Repo Valuation (Floating) ......................................................................................... 854 Repurchase Agreement ............................................................................................ 854 Repurchase Agreement (Floating) ........................................................................... 856 Result ....................................................................................................................... 856 Result with Classification .......................................................................................... 857 RiskManager position template ................................................................................ 857 Risk Setup (BOND) .................................................................................................. 858 Risk Setup (FRN) ..................................................................................................... 858 Risk Venture Capital ................................................................................................. 859 Risk Yield .................................................................................................................. 859 Schedule Data .......................................................................................................... 859 Schedule Template Setup ........................................................................................ 859 Schuldschein ............................................................................................................ 860 Security Identifiers .................................................................................................... 860 Security Info .............................................................................................................. 861 Security Loan ............................................................................................................ 861 Settlement Setup ...................................................................................................... 861 Short Term Loan ....................................................................................................... 862 Short Term Loan Margin Result ............................................................................... 863 Short Term Loan Valuation ....................................................................................... 863 Single Swap Valuation .............................................................................................. 863 Special Issue ............................................................................................................ 864 © Wall Street Systems IPH AB - Confidential A.2.304 A.2.305 A.2.306 A.2.307 A.2.308 A.2.309 A.2.310 A.2.311 A.2.312 A.2.313 A.2.314 A.2.315 A.2.316 A.2.317 A.2.318 A.2.319 A.2.320 A.2.321 A.2.322 A.2.323 A.2.324 A.2.325 A.2.326 A.2.327 A.2.328 A.2.329 A.2.330 A.2.331 A.2.332 A.2.333 A.2.334 A.2.335 A.2.336 A.2.337 A.2.338 A.2.339 A.2.340 A.2.341 A.2.342 A.2.343 Spot Date Setup ....................................................................................................... 864 Spread Curve Setup ................................................................................................. 865 Substitution ............................................................................................................... 865 Swap ......................................................................................................................... 866 Swap (Book, FX Rate) .............................................................................................. 867 Swap (Deal, FX Rate) ............................................................................................... 867 Swap Valuation ......................................................................................................... 867 Swaption Valuation ................................................................................................... 868 Swaption Pricing ....................................................................................................... 868 Swap Per Leg Valuation ........................................................................................... 868 Swap Pricing ............................................................................................................. 868 Swaption ................................................................................................................... 869 Swap, Upfront ........................................................................................................... 869 Swedish Index-Linked Treasury Bond ...................................................................... 869 Swedish Index-Linked Bond Valuation ..................................................................... 870 Ticks Netting ............................................................................................................. 870 Trading Unit (Derivative) ........................................................................................... 871 Trading Unit (Equity) ................................................................................................. 871 Trading Unit (Index) .................................................................................................. 872 Trading Yield ............................................................................................................ 872 Transaction Charges ................................................................................................ 873 Transaction Conversion ............................................................................................ 873 Transfer (cash) ......................................................................................................... 874 TRS - Total Return Swap ......................................................................................... 875 TRS Deferred ........................................................................................................... 875 UK ILG (3M) ............................................................................................................. 876 UK ILG (8M) ............................................................................................................. 876 UK Index-Linked Bond (3M) Valuation ..................................................................... 876 UK Index-Linked Bond (8M) Valuation ..................................................................... 877 US Index-Linked Bond Valuation .............................................................................. 877 US TIPS .................................................................................................................... 877 US TIPS (with Rounding) ......................................................................................... 877 VaR Mapping Type ................................................................................................... 878 Valuation Curve Setup .............................................................................................. 878 Valuation Setup (Floating) ........................................................................................ 879 Value Date Setup ..................................................................................................... 879 Volatility Surface Setup ............................................................................................ 880 XAU Loan ................................................................................................................. 880 Yield .......................................................................................................................... 881 Z-DM/Spread Setup .................................................................................................. 882 Appendix B: Schedules .........................................................................................................883 B.1 Schedule parameters ......................................................................................................... 883 B.2 Templates ............................................................................................................................ 889 B.2.1 System-defined templates ............................................................................................ 889 B.2.2 User-defined templates ................................................................................................ 909 B.3 Schedule template groups ................................................................................................. 910 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 17 Appendix C: Option schedules .............................................................................................911 C.1 Option schedule parameters ............................................................................................. 911 C.2 Templates ............................................................................................................................ 913 C.2.1 System-defined templates ............................................................................................ 913 C.2.2 User-defined templates ................................................................................................ 915 C.3 Option schedule template groups .................................................................................... 915 Appendix D: Expressions......................................................................................................917 D.1 Expression syntax .............................................................................................................. 917 D.2 Market references in expressions ..................................................................................... 917 D.2.1 Using Fixing Quote ....................................................................................................... 917 D.2.2 Not using Fixing Quote ................................................................................................. 918 D.3 Constants in expressions .................................................................................................. 919 D.4 Functions in expressions .................................................................................................. 920 D.4.1 Basic functions ............................................................................................................. 920 D.4.2 Referring functions ....................................................................................................... 921 D.4.3 Special functions .......................................................................................................... 922 D.4.4 Special characters ........................................................................................................ 929 18 © Wall Street Systems IPH AB - Confidential Preface Welcome to the Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations guide. This guide describes the following for TRM: • The financial instruments that TRM supports and their required setup. • The calculations that TRM performs to produce the key-figures–market value, risk exposure, and profit/loss–used to analyze a position. Intended audience This guide is intended for TRM users who require information to support the following tasks: • Set up and customize instruments: For users with back office and middle office experience who have a good understanding of TRM. • Valuation: For experienced TRM users who need to understand how calculations are performed in TRM. Associated documents Associated documents can be accessed from the Help menu of the Wallstreet Suite’s applications. • TRM User Guide • TRM System Administration Guide • ACM User Guide • CLM User Guide • WebSuite User Guide. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 19 Change history Edition Date Changes Updated By 0.1 April 2011 Initial release 7.3.14. Features: Positive spread, Negative spread Bonds: Asset swap (minor changes) Dual currency: FX Fixing and Generic IR Valuation Risk profiles: Output (replaced the description) AI method: Australian Floater (3 decimals) Bond Futures: Position monitoring setup, Risk Setup (BOND) Yield/price conversion: Malaysian government bonds Bank Account, Cost of Carry, and Funds: Update Realization Date TRM Dev Team 0.2 May 2011 Israeli Index-Linked Bonds: time-dependent, Index Rebase TRM Dev Team 20 © Wall Street Systems IPH AB - Confidential Chapter 1 Concepts In the Wallstreet Suite Transaction & Risk Management Module (TRM), all instruments rely on the same key concepts. It is important to be familiar with these concepts to understand how the system works and to be able to use it effectively. TRM’s concepts are referred to frequently throughout this guide. Each one is explained in more detail in the relevant section. 1.1 Instruments In TRM, all instruments share several main characteristics: • Unique ID (and an optional Name) • Instrument Type (mandatory) (see 1.2 Classes and types on page 21 for more information) • Active From / Active To period (from/to dates inclusive) to restrict the period in which the • Instrument Group for use in rules, monitoring, and reporting • Labeling for Buy/Sell transactions (optional Buy Label and Sell Label naming) to override the default settings. instrument can be traded in TRM (optional) The following information is also available for each instrument: • History of all modifications made to an instrument since it was defined in the system • Links to documents or Web pages attached to the instrument which can be opened through the editor • User-defined properties that can be added to the instrument. Finally, an instrument is made up of features. Features are the most important of the key concepts. They are the building blocks of an instrument and are responsible for driving the processes in TRM. Features are explained in a later section of this chapter. First however, it is important to understand the concepts of instrument classes and types. 1.2 Classes and types The notion of instrument class is specific to TRM. Instrument classes denote the different categories of instruments which are supported by TRM. They are pre-defined in the system and cannot be changed by the user. An instrument class is only used as a basis on which to define an instrument type. Once the types have been defined, the instrument classes are no longer used. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 21 1 Concepts 1.2 Classes and types 1.2.1 Creating types The first step in defining instruments involves creating all the instrument types that are necessary to use the system. It is possible to create an infinite number of types with each class. However, it is not recommended to create instrument types that are based on an instrument class that you do not need. In contrast, you may wish to create more than one instrument type based on the same class to create more specific instrument definitions. For example, the Bond instrument class is used to define many different types of bonds instruments, such as fixed-rate bonds, floating-rate bonds, dual-currency bonds, and so on. Creating and customizing an instrument type for each type of bond makes it easier to define the instruments. Nevertheless, it is still possible to have only one instrument type, and differentiate the setup later, when the instrument is created. 1.2.2 Customizing types As mentioned in the earlier section, features are the most important of the key concepts. Features drive the behavior of an instrument in TRM. Each instrument class contains a set of available features: some features are mandatory, some are assigned by default, and others are optional. An instrument type is derived from an instrument class. The type inherits all the features contained in the instrument class automatically. Apart from mandatory features, which cannot be changed or removed, the default and optional features within the list can be modified as follows: • Default features can be made mandatory, optional, or be removed completely • Optional features can be made mandatory, default, or be removed completely. When the instrument type is assigned to an instrument, the instrument inherits the features as follows: • Mandatory features from the instrument type are assigned to the instrument and cannot be removed • Default features from the instrument type are assigned to the instrument but may be removed • Optional features from the instrument type can be manually applied to the instrument if required. For example, assume you need to define some fixed-rate bonds, some FRNs, and some dual-currency bonds in your system. You could simply create one Bond instrument type that exactly replicates the Bond instrument class. It will then be possible to set up any kind of bond instrument using this type. However, you may prefer to simplify the setup of bond instruments by creating three different instrument types based on the same instrument class. You could modify the set of features in the instrument class by selecting only the relevant features for each type of bond: • For the fixed-rate bond, you remove the features related to dual-currency, and everything related to floating-rates • For the FRN instrument, you assign as mandatory the FRN valuation method, and remove all features related to dual-currency, and anything else not related to an FRN • For the dual-currency bond, you assign as mandatory the Dual Currency feature, and remove anything else not related to the instrument you want to set up. By customizing an instrument type to correspond to a particular category of instrument, a significant part of the set up is done at type level making the task of setting up instruments much easier. It is important to keep in mind that the instrument type is a visible attribute of the instrument. Its definition is an important step in the process of instrument setup and therefore must be made with care. 22 © Wall Street Systems IPH AB - Confidential 1 Concepts 1.3 Instrument templates 1.3 Instrument templates Instrument templates use the framework of static data template editors. In the context of instrument setup, templates can be used to define more closely the characteristics of instruments that can be set up using a given instrument type, as follows: • The selected optional and default features of the given type can be modified to reflect more accurately the nature of instruments for which the template is designed. • Subentities and individual fields can be identified as mandatory or frozen in the instrument setup in a similar way to the features. Thus, you can control the instrument at the field level. • Values for default or frozen setup of the instrument can be already defined in the template. Thus, instruments based on a template, already inherits these configured values. As in with other static data templates, when you select a template in Instrument Editor, the template will automatically load all configured information, so that you only have to provide a limited set of values when you create the new instrument. For information about using the Instrument Template Editor, see TRM User Guide. 1.4 Groups Instrument groups facilitate reporting and monitoring of instruments and their subsequent transactions. They are also used in the setting up of rules as a means to identify individual cashflows in order to direct them to the correct place in the transaction flow. Each instrument is assigned to an instrument group during the setup process. Instrument groups are arranged into a simple hierarchy, where each group is assigned one parent. Instruments can only be assigned to a single instrument group in the hierarchy. Default instrument groups for the first level in the hierarchy are pre-defined in the system, but can be modified at implementation according to your organization’s requirements. You then create further instrument groups for the lower levels of the hierarchy to reflect the requirements of your organization. The first level of the hierarchy could typically represent the class of instruments in which you trade; such as Debt Instrument, Foreign Exchange, and Equity. Instrument groups in the second level could correspond to different types of instruments traded in these markets, and any lower levels would usually be created for instruments, which are derived from the same instrument type, but have different characteristics. Instrument groups from any level in the hierarchy can be used as a parameter when setting up reports or rules, and when monitoring instruments. The instrument group you use depends on how specific the rule, report, or position needs to be. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 23 1 Concepts 1.5 Features Consider the following example which illustrates how an instrument group hierarchy may be set up and used. Level 1 Level 2 Level 3 Level 4 In the example hierarchy, if the Government instrument group in level 4 is used as one of the parameters to run a report, the generated report will only contain data resulting from any Government Bonds assigned to this instrument group. Alternatively, if the Fixed-Rate Bond instrument group in level 3 is used as the start-up parameter, the resulting report will include data from both Corporate and Government Bonds. If an overview of all debt instruments is required in the report, the Debt Instrument group in level 1 should be selected. 1.5 Features The notion of the Instrument Class/Feature association is specific to TRM. Features are an integral part of setting up instruments. Features are system-defined entities used to give instruments their distinctive functionality and enable deal capture, transaction processing, and position monitoring. A feature is a combination of Setup and Process: • Setup refers to the number of database tables that are attached to a feature. It is only possible to populate the information related to these tables in the editor if the feature is attached to the instrument. • Process refers to the number of units of processing that are attached to a feature. The code that is linked to the feature is triggered only when the feature is attached to the instrument. The major benefits of this architecture are two-fold: • Setting up instruments becomes much easier because the system only proposes the necessary information according to the behavior required by the user for the instrument. • Processing is completely modular. This means that many independent units of code are triggered in sequence to handle the processing of the deals. This very low level dependency ensures an 24 © Wall Street Systems IPH AB - Confidential 1 Concepts 1.6 Schedules improved stability of the system should any modifications be made, and also an improved capacity for the addition of new processing features. Features are organized into the following categories: Primary, Trading, Action, Valuation, and Valuation Setup. These categories are pre-defined in the system and cannot be modified by the user. Features are frequently referred to throughout this guide. The combination of features associated with an instrument completely defines the instrument’s characteristics. Any parameters that need to be defined for the set up and processing of the features and their related actions are explained in more detail in the relevant section. Note: In Appendix A Features on page 713 you can find a list of the available features together with an explanation of how they are used. 1.5.1 Primary and trading features Primary features are responsible for the core deal generation (such as, transaction and cashflows), and core instrument setup. There can be only one primary feature associated with an instrument. Primary features contain the largest part of the business logic. They are used during instrument setup and throughout deal-entry. For example, the primary feature Bond enables the setup of the main characteristics of a bond and its associated cashflows. It also manages the creation and modification of a bond deal by calculating amounts and generating the cashflows. Trading features introduce additional setup possibilities and some additional rules for deal management. More than one trading feature can be applied to an instrument, and some trading features can be used for several different classes of instrument. For example, the trading feature Trading Unit enables the setup of a denomination size, a minimum bid size, and a minimum price unit for an instrument. It also ensures that this setup is verified when a deal is entered and will adjust the deal accordingly if the deal does not correspond to the setup. The processing units of primary and trading features are assigned with a priority number. This number ensures that the processes are executed in the correct order. 1.5.2 Action features Action features enable deal processing, some of which are also linked to a setup. The parameters defined in the setup are used when the action is performed. Action features are called each time the user wants to execute a business process. For example, the action feature Allow Roll Over (FX) enables roll over of FX forwards and FX swaps. 1.5.3 Valuation approach and valuation setup features Valuation Approach and Valuation Setup features work together: they determine which valuation approach is used for the instrument. With these features, it is possible to specify the market variables used in the valuation, such as yield curves, date basis, and discounting methods. Valuation can still be performed on an instrument even without any specific setup. In this case, the default settings for valuation are employed to find the market variables used to value the instrument. Note that, in TRM, as well as being responsible for calculating market value, the valuation approach is also responsible for calculating other figures, such as unrealized results and risk figures. 1.6 Schedules The concept of Schedules is used in several places in TRM. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 25 1 Concepts 1.6 Schedules There are two types of schedules; Schedules and Option Schedules: • Schedules are used for most debt instruments (and their derivatives): Asset Backed Securities, Bonds, Caps, Floors, and Collars, Loans, and Commercial Loans, Swaps, Total Return Swaps, and Swaptions. • Option Schedules are used for Exotic FX Options. Option schedules are a simplified version of schedules. They are used to enable the definition of option events, such as barriers or Bermudan exercise periods. In TRM, schedules and option schedules drive the generation of a set of cashflows. When the cashflow structure is frozen for an instrument, as is the case for Asset Backed Securities and Bonds, schedules are linked to the instrument itself, together with the generated cashflows. When the cashflow structure is not frozen (for example, with instruments such as Caps, Floors, and Collars, Loans, FX Options with Barriers, and so on), schedules can be associated with the deal instead of with the instrument. The cashflows are then generated at deal entry. Schedules contain a number of values that determine how a set of cashflows are generated. The information that can be defined in a schedule is explained in the appendices. TRM provides a number of Schedule Templates and Option Schedule Templates. A template groups together the prepackaged set of individual schedules that are necessary to set up a deal or type of instrument. Some of the characteristics of the deal or instrument are then used to automatically update many of the values in the schedule. When a template is applied, the schedules included in the template are simply copied onto the deal or instrument. Consequently, there is not a dynamic link between the deal or instrument and the schedule template. If any changes are subsequently made to a template, they are not reflected in the characteristics of the deal or instrument to which it had previously been applied. Many templates are provided by the system and users can use these as a basis on which to create their own. The following simple example illustrates the concept of schedules in TRM: • A 3-year fixed-rate loan paying 5% interest per annum with a bullet repayment of the principal amount A deal involving this instrument has two distinct types of cashflow: interest cashflows, and the principal payback cashflow. Two schedules need to be associated to the deal: one schedule to drive the creation of the interest cashflows, and another schedule to drive the creation of the principal payback cashflow. The following information is required for the interest schedule: 26 Type: Interest Category: Payback Start Date: Value date of the deal End Date: Maturity date of the deal Currency: Currency of the deal Method: Times/Year Frequency: 1 Rate Type: Interest Rate Rate: 5 © Wall Street Systems IPH AB - Confidential 1 Concepts 1.7 Deal capture The following information is required for the principal schedule: Type: Principal Category: Payback Start Date: Value date of the deal End Date: Maturity date of the deal Currency: Currency of the deal Method: Bullet TRM provides a system template (called Fixed, Bullet Repayment) which contains both these schedules. The template also contains some defaulting rules. As a result, when the schedule is applied to the instrument most of the information relating to the cashflow structure is defaulted automatically by TRM. Note: For more details about system templates and how they can be grouped or specialized into user templates, see Appendix B Schedules on page 883 and Appendix C Option schedules on page 911.) 1.7 Deal capture In TRM, dealing is carried out in Transaction Manager or in Enter Board. 1.7.1 Input data Some deal information that needs to be input is common to all transaction types, no matter what type of instrument is involved. This generic input data includes the following: • Instrument to be used in the deal • Opening Date of the deal when it is taken into account in the system • Portfolio that is impacted by the deal • Counterparty, that is, the other party involved in the deal. Other required input data is specific to an instrument type, for example, premium flow parameters for option transactions. Some input data can be defined either in the instrument definition or it can be specified at deal entry. 1.7.2 Generated data Some information is automatically set by the system on a new deal when the deal has been saved, such as: • Transaction Number which identifies the deal in the system • State which shows the transaction’s position in the workflow • Status, which gives additional information about the status of the deal. The deal’s associated cashflows, for example, interest flows, settlement or premium amounts, and position flows are generated, according to the instrument and its setup. Note: Deal capture information that is specific to an instrument type is explained in the relevant Deal capture section of this guide. For information about entering deals that is common to all instruments: see the TRM User Guide. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 27 1 Concepts 1.8 Processing 1.8 Processing Processing deals in TRM is mainly done through Transaction Manager; although some back office operations are performed using activities. There are a number of commands that can be performed on all deals. These commands are used to save, reject, or cancel a deal and move the deal through TRM’s process flow, and include: • Apply, Commit, Accept, Reject, Re-Open, and so on These commands are used to move a transaction to a different state in the workflow. The new state of the transaction when one of these actions is performed depends on how the transaction flow has been defined for the system. • Reset The Reset command resets all changes made to a deal since the last time it was saved in the system. If the reset command is performed on a new deal, the deal is removed. • Cancel Using this command, it is possible to cancel a deal which has been entered in error. Another of the concepts on which TRM is based is that of actions. An action is something you can execute on a deal (or several deals) in order to perform a business task. Some actions are available for all instruments, either by default, or through the addition of a feature: • Duplicate This action creates a new deal with the same characteristics as the initial transaction, apart from Transaction Number and State. After the deal has been duplicated, it is possible to change some of the characteristics of the new deal. This is a useful function when you need to create many deals with similar characteristics using the same instrument. • Package The Package action assigns a deal to a package. Packaging several deals together creates a link between them. Packages can be used as criteria in position monitoring or reports. • Add Transaction Charge or Cashflow Charge These actions allow you to add one or more charges to a deal. They are available when the respective feature is applied to the instrument. The charges are stored as separate cashflows. Many actions are specific to certain instruments, and details of these can be found in the relevant Processing section of this guide. Examples of instrument-specific actions in TRM are: Early Expiration of a loan; Exercise of an option; Fixing of a cashflow; and the Netting of a future. These actions are often only available once the deal has reached a certain stage in the process flow. Note: See the TRM User Guide for more information about executing actions on deals and processing deals through the transaction flow. 1.8.1 Setup The ability to execute certain actions on an instrument can either be linked to the presence of instrument-specific features applied to the instrument definition, or for other instruments, the execution is automatically included in the instrument setup. In all cases, the availability of an action can be made dependent on the state of the transaction. For example, it is possible to allow a tax to be added for newly entered transactions, but not for confirmed ones. 28 © Wall Street Systems IPH AB - Confidential 1 Concepts 1.9 Valuation and results 1.8.2 Execution The availability of the action is also often driven by certain conditions that are built into the action itself. The exercise of an option for example, recognizes that it can only be executed during the exercise period. The exercise action is unavailable outside the exercise period. Many frequently performed actions can be automated through batch activities. It is important to note that the batch activity executes exactly the same code as the user for the execution of the action. 1.8.3 Cancellation Sometimes, it is necessary to cancel the execution of an action. In TRM, all actions can be canceled or reversed. 1.9 Valuation and results 1.9.1 Market value In TRM, market value can be calculated using two different valuation methods: • Quoted valuation method which is a direct mark-to-market quote of an instrument • Theoretical valuation method which is a theoretical valuation model defined in the system. Generally, quotes can be obtained from the market for exchange-traded (listed) instruments and can be applied directly to establish the market value of a position, whereas over-the-counter (OTC) transactions need to be valued using a theoretical model. Theoretical models are set up in TRM and can range from models used for simple discounting of cashflows to complex multi-factor option valuation models. Regardless of the approach taken, users have two additional decisions to make that will have a minor impact on the market value of each position. More specifically, for each instrument, the following needs to be defined: • • Market value calculation period – If market value is calculated to the spot date (as of the valuation date) of the instrument – If market value is discounted from the spot date to the valuation date of the instrument. Market value calculation of foreign currency positions (into the base currency of the portfolio or another currency) – If market value is calculated using the spot rate between the two currencies – If the spot rate is further adjusted by O/N and T/N points – If the spot rate is adjusted by the interest rate differential between the two currencies from valuation date to spot date. 1.9.2 Profits and results The market value is used when calculating the total profit of a position. In TRM, the term profit refers to the profit/loss on a position at a given point in time since its inception or since a subsequent realization (for example, the payment of interest). The term result refers to the profit/loss over a specific period of time (for example, from January 1 to January 31). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 29 1 Concepts 1.9 Valuation and results In general terms, the market value of a position is compared to capital invested, and the difference is the total profit of the position. Total profit is further split into the following components (the exact description of each component may vary slightly according to the instrument): Profit Description Accrued Interest Interest accrued since the value date of the transaction or the previous coupon date until the valuation date. Accrued Profit Accrued/amortized discount/premium, accrued fees, or amortized option premiums since the value date of the transaction or the payment date of the premium/fee, until the valuation date. MtoM Profit Profit/loss resulting from the difference between market valuation (excluding accrued interest and accrued profit) and capital invested. For example, for instruments with a market quotation, MtoM profit is generally the difference between the market price and the deal price.However, when accruals and fees need to be taken into account, the calculation of MtoM Profit becomes more complex. MtoM profit is calculated to the spot date of the instrument, and not discounted to the valuation date. Note: For details of the MtoM Profit calculation for a particular type of instrument, see the relevant section of this guide. FX Profit Profit/loss resulting from the change in FX rates, between the value (or trade) date and the valuation date, calculated on the invested amount. Other Profit The residual profit/loss after the above components are separated from total profit. This residual is usually the end-product when total result is calculated correctly theoretically, but the other components are calculated according to general accounting practices. For example, the market value for a bond includes the accrued interest calculated until the spot date of the instrument (that is, the amount which would be received if the bond was sold today), while accrued interest includes the interest accrued until the valuation date. 1.9.3 Valuation modes Sometimes, it is necessary to calculate market value and results in different ways. For example, even if market value can be obtained from market quotes, occasionally it may be useful to run the valuation using a theoretical model. Furthermore, for accounting purposes, it may also be necessary to do the valuation using specific benchmark yield curves, and to apply specific accounting treatment for the difference between normal and benchmark valuation. Valuation modes allow users to define different valuation methods and models and to use different market parameters to value the same instrument. Every time valuation is requested by a user, the user specifies the valuation mode, and the system performs the valuation using the setup applicable to that mode. The standard system provides three different valuation modes: • Default • Theoretical • Benchmark. The valuation modes themselves are simply identifiers. Users need to specify the type of valuation that is to be carried out at instrument level. For example, if the Theoretical valuation mode is selected, the system will not switch automatically to a theoretical model. Rather, the user needs to link the appropriate valuation methods and models for each instrument, which are then called each time theoretical valuation is requested. Valuation Mode can be used as a start-up parameter for monitoring the treasury position, for running profit/loss reports, and for closing-the books. If no mode is specified, the system’s Default valuation mode is used. 30 © Wall Street Systems IPH AB - Confidential 1 Concepts 1.9 Valuation and results New valuation modes can be added during implementation according to your organization’s requirements. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 31 1 Concepts 1.9 Valuation and results 32 © Wall Street Systems IPH AB - Confidential Chapter 2 Market standards and calculations 2.1 Market standards 2.1.1 Date basis Date bases are used to calculate the length, in years, of the period between two dates. The formula for this calculation is t=d/B, where d is the number of days in the period, and B is the basis denominator. Both d and B depend on the date basis used. Different date bases may result in different values for d and B for the same period and, consequently, in different period lengths. TRM uses date bases when an interest rate is defined over a period. The definition of the rate must include how the length of the period is calculated. • 360 date bases In these date bases, the denominator B is always 360, but the calculation of the numerator varies. However, there is a difference in the way the 31st day at the beginning and at the end of the period under consideration is handled. The formulas used show how the period d between date1 (y1, m1, d1) and date2 (y2, m2, d2) is calculated: yi, mi, and di represent the year, month, and day, respectively; and min is the minimum value in the set. For example, min(d2, 30) means "use the lesser value of d2 and 30." • Actual date bases Actual date bases allow for different lengths of months and are, therefore, more accurate than the 360 date bases. The Actual date bases generally differ in the way that they handle leap years. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 33 2 Market standards and calculations 2.1 Market standards Example period 1991-06-30 to 1996-01-31 The period 1991-06-30 to 1996-01-31 is used in some of the following examples to show how the various date bases calculate the number of days between two dates. Name Description 30E/360 Any 31st day of the month is considered to be the 30th of the month. The formal definition is: d = min(d2,30) - min (d1,30) + 30(m2 - m1) + 360(y2 - y1) For the example period: d = min(31,30) - min(30,30) + 30*(1 - 6) + 360*(1996 -1991) = 1650 The length of the period in years is 1650/360 = 4.583 30E/360 EOM This is a variation of the 30E/360 basis, with the month of February having an invariable 30 days. Example: For the 2003-08-31 through 2004-02-29: d = min(30,30) min (31,30 + 30*(2 - 8 360*(2004 - 2003 = 180 The length of the period in years is 180/360 = 0.5 30/360 This is a variation of the 30E/360 basis. The difference occurs when d1 < 30. In this case, no rounding of the date occurs, and the above equation is replaced by: d = d2, - d1 + 30(m2 - m1) + 360(y2 - y1) For the example period: d1 = 30, so the 30E/360 formula is used and d = 1650 However, if the beginning of the period was the 29th instead of the 30th, the result would be: d = 31 - 29 + 30*(1 - 6) + 360*(1996 - 1991) = 1652 The length of the period in years would then be 1652/360 = 4.589. 30E+/360 This is a variation of the 30E/360 basis. The difference is that rounding is applied only to the earlier date. The equation is then: d = d2 - min(d1,30) + 30(m2 - m1) + 360(y2 - y1) For the example period: d = 31 - min(31,30) + 30*(1 - 6) + 360*(1996 -1991) = 1651 The length of the period in years is 1651/360 = 4.586 Actual/Actual ISDA If no leap year is involved in the calculation, then t = d/B where d = the actual number of days and B = 365. If there is a leap year, then t = d1/B1 + d2/B2, where d1 = the actual number of days in the leap year and B1 = 366 d2 = the actual number of days in the non-leap year and B2 = 365 Actual+/Actual ISDA Actual-/365 This is a variation on Actual/Actual ISDA, for which the first day is excluded for the day count. d = the actual number of days excluding all leap days (29th of February). B = 365 days. For the example period: The number of days between 1991-06-30 and 1996-01-31 is 1676, but since there is one leap day within that period, d = 1675. The length of the period in years, t, is 1675/365 = 4.589 Actual-/365+ d = the actual number of days excluding all leap days (29th of February). B = the number of days in the year in which the coupon value date falls. 34 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards Name Description Actual-/365L d = the actual number of days excluding all leap days (29th of February). B = 366 if the last partial year of the period contains a leap day; otherwise, B = 365. The last partial year is the remaining period when the maximum number of full years have been counted off, starting from the beginning of the period. For the example period: The last partial year is the period from 1995-06-30 to 1996-01-31, which does not contain a leap day, so B = 365. The number of days between 1991-06-30 and 1996-01-31 is 1676, but since there is one leap day within that period, d = 1675. The length of the period in years, t, is 1675/365 = 4.589. If, instead, the end of the period were on 1996-02-29, the number of days would be 1675+29-1=1703 (the leap day is not counted), and the last partial year would contain a leap day, so that t would be 1703/366 = 4.653. Actual/360 d = the actual number of days. B = 360 days. For the example period: d = 1676 and B = 360, so t = 1676/360 = 4.656 Actual/365 d = the actual number of days. B = 365 days. For the example period: d = 1676 and B = 365 so t = 1676/365 = 4.592 Actual/365+ d = the actual number of days. B = 366 if the end of the period falls on a leap year; otherwise, B = 365. For the example period: The number of days between 1991-06-30 and 1996-01-31 is 1676. B = 366 since 1996 is a leap year. So t = 1675/366 = 4.577 Actual/365L d = the actual number of days. B = 366 if the last partial year of the period contains a leap day; otherwise B = 365. The last partial year is the remaining period when the maximum number of full years have been counted off, starting from the beginning of the period. For the example period: The last partial year is the period from 1995-06-30 to 1996-01-31, which does not contain a leap day, so B = 365 and t = 1676/365 = 4.592 Actual/Actual ISDA If no leap year is involved in the calculation, then t = d/B where d = the actual number of days and B = 365. If there is a leap year, then t = d1/B1 + d2/B2, where d1 = the actual number of days in the leap year and B1 = 366 d2 = the actual number of days in the non-leap year and B2 = 365. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 35 2 Market standards and calculations 2.1 Market standards Name Description Actual/Actual (n) The variable n is 1, 2, or 4, specifying the frequency of coupons. The corresponding coupon periods are 12, 6, and 3 months (= 12 / n), respectively. The time between the dates d1 and d2 is calculated by first calculating the number (p) of the whole periods that fit into the interval (d1, d2), from the date (d2) backwards, and then by adding the length of the first fractional period. The end and start dates of the periods are generated by repeatedly subtracting 12, 6, or 3 from the month number of d2. If the month thus generated has fewer days than the day of month of the end date (d2), the period end date is the end date of the month in question. That is, if d2 = 2008-05-31 and n = 4, then the start date of the last period is 2008-02-29. If the date (d1) is a start date of a whole period, then the time in years between d1 and d2 is simply the number of whole periods: Equation 2-1 Actual/Actual (n): number of whole periods t = p⁄n Otherwise, let ds and de be the start and end dates of the whole period wherein the date (d1) falls. Then the time in years between d1 and d2 is: Equation 2-2 Actual/Actual (n): time in years between d1 and d2 de – d1 t = p ⁄ n + -----------------------n ( de – ds ) Example Let the start and end dates be d1 = 2008-03-31 and d2 = 2009-09-30, and the frequency be n = 2. Then, the dates generated are as follows: • 2009-09-30 • 2009-03-30 • 2008-09-30 = de • 2008-03-30 = ds There are two (2) whole periods, and the time between d1 and d2 is: Equation 2-3 Actual/Actual (n): Example with 2 whole periods Actual/Actual (n) EOM Note: The Actual/Actual (n) EOM data basis is TRM-specific, i.e. non-market standard. This date basis is similar to Actual/Actual (n) except that the period end and start dates are moved to the last date of the month in question. That is, all the whole periods begin and end at the last day of the month. Example Let the start and end dates be d1 = 2008-03-31 and d2 = 2009-09-30, and frequency be n = 2. Then the dates generated are as follows: • 2009-09-30 • 2009-03-31 • 2008-09-30 = de • 2008-03-31 = ds That is, the dates in March have been moved to the end of March. There are three (3) whole periods, and no fractional part. Therefore, time in years is as follows: Equation 2-4 Actual/Actual (n) EOM: Example with 3 whole periods t = 3 ⁄ 2 = 1.5 36 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards Name Description BRL/252 This date basis calculates time as business days according to the Brazilian (BRL) calendar divided by 252. Example Take the period between 2003/12/16 and 2004/02/02. For this period, the BRL calendar is set up with the following public holidays: 2003/12/25, 2003/12/26, and 2004/01/01, as well as 14 weekend days. Therefore, there are 31 business days in the period, and so, using this date basis, the resulting time is: 31/252 = 0.123015873 (instead of 48/365 = 0.131506849 if the Actual/365 date basis was used). 2.1.2 Interest types Name Discount factor in terms of interest rate Annually Compounded Rate Semi-Annually Compounded Rate Quarterly Compounded Rate Monthly Compounded Rate Daily Compounded Yield (B = denominator of date basis) r –t D = ⎛ 1 + ---------⎞ ⎝ 100⎠ r = 100 ( D r – 2t D = ⎛ 1 + ---------⎞ ⎝ 200⎠ r = 200 ( D – 1 ⁄ ( 2t ) – 1) r – 4t D = ⎛ 1 + ---------⎞ ⎝ 400⎠ r = 400 ( D – 1 ⁄ ( 4t ) – 1) r –12t D = ⎛ 1 + ------------⎞ ⎝ 1200⎠ r = 1200 ( D r –Bt D = ⎛ 1 + -------------⎞ ⎝ 100B⎠ r = 100B ( D Continuous Yield D = e Discount Rate Interest Rate Periodic Rate Interest rate in terms of discount factor r – --------- t 100 r D = 1 – --------- t 100 –1 ⁄ t – 1) – 1 ⁄ ( 12t ) – 1) – 1 ⁄ ( Bt ) – 1) 100 r = – --------- log D t 1–D r = 100 ------------t Depending on time: • Periodic Rate for maturities less than one year • Continuous Yield for maturities equal to or over one year. 1 D = -------------------r 1 + --------- t 100 100 1 r = --------- ⎛ ---- – 1⎞ t ⎝D ⎠ Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 37 2 Market standards and calculations 2.1 Market standards Name Discount factor in terms of interest rate Semi-Annual/Periodic Rate These interest types work in a similar way to interest type Interest Rate: Quarterly/Periodic Rate • If time is shorter than six months/three months/month, then the discount factor is periodic: • If time is longer than six months/three months/month, then the discount factor is compounded with frequency of 2, 4, or 12: Monthly/Periodic Rate Interest rate in terms of discount factor 1 / (1 + rate/100 * time) (1 + rate / (frequency * 100))^(-frequency * time) ("^" means to the power) Note: The number of months is calculated as calendar months. For example, from 15 February to 15 March is one month, regardless of date basis. This interest type works in a similar way to interest type Periodic Rate except that the last coupon period is one day longer, i.e. it includes both first and last date. ISDA CDS 2.1.3 Price types 2.1.3.1 Trading Margin The conversion of the quotation (trading margin) into the price is handled by specific quote handlers for Australian FRNs and MBS. The formula used to convert the trading margin (market quote) to the instruments price is described in 3.1.3 Australian floating rate note on page 236 and 3.7.5 Australian MBS on page 302 respectively. 2.1.4 Yield/price conversions Bonds are traded on either yield or price depending on the market conventions. At deal entry, the user can enter either the yield or the price of the bond, the missing value is then calculated from the entered one. For example, if you enter the price then the yield is calculated, and vice versa. The yield/price conversion of a bond is set by including the Trading Yield feature and associating the relevant yield convention with the instrument in the Instrument Editor. The convention determines which price and yield method are used for the conversion. When no convention is selected at the instrument level, the default convention for calculating the yield (deal rate) is ISMA with Actual/Actual date basis and Annually Compounded yield. The following information is provided in this section for each convention: Field Description Name The name of the convention as it appears in TRM. Description General description of the method and standard calculations. Usage Describes with which instrument this method is typically used. 2.1.4.1 Price/yield conversion The yield y is in most cases converted from the clean price Pc of a fixed rate bond by using either the ISMA or the Simple Yield formula. This section describes these two calculations. 38 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards 2.1.4.1.1 ISMA (financial/instrument/isma@yield) Information Description Name ISMA Description The ISMA yield uses a goal seeker method id in the system seeks for the yield which gives the input price. The algorithm iterates the yield y until the equation equals zero: Equation 2-5 ISMA method where Usage • p c is the clean market price • c i and d i represent the ith cashflow and its date (coupon date) • D • I a is the accrued interest is the discount factor for that cashflow This method applies to all bonds except Japanese government bonds, which use the simple yield. See 2.1.4.2 Yield/price conversion on page 40. 2.1.4.1.2 Simple Yield (financial/instrument/simple-yield@yield) Information Description Name Simple Yield Description The simple yield calculates the yield from the clean market price as follows: Equation 2-6 Simple Yield where • r is the coupon rate • p c is the clean market price • t m is the time in years from the valuation date to maturity From this, the conversion equation for simple yield is: Equation 2-7 Simple Yield: conversion equation Usage This method applies only to Japanese government bonds (GOVT-JP). See 2.1.4.2.29 GOVT-JP (financial/instrument/simple-yield@price) on page 59. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 39 2 Market standards and calculations 2.1 Market standards 2.1.4.2 Yield/price conversion The clean price Pc of a fixed rate bond is in most cases converted from the yield y by the formula: Equation 2-8 Yield/price conversion: clean price where • p c is the clean market price • c i and d i represent the ith cashflow and its date (coupon date) • D • I a is the accrued interest. is the discount factor for that cashflow If the dirty price is used, then accrued interest in the above equation is dropped. The methods of calculating the discount factor and the accrued interest may depend on market conventions as explained in the following sections. Hint: For the following bond conventions, when the yield is not specifically mentioned then the convention uses ISMA. 2.1.4.2.1 *ISMA-30/360-BIMONTHLY (financial/instrument/isma@price) Field Description Name *ISMA-30/360-BIMONTHLY Description *ISMA-30/360-BIMONTHLY bonds are regular fixed coupon securities with bi-monthly coupons and 30/360 date basis. With *ISMA-30/360-BIMONTHLY, the coupons for the ith cashflow on date di are discounted using the following formula: Equation 2-9 European bonds before the Euro t D ( y, d i ) = ( 1 + y ⁄ 6 ) i where • Usage t i is the time in years between the value date and the coupon date di . Convention used for australian bonds. 2.1.4.2.2 *ISMA-30E360-ANNUAL (financial/instrument/isma@price) Field Description Name *ISMA-30E360-ANNUAL Description *ISMA-30E360-ANNUAL bonds are regular fixed coupon securities with annual coupons and 30E/360 date basis. With *ISMA-30E360-ANNUAL, the coupons for the ith cashflow on date di are discounted using the following formula: Equation 2-10 European bonds before the Euro t D ( y, d i ) = ( 1 + y ) i where • 40 t i is the time in years between the value date and the coupon date di . © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards Field Description Usage Convention used for European bonds (Belgium, Finland, and Germany) issued before the introduction of the Euro. 2.1.4.2.3 *ISMA-30E360-SEMI-ANNUAL (financial/instrument/isma@price) Field Description Name *ISMA-30E360-SEMI-ANNUAL Description *ISMA-30E360-SEMI-ANNUAL bonds are regular fixed coupon securities with semi-annual coupons and 30E/360 date basis. With *ISMA-30E360-SEMI-ANNUAL, the coupons for the ith cashflow on date di are discounted using the following formula: Equation 2-11 Sovereign and corporate bonds t D ( y, d i ) = ( 1 + y ⁄ 2 ) i where • Usage t i is the time in years between the value date and the coupon date di . Convention used for some sovereign or corporate bonds. 2.1.4.2.4 *ISMA-30E360-QUARTERLY (financial/instrument/isma@price) Field Description Name *ISMA-30E360-QUARTERLY Description *ISMA-30E360-QUARTERLY bonds are regular fixed coupon securities with quarterly coupons and 30E/360 date basis. With *ISMA-30E360-QUARTERLY, the coupons for the ith cashflow on date di are discounted using the following formula: Equation 2-12 ISMA 30E360 Quarterly bonds y ti D ( y, d i ) = ⎛ 1 + ---⎞ ⎝ 4⎠ where • Usage t i is the time in years between the value date and the coupon date d . i Supranational or regional bond issuer, for example, German Landesbank. 2.1.4.2.5 *ISMA-ACTACT-ANNUAL (financial/instrument/isma@price) Field Description Name *ISMA-ACTACT-ANNUAL Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 41 2 Market standards and calculations 2.1 Market standards Field Description Description This yield convention is used according to the Eurozone. With *ISMA-ACTACT-ANNUAL, the coupons for the ith cashflow on date di are discounted using the following formula: • If t m > 1 Equation 2-13 Standard Eurozone: when time in years is more than 1 • If t m ≤ 1 Equation 2-14 Standard Eurozone: when time in years is less than or equal to 1 where Usage • t i is the time in years between the value date and the coupon date d i • t m is the time in years from the valuation date to the maturity of the bond. Standard Euro Zone convention that can be applied to other corporate bonds. 2.1.4.2.6 *ISMA-ACTACT-QUARTERLY (financial/instrument/isma@price) Field Description Name *ISMA-ACTACT-QUARTERLY Description *ISMA-ACTACT-QUARTERLY bonds are regular fixed coupon securities with quarterly coupons and Act/Act date basis. With *ISMA-ACTACT-QUARTERLY the coupons for the ith cashflow on date di are discounted using the following formula: Equation 2-15 ISMA Act/Act Quarterly bonds y ti D ( y, d i ) = ⎛⎝ 1 + ---⎞⎠ 4 where • Usage t i is the time in years between the value date and the coupon date d . i Supranational or regional bond issuer, for example, EIB. 2.1.4.2.7 *ISMA-ACTACT-SEMI-ANNUAL (financial/instrument/isma@price) Field Description Name *ISMA-ACTACT-SEMI-ANNUAL 42 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards Field Description Description ISMA-ACTACT-SEMI-ANNUAL bonds are regular fixed coupon securities with semi-annual coupons and Act/Act date basis. With *ISMA-ACTACT-SEMI-ANNUAL, the coupons for the ith cashflow on date di are discounted using the following formula: Equation 2-16 Standard UK government bondS where • Usage t i is the time in years between the value date and the coupon date d i Standard UK government bond convention that can be applied by other corporate bonds. 2.1.4.2.8 *ISMA-ACT360-ANNUAL (financial/instrument/isma@price) Field Description Name *ISMA-ACT360-ANNUAL Description ISMA-ACT360-ANNUAL bonds are regular fixed coupon securities with annual coupons and Act/360 date basis. ISMA-ACT360-ANNUAL bonds are calculated using the same formula as ISMA-30E360-ANNUAL, see 2.1.4.2.2 *ISMA-30E360-ANNUAL (financial/instrument/isma@price) on page 40. Usage This convention is used for bond instruments bonds (Interest FIXBIS) issued by sovereign issuers such as the Bank for International Settlement (BIS). 2.1.4.2.9 *ISMA-ACT365-ANNUAL (financial/instrument/isma@price) Field Description Name *ISMA-ACT365-ANNUAL Description *ISMA-ACT365-ANNUAL bonds are regular fixed coupon securities with annual coupons and Act/365 date basis. ISMA-ACT360-ANNUAL bonds are calculated using the same formula as ISMA-30E360-ANNUAL, see 2.1.4.2.2 *ISMA-30E360-ANNUAL (financial/instrument/isma@price) on page 40. Usage This convention is used for some sovereign bond instruments. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 43 2 Market standards and calculations 2.1 Market standards 2.1.4.2.10 *U.S.STREET-ACT365-SEMIANNUAL (financial/instrument/us-street@price) Field Description Name *U.S.STREET-ACT365-SEMIANNUAL Description U.S.STREET-ACT365-SEMIANNUAL bonds are regular or irregular securities with Act/365 date basis. With *U.S.STREET-ACT365-SEMIANNUAL, the coupons for the ith cashflow on date di are discounted using the following formula: Equation 2-17 U.S. Treasury Notes where • k is the compounding frequency of the yield. For example, k = 2 for semi-annual yield) • t0 is the time in years from the value date to d 0 the first coupon date. t 0 is calculated using the following formula: Equation 2-18 U.S. Treasury Notes: time in years where - t v, 0 is the period in years between the valuation date and the first coupon date t p, 0 is the period in years between the previous and the next coupon date, calculated using the date basis Act/365. • n is the number of coupon periods between d 0 and d i , the ith coupon date. n is calculated using: Equation 2-19 U.S. Treasury Notes: number of coupon periods n = round ( k × t i ) where Usage 44 t i is the time (in years) between d 0 and d i . U.S. Treasury Notes market convention on the secondary market. © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards 2.1.4.2.11 *U.S.STREET-ACTACT-SEMIANNUAL (financial/instrument/us-street@price) Field Description Name *U.S.STREET-ACTACT-SEMIANNUAL Description U.S.STREET-ACTACT-SEMIANNUAL bonds are based on the same formula as U.S.STREET-ACT365-SEMIANNUAL, but have Act/Act date basis. See 2.1.4.2.10 *U.S.STREET-ACT365-SEMIANNUAL (financial/instrument/us-street@price) on page 44. Usage Zero-coupon markets, such as, the U.S. and the UK strips. 2.1.4.2.12 *U.S.STREET-ACTACT-ANNUAL (financial/instrument/us-street@price-1) Field Description Name *U.S.STREET-ACTACT-ANNUAL Description U.S.STREET-ACTACT-ANNUAL bonds are based on the same formula as U.S.STREET-ACT365-SEMIANNUAL, but have annual coupon and Act/Act date basis. See 2.1.4.2.10 *U.S.STREET-ACT365-SEMIANNUAL (financial/instrument/us-street@price) on page 44. Usage Some sovereign bonds, for example, on the Euro Dollar market. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 45 2 Market standards and calculations 2.1 Market standards 2.1.4.2.13 *U.S. Treasury (financial/instrument/us-treasury@price) Field Description Name *U.S.TREASURY Description U.S.TREASURY bonds are regular and irregular fixed coupon securities with semi-annual coupons and Act/365 date basis. With *U.S.TREASURY, a periodic rather than compound rate is used for discounting over the partial period from the value date to the next coupon date di : Equation 2-20 U.S. Treasury notes and bonds where • t 0 is the time in years from the value date to the next coupon date (calculated as in *U.S.STREET-ACT365-SEMIANNUAL, see 2.1.4.2.10 on page 44) • t i is time in years from the value date to the coupon date. U.S. Treasury notes and bonds may have an odd first coupon, that is, the length of the first coupon period may be longer or shorter than the normal coupon period: • If the first coupon period is shorter, the coupon amount is calculated as: Equation 2-21 U.S. Treasury notes and bonds: shorter first coupon period c 1 = rt 1 where • - r is the nominal interest rate as a percentage of the par value - t 1 is the time (in years) between the value date of the interest accrual (i.e. beginning of interest accrual) and the first coupon date. If first coupon periods longer than the regular coupon period, the first coupon amount is given by: Equation 2-22 U.S. Treasury notes and bonds: longer first coupon period where - r is the nominal interest rate as a percentage of the par value - t 0 is time (in years) between the value date of the interest accrual and the date six months before the first coupon date. Note: If the first coupon period is exactly half a year, both equations give the same result. Usage 46 Standard U.S. Treasury Notes and bonds convention that can be applied to other corporate bonds. © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards 2.1.4.2.14 BOND-BR-LFT (financial/instrument/isma@price) Information Description ID BOND-BR-LFT Name Brazilian LFT Description BOND-BR-LFT bonds are Brazilian Zero Coupon Bonds linked to the O/N-SELIC-interest rate. The maturities can be over 2 years. They are traded and quoted in 1000's (Dirty Price, Date basis: Business Days/252) and have a unique security ID (ISIN number), issue date and maturity date. The price is derived from the traded yield according to the following equation: Equation 2-23 Brazilian zero coupon bond where Usage • P is the price (as a percentage of the par value) • y is the annual yield-to-maturity (as a percentage) • d denotes the number of business dates from settlement date to maturity date. Brazilian Zero Coupon Bonds Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 47 2 Market standards and calculations 2.1 Market standards 2.1.4.2.15 BOND-BR-NBC (financial/instrument/isma@price) Information Description ID BOND-BR-NBC Name Brazilian NBC Description BOND-BR-NBC bonds are fixed rate bonds linked to the PTAX-index (FX-rate). The maturities are 2Y, 3Y and 5Y. The fixed rate is 12% p.a. They are traded and quoted in 1000’s and have a unique security ID (ISIN number), issue date and maturity date. The price is calculated as a dirty price and is derived from the traded market rate quoted as a semiannual yield according to the following equation: Equation 2-24 Brazilian NBC bonds where Usage • P is the price (as a percentage of the par value) • y is the annual yield-to-maturity (as a percentage) • d360(k) is the number of days between settlement date and cashflow value date according to 30/360 date basis • c is the coupon rate (12%) • L is the number of future coupons • PTAX(t-1) is the PTAX-index rate valid at time t-1, and ID is the issue date • PTAX(ID-1) is the PTAX-index rate valid at Issue Date-1. Brazilian NBC Bonds 2.1.4.2.16 BOND-BR-NTN (financial/instrument/isma@price) Information Description ID BOND-BR-NTN Name Brazilian NTN 48 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards Information Description Description BOND-BR-NTN bonds are bonds linked to the IGPM-index (NTN-C) and the ICPA-index (NTN-B). The maturities are 2Y, 3Y and 5Y. The fixed rate is 12% p.a. or 6% p.a. They are traded and quoted in 1000’s and have a unique security ID (ISIN number), issue date and maturity date. The price is calculated as a dirty price and is derived from the traded market rate quoted as a compound yield according to the following equation: Equation 2-25 Brazilian NTN bonds where • P is the price (as a percentage of the par value) • y is the annual yield-to-maturity (as a percentage) • bd(k) is the number of business days between settlement date and cashflow value date • L is the number of future coupons. • c is the coupon rate (12% or 6%) The nominal value is 1 000 at issue date for both NTN-B and NTN-C instruments. The nominal value is then adjusted by the IGPM-rates (NTN-C) and IPCA-rates (NTN-B) respectively. These rates are inflation rates published every month as a monthly (p.m.) rate. Usage Brazilian NTN Bonds Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 49 2 Market standards and calculations 2.1 Market standards 2.1.4.2.17 GOVT-AU (financial/instrument/australian@price) Information Description ID GOVT-AU Name Australian Government bond Description GOVT-AU bonds are medium to long-term debt securities with a fixed coupon paid semi-annually in arrears, redeemable at face value on the maturity date. Treasury Bonds are traded on a yield to maturity basis with the price per $100 face value calculated using the following pricing formulae: • Basic formula Equation 2-26 Australian government bond: Basic formula • Ex interest bonds Equation 2-27 Australian government bond: Ex interest bonds • Near-maturity bonds: Specifically, those entitling a purchaser to only the final coupon payment and repayment of principal. Equation 2-28 Australian government bond: Near-maturity bonds where • P is the price per $100 face value (the computed price is rounded to 3 decimal spaces) • v is 1 + i • i is the annual percentage yield to maturity divided by 200 in Equation 2-26 on page 50 and Equation 2-27 on page 50, or the annual percentage yield to maturity divided by 100 in Equation 2-28 on page 50 • f is the number of days from the date of settlement to the next interest payment date in Equation 2-26 on page 50 and Equation 2-27 on page 50 or to the maturity date in Equation 2-28 on page 50. • If the next interest payment date or maturity date falls on a non-business day, the next good business day (a day on which banks are open for business in Melbourne or Sydney, i.e. not a Saturday or Sunday) is used in the calculation of f. • d is the number of days in the half year ending on the next interest payment date • g is the half-yearly rate of coupon payment per $100 face value • n is the term in half years from the next interest-payment date to maturity 1 ----------- Settlement amounts are rounded to the nearest cent (0.50 cent is rounded up). That is, the pricing formula used for computing the price from the yield is the ISMA method. But in the case of near maturing bonds, i.e. when the bond is settled six months plus seven days before maturity, it is treated as a special case, using the pricing of Treasury Notes. Equation 2-29 Treasury Notes equation 50 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards Information Description Usage Australian government bond 2.1.4.2.18 GOVT-CA (financial/instrument/canadian@price) Information Description ID GOVT-CA Name Canadian Government bond Description GOVT-CA bonds are regular, fixed-coupon securities with equal, semi-annual coupon payments and Act/365 date basis. These bonds are traded on a clean price basis. Although Canadian government bonds share similarities with U.S. Treasury bonds, they differ in the accrued interest calculation. The accrued interest on Canadian Government bonds is calculated as follows: Equation 2-30 Canadian government bonds where • AI is the accrued interest • r is the nominal interest rate (to be paid at time i) as a percentage of the par value • PAI is the number of accrued interest days computed in the following way: where - coupon days (pc) is the actual number of days in the current coupon period, calculated as coupon value date minus the start of the current coupon period - p AI is the actual number of days in the period over which the accrued interest is act calculated (calculated as accrued interest date minus the start of the current coupon period). Then: Usage act act - if p AI is less than or equal to 182, then p AI = p AI , or - if p AI is greater than 182, then p AI = ( 182.5 – ( p c – p AI ) ) act act Canadian government bond Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 51 2 Market standards and calculations 2.1 Market standards Information Description Yield The following algorithm is used to calculate the yield (Y) based on the price of Canadian Government bonds: • If one coupon payment remains, then the following algorithm is used to calculate the yield (Y) based on the price of Canadian Government bonds: Equation 2-31 Canadian government bonds: one coupon payment remains where • y is the annual yield-to-maturity (as a percentage) r is the nominal interest rate (to be paid at time i) as a percentage of the par value P is the clean price (as a percentage of the par value) DSM is the days from settlement date to maturity date AI is the accrued interest calculated as described in Equation 2-30 on page 51. If the first coupon is a short coupon, then the Yield formula of Canadian Bond (yield convention GOVT-CA) takes into account the first coupon as follows: Equation 2-32 Canadian government bonds: if first coupon is a short coupon Where - r is the nominal interest rate - t1 is the time (in years) between the beginning of the interest accrual and the first coupon date and then applies to the following Yield/Price formula: Equation 2-33 Canadian government bonds: Yield/Price formula Where - P is the clean price (as a percentage) of the Par value - y is the annual Yield-to-Maturity (as a percentage) - p1 is the number of days from the settlement date to the first coupon date - is the number of days in the quasi-coupon period ending on the first coupon payment date r is the nominal interest rate - n is the number of coupon payments remaining • 52 is the number of days from interest accrual date to first payment date is the number of days from the interest accrual date to the settlement date. If more than one coupon payment remains, the US Treasury bond market conventions (i.e. US Street calculation method) are used for the price/yield calculations. See 2.1.4.2.10 *U.S.STREET-ACT365-SEMIANNUAL (financial/instrument/us-street@price) on page 44. © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards 2.1.4.2.19 GOVT-CH (financial/instrument/isma@price) Information Description ID GOVT-CH Name Swiss Government bond Description GOVT-CH bonds are regular, fixed-coupon securities with equal, annual coupon payments and 30E/360 date basis (the date basis where the 31st of the month is treated as the 30th.) With GOVT-CH, the coupons for the ith cashflow on date d i are discounted using the following formula: Equation 2-34 Swiss government bonds where • Usage t i is the time in years between the value date and the coupon date d i Swiss government bond. 2.1.4.2.20 GOVT-DK-OLD-30E360 (financial/instrument/isma@price) Information Description ID GOVT-DK-OLD-30E360 Name Danish Government 30E360 before 8 February 2001 Description GOVT-DK-OLD-30E360 bonds are regular, fixed-coupon securities with annual coupon payments and 30E/360 date basis (the date basis where the 31st of the month is treated as the 30th). With GOVT-DK-OLD-30E360, the coupons for the ith cashflow on date d i are discounted using the following formula: Equation 2-35 Danish government bond issued before 8 February 2001 where • t i is the time in years between the value date and the coupon date With GOVT-DK-OLD-30E360, the Accrued Interest calculation is calculated using a 30E/360 date basis: Equation 2-36 where • I a is the accrued interest • r is the nominal interest rate (to be paid at time i) as a percentage of the par value • t a is the number of calendar days between the previous coupon payment (inclusive) and the settlement date (exclusive). • t i equals 360. It represents the number of days between the last and next coupon dates. 360 is also used for leap years. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 53 2 Market standards and calculations 2.1 Market standards Information Description Usage Danish government bond issued before 8 February 2001. 2.1.4.2.21 GOVT-DK (financial/instrument/isma@price) Information Description ID GOVT-DK Name Danish Government bond issued after 8 February 2001. Description GOVT-DK bonds are regular, fixed-coupon securities with equal, annual coupon payments and Act/Act date basis. With GOVT-DK, the coupons for the ith cashflow on date d i are discounted using the following formula: • If t m > 1 , then Equation 2-37 • If t m ≤ 1 , then Equation 2-38 where Usage 54 • t i is the time in years between the value date and the coupon date d i • t m is the time in years from the valuation date to maturity of the bond. Danish government bond. This corresponds to the standard Euro Zone convention. From 8 February 2001 the Danish Government bonds follow the Euro Zone convention. See 2.1.4.2.22 GOVT-EUROZONE (financial/instrument/isma@price) on page 55 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards 2.1.4.2.22 GOVT-EUROZONE (financial/instrument/isma@price) Field Description Name GOVT-EUROZONE Description Euro Zone government bonds are regular, fixed-coupon securities with equal, annual coupon payments and a bullet redemption using Act/Act date basis. These bonds are traded on a clean-price basis. With GOVT-EUROZONE, the coupons for the ith cashflow on date di are discounted using the following formula: • If t m > 1 Equation 2-39 GOVT-EUROZONE: time in years is more than 1 • If t m ≤ 1 Equation 2-40 EGOVT-EUROZONE: time in years is less than or equal to 1 where - t i is the time in years between the value date and the coupon date d i - t m is the time in years from the valuation date to the maturity of the bond. With GOVT-EUROZONE, the Accrued Interest is calculated as follows according to ISMA Rule 251: Equation 2-41 GOVT-EUROZONE: Accrued Interest where • I a is the accrued interest • r is the nominal interest rate (to be paid at time i) as a percentage of the par value • t a is the actual number of days between the last coupon payment date (inclusive) and the current value date (exclusive) • t i is the actual number of days in the coupon period between the last (inclusive) and next (exclusive) coupon dates multiplied by the number of coupon periods in the year. However, the denominator calculation is subject to exceptions in relation to irregular coupon periods (see below) • Usage n c is the number of coupon periods in the year. This is the standard Euro Zone convention. This convention applies to the following government bonds: Austria, Belgium, Cyprus, Finland, France (BTAN), German, Greece, Ireland, Luxembourg, Malta, Netherlands, Portugal, Slovakia, Slovenia, Spain. Note: France (OAT) and Italy also belong to the Eurozone, but apply small variants to the Euro Zone convention. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 55 2 Market standards and calculations 2.1 Market standards 2.1.4.2.23 GOVT-FR-OAT-OLD-AIR3 (financial/instrument/isma@price) Information Description ID GOVT-FR-OAT-OLD-AIR3 Name French Government OAT Old. Description GOVT-FR-OAT-OLD-AIR3 bonds are regular, fixed-coupon securities with equal, annual coupon payments, and Act/Act date basis. These bonds are traded on a clean price basis. With GOVT-FR-OAT-OLD-AIR3, the accrued interest calculation is rounded to 3 decimals using an Actual/Actual date basis: Equation 2-42 Old French OAT convention where • I a is the accrued interest • r is the nominal interest rate (to be paid at time i) as a percentage of the par value • t a is the time in years between the last coupon date (inclusive) and the value date (exclusive), calculated using the accrual date basis, • Usage t i is the time in years between the last (inclusive) and next (exclusive) coupon dates, calculated using the appropriate Actual/Actual date basis. Old French OAT convention for bonds issued before 18 April 2005, where the convention required an Accrued Interest calculation rounded to 3 decimals using an Actual/Actual date basis. This convention has been replaced by a rounding to 7 decimals. The old 3-decimal rounding is still accepted. 2.1.4.2.24 GOVT-FR-OAT (financial/instrument/isma@price) Information Description ID GOVT-FR-OAT Name French Government OAT Description French government OATs follow the Euro Zone standard convention. However, in the GOVT-FR-OAT method the accrued interest calculation is rounded to 7 decimals using an Actual/Actual date basis: Equation 2-43 French government OAT where • I a is the accrued interest • r is the nominal interest rate (to be paid at time i) as a percentage of the par value • t a is the time in years between the last coupon date (inclusive) and the value date (exclusive), calculated using the accrual date basis • Usage 56 t i is the time in years between the last (inclusive) and next (exclusive) coupon dates, calculated using the appropriate Actual/Actual date basis. French OAT convention for bonds issued after 18 April 2005 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards 2.1.4.2.25 GOVT-GR-OLD-30E360 (financial/instrument/isma@price) Information Description ID GOVT-GR-OLD-30E360 Name Greek Government 30E360 before 1 January 2001 Description GOVT-GR-OLD-30E360 bonds are fixed-coupon securities with annual coupon payments, and 30E/360 date basis (the date basis where the 31st of the month is treated as the 30th). These bonds are traded on a clean price basis. With GOVT-GR-OLD-30E360, the coupons for the ith cashflow on date d i are discounted using the following formula: Equation 2-44 Greek government bond where • Usage t i is the time in years between the value date and the coupon date d i . Greek government bond issued before 1 January 2001. 2.1.4.2.26 GOVT-HU (financial/instrument/isma@price) Field Description ID GOVT-HU Name Hungarian Government Description With this yield convention, the coupons for the ith cashflow on date di are discounted using the following formula: • If t m > 1 Equation 2-45 Hungarian government bonds: when time in years is more than 1 • If t m ≤ 1 Equation 2-46 Hungarian government bonds: when time in years is less than or equal to 1 where Usage • t i is the time in years between the value date and the coupon date d i • t m is the time in years from the valuation date to the maturity of the bond. Hungarian government bonds. This convention uses the accrued interest method Hungarian (4 decimals), see Hungarian (4 decimals) on page 75. 2.1.4.2.27 GOVT-IT (financial/instrument/isma@price) Information Description ID GOVT-IT Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 57 2 Market standards and calculations 2.1 Market standards Information Description Name Italian Government Description GOVT-IT bonds are regular, fixed-coupon securities with equal, semi-annual coupon payments, and Actual/Actual date basis. With GOVT-IT, the coupons for the ith cashflow on date d i are discounted using the following formula: Equation 2-47 Italian government bonds where • t i is the time in years between the value date and the coupon date d i Equation 2-48 Italian government bonds: time in years - d i is the number of days between the value date and the coupon date d - n is the number of coupons i.e. 2. - d c is the number of days during the coupon period With GOVT-IT, the accrued interest calculation is rounded to 5 decimals using an Actual/Actual date basis: Equation 2-49 Italian government bonds: accrued interest calculation • I a is the accrued interest • r is the nominal interest rate (to be paid at time i) as a percentage of the par value • t a is the time in years between the last coupon date (inclusive) and the value date (exclusive), calculated using the accrual date basis • Usage t i is the time in years between the last (inclusive) and next (exclusive) coupon dates, calculated using the appropriate Actual/Actual date basis. Italian government bonds. 2.1.4.2.28 GOVT-IT-ZC (financial/instrument/isma@price) Field Description ID GOVT-IT-ZC Name Italian Government Zero Coupon 58 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards Field Description Description This yield convention is used for the Italian Government Bond with Zero Coupon. The date basis is Actual-/365 and the discount factor is calculated according to the following formula: • If t m > 1 Equation 2-50 Italian ZC government bonds: when time in years is more than 1 • If t m ≤ 1 Equation 2-51 Italian ZC government bonds: when time in years is less than or equal to 1 where Usage • t i is the time in years between the value date and the coupon date d i • t m is the time in years from the valuation date to the maturity of the bond. Italian Government Bond with Zero Coupon 2.1.4.2.29 GOVT-JP (financial/instrument/simple-yield@price) Information Description ID GOVT-JP Name Japanese Government Description GOVT-JP bonds are regular, fixed-coupon securities with equal, annual coupon payments, and Actual-/365 date basis. These bonds are traded on a clean price basis. With GOVT-JP, the Accrued Interest calculation is truncated to 7 decimals using Actual/365 date basis: Equation 2-52 Japanese government bonds • I a is the accrued interest • r is the nominal interest rate (to be paid at time i) as a percentage of the par value • t a is the time in years between the last coupon date (inclusive) and the value date (exclusive), calculated using the accrual date basis • t i is the time in years between the last (inclusive) and next (exclusive) coupon dates, calculated using the appropriate Actual/365 date basis. Usage Japanese government bonds Yield Simple Yield Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 59 2 Market standards and calculations 2.1 Market standards 2.1.4.2.30 GOVT-MALAYSIA (financial/instrument/isma@price) Information Description Name GOVT-MALAYSIA Usage Used to support Malaysian Government bonds. These bonds have semi-annual coupon payments with Act/2Act date basis. 2.1.4.2.31 GOVT-NO (financial/instrument/norwegian@price) Information Description Name GOVT-NO Description Norwegian government bonds are regular, fixed-coupon securities with equal, annual coupon payments and a bullet redemption on an Act/365 date basis. These bonds are traded on a clean-price basis. With GOVT-NO, the coupons for the ith cashflow on date di are discounted using the following formula: Equation 2-53 Norwegian government bonds where • t i is the time in years between the value date and the coupon date calculated using the date basis Actual/365 With GOVT-NO, the Accrued Interest calculation is calculated using date basis Actual/365: Equation 2-54 Norwegian government bonds: Accrued Interest where • I a is the accrued interest • r is the nominal interest rate (to be paid at time i) as a percentage of the par value • t a is the actual number of calendar days between the previous coupon payment and the settlement date. The actual number of calendar days include leap years • t i is equal to 365 and represents the number of days between the last and next coupon dates. Note: 365 is also used for leap years. Usage Norwegian government bonds 2.1.4.2.32 GOVT-NZ (financial/instrument/isma@price) Information Description ID GOVT-NZ Name New Zealand Government Bond 60 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards Information Description Description GOVT-NZ bonds are regular, fixed-coupon securities with semi-annual coupon payments, and Actual/Actual date basis. These bonds are traded on a clean price basis. With GOVT-NZ, the coupons for the ith cashflow on date d i are discounted using the following formula: Equation 2-55 New Zealand government bonds where • Usage t i is the time in years between the value date and the coupon date d i calculated using the date basis Actual/Actual. New Zealand government bonds 2.1.4.2.33 GOVT-SE (financial/instrument/isma@price) Information Description ID GOVT-SE Name Swedish Government Bond Description GOVT-SE bonds are regular, fixed-coupon securities with equal, annual coupon payments, and 30E/360 date basis (the date basis whereby the 31st of the month is treated as the 30th). These bonds are traded on a clean price basis. With GOVT-SE, the coupons for the ith cashflow on date d i are discounted using the following formula: Equation 2-56 Swedish government bonds where • t i is the time in years between the value date and the coupon date d i With GOVT-SE, the accrued interest calculation is calculated using an 30E/360 date basis: Equation 2-57 where Usage • I a is the accrued interest • r is the nominal interest rate (to be paid at time i) as a percentage of the par value • t a is the number of calendar days between the previous coupon payment (inclusive) and the settlement date (exclusive) • t i equals 360. It represents the number of days between the last and next coupon dates. 360 is also used for leap years. Swedish government bonds. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 61 2 Market standards and calculations 2.1 Market standards 2.1.4.2.34 GOVT-SG (financial/instrument/us-street@price) Field Description Name GOVT-SG Description Singaporean Government Bonds are based on the same formula as U.S.STREET-ACTACT-SEMIANNUAL. See 2.1.4.2.11 *U.S.STREET-ACTACT-SEMIANNUAL (financial/instrument/us-street@price) on page 45. Usage Singaporean government bond convention. This convention uses the accrued interest method Singaporean (8 decimals), see Singaporean (8 decimals) on page 77. 2.1.4.2.35 GOVT-UK (financial/instrument/isma@price) Information Description ID GOVT-UK Name UK Government Bond Description GOVT-UK bonds are regular, fixed-coupon securities with equal, semi-annual coupon payments, and Actual/Actual date basis. These bonds are traded on a clean price basis. With GOVT-UK, the coupons for the ith cashflow on date d i are discounted using the following formula: Equation 2-58 where • t i is the time in years between the value date and the coupon date d i Equation 2-59 where Usage - d i is the number of days between the value date and the coupon date d - n is the number of coupons i.e. 2. - d c is the number of days during the coupon period UK government bond convention. 2.1.4.2.36 GOVT-US (financial/instrument/us-street@price) Information Description ID GOVT-US Name United States Government 62 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards Information Description Description U.S. Treasury government bonds are regular and irregular fixed-coupon securities with semi-annual coupon payments and Actual/365 date basis. These bonds are traded on a clean price basis. With GOVT-US, a periodic rather than compound rate is used for discounting over the partial period from the value date to the next coupon date d i : Equation 2-60 U.S Treasury government bonds where • t 0 is the time in years from the value date to the next coupon date (calculated as in the U.S. Street method) • t i is the time in years from the value date to d i . U.S. Treasury notes and bonds may have a first coupon of an unequal length. That is, the length of the first coupon period may be longer or shorter than the normal coupon period. • If the first coupon period is shorter, the coupon amount is calculated as follows: Equation 2-61 First coupon period shorter c 1 = rt 1 where - r is the nominal interest rate - t 1 is the time (in years) between the dated date (the beginning of interest accrual) and the first coupon date. • If the first coupon period is longer, the first coupon amount is calculated as follows: Equation 2-62 First coupon period longer c 1 = r ⁄ 2 + rt 0 where - t 0 is time (in years) between the dated date and the date six months before the first coupon date. • Usage If the first coupon period is exactly half a year, both equations give the same result. This is the US government bond convention based on U.S. Street Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 63 2 Market standards and calculations 2.1 Market standards 2.1.4.2.37 GOVT-USAGENCY (financial/instrument/isma@price) Information Description ID GOVT-USAGENCY Name United States Government Agency Description GOVT- USAGENCY bonds are fixed-coupon securities with annual coupon payments, and 30/360 date basis. These bonds are traded on a clean price basis. With GOVT-USAGENCY, the accrued interest is calculated as follows using a 30/360 date basis: Equation 2-63 United States Government Agency where • I a is the accrued interest • r is the nominal interest rate (to be paid at time i) as a percentage of the par value • t i is the length of the coupon period calculated using the accrual date basis of 30/360 (or coupon date basis if the former is missing) • Usage 64 t r is the length of the remaining accrual period (i.e. the time between the accrual date and the end date of the coupon). US government Agencies bond convention © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards 2.1.4.2.38 GOVT-ZA (financial/instrument/south-african@price) Information Description ID GOVT-ZA Name South African Government bond Description GOVT-ZA bonds are regular, fixed-coupon securities with semi-annual coupon payments, and Actual/365 date basis. These bonds are traded on a clean price basis. With GOVT-ZA, the Accrued Interest calculation is rounded to 5 decimals using an Actual/365 date basis: Equation 2-64 South African Government bond where • I a is the accrued interest • r is the nominal interest rate (to be paid at time i) as a percentage of the par value • t a is the time in years between the last coupon date (inclusive) and the value date (exclusive), calculated using the accrual date basis • t i is the time in years between the last (inclusive) and next (exclusive) coupon dates, calculated using the appropriate Actual/365 date basis. With GOVT-ZA, the coupons for the ith cashflow on date d i are discounted using the following formula: Equation 2-65 where • k is the compounding frequency of the yield (for example, k=2 for semi-annual yield) • t 0 is time in years from the value date to d 0 , the first coupon date. t 0 is calculated using the following formula: Equation 2-66 Time in years from value date to first coupon date t v, 0 t 0 = --------t p, 0 where - t v, 0 and t p, 0 are the periods in years between the valuation date and the first coupon date, and between the previous and the next coupon date, respectively, calculated using the date basis Act/365 - n is the number of coupon periods between d 0 and d i , the ith coupon date. The number of coupon periods is calculated using: n = round ( kxt i ) where t i is the time (in years) from the next coupon date to the maturity of the bond, and round rounds the number to the nearest integer. Usage South African Government bond convention Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 65 2 Market standards and calculations 2.1 Market standards 2.1.4.2.39 INDEX-UK (function/index-uk@price) ID INDEX-UK Name Index-linked UK Government bond Description The prevailing market conventions for price/yield calculations in the UK index-linked market are different from the conventions used for the Swedish and US index-linked markets. The market practice is to assume that all future semi-annual coupon periods have the same length as the present accrued period. Therefore, the overall period T si between settlement and the ith coupon, in the date basis actual/365, is given by: Equation 2-67 Index-linked UK Government bond The market quoted clean price and the semi-annual nominal yield to maturity Y nominal are calculated by the following price/yield formula: Equation 2-68 Price/yield equation where • C IndexAdj is the index adjusted coupons • R IndexAdj (prolonged RPI index figures) is the redemption. Given the price, the nominal yield is obtained by numerical methods. The real yield to maturity y Real is derived from the nominal yield and the assumed inflation rate using the Fisher equation: Equation 2-69 Fisher equation Usage Index-linked UK Government bonds 2.1.5 Discount Margin Discount margin is the spread that, when added to the discounting zero curve, will equate the theoretical value of a floating rate note (see 3.1.2 Floating rate note on page 228) to the quoted price. Discount Margin is calculated at instrument level and shown in Rate Monitor or in Transaction Manager (Figure Discount Margin). In this calculation, the day count method and yield type specified in Discount Margin page are used, and the spread is added to the discounting curve defined in this page. When discount margin is used in the valuation, it is added to the valuation curve specified for the instrument, and the day count method and yield type used are taken from the interpolation method of this valuation curve. For the results to be consistent, the day count method and yield type specified in Discount Margin page should match these. Also, the instrument's valuation curve should 66 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards be used for discount margin calculation. Discount margin valuation is enabled by the feature FRN Valuation, see A.2.164 FRN Valuation on page 791. At instrument level, discount margin m is calculated by solving the equation: Equation 2-70 Discount margin Where: – Pd The dirty price (at spot) of the bond, based on the market quote. – d i The coupon dates. – ci The fixed or estimated coupons. y D i The discount factors (from spot) from the discounting curve on dates d i . – Note: Coupons have to be fixed in Instrument Editor for the fixing to have an effect on the discount margin calculation. – and are the rate-to-discount-factor and discount-factor-to-rate conversions (from spot date) using the day count method and yield type specified in the discount margin setup. 2.1.6 Calculation methods 2.1.6.1 Accrued interest calculations The generic formula for accrued interest AI is: Equation 2-71 Accrued interest (generic formula) t AI = --- × C T where C is the coupon amount, T is the length of the coupon period (in years, calculated with the appropriate date basis), and t is the length of the accrual period (in years). There are many variations of this basic formula. Note: For bonds, the method used for the accrued interest calculation is specified in the AI Method field in Instrument Editor’s Bond page. The date basis used for period length calculations is specified in the Cashflow page (Accrual Date Basis field). If the accrual date basis is not defined, then the date basis of the cashflow is used. Both these pages are available in the editor when the Bond feature is present in the instrument definition (see A.2.51 Bond on page 734). Some AI methods use neither the accrual nor the cashflow’s date basis. This is because the day count method is built in the method. The following table lists the symbols used in the accrued interest calculations: Symbol Description P Principal on which the coupon amount and accrued interest are calculated. C Coupon amount. r Coupon interest rate (as a decimal number). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 67 2 Market standards and calculations 2.1 Market standards Symbol Description T Coupon period in years. t Accrual period in years. D Coupon period in days. d Accrual period in days. 2.1.6.1.1 Generic methods The following sections describe the generic methods for calculating accrued interest in TRM. Linear Equation 2-72 Accrued Interest: Linear t AI = --- × C T Linear 30/360 EOM The Linear 30/360 EOM method ensures that the calculation of accrued interest follows the same month-end behavior as accrued interest used in the calculation of accrued profit. This method is used when defining the Result IR setup for a result treatment (in Result Editor). It achieves a constant yield when a 30E/360 EOM date basis is selected (in Result Editor’s Accrual Yield page). See the TRM User Guide for more information about setting up result treatments. Linear (Closing) The Linear (Closing) method ensures that in closing the books, February is considered as having 30 days when 30-day date bases (such as, the 30/360 and 30E/360 date bases) are used. This means that in accounting, these date bases result in equal interest accrual amount postings in each month. Actual/Actual Equation 2-73 Accrued Interest: Actual/Actual d AI = ---- × C D where D is the interest period length in actual days, and d is the length of the accrual period in actual days. This method will ignore any date basis conventions associated with the coupon. Actual/Actual (Inclusive) This method accrues interest linearly over the interest period, including the first day and excluding the last day of the period. Actual/Actual Annually In the following methods, Actual/Actual Annually, Actual/Actual Semi-Annually, and Actual/Actual Quarterly, the basic formula is used, but the period length calculation is more complicated, as follows: • 68 The coupon period is divided into 12/N -month segments, starting from the end of the coupon period. © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards • The number of months in each segment, 12/N, may be 12, 6, or 3, depending on the method chosen (respectively, Annually, Semi-Annually, or Quarterly). • The segments are created by moving the coupon end date back in 12/N -month steps. • If a date created by such a move does not exist (that is, it falls after the end of month), the end-of-the-month date is substituted for it. Let ith such segment span dis days, and the part of the period within the segment contain dip days; then the total period length in years is: Equation 2-74 Accrued Interest: Actual/Actual Annually - total period length i dp t = ∑ -------i d N i s Note: If the period extends over an entire segment, then dip = dis and the contribution to the total period length of that segment is simply 1/N years. This calculation is repeated for the coupon period (T) and for the accrual period (t), and finally the accrued interest is: Equation 2-75 Accrued Interest: Actual/Actual Annually t AI = --- × C T These methods will ignore any date basis conventions associated with the coupon. Actual/Actual Annually (5 decimals) Non-government Italian bonds are based on annual coupon and Actual/Actual accrual date basis with a rounding to the fifth decimal. This method can be used for more generic purposes as well as for non-government Italian bonds. Accrued Interest is calculated as follows: Equation 2-76 Actual/Actual Annually (5 decimals): accrued interest AI = R 7 [ r × d ⁄ D ] × P Where AI Accrued interest r Nominal interest rate (to be paid at time i) as a real number. d Time in years between the last coupon date (inclusive) and the value date (exclusive), calculated using the accrual date basis. D Time in years between the last (inclusive) and next (exclusive) coupon dates, calculated using the appropriate Actual/Actual date basis. P Principal Index ratio: Equation 2-77 Actual/Actual Annually (5 decimals): index ratio Index IndexRatio = R 5 ⎛⎝ -----------------------------⎞⎠ IssueIndex Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 69 2 Market standards and calculations 2.1 Market standards Index Accrued Interest: Equation 2-78 Actual/Actual Annually (5 decimals): index accrued interest IndexAI = IndexRatio × AI Coupon % methods With the Coupon % methods, the accrued interest is calculated directly from the principal (P) and the coupon rate (r). It may happen that the accrued interest thus calculated is larger than the actual coupon amount (for example, if the date basis used in the AI calculation is different from the date basis used for the calculation of the coupon amount). In this case, accrued interest is capped at the coupon amount, and the daily accrual towards the end of the coupon period may be zero. • Coupon % Equation 2-79 Accrued Interest: Coupon % AI = min [ r × t × P ,C ] • Coupon % Relative Semi-Annually Equation 2-80 Accrued Interest: Coupon % Relative Semi-Annually r×t×P AI = min ------------------- ,C 2T Here T is calculated using the date basis of the cashflow, not the accrual date basis. • Coupon % Relative Quarterly Equation 2-81 Accrued interest: Coupon % Relative Quarterly r×t×P AI = min ------------------- ,C 4T Here T is calculated using the date basis of the cashflow, not the accrual date basis. • Coupon % Compound Annually Equation 2-82 Accrued interest: Coupon % Compound Annually t AI = min [ ( 1 + r ) – 1 ,C ] • Coupon % Compound Semi-Annually Equation 2-83 Accrued interest: Coupon % Compound Semi-Annually 2t AI = min [ ( 1 + r ⁄ 2 ) – 1 ,C ] • Coupon % Compound Quarterly Equation 2-84 Accrued interest: Coupon % Compound Quarterly 4t AI = min [ ( 1 + r ⁄ 4 ) – 1 ,C ] Expression If the coupon is fixed in arrears, the fixing rate is not known when figure accrued interest is calculated. As an estimate, the system uses the current market rate for the fixing period. 70 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards The formula for accrued interest is then: Equation 2-85 Accrued interest: Coupon % Expression t AI = A × --T where: – t is the time in years between the start of the coupon period and the valuation date – T is the length in years of the coupon period – A is the coupon amount calculated using the expression defined for the coupon cashflow. Dual currency • Dual-Currency Estimated The settlement amount is calculated using the forward FX rates. • Dual-Currency Last The settlement amount is calculated using the FX rate of the previous FX fixing. Note: Both methods round the figure value in the cashflow currency before converting it into the settlement currency. Range For range accrual transactions, several specific accrued interest calculation methods exist. They are all based on the principle that the interest (coupon) rate has to be scaled down by a factor depending on the number of days the market variable being observed has been within the range. Once the interest rate has been scaled down, the accrued interest is calculated linearly based on the time spent until valuation date, the total interest period and the date basis of the cashflow. The accrued interest methods and the corresponding factors are: • Range Proportional Days In Range / Observation Days until valuation date • Range So Far In Days In Range / Total Interest Period • Range So Far Out (Total Interest Period - Days Out of Range) / Total Interest Period • Range Fixing Assumes the variable observed will remain in the same state as on valuation date, i.e. So Far In if it is out of range and So Far Out otherwise. Note that the default observation period includes the first date of the interest period and excludes the last date (i.e payment date) of the interest period. For example: Let us consider the interest period from 01/06/2003 until 01/12/2003 with the interest calculation expression as: max[0, 4.85 * range(Euribor/6M, 0, 4.00, up-in/down-in, 2, EUR, ACT/365)] Valuation date is 30/06/2003, i.e. there have been 30 observation days, and 29 days on interest accrual. The total interest period is 183 days. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 71 2 Market standards and calculations 2.1 Market standards Assume that the 6M Euribor rate was in the range 20 times. The accrued interest would be (using date basis Act/365): • Range Proportional method: 4.85% * 20/30 * 29/365 * Nominal Amount • So-Far-In method: 4.85% * 20/183 * 29/365 * Nominal Amount • So-Far-Out method: 4.85% * (183 - 10)/183 * 29/365 * Nominal Amount, i.e. 4.85% * 173/183 * 29/365 * Nominal Amount Yield Accrued Interest This yield based method is used only for the yield accrual of discount/premium – it is not to be used for actual accrued interest calculation. It converts the coupon rate to the same basis as with which yield to maturity is calculated (in a manner that the total coupon remains the same, but the rate of accrual changes). Yield accrual is then based on the coupon accruing with this rate. ISDA CDS The ISDA CDS method is used with credit default swap. This AI method is based on the Linear AI method except that the last period coupon is one day longer, i.e. it includes both the first and last dates in the AI calculation. 2.1.6.1.2 Market-specific methods The following sections describe the market-specific methods for calculating accrued interest in TRM. Note: With regards to rounding, we use the symbol Rn to indicate the rounding to n decimal places. In the applications the interest rate r is given as a % (e.g. r = 3.85 is treated as 3.85% = 0.0385). In the calculation, the system uses the real number. This means that an AI Method (3 decimals) corresponds to a rounding (R5) of the real number to 5 decimals. Australian (3 decimals) This is the AI method rounded to 3 decimals using the Actual/Actual date basis: Equation 2-86 Accrued interest: Australian (3 decimals) AI = R 5 [ ( r ⁄ 2 ) × d ⁄ D ] × P where d is the length of the accrual period in actual days and D is the interest period length in actual days. Australian Floater (3 decimals) This is the method used for australian domestic floating rate note, rounded to 3 decimals using instrument date basis. Equation 2-87 Accrued interest: Australian Floater (3 decimals) AI = R 5 [ r × t ] × P where 72 – r is the fixing rate of the current coupon – P is the Principal © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards – t is the length of the accrual period in years, calculated using the coupon date basis. Moreover, during the ex coupon period, accrued interest is based directly on the number of remaining days to the next coupon using the following equation: Equation 2-88 Accrued interest: Australian Floater (3 decimals): ex coupon period AI = R 5 [ r × t ] × P Where – P is the principal – t is the length of the remaining period (to the next coupon) in years, calculated using the coupon date basis. Australian Index Linked These are the Australian Index Linked (IAB) or Australian Index Linked (CIB) AI methods used for Australian index-linked bonds or Australian capital indexed bonds respectively. Note: For three decimal places rounding, use AI method Australian Index Linked (IAB) (3 dec). Belgian The following calculation applies for all coupon lengths (except short coupons); see Equation 2-74 on page 69 for more details: For short coupons, the calculation is the following; see Equation 2-79 on page 70 for more details: Canadian The Actual/365 (Canadian Bond) date basis considers a year to have 365 days, whereas the length of a coupon period is represented by 365 divided by the number of coupon periods in a year. For the most common Canadian domestic bond structures, which pay a semi-annual coupon, this implies the length of a coupon period is 365/2 = 182.5 days. Where f is the annual payment frequency (or number of coupon periods per year), the Actual/365 Canadian Bond measures the fraction of a coupon period represented by a given number of days as follows: • If the number of days of interest accrual is less than the actual number of days in the coupon period: Equation 2-89 Accrued Interest: Canadian { frac } pc d×f = ----------365 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 73 2 Market standards and calculations 2.1 Market standards Which, for semi-annual pay bonds where f = 2 , reduces to: Equation 2-90 Accrued Interest: Canadian semi annual pay bonds { frac } pc d = ------------182.5 Then Equation 2-91 Canadian AI calculation { frac } AI = A c × p c • If the number of days of interest accrual exceeds 365/f, or 182.5 days for a semi-annual pay bond: Equation 2-92 Accrued Interest: Canadian when interest accrual exceeds 365/f or 182.5 days { frac } pc df × f = 1 – ------------365 Where – d f is the actual number of days from the valuation date to the next coupon date. Then Equation 2-93 Canadian AI calculation when interest accrual exceeds 365/f or 182.5 days { frac } AI = A c × p c French (3 decimals) Equation 2-94 Accrued interest: French (3 decimals) AI = max [ ( R 5 [ 1 + rt ] – 1 ) × P ,C ] where t is the length of the accrual period in years, calculated using the accrual date basis, operator R5 signifies the rounding, and Tc and t are the length of the coupon period calculated using the coupon date basis and the accrual date basis, respectively. French (4 decimals) This method is the same as French (3 decimals) except that the rounding operator = R6. French (7 decimals) This method is the same as French (3 decimals) except that the rounding operator = R9. Greek (3 decimals) Greek index-linked bonds are based on the annual coupon and Actual/Actual Accrual date basis with a rounding to the third decimal. This method is used for Greek index-linked bonds. Accrued Interest is calculated as follows: Equation 2-95 Accrued interest: Greeks (3 decimals) AI = R 5 [ r × d ⁄ D ] × P 74 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards Where AI Accrued interest r Nominal interest rate (to be paid at time i) as a real number. d Time in years between the last coupon date (inclusive) and the value date (exclusive), calculated using the accrual date basis. D Time in years between the last (inclusive) and next (exclusive) coupon dates, calculated using the appropriate Actual/Actual date basis. P Principal Index ratio: Equation 2-96 Accrued interest: Greeks (3 decimals) - index ratio Index IndexRatio = R 3 ⎛⎝ -----------------------------⎞⎠ IssueIndex Index Accrued Interest: Equation 2-97 Accrued interest: Greeks (3 decimals) - index accrued interest IndexAI = IndexRatio × AI Hungarian (4 decimals) This is the AI method rounded to 4 decimals using the Actual/Actual accrual date basis: Equation 2-98 Accrued interest: Hungarian (4 decimals) AI = max [ ( R 6 [ 1 + rt ] – 1 ) × P ,C ] where t is the length of the accrual period in years, calculated using the accrual date basis, the operator R6 signifies the rounding, and Tc and t are the length of the coupon period calculated using the coupon date basis and the accrual date basis, respectively. Israeli (Annual Compound, 5 decimals) • Bond Bond coupon rate r (in %) is converted to the annual compound rate as follows: Equation 2-99 Accrued Interest: Israeli (Annual Compound, 5 decimals) Bond Where: t = Time in years between the last (inclusive) and next (exclusive) coupon dates, calculated using the appropriate Actual/365 date basis. r = nominal interest rate Then, the AI is computed as follows: Equation 2-100 Israeli (Annual Compound, 5 decimals) Bond - AI calculation Where P is the principal. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 75 2 Market standards and calculations 2.1 Market standards • Index Linked Bond Coupon rate r (in %) is converted to the annual compound rate as follows: Equation 2-101 Israeli (Annual Compound, 5 decimals) Index Linked Bond Then, the Index AI is computed as follows: Equation 2-102 Israeli (Annual Compound, 5 decimals) Index Linked Bond - AI calculation Where P is the principal. Israeli (Linear, 5 decimals) This is the AI method rounded to 5 decimals using the Actual/365 date basis: Equation 2-103 Accrued Interest: Israeli (Linear, 5 decimals) AI = R 7 [ r × d ⁄ D ] × P where AI Accrued interest r Nominal interest rate (to be paid at time i) as a real number. d Time in years between the last coupon date (inclusive) and the value date (exclusive) calculated using the accrual date basis. D Time in years between the last (inclusive) and next (exclusive) coupon dates, calculated using the appropriate Actual/365 date basis. P Principal The index (inflation-adjusted) Accrued Interest is rounded to 5 decimals using Actual/365 date basis: • Index Ratio Equation 2-104 Accrued Interest: Israeli (Linear, 5 decimals) - index ratio Index IndexRatio = R 9 ⎛ -----------------------------⎞ ⎝ IssueIndex⎠ • Index Accrued Interest % Equation 2-105 Accrued Interest: Israeli (Linear, 5 decimals) - index accrued interest % IndexAI = IndexRatio × AI 76 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards Italian (5 decimals) This is the Actual/Actual AI method rounded to 5 decimals: Equation 2-106 Accrued interest: Italian (5 decimals) AI = R 7 [ ( r ⁄ 2 ) × d ⁄ D ] × P where d is the length of the accrual period in actual days and D is the interest period length in actual days. Japanese Yield (7 decimals) This is the Coupon % AI method ( Coupon % methods on page 70) truncated to 7 decimals: Equation 2-107 Accrued Interest: Japanese Yield AI = min [ ( R 9 ( 1 + r t ) × P – P ), C ] where t is the length of the accrual period in years. Norwegian The Norwegian accrued interest method is calculated during ex-coupon and based directly on the number of remaining days next to the coupon using the following equation: Equation 2-108 Accrued Interest: Norwegian t AI = C × --------365 Where C The coupon interest percent per annum. t-------365 The actual number of calendar days from the settlement date (transaction value date) to the next coupon payment date divided by 365. Singaporean (8 decimals) This is the Actual/Actual AI method rounded to 8 decimals: Equation 2-109 Accrued interest: Singaporean (8 decimals) AI = R 10 [ ( r ⁄ 2 ) × d ⁄ D ] × P where – d is the time in years between the last coupon date (inclusive) and the value date (exclusive), calculated using the accrual date basis. – D is the time in years between the last (inclusive) and next (exclusive) coupon dates, calculated using the appropriate Actual/Actual date basis. South African (5 decimals) This is the Coupon % AI method truncated to 5 decimals: Equation 2-110 Accrued interest: South African (5 decimals) AI = min [ ( R 7 ( 1 + r t ) – 1 )P ,C ] Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 77 2 Market standards and calculations 2.1 Market standards where t is the length of the accrual period in years. US Agency Equation 2-111 Accrued interest: US Agency AI = r × ( T – t r ) × P where T is the length of the coupon period calculated using the accrual date basis (or coupon’s date basis if the former is missing), and tr is the length of the remaining accrual period (that is, the time between the accrual date and the end date of the coupon). 2.1.6.2 Annuity calculations Annuity calculations are based on all interest cashflows having Kind = Annuity Component and a matching value date, with the amortization cashflows also having Kind = Annuity Component. This allows cashflows from several interest schedules to be included in the calculation. Grace periods can be handled by setting up a forward starting amortization schedule: the coupon dates before will not match the amortization dates and will therefore behave outside any annuity calculation. The later ones will be part of the annuity calculation. In practical terms, this means one of the following: • Instrument setup can start from a normal fixed rate loan and be defined so that interest and amortization share the value dates, or create a reference interest schedule from the amortization schedule • Select the calculation methods (either Annuity or Fixed Annuity), on both schedules (P stands for Principal, Ri for the repayment as i-th value date, Ci for the coupon amount, n the number of dates). See the following sections for more information. 2.1.6.2.1 General annuity calculation This works for any date basis, irregular dates, varying interest rate, and so on, when Interest and Amortization Calculation Method = Annuity. Ri + Ci = Ri-1 + Ci-1 whenever i and sum(Ri) = -P Ci is calculated as usual from the outstanding nominal (that is, P+sum(Ri) where i from 1 to i-1) Ri and Ci are rounded according to the Leg Amount Precision Rn is adjusted so that Rn = P + sum(rounded(Ri)) where i from 1 to n-1 – If the 1st coupon period is short, then you get a "big" amortization and a small coupon amount – Rounded(Ri) + rounded(Ci) are not always equal because of the rounding effect (couple of rounding units difference maximum) Note that the cashflow part of the calculation is given the attribute Kind = Annuity Component. For an irregular annuity, if a rate is specified in the principal schedule, the annuity is computed equally across all flows, except for the last one. The last payment is adjusted according to the outstanding principal amount (100 - r). 2.1.6.2.2 Fixed annuity calculation This works only when the same discount factor is used for all periods, that is, the same interest rate and date bases, so all periods are worth the same (for example, 30/360 for semi-annual or quarterly, Actual/Actual for yearly, and so on), when Interest and Amortization Calculation Method = Fixed Annuity. 78 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.1 Market standards The calculation always uses the last interest period to calculate the annuity amount. It calculates the repayment amount from a direct formula that assumes that you have the same discount factor for all periods. The calculation will not work if there are different periods or uneven date bases. The simplified formula is: Ri = P * (D-1) * D^(i-1) / (1 – D^n) D being the discount factor for 1 period, that is (1+rate*180/360), for a semi-annual 30/360 interest. Therefore, the annuity amount is calculated from: Cn+Rn = Rn*(D-1) + Rn = Rn * D = P * (D-1) * D^(n-1) / (1 – D^n) * D = P * (D-1) * D^n / (1 – D^n) This accumulated annuity is used as the reference annuity amount for all value dates in the rest of the calculation. Once amortizations are calculated (using the direct formula), for each date, the remaining amount from the reference annuity is distributed between interest flows that have Kind = Fixed Annuity, in relation to their Amount % value (in the case where there are many interest amounts for the same date). To handle the short 1st coupon, the attribute 1st Coupon Excluded must be set on the interest schedule: this removes the Fixed Annuity kind so that the interest amount is calculated as usual, based on the principal. Note that the cashflows part of the calculation is given the Fixed Annuity kind as well as the Annuity Component kind. 2.1.6.2.3 Annuity calculation with rounded repayment factors This works when Interest Calculation Method = Annuity, and Amortization Calculation Method = Fixed Annuity. The calculation precision is set to the number of decimals for the repayment/principal ratio %. The amortization calculation is similar to the fixed annuity calculation, except that the Ri/P calculation is rounded to the specified precision. The interest amounts have to be calculated from the outstanding nominal (requires the Annuity calculation method) and the sum of repayment and interest varies significantly because of the repayment ratio% rounding effect. The same attribute is used to handle the short 1st coupon. 2.1.6.3 FX rate calculation The following three methods are available for the calculation of valuation date's FX rate (Sv) from FX Spot rate (S): • Spot Rate: This method uses the FX Spot Rate to convert the cashflow currency to the valuation currency, i.e. the rate is unchanged from the default method. Equation 2-112 FX method: Spot Rate calculation Sv = S • Today's Rate (Forward Points): This method modifies the FX Spot rate with forward points between the valuation date and the spot date. Equation 2-113 FX method: Today’s Rate (Forward Points) calculation S v = S – p × 0.0001 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 79 2 Market standards and calculations 2.1 Market standards where p is the forward points. Typically there are O/N and T/N quotes between the valuation date and the spot date, in which case: Equation 2-114 FX method: Today’s Rate (Forward Points) calculation a b a b p = ( p1 + p1 ) ⁄ 2 + ( p2 + p2 ) ⁄ 2 where the superscripts refer to O/N and T/N. • a and b refer to Ask and Bid quotes respectively, and subscripts 1 and 2 Today's Rate (IR Differential): This method modifies the FX Spot rate with the ratio of the two currencies' discount factors. Equation 2-115 Today's Rate (IR Differential) calculation v S v = SD ⁄ D c where – Dv is the valuation currency discount factor between the valuation date and the spot date – Dc is the cashflow currency discount factor between the valuation date and the spot date. 2.1.6.3.1 Example of FX rate calculation The following example shows the calculations using the following market date (Rate Monitor): • • FX Rate Spot S = 1.5 O/N points • p 1 = 0.02 T/N points • p 2 = – 0.03 b b a Bid • p 1 = 0.06 Bid • p 2 = – 0.01 a Ask Discount Factors O/N • Ask T/N c • D 2 = 0.999985555764 v • D 2 = 0.999948197128 Cashflow Currency • D 1 = 0.999992955609 Valuation Currency • D 1 = 0.999964445709 c v Forward Points Equation 2-116 Example - FX method: Today’s Rate (Forward Points) calculation a b a b p = ( p 1 + p 1 ) ⁄ 2 + ( p 2 + p 2 ) ⁄ 2 = 0.02 S v = S – p × 0.0001 = 1.499998 80 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves • IR Differential Equation 2-117 Example - FX method: Today's Rate (IR Differential) calculation c c c v v v D = D 1 D 2 = 0.999977500389355 D = D 1 D 2 = 0.999912644678814 v c S v = SD ⁄ D = 1.49990271424530 2.2 Yield curves TRM boot straps zero coupon yield curves in order to carry out valuations that are based on discounting future cashflows and/or estimating the amounts of unfixed future cashflows. Three types of bootstrapped zero coupon yield curves exist in TRM: • Yield Curves, i.e. zero coupon yield curves calculated from IR quotes (e.g. deposit, swap and FRA quotes) MM futures and/or bonds. These curves are generally used for discounting (and estimating) any arbitrary set of cashflow. • Tenor Basis Swap Curve, i.e. zero coupon yield curves calculated from tenor basis swap quotes and a base yield curve. These curves are used as estimation curves in tenor basis swap valuation (of the leg for which the spread is quoted) in order to capture the affect of the tenor basis spread quotes. • Cross Currency Basis Swap Curve, i.e. zero coupon yield curves calculated from cross currency basis swap quotes and a base yield curve. These curves are used as valuation curves in cross currency basis swap valuation (of the leg for which the spread is quoted) in order to capture the affect of the cross currency basis spread quotes. The bootstrapping logic for all these yield curves is explained below. Note: See the TRM User Guide for general information about setting up yield curves. 2.2.1 Yield curve A yield curve is a curve that gives the prices of discount bonds maturing in the future as a function of time. Since any cashflow maturing in the future can be regarded as a discount bond, a yield curve can be used to value any instrument that can be represented as a collection of cashflows. In principle, it is also possible to price linear derivatives which have a price that only depends on forward interest rates (for example, short futures, ignoring convexity adjustment) using forward rates derived from the zero curve. In practice, however, this should be treated with caution since the derived forward rate will depend on the method used in the construction of the zero curve much more than the spot rates depend on it. The information on interest rates that can be observed in the market comes in various forms. There are deposit rates that give the discount bond prices directly, but these are mainly available only for Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 81 2 Market standards and calculations 2.2 Yield curves maturities shorter than one year. Longer interest rates are embedded in the swap rates, FRA and short future rates, and bond prices. The objective of yield curve construction is to recover the discount bond price information from the market information. The guiding principle is that when the quoted instruments are priced against the zero coupon curve, the original quotes should be reproduced. Since this requirement does not uniquely define the zero curve, some additional conditions on the functional form and the smoothness of the curve have to be imposed. Discount factors are the fundamental elements on which most valuation calculations are based. If valuation needs for example an interest rate over a period in order to calculate the market value of a caplet, it is the discount factors for the start and end dates of that period that are given as input to valuation, and the desired interest rate is derived from these. 2.2.1.1 Input The starting point of a bootstrap curve is a given set of interest rate related market information. This information may consist of deposit prices, bond prices, or swap prices, for example. In general, any instrument for which a liquid quote exists, and the theoretical price can be calculated using only zero-coupon information, can be used. Normally, it is assumed that all the instruments have the same risk offset. That is, the bootstrap calculation produces a zero curve that is the sum of the risk-free rate and the spread. Each price quote creates a set of cashflows, which are used as input for the bootstrap algorithm (see 2.2.1.3 Bootstrap algorithm on page 83). 2.2.1.1.1 Deposit quotes A deposit quote generates a negative unit cashflow at spot, and a positive unit plus interest cashflow at the maturity of the deposit. The interest amount corresponds to the interest type defined for the deposit quote. The maturity date of the deposit follows the definition of the tenor of the deposit. 2.2.1.1.2 Swap quotes A swap quote creates a negative unit cashflow at spot, and a positive unit cashflow at the maturity of the swap. In addition, the fixed coupons (yearly, semi-annual, and so on) of the swap are created, and their amounts calculated using the date basis and interest type of the quote. 2.2.1.1.3 FRA quotes Each FRA creates a node point at its maturity. The bootstrap curve will have the property that the discount factor over the FRA period is equal to the discount factor implied by the FRA quote. The market quote of an FRA provides an estimate of the interest rate between two dates in the future: the value date and the maturity date of the FRA. This can be converted into the forward price on the value date of a zero-coupon bond on the maturity date of the FRA. Given the market quote of the FRA (r) and the length of the FRA period (t) (calculated using the appropriate date basis), the price on the value date (dv) of a discount bond that matures on the maturity date (dm) of the FRA is given by: Equation 2-118 FRA quotes 1 P ( d v ,d m ) = ------------1 + rt 2.2.1.1.4 Money market future quotes Each MM future creates a node point at its maturity. The bootstrap curve will have the property that the discount factor over the future period is equal to the discount factor implied by the future quote. The market quote of the price of the future provides an estimate of the forward interest rate over the period of the future. This can be converted into a discount factor between the start and the end of the future period. 82 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves Given the MM future quote (F), the corresponding interest rate over the period of the future is r =100 - F, from which the discount price over the period can be calculated, either using the equation for FRA quotes, or if the quote is of the discount type using: P ( d v, d m ) = 1 – rt Equation 2-119 Money market figure quotes 2.2.1.2 Bootstrap date basis and interest type If a cashflow of a bootstrapping instrument (swap, bond, FRA, or MM future) does not fall on a node point of the bootstrap curve, interpolation is needed to find the discount factor for the date in question. Note: The base date for interpolation is the spot date corresponding to the figure date of the calculation. 2.2.1.3 Bootstrap algorithm The bootstrap curve has the following properties: • The (zero coupon) market prices derived from the bootstrap curve will be equal to the given market prices. • The bootstrap curve follows a given functional format and satisfies a smoothness condition (bootstrap curve is continuous). Within each interval, the chosen bootstrap rate is given by: y ( t ) = ai + bi ( t – ti ) Equation 2-120 Bootstrap algorithm where: – ai and bi are parameters calculated by the bootstrap process, and ti is the starting point of the interval in question. – The default interest type is Continuous Yield. 2.2.1.3.1 Node points The maturities of the input instruments are always used as node points. 2.2.1.4 Example: Bootstrapping zero-coupon curve In this example, the zero-coupon curve is based on deposit quotes for the short end (for maturity periods of up to one year) and swap quotes for the long end (for maturity periods of two years and longer). Note: The number of periods in the curves has been kept to a minimum in order to simplify the illustration of the method. In reality, the curves would have many more periods defined. • Depo Quotes For the deposit quotes, the following periods have been defined: Tenor Date Basis Interest Type Interest Structure O/N Actual/360 Periodic Rate At Maturity T/N Actual/360 Periodic Rate At Maturity 6M Actual/360 Periodic Rate At Maturity 1Y Actual/360 Periodic Rate At Maturity Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 83 2 Market standards and calculations 2.2 Yield curves • Swap Quotes For the swap quotes, the following periods have been defined: • Period Date Basis Interest Type Interest Structure 2Y 30/360 Periodic Rate Annual 3Y 30/360 Periodic Rate Annual Parameters Interpolation method is Linear (with flat rate extrapolation), based on Continuous Yield, date basis 30/360. The deposit and swap quotes are as follows: Period Deposit Swap Bid Ask Bid Ask O/N 4.8 4.88 T/N 4.78 4.84 6M 5.1 5.1 1Y 5.161 5.161 2Y 5.257 5.257 3Y 5.32 5.32 The yield curve uses the average of the bid and ask quotes as input. The deposit quotes are already zero-coupon quotes, thus the resulting yield curve is simply the average of the deposit bid and ask quotes: Period Deposit Swap Bid Yield Curve Bid Ask Ask O/N 4.8 4.88 4.84 T/N 4.78 4.84 4.81 6M 5.1 5.1 5.1 1Y 5.161 5.161 5.161 2Y 5.257 5.257 3Y 5.32 5.32 Average The remaining rates for the yield curve, for the 2Y and 3Y periods, have to be solved from the existing rates using bootstrapping. 2.2.1.4.1 Finding the 2-year rate The object of the zero-coupon curve calculation is to derive a set of rates that, when used to price the fixed leg of the swap specified in the underlying swap curve, will price all the fixed-leg payments at par on the spot date. 84 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves To calculate the market value at spot MVspot of the fixed leg of a 2-year swap, the following equation is used: Equation 2-121 2-year swap: market value at spot MVspot A × r 2s × cp 1 A × ( 1 + r 2s × cp 2 ) MV spot = -------------------------------- + ----------------------------------------------D 1Y D 2Y where: – A = nominal amount – r2s = 2-year swap rate – cp1 = period from the spot date to the first coupon date – cp2 = period from the first coupon date to the second coupon date – D1Y = discount factor for the period between the spot date and the 1 year date – D2Y = discount factor for the period between the spot date and the 2 year date. If the swap is priced at par, then the market value at par is equal to the nominal amount: Equation 2-122 Swap priced at par A × r 2s × cp 1 A × ( 1 + r 2s ) × cp 2 A = -------------------------------- + ----------------------------------------------D 1Y D 2Y r 2s × cp 1 ( 1 + r 2s × cp 2 ) therefore: 1 = --------------------- + -----------------------------------D 1Y D 2Y Since the 1 year zero-coupon rate is already known (it is taken directly from the underlying deposit quotes), the 1 year discount factor can be calculated. This equation can be rearranged to solve D 2Y as follows: Equation 2-123 ( 1 + r 2s × cp 2 ) D 2Y = -------------------------------------------------------( 1 – ( r 2s × cp 1 ⁄ D 1Y ) ) The coupon periods cp1 and cp2 are calculated from the spot date and the swap coupon dates using the date basis of the swap quote (30/360). The date counts for the swap coupons are as follows: Period Date Days from spot (30/360 date basis) Days from spot (Actual/360 date basis) Spot 24-11-2000 0 0 1Y coupon 26-11-2001 362 367 2Y coupon 25-11-2002 721 731 Since the 30/360 date basis is used for the interpolation, the period lengths are: cp 1 = 362 / 360 cp 2 = (721 - 362) / 360 = 359 / 360 The 2-year swap rate (from the swap quotes) r 2s = 5.257%. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 85 2 Market standards and calculations 2.2 Yield curves The discount factor for the 1 year rate, D1Y, can be calculated from the 1 year rate (5.161%), using the date basis (Actual/360) and interest type (Periodic Rate) defined for that tenor: 5.161 367 D 1Y = ⎛ 1 + ------------- × --------- ⎞ = 1.05261353 ⎝ 100 360 ⎠ The discount factor D2Y then becomes: ( 1 + 0.05257 × 359 ⁄ 360 ) D 2Y = --------------------------------------------------------------------- = 1.1080711 × 362 ⁄ 360 ⎞ ⎞ ⎛ 1 – ⎛ 0.05257 ----------------------------------------------⎝ ⎝ ⎠⎠ 1.0526135 From this the 2-year zero-coupon rate r2Y can be calculated, using the date basis (30/360) and interest type (Compound Yield) defined for that tenor: ( 1 + r 2Y ) ( 721 ⁄ 360 ) = D 2Y therefore: r 2y = 1.1080711 ( 360 ⁄ 721 ) – 1 = 0.05257465 2.2.1.4.2 Finding the 3-year rate The zero-coupon curve must also price the 3-year swap at par, and so the 3 year discount factor D3Y for the period from the spot date to the 3-year date must satisfy the following condition: r 3s × cp 1 r 3s × cp 2 ( 1 + r 3s × cp 3 ) 1 = --------------------- + --------------------- + -----------------------------------D 1Y D 2Y D 3Y where: – r3s = the 3-year swap rate – cp1 = the period from the spot date to the first coupon date – cp2 = the period from the first coupon date to the second coupon date – cp3 = the period from the second coupon date to the third coupon date – D1Y = the discount factor for the period between the spot date and the 1 year date: – D2Y = the discount factor for the period between the spot date and the 2 year date: This equation can be rearranged to solve D3Y as follows: ( 1 + r 3s × cp 3 ) D 3Y = -------------------------------------------------------------------------------------------------------( 1 – ( r 3s × cp 1 ⁄ D 1Y ) – ( r 3s × cp 2 ⁄ D 2Y ) ) The coupon periods cp1, cp2, and cp3 are calculated from the spot date and the swap coupon dates using the date basis defined for the bootstrapping (30/360). The following date counts for the swap instrument coupons are as follows: Period Date Days from spot (30/360 date basis) Days from spot (Actual/360 date basis) Spot 24-11-2000 0 0 1Y coupon 26-11-2001 362 367 2Y coupon 25-11-2002 721 731 3Y coupon 24-11-2003 1080 1095 Since the 30/360 date basis is used for the interpolation, the period lengths are: cp1 = 362 / 360 86 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves cp2 = (721 - 362) / 360 = 359 / 360 cp3 = (1080 -721) / 360 = 359 / 360 The 3-year swap rate (from the swap quotes) r3s = 5.32%. The discount factors for the 1 year and 2 year rates (D1Y and D2Y) have already been calculated: D1Y = 1.0526135 D2Y = 1.1080711 So the discount factor D3Y becomes: ( 1 + 0.0532 × 359 ⁄ 360 ) D 3Y = ---------------------------------------------------------------------------------------------------------------------------- = 1.1683699 0.0532 × 362 ⁄ 360 ⎞ ⎛ 0.0532 × 359 ⁄ 360 ⎞ ⎞ ⎛ 1 – ⎛ --------------------------------------------------------------------------------------⎝ ⎝ ⎠ –⎝ ⎠⎠ 1.0526135 1.1080711 From this the 3-year zero-coupon rate r3Y, can be calculated using the date basis 30/360 and the interest type Continuous Yield defined for that tenor: ( 1 + r 3Y ) ( 1080 ⁄ 360 ) = D 3Y therefore: r 3Y = 1.1683699 ( 360 ⁄ 1080 ) – 1 = 0.05323865 The complete zero-coupon curve is shown in the table below: Period Deposit Swap Bid Yield Curve Bid Ask Ask Average O/N 4.8 4.88 4.84 T/N 4.78 4.84 4.81 6M 5.1 5.1 5.1 1Y 5.161 5.161 5.161 2Y 5.257 5.257 5.257465 3Y 5.32 5.32 5.323865 2.2.1.4.3 Finding the 3-year rate The zero-coupon yield curve must also price the 3-year swap at par, and so the 3 year discount factor D3Y for the period from the spot date to the 3-year date must satisfy the following condition: r 3s × cp 1 r 3s × cp 2 ( 1 + r 3s × cp 3 ) 1 = --------------------- + --------------------- + -----------------------------------D 1Y D 2Y D 3Y where: – r3s = the 3-year swap rate – cp1 = the period from the spot date to the first coupon date – cp2 = the period from the first coupon date to the second coupon date – cp3 = the period from the second coupon date to the third coupon date – D1Y = the discount factor for the period between the spot date and the 1 year date: – D2Y = the discount factor for the period between the spot date and the 2 year date: Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 87 2 Market standards and calculations 2.2 Yield curves This equation can be rearranged to solve D3Y as follows: ( 1 + r 3s × cp 3 ) D 3Y = -------------------------------------------------------------------------------------------------------( 1 – ( r 3s × cp 1 ⁄ D 1Y ) – ( r 3s × cp 2 ⁄ D 2Y ) ) The coupon periods cp1, cp2, and cp3 are calculated from the spot date and the swap coupon dates using the date basis defined for the bootstrapping (30/360). The following date counts for the swap instrument coupons are as follows: Period Date Days from spot (30/360 date basis) Days from spot (Actual/360 date basis) Spot 24-11-2000 0 0 1Y coupon 26-11-2001 362 367 2Y coupon 25-11-2002 721 731 3Y coupon 24-11-2003 1080 1095 Since the 30/360 date basis is used for the bootstrapping, the period lengths are: cp1 = 362 / 360 cp2 = (721 - 362) / 360 = 359 / 360 cp3 = (1080 -721) / 360 = 359 / 360 The 3-year swap rate (from the swap quotes) r3s = 5.32%. The discount factors for the 1 year and 2 year rates (D1Y and D2Y) have already been calculated: D1Y = 1.0526135 D2Y = 1.1080711 So the discount factor D3Y becomes: ( 1 + 0.0532 × 359 ⁄ 360 ) D 3Y = ---------------------------------------------------------------------------------------------------------------------------- = 1.1683699 × 362 ⁄ 360 ⎞ ⎛ 0.0532 × 359 ⁄ 360 ⎛ 1 – ⎛ 0.0532 -------------------------------------------– -------------------------------------------- ⎞ ⎞ ⎝ ⎝ ⎠ ⎝ ⎠⎠ 1.0526135 1.1080711 From this the 3-year zero-coupon rate r3Y, can be calculated using the date basis 30/360 and the interest type Continuous Yield defined for that tenor: ( 1 + r 3Y ) ( 1080 ⁄ 360 ) = D 3Y therefore: r 3Y = 1.1683699 ( 360 ⁄ 1080 ) – 1 = 0.05323865 The complete zero-coupon curve is shown in the table below: Period Deposit Swap Bid Ask O/N 4.8 4.88 4.84 T/N 4.78 4.84 4.81 6M 5.1 5.1 5.1 1Y 5.161 5.161 5.161 2Y 88 Bid Yield Curve 5.257 Ask 5.257 Average 5.257465 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves Period Deposit Bid Swap Ask 3Y Yield Curve Bid Ask Average 5.32 5.32 5.323865 2.2.1.5 Example: Yield Curve calculated using bonds Consider this example of a bootstrap yield curve calculated using bond prices, with the following definition: Data Value Spot Days 2 Calculation Date 18-07-2005 Effective Date 20-07-2005 For the deposit, there is the following data: Periods Dates Date Basis Rate Discount Factor 0/N 19-07-2005 Actual/360 4 0.9998889012 T/N 20-07-2005 Actual/360 4.1 0.9998861241 1W 27-07-2005 Actual/360 4.12 0.9989747482 1M 22-08-2005 Actual/360 4.14 0.9959952360 2M 20-09-2005 Actual/360 4.15 0.9926801325 3M 20-10-2005 Actual/360 4.16 0.9892581249 6M 20-01-2006 Actual/360 4.17 0.9789111777 9M 20-04-2006 Actual/360 4.18 0.9689484804 1Y 20-07-2006 Actual/360 4.19 0.9590334329 In addition, two bond instruments are used as input for the curve. • The cashflow structure of the first bond is: Amount Value Date Time -99.014305 20-07-2005 0.005479452 5.0694444 08-04-2006 0.723287671 5.069444 08-04-2007 1.723287671 100 08-04-2007 1.723287671 The first cashflow is the dirty price of the bond at the effective date. • The cashflow structure of the second bond is: Amount Value Date Time -98.01367611 20-07-2005 0.005479452 4.84639 08-04-2006 0.723287671 4.84639 08-04-2007 1.723287671 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 89 2 Market standards and calculations 2.2 Yield curves Amount Value Date Time 4.85967 08-04-2008 2.726027397 4.84639 08-04-2009 3.726027397 100 08-04-2009 3.726027397 The first cashflow is the bond dirty price at the effective date. The assumption is that the zero curve is piecewise linear between two node points. In this specific case, it is assumed that the zero rate is continuously compounding and the date basis is Actual/365. The maturity of the instrument is used as node points in the bootstrap algorithm: see 2.2.1.5.1 Scenario 1 - Maturity of bonds as node points on page 90. 2.2.1.5.1 Scenario 1 - Maturity of bonds as node points For the period [20/07/2006,08/04/2007] For the first bond, the coupon date 08-04-2006 falls between the 6M and the 9M periods. The discount factor is converted into continuous compound rate and the rate is interpolated to derive the discount factor at 08-04-2006: Date Discount Factor Time Rate 20-01-2006 0.50958904 0.041826583 0.9789111777 08-04-2006 0.72328767 0.041730381 0.9702678903 20-04-2006 0.75616438 0.041715581 0.9689484804 Since the zero rate is piecewise linear between the node points, that is, between one year and bond maturity [20/07/2006,08/04/2007], the one year discount factor needs to be converted into a continuous compound rate: Date Discount Factor Time Rate 20-07-2006 0.959033433 1.005479452 0.041601389586 Let us denote the slope by b, so the Pricing equation for the first bond can be written as: – 99.0143 × 0.99977504 = 5.069444 × 0.97026789 + 105.069444 × exp ( – ( 0.04160139 + b × ( 1.72328 – 1.0054794 ) ) × 1.72328 ) From this we can deduce that b = 0.031411691 The rate and the discount factor at the first bond maturity are as follows: 0.04160139 + b × ( 1.7232877 – 1.0054794 ) = 0.06414896 exp ( – ( 0.04160139 + b × ( 1.7232877 – 1.0054794 ) ) × 1.7232877 ) = 0.89534415 For the period [08/04/2007,08/04/2009] At the beginning of the period, we have: Date Discount Factor Time Rate 08-04-2007 0.895344149 1.723287671 0.064148959214 90 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves Again, since the zero rate is a piecewise linear function, the slope of the line needs to be found so that the Pricing equation for the second bond is satisfied: – 98.01368 × 0.99977504 = 4.84639 × 0.97026789 + 4.84639 × 0.89534415 + 4.85967 × exp ( ( – ( 0.06414896 + b × ( 2.7260274 – 1.7232877 ) ) × 2.7260274 ) ) + 104.84639 × exp ( ( – ( 0.06414896 + b × 3.7260274 – 1.7232877 ) ) × 3.7260274 ) ) The slope b is then calculated as -0.00364043. The time between the effective date 18-07-2005 and the 2Y node point 20-07-2007 is 2.005479452. The 2Y rate and discount factor at the value date 20-07-2007 can be calculated as: 0.06414896 + b × ( 2.0054795 – 1.7232877 ) = 0.06312166 exp ( – ( 0.06414896 + b × ( 2.0054795 – 1.7232877 ) ) × 2.0054795 ) = 0.88109556 The time between the 18-07-2005 and the maturity of the second bond (08-04-2009) is 3.726027397. The rate and the discount factor are then: 0.06414896 + b × ( 3.7260274 – 1.7232877 ) = 0.05685813 exp ( – ( 0.06414896 + b × ( 3.7260274 – 1.7232877 ) ) × 3.7260274 ) = 0.80908206 For the period [08/04/2009, ∞ +[ 08-04-2009 is the last node point. The algorithm makes a flat extrapolation based on the continuous compound rate (that is, 0.056858126). Therefore, the 5Y discount factor corresponding to 20-07-2010 (that is, for time 5.008219178), is: exp ( – ( 0.05685813 ) × 5.0082192 ) = 0.75219629 2.2.2 Basis swaps 2.2.2.1 Tenor Basis Swap Curve This section describes the algorithm used in converting tenor basis swap spreads into discount factors. The input to the algorithm consists of a base yield curve and a series of tenor basis spread quotes, resulting in a tenor basis swap curve. We search for a series of discount factors such that the value of the tenor basis swap is at par. The estimation curve method is used in tenor basis swaps, i.e. the underlying curve is used for discounting, and the derived tenor basis swap curve for the estimation of the swap coupon amounts (for the leg for which the spread is quoted). 2.2.2.1.1 Input • Spot date • Basis swap quotes: These are tuples (start date, maturity, spread, coupon frequency), with some implicit rules for the generation of coupons. Discount curve: A fixed curve that provides discount factors ( Dd ) for required dates. • • Coupon estimation: This is a function E [ D 1, D 2, s, ϒ ] that returns a coupon estimate, given two discount factors, coupon period, and a spread. The bootstrap algorithm input is generated from this data. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 91 2 Market standards and calculations 2.2 Yield curves For each swap quote we generate the coupon date data (see Equation 2-124 on page 92), corresponding to the start, end, and payment dates, and the length of the coupon period of the ith coupon of the jth quote. Equation 2-124 Coupon date data We shall also need the discount factors derived from the discount curve for all payment dates: Equation 2-125 Discount factors for all payment dates Given the interpolation date basis, all dates are transformed into times from spot date, so that we have coupon time triplets (Equation 2-126 on page 92) and swap maturity times (Equation 2-127 on page 92). Equation 2-126 Coupon time triplets Equation 2-127 Swap maturity times 2.2.2.1.2 Algorithm Initially, set T, the last known node point, to zero (i.e. spot). 1. Choose the smallest maturity greater than the last known node point T, i.e. choose J: Equation 2-128 Smallest maturity There could, in principle be more than one, but start by assuming that J is unique. 2. For all i such that t ei ≤ T , calculate the coupon estimate based on the known part of the J bootstrap curve: Equation 2-129 Coupon estimate Where some interpolation may be needed, use the interpolation method specified for the derived curve. 3. Calculate the stub price of the swap as the sum of the known coupons of each leg: Equation 2-130 Stub price of the swap Note: For discounting, we use the discount curve that was given as input. The term Dd [ TJ ] can be interpreted as the discounted value of the redemption payment, in which case the other 92 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves leg has value 1. Likewise, we may interpret the term 1 – Dd [ T J ] as the value of the other leg in case there is no principal exchange. 4. Initialize iteration: Create a new node point for the bootstrap curve at T J , with initial value Dn = 0.00001 5. For each coupon with t ei J > T , calculate the estimate based on D e [ T ] (known) and Dn , see Equation 2-129 on page 92. where the discount factors may have to be interpolated from D e [ T ] and Dn , using the interpolation method specified for the derived curve. Calculate the value of the swap: Equation 2-131 Swap value If P n is positive, let D p = D n , and P p = P n . If P n is negative, stop. 6. Repeat step 5. on page 93 using Dn = 1 . If P n is negative let D l = D n and P l = P n . If P n is positive, stop. 7. Generic step: Use a goal seek algorithm and the method described in step 5. on page 93 to find D n so that the value of the Jth swap is zero. 8. Set T = T J and create new node D e [ T J ] = D n . If T < max j [ T j ] , then go to step 1. on page 92, otherwise stop. 2.2.2.2 Cross Currency Basis Swap Curve This section describes the algorithm used in converting cross currency basis swap spreads into discount factors. The input to the algorithm consists of a base yield curve and a series of cross currency basis spread quotes, resulting in a cross currency basis swap curve. We search for a series of discount factors such that the value of the cross currency basis swap is at par. The discount curve method is used in cross currency basis swaps, i.e. the underlying curve is used for estimating the swap coupon amounts, and the derived cross currency basis swap curve for discounting (the leg for which the spread is quoted). 2.2.2.2.1 Input • Spot date • Cross currency basis swap quotes: These are tuples (start date, maturity, spread, coupon frequency), with some implicit rules for the generation of coupons. • Estimation curve: A fixed curve that provides discount factors ( D e ) for the required dates. Coupon estimation: This is a function E [ D 1, D 2, s, ϒ ] that returns a coupon estimate, given two discount factors, coupon period, and a spread. • The bootstrap algorithm input is generated from this data. For each swap quote, we generate the coupon date data (see Equation 2-124 on page 92), corresponding to the start, end, and payment dates; and the length of the coupon period of the ith coupon of the jth quote. Then, using the estimation method, together with the estimation curve discount factors for the start and end dates of the coupon, and , we can create the corresponding coupons using Equation 2-129 on page 92. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 93 2 Market standards and calculations 2.2 Yield curves Given the interpolation date basis, all dates are transformed into times from spot date, so that we have coupon payment times and swap maturity times (Equation 2-127 on page 92). 2.2.2.2.2 Algorithm Initially, set T, the last known node point, to zero (i.e. spot). 1. Choose the smallest maturity greater than the last node point: That is, choose J so that T J = minj [ T j > T ] . There could, in principle be more than one, but start by assuming that J is unique. 2. Calculate the stub price of the swap as the sum of the known discounted coupons minus the known price of the other leg (assumed at par, i.e. principals are exchanged). Equation 2-132 Discount curve: stub price 3. Initialize iteration: Create a new node point for the bootstrap curve at T J , with initial value D n = 1.0 . 4. Calculate the value of swap: Equation 2-133 Discount curve: swap value where the discount factors may have to be interpolated from D d [ T ] and D n , using the interpolation method specified for the derived curve. The last term is the principal payment: in this method, we always assume that principals are exchanged. If P n is positive, let D p = D n and P p = P n . If P n is negative, stop. 5. Repeat step 4. on page 94 using D n = 0.0000001 . If P n is negative, let let D l = D n and P l = P n . If P n is positive, stop. 6. Generic step: Use a goal seek algorithm and the method described in step 4. on page 94 to find D n so that the value of the Jth swap is zero. 7. Set T = T J and create new node D d [ T J ] = D n . If T < maxj [ Tj ] go to step 1. on page 94, otherwise stop. 2.2.2.3 Basis swap bootstrapping This section describes the algorithm used in converting basis swap spreads into discount factors. Two different approaches are presented: estimation curve bootstrapping and discount curve bootstrapping. In both approaches, the input to the algorithm consists of an underlying zero curve and a series of basis spread quotes. In both algorithms, we search for a series of discount factors such that the value of the calculated spread leg is at par. (Section 2.2.2.3.3 Non-par market value on page 97 addresses the case when the other leg is not at par.) The estimation curve method is used in tenor basis swaps, while the discount curve method is used in cross currency basis swaps. 94 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves 2.2.2.3.1 Estimation curve bootstrapping This section describes the bootstrap algorithm for estimation curve bootstrapping. In estimation curve bootstrapping, we use the underlying curve for discounting, and the bootstrapped curve for the estimation of the swap coupon amounts. This method is used in tenor basis swaps. Input data generation • Spot date • Basis swap quotes: These are tuples (start date, maturity, spread, coupon frequency), with some implicit rules for the generation of coupons. • Discount curve: A fixed curve that provides discount factors (Dd) for the required dates. • Coupon estimation: This function discount factors, coupon period, and a spread. returns a coupon estimate, given two The bootstrap algorithm input is generated from this data. For each swap quote, we generate the coupon date data ( ), corresponding to the start, end, and payment dates and the length of the coupon period of the ith coupon of the Jth quote. We shall also need the discount factors derived from the discount curve for all payment dates: . Given the interpolation date basis, all dates are transformed into times from the spot date, so that we have coupon time triplets ( ), and swap maturity times ( ). The algorithm Initially, set T, the last known node point, to zero (i.e. spot). 1. Choose the smallest maturity greater than the last known node point T. That is, choose J so that TJ=minj[Tj > T]. There could, in principle, be more than one, but start by assuming that J is unique. 2. For all i such that bootstrapped curve: , calculate coupon estimate based on the known part of the Equation 2-134 Estimation curve bootstrapping: coupon estimate – If interpolation is needed, use the interpolation method specified for the bootstrapped curve. 3. Calculate the stub price of the swap as the sum of the known coupons of each leg: Equation 2-135 Estimation curve bootstrapping: calculated stub price of the swap Note: For discounting, we use the discount curve given as input. The term can be interpreted as the discounted value of the redemption payment, in which case the other leg has value Dd[TJ]. Similarly, we may interpret the term as the value of the other leg in case there is no principal exchange. 4. Initialize iteration: Create a new node point for the bootstrap curve at TJ, with initial value Dn=0.00001 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 95 2 Market standards and calculations 2.2 Yield curves 5. For each coupon with , calculate the estimate based on De[T] (known) and Dn: Equation 2-136 Estimation curve bootstrapping: calculate the estimate – Where the discount factors may have to be interpolated from De[T] and Dn, using the interpolation method specified for the bootstrapped curve, calculate the value of swap: Equation 2-137 Estimation curve bootstrapping: calculate the value of the swap – If the value is negative, stop. Otherwise, let Dp=Dn and Pp=Pn 6. Repeat step 5. on page 96 using Dn=1. If the resulting price is positive, stop. Otherwise, let and Dl=Dn and Pl=Pn 7. Generic step: Use a goal seeker algorithm and the method described in step 5. on page 96 to find Dn so that the value of the Jth swap is zero. 8. Set T = TJ and create the new node De[TJ]=Dn. If T < maxj[Tj] go to step 1. on page 95, otherwise stop. 2.2.2.3.2 Discount curve bootstrapping This section describes the bootstrap algorithm for discount curve bootstrapping. In discount curve bootstrapping these roles are exchanged: the underlying curve generates the coupon estimates, and the bootstrapped curve is used in discounting. The discount curve method is used in cross currency basis swaps. Input data generation • Spot date • Basis swap quotes: These are tuples (start date, maturity, spread, coupon frequency), with some implicit rules for the generation of coupons. • Estimation curve: A fixed curve that provides discount factors (De) for required dates. • Coupon estimation: This is a function two discount factors, coupon period, and a spread. that returns a coupon estimate, given The bootstrap algorithm input is generated from this data. For each swap quote, we first generate the coupon date data ( ), corresponding to the start, end, and payment dates, and the length of the coupon period ith of the coupon jth of the quote (sj). Then, using the estimation method with the estimation curve discount factors for the start and end dates of the coupon, and , we can create the corresponding coupons using the following equation: Equation 2-138 Discount curve bootstrapping: creating the coupons Given the interpolation date basis, all dates are transformed into times from spot date, so that we have coupon payment times ( 96 ) and swap maturity times ( ) © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves The algorithm Initially, set T, the last known node point, to zero (i.e. spot). 1. Choose the smallest maturity greater than the last node point: That is, choose J so that TJ=minj[Tj>T]. There could, in principle be more than one, but start by assuming that J is unique. 2. Calculate the stub price of the swap as the sum of the known discounted coupons minus the known price of the other leg (assumed at par, i.e. the principals are exchanged). Equation 2-139 Discount curve bootstrapping: stub price 3. Initialize iteration: Create a new node point for the bootstrap curve at Tj, with initial value Dn=1.0. 4. Calculate the value of swap: Equation 2-140 Discount curve bootstrapping: value of the swap – Where the discount factors may have to be interpolated from Dd[T] and Dn, using the interpolation method specified for the bootstrapped curve. The last term is the principal payment: in this method, we always assume that the principals are exchanged. – If the value is negative, stop. Otherwise, let Dp=Dn and Pp=Pn. 5. Repeat step 4. on page 97 using Dn=0.0000001. If the resulting price is positive, stop. Otherwise, let Dl=Dn and Pl=Pn. 6. Generic step: Use a goal seeker algorithm and the method described in step 4. on page 97 to find Dn so that the value of the swap is zero. 7. Set T=TJ and create the new node Dd[TJ]=Dn. If T < maxj[Tj]. If go to step 1. on page 97, otherwise stop. 2.2.2.3.3 Non-par market value The bootstrapping algorithm described in section 2.2.2.3 Basis swap bootstrapping on page 94 applies to the basic setup, where we want to bootstrap a new curve (estimation or discounting) for the spread leg, and assume that the other leg (i.e the leg whose value is taken as an input to the bootstrapping algorithm) of the swap is valued at par. There are cases when this assumption is no longer valid: • Case 1. Instead of spread leg, we calculate the new curve for the flat leg. In this case the other leg is the spread leg, which is not at par. • Case 2. We want to use two different curves for estimation and discounting of the other leg, which will then have a non-par value. In these cases the value of the other leg needs to be calculated: We have to generate its cashflows (using the estimation curve defined for the other leg) and discount them (using the discount curve defined for the other leg). The coupon structure of the other leg may differ from the structure of the calculated leg and is given in IR Quote and Yield Curve Editor's Tenor page. The estimation and calculation curves are given in IR Quote and Yield Curve Editor's Other Leg Yield Curves page once the optional feature Other Leg Yield Curves is selected. For more information about this editor, see TRM User Guide. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 97 2 Market standards and calculations 2.2 Yield curves Using the same notation as above, but with bars above the symbols to indicate that they refer to the other leg and are known in advance, the value of the other leg becomes: Equation 2-141 Non-par market value This value has to replace the value in Equation 2-135 on page 95, which becomes: Equation 2-142 Non-par market value Otherwise, bootstrapping follows the same steps as described previously. 2.2.2.4 Interpolation before first swap quote The first calculated node of a basis swap curve is usually at one year. Without any additional information, one would use the interest rate of the bootstrapped curve at the first node for all dates before it. However, it is reasonable to assume that instead of being flat, the bootstrapped curve should follow the underlying curve. To achieve this, the yield creation algorithm creates an additional virtual quote for each gap of the underlying curve that is no closer than 14 days before the first actual quote. Each virtual quote has the same value as the first actual quote, but they are treated as deposits instead of swaps. The virtual quotes are included in the bootstrapping process, and their presence causes the bootstrapped curve to follow the shape of the underlying curve also before the first spread quote. 2.2.3 Yield Curve interpolation An interpolation method is a way of estimating the shape of a yield curve between points for which quotes exist. TRM performs interpolation to calculate these rates from the closest known quotes according to the variables specified in the interpolation method. The default interpolation method of yield curves is Linear, Flat Rate Extrapolation with date basis Actual/365 and interest type Continuous Yield. 2.2.3.1 Interpolation periods The starting point of yield curve interpolation is a set of known yields for a number of periods (the node points), all having the same start date (spot date). The objective is to find the discount factor between the spot date and another date for which there is no direct data. All input quotes are first converted into discount factors between the spot date and the end date of the quote period (or start date, if the quote is for a period before the spot). Quotes that do not start or end at the spot date can be used if there is also a series of quotes starting from or ending at the spot date (for example, T/N and S/N in markets where the spot date is today). By combining the discount factors from the spot to the end dates of the forward quotes, a synthetic quote from the spot can be obtained. This can then be used in the same way as regular quotes from the spot. Before the first input period and after the last, extrapolation is required. The methods required are specified in the interpolation method definition. 98 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves 2.2.3.2 Interpolation date basis The interpolation algorithm uses the period lengths, between the common starting point of all periods and the end point of each period, as input data. When the interpolation result is requested for a target date, the period length between the common start date and the target date is needed. To calculate these period lengths, a date basis is required. The same date basis is used for all periods, regardless of the date basis used for the discount factor. The date basis specified in the interpolation method definition is used both for the calculation of the interpolation period lengths and to convert discount factors into the interpolation rate (except, of course, if the interpolation rate is a discount factor, in which case, conversion is not needed). 2.2.3.3 Interpolation over spot date When we seek a discount factor for a date after spot and before the first forward quote (most often the one week quote), the nearest known discount factor before the target date is for spot (D=1). However, that discount factor cannot be converted into rate, since the period length is zero. Therefore, the previous existing quote (usually, O/N) is used as if it were the quote for the zero-length period from spot to spot. 2.2.3.4 Type of interpolation 2.2.3.4.1 Linear To calculate the interest rate for a date for which no direct quote exists, linear interpolation is used to calculate the interest rate rm for the period tm (to spot date) between the closest quoted periods t1 and t2 such that t1 < tm < t2. Interest % r2 rm r1 Period t1 tm t2 1. The rates r1 and r2 need to be converted to the correct interest type before they can be used in the linear interpolation. To do this, two calculations need to be done: a. Calculate the discount factors D1 and D2 for the periods t1 and t2. For example, if the interest type is Annually Compounded Rate and the date basis is Actual/365, then the discount factors D1 and D2 are calculated as follows: Equation 2-143 Linear interpolation: Discount factor D1 –d --------1- r 1 365 D 1 = ⎛ 1 + ---------⎞ ⎝ 100⎠ Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 99 2 Market standards and calculations 2.2 Yield curves and Equation 2-144 Linear interpolation: Discount factor D2 –d --------2- r 2 365 D 2 = ⎛⎝ 1 + ---------⎞⎠ 100 where d1 and d2 are the actual number of days between the spot date and the period end dates for the periods t1 and t2. b. From these discount factors D1 and D2, the rates can be calculated with the correct interest type (r1C and r2C). The interest type and date basis that you selected for the interpolation of the yield curve will be used. Here, we use the interest type Continuous Yield date basis Actual/365: Equation 2-145 Linear interpolation: interest type r1C – 100 r 1C = ------------ 1nD 1 t1 and Equation 2-146 Linear interpolation: interest type r1C – 100 r 2C = ------------ 1nD 2 t2 2. Linear interpolation is then used to calculate the rate rmc. The date basis used is the one selected in the interpolation setup. The interpolation setup is described in the TRM User Guide. This rate will have the same interest type as r1C and r2C: Equation 2-147 Linear interpolation: calculated rate rmc ( t 2 – t m )r 1C + ( t m – t 1 )r 2C r mc = ---------------------------------------------------------------t2 – t1 3. The discount factor Dm, from the cashflow value date to the spot date, is calculated from the linearly interpolated rate rmc. The form of the equation is based on the date basis and interest type of the linear interpolation method. For continuous yield: Equation 2-148 Linear interpolation: Continuous Yield Dm = e – r mc -----------t m 100 4. The discount factor Dm derived from the linearly interpolated rate rmc is multiplied by the discount factors for the period from the spot date to the valuation date, using market quotes. For example, if the number of spot days is 2, we would use DO/N and DT/N: D = DO/NDT/NDm 100 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves Example: Interest rate interpolation In this example, the interest rate for a cashflow at 1.5 years is calculated using two IR quotes at 1 and 2 years. Note: In this example, all calculated amounts are rounded. Data Symbol Value Value Date 22-11-2000 Spot Days 2 Spot Date 24-11-2000 IR quote (1Y) r1 5.161% Date basis of 1Y quote d/B Actual/360 Number of days from spot date to 1Y cashflow on 26-11-2001 367 Interest type of 1Y quote Periodic IR quote (2Y) r2 5.2575% Date basis of 2Y quote d/B 30/360 Number of days from spot date to 2Y cashflow on 25-11-2002 721 Interest type of 2Y quote Annually Compounded Rate O/N quote rO/N 4.84% T/N quote rT/N 4.81% Date basis of O/N and T/N quotes d/B Actual/360 Instrument date basis d/B Actual/360 Number of days from spot date to 1.5Y on 24-05-2002 using instrument date basis 546 For this example, it is assumed that a linear interpolation method has been defined with the date basis Actual/365 and interest type of Continuous Yield. • Step 1 - Convert the reference rates to continuous yield rates To convert the reference rates r1 and r2 to continuous yield rates, first the discount factors for these rates is calculated, using the date bases and interest types defined for these two quotes. – The 1Y quote has an Actual/360 date basis and Periodic Rate interest type. This gives the following formula: Equation 2-149 Example: Interest Rate Interpolation r1 d1 D 1 = ⎛ 1 + --------- × ---------⎞ ⎝ 100 360⎠ – –1 5.161 367 –1 = ⎛ 1 + ------------- × ---------⎞ = 0.950016 ⎝ 100 360⎠ The 2Y quote has a 30/360 date basis and Annually Compounded Rate interest type. This gives the following formula: Equation 2-150 Example: Interest Rate Interpolation –d --------2- r 2 360 5.2575 D 2 = ⎛⎝ 1 + ---------⎞⎠ = ⎛⎝ 1 + ----------------⎞⎠ 100 100 – 721----------360 = 0.902469 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 101 2 Market standards and calculations 2.2 Yield curves – Next, the continuous yield rates r1C and r2C are calculated from these discount factors, using the interpolation method date basis Actual/365 and interest type Continuous Yield): Equation 2-151 Example: Interest Rate Interpolation – 100 – 100 r 1C = ------------ 1nD 1 = ---------------------- 1n ( 0.950016 ) = 5.0997 t1 367 ⁄ 365 Equation 2-152 Example: Interest Rate Interpolation – 100 – 100 r 2C = ------------ 1nD 2 = -------------------------- 1n ( 0.902469 ) = 5.124 t2 ( 731 ) ⁄ 365 • Step 2 - Linear interpolation Linear interpolation with the recalculated reference rates from the first step is used to calculate the continuous yield rate rmc. Note: tm is recalculated using the interpolation method date basis Actual/365. Equation 2-153 Linearly interpolated rate rmc r mc • – 546 546 – 367 ⎛ 731 ------------------------⎞ 5.0997 + ⎛ ------------------------⎞ 5.124 ⎝ 365 ⎠ ⎝ 365 ⎠ ( t 2 – t m )r 1C + ( t m – t 1 )r 2C = ---------------------------------------------------------------- = ------------------------------------------------------------------------------------------------ = 5.11165 t2 – t1 – 367-⎞ ⎛ 731 ----------------------⎝ 365 ⎠ Step 3 - Discount factor to spot date (Dm) The discount factor Dm, from the cashflow value date to the spot date, is calculated from the linearly interpolated rate rmc from the previous step (Equation 2-153 on page 102). The equation in this example is based on the interpolation interest type Continuous Yield and date basis Actual/365: Equation 2-154 Discount factor to spot date Dm = e • r mc ⎞ - t – ⎛ -------⎝ 100⎠ m = e 5.11165 – ⎛⎝ -------------------⎞⎠ ( 546 ⁄ 365 ) 100 = 0.926386 Step 4 - Discount factor to valuation date (D) To get the discount factor to the valuation date, the discount factor Dm to the spot date is multiplied by the discount factors for the period from the spot date to the valuation date, DO/N and DT/N. The number of spot days is 2. This gives the following equation: D = DO/NDT/NDm The discount factors DO/N and DT/N are calculated from the O/N and T/N rates, using the date basis and interest type defined for the quotes. In this case, they have both been defined with date basis Actual/360 and interest type Periodic Rate. Equation 2-155 Discount factors DO/N 4.84 1 –1 D O ⁄ N = ⎛ 1 + ---------- × ---------⎞ = 0.9998656 ⎝ 100 360⎠ 102 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves and Equation 2-156 Discount factors DT/N 4.81 1 –1 D T ⁄ N = ⎛⎝ 1 + ---------- × ---------⎞⎠ = 0.9998664 100 360 D = DO/NDT/NDm = 0.926386 * 0.9998656 * 0.9998664 = 0.926137 If a discount factor between two dates is needed, neither of which is the spot, the two discount factors between the spot and the two days in question are calculated, and divided one by the other. 2.2.3.4.2 Cubic splines interpolation The interpolation method is defined by choosing the optional feature Yield Curve Interpolation Setup, and then, in the Interpolation page, by selecting one of the interpolation methods. Choices for cubic spline are: Hermite Spline (Two Points), Hermite Spline (Three Points) or Cubic Spline. The first two refer to Hermite Spline ( Hermite spline on page 105) with slopes at node points (mi) defined by either a two-point difference or a three-point difference, as explained in section Setting the slopes at node points on page 106. The third option (Cubic Spline) corresponds to classic spline described in section Classic spline on page 104. For more information about setting up yield curves, see TRM User Guide. The input to the interpolation module is a set of points, usually giving the value of interest rate at a set of times. The task of the interpolator is to provide the value of the dependent variable (e.g. interest rate) at an arbitrary point, i.e. to extend a function defined at a restricted number of points to a function defined everywhere (or more typically, for non-negative numbers when we are dealing with time as an independent variable). The interpolation function will go through the points given as input. In the quasi-cubic spline interpolation, we also require that the interpolation function be continuous and differentiable at all points. Furthermore, a classic spline will have a continuous second derivative at all points. The yield curve interpolation is used in two different settings: where the input points are known in advance and when the shorter end of the curve is needed to construct new points in the longer end. The latter situation takes place in bootstrapping when there are coupons falling on dates, which are not maturity dates of the input quotes. (That is, we need to interpolate from the existing curve to discount such coupons.) The classic spline has the property that when any input point is changed, the whole curve moves. On the other hand, Hermite splines depend only on two or four points around the interval to be interpolated, and are therefore easier to use in bootstrapping. Technical definition Given a set of points (with and , a cubic spline is a continuous function that goes through the points in I, and is a cubic polynomial within each interval intervals altogether), and is either continuously differentiable (quasi-cubic spline) or has a continuous second derivative (classic cubic spline). Boundary conditions Let us call Pi the cubic polynomial forming the spline within interval Ii. Then, a quasi-cubic spline satisfies the following conditions: Equation 2-157 Cubic spline: conditions Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 103 2 Market standards and calculations 2.2 Yield curves This gives us 3N - 4 conditions. For classic splines, the continuity of the second derivative provides another N - 2 conditions: Equation 2-158 Cubic spline: classic splines To determine all N - 1 cubic polynomials, 4N - 4 parameters need to be set. This means that for classic spline, two additional conditions are needed, while for quasi-cubic splines N additional conditions are necessary. With classic spline, the additional two conditions are usually set at either boundary, for example: Equation 2-159 Cubic spline: natural condition and clamped spline where λ 1 and λ N are the slope of the curve at either end. For the bootstrapping algorithm, it is convenient to be able to set the two additional conditions at the short end of the curve: Equation 2-160 Cubic spline: bootstrapping algorithm conditions Classic spline The value of the spline at a point is given in terms of the second derivatives at node points (zi) as shown in Equation 2-161 on page 104: Equation 2-161 Classic spline: value of spline where 104 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves The parameters zi can be solved by requiring that the derivatives at interior nodes ( ) be continuous: Equation 2-162 Classic spline: continuous derivatives at interior nodes and that the boundary conditions are satisfied, which in case of clamped boundary conditions means: Equation 2-163 Classic spline: clamped boundary conditions In matrix form, Equation 2-162 on page 105 and Equation 2-163 on page 105 can be written as follows: Equation 2-164 Classic spline: matrix Hermite spline In each sub interval Ii, we can normalize the argument t by mapping it to the interval [0, 1] Equation 2-165 Classic spline: normalize t where Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 105 2 Market standards and calculations 2.2 Yield curves Then, we may represent the cubic polynomial as a linear combination of the third order Hermite polynomials over the normalized interval [0, 1]: Equation 2-166 Classic spline: third order Hermite polynomials where mi is the derivative at point ti. It is the setting of these N derivatives at the node points that uniquely determines the quasi-cubic spline. From Equation 2-166 on page 106 we can find the value of the second derivative of the curve at each node. The left hand-side derivative is: Equation 2-167 Classic spline: Left hand side derivative • Setting the slopes at node points There are various methods for determining mi, and we shall consider the following four: – Three-point difference Equation 2-168 Cubic spline: three-point difference method If we use clamped initial and final conditions, then: Equation 2-169 Cubic spline: three-point difference method, clamped 106 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves – Two-point difference Equation 2-170 Two-point difference If we use clamped initial and final conditions, then: Equation 2-171 Two-point difference: clamped initial and final conditions For the classic (continuous second derivative) case, we have the additional N - 2 conditions that the second derivative at each interior node point is continuous: Equation 2-172 Two-point difference: Classic – With clamped boundary conditions following set of equations: , mi can be solved from the Equation 2-173 Clamped boundary conditions: equations Note: Equation 2-173 on page 107 is equivalent to Equation 2-162 on page 105 and Equation 2-163 on page 105, except that here we use the slopes as parameters, while in the classic formulation second derivatives are used. – Replacing the long end boundary condition (mN = 2) with an initial condition on the second derivative () we have the following set of equations, which can be solved sequentially: Equation 2-174 Clamped boundary conditions: initial condition on the second derivative Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 107 2 Market standards and calculations 2.2 Yield curves Extrapolation For values t < t1 and t > tN we have to use extrapolation. For yield curve interpolation it makes sense to use linear interpolation, typically with zero slope. In this case, to maintain continuity of the first derivative, clamped boundary conditions are appropriate for the spline itself. If we apply two initial conditions for a classic spline, we have no control over the slope at the long end of the curve, and the first derivative will be discontinuous. 2.2.3.4.3 Spline building algorithm The structure of the spline building algorithm depends on whether the node points (ti, fi) are all known in advance, or whether we have to solve the values if as we go along (as in bootstrapping). There are three cases: • All node points are known: In case the values at the node points are known, we can use the methods described in Setting the slopes at node points on page 106 directly. • Bootstrapping is required to construct the curve, but interpolation is not necessary during curve construction. • Bootstrapping uses interpolation. If interpolation is needed during bootstrapping, there are two possibilities: – If the information up to a given point fully defines the interpolation curve up to that point, then we can use sequential bootstrapping ( Sequential bootstrapping on page 108). – If the information beyond the current node is necessary for the interpolator, we need an iterative algorithm ( Iterative algorithm on page 109). Sequential bootstrapping If we have to boot strap the values at node points, or if we use classic spline, a sequential algorithm is needed. We only consider classic case with initial conditions ( ) and quasi-cubic case with the two-point difference, since these are the cases amenable to the bootstrapping type of algorithm. Classic spline with boundary conditions and quasi-cubic spline with three-point difference are described in section Iterative algorithm on page 109. Set Equation 2-175 Spline building algorithm: sequential bootstrapping Equation 2-176 Spline building algorithm: sequential bootstrapping - Classic case only For the ith interval, given the value fi+1 at the right-hand end of the interval, we set for the classic case: Equation 2-177 Spline building algorithm: sequential bootstrapping - ith interval where for i > 1: Equation 2-178 Spline building algorithm: sequential bootstrapping (i > 1) 108 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves And for the quasi-cubic case: Equation 2-179 Spline building algorithm: sequential bootstrapping (quasi-cubic case) In either case, the ith spline is now given in terms fi+1. If fi+1 is known, then the sequential bootstrapping is finished. Otherwise, this function can now be used iteratively to solve the bootstrapping step, yielding a value fi+1 that provides the market price for the ith bootstrapping instrument. Iterative algorithm The sequential algorithm for classic spline, while well adapted to the solving of the bootstrap problem, cannot be made to satisfy the boundary condition at the long end of the curve. On the other hand, for quasi-cubic spline with three-point differences the sequential algorithm cannot be applied at all. For these cases we need an iterative approach. • Quasi-cubic spline In this algorithm, we solve the problem of missing node values by using the values from the previous iteration round. To initialize the values, we use sequential bootstrapping with two-point differences. – Bootstrap using the sequential algorithm with two-point differences. – Bootstrap using the sequential algorithm with three-point differences. Takes the values for nodes beyond the current one from the previous iteration round. Repeat until slopes no longer change. In practice, only one iteration is needed. • Classic spline The objective here is to use the sequential algorithm iteratively to find a classic spline with the proper slope at the long end of the curve. The idea is to apply sequential bootstrapping with the given initial slope and to adjust the initial second derivative so that the final slope, which is determined by the initial conditions and the sequential bootstrapping process, will be equal to the requested value. To ensure a good initial guess, we first carry out bootstrapping using linear interpolation and create a cubic spline through its node points. We then use the second derivative at the first node point as the initial value ( η ) for the iteration algorithm. Iteration algorithm 1. Initialize: Set the initial slope and second derivative: Equation 2-180 Cubic spline interpolation: Iteration algorithm 2. Sequential bootstrapping: Using the initial conditions and sequential bootstrapping (see Sequential bootstrapping on page 108), find the interpolation curve. 3. Iteration k: Find the error in the end condition slope: Equation 2-181 Cubic spline interpolation: Iteration algorithm Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 109 2 Market standards and calculations 2.2 Yield curves k where λ 1 is the target value, and m N is the slope at the kth iteration. If |ek| is small enough, stop, otherwise adjust the free initial variable: Equation 2-182 Cubic spline interpolation: Iteration algorithm Slope to a change in the initial second derivative. Go to 2. on page 109. 2.2.3.4.4 Reference time In interpolating a yield curve, the value to be interpolated is either the discount factor between two dates or the corresponding interest rate. One of these dates has to be common to all interpolated values, and the interpolation results depend on the choice of the common date. Since usually most of the market quotes used in the construction of the curve are from the spot, TRM uses the spot date as the common reference point for all interpolated values. This leads to a two-phased bootstrapping process: • Before spot: In the first phase, we use the valuation date as reference and apply bootstrapping only to the input quotes with maturity on or before the spot date, thus creating a stub yield curve between the valuation date and spot date. • After spot: In the second phase, we move the reference date to spot, and apply bootstrapping to all input quotes with maturity after the spot date. To these quotes, we add the discount factors between the spot date and each date from the valuation date to the spot date (including the former and excluding the latter) derived from the stub curve constructed in the first phase. Whenever a discount factor between two dates (d1 and d2) is needed, the following steps are taken: 1. Find the discount factor (D1) between the spot date (ds) and d1. To do this, calculate the length of period between ds and d1 in year using the interpolation date basis defined for the curve, and find the value of the interpolation variable at that point of time. If the interpolation variable is not a discount factor but a rate, convert the rate into discount factor by using the rate type and date basis defined for the curve. 2. Similarly, find the discount factor (D2) between ds and d2. 3. Finally, the discount factor between dates d1 and d2 is D12 = D2/D1. 2.2.3.4.5 Exponential splines If scaling is set to Logarithmic (interpolation setup), then the interpolation is carried out on the logarithms of the original values. The interpolation curve then has the form: Equation 2-183 Exponential splines: interpolation curve y(x) = e 2 a + bx + cx + dx 3 where: • The parameters a, b, c, d vary from interval to interval. 2.2.4 FX rate interpolation Forward FX rates are the result of interest rate differences. When a market FX exchange rate is needed on a date for which no direct quote is available, the exchange rate needs to be interpolated from other quotes. In FX markets, all market rates except S (spot) are quoted in terms of 110 Δ F (forward points) that are to be added to S. © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.2 Yield curves To find out, on valuation date dr, a market rate F on a future date d, one of the following methods is used: • If d is before the next banking day, then: Equation 2-184 FX rate interpolation: market rate ( d – dr ) F = S – ΔF T/N – ΔF O/N -----------------d O/N where: – dO/N is the number of days from the valuation date to the next business day. Note: For FX rates before the spot date, the forward points are taken from the opposite side of the spread. That is, the bid rate is calculated from the bid spot rate and ask points and the ask rate is calculated from the ask spot rate and bid points. • If d is before the spot date but after the next business day, then: Equation 2-185 FX rate interpolation: before spot date. after business day ( d – dT ) F = S – Δ F T/N --------------------d T/N where: – • dT is the next business day and dT/N is the number of days from the next business day to the spot. If d is the spot date, then: F=S • If there is an exact quote Δ Fd (number of forward points) for date d, then: Equation 2-186 FX rate interpolation: exact number of forward points F = S + Δ Fd • If there are two market quotes Δ Fd1 and Δ Fd2 such that d1 < d < d2 then: Equation 2-187 FX rate interpolation: two market quotes Δ F d2 – Δ F d1 - ( d – d1 ) F = S + Δ F d 1 + -------------------------d2 – d1 This is illustrated in the following figure. Forward points % ΔFd2 ΔFd ΔFd1 Period • d1 d d2 If the quote for d1 is S, then ΔF d1 = 0 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 111 2 Market standards and calculations 2.3 Key-figures If the date d is after the last quoted rate, then we extrapolate linearly using the slope between the two last quotes: • Equation 2-188 FX rate interpolation: after last quoted rate where dN is the last quote date and d N– 1 is the penultimate quote date. 2.2.4.1 Example: FX rate interpolation In this example, the USD/JPY exchange rate is calculated at a date 121 days after spot, with spot date 11-01-1999. We have the following data: Data Symbol Value Maturity d 121 days USD/JPY spot rate S 137.9 Quote for 3 months in forward points ΔF d1 -190 Quote for 6 months in forward points ΔF d2 -380 Date basis for currency Actual/360 d1 = 31 + 28 + 31 = 90 d2 = 31 + 28 + 31 + 30 + 31 + 30 = 181 Therefore, using the following equation: Equation 2-189 FX rate interpolation: interpolated forward rate Δ Fd2 – Δ Fd1 - ( d – d1 ) F = S + Δ F d 1 + -------------------------d2 – d1 The interpolated forward rate for 121 days = 137.65: Equation 2-190 FX rate interpolation: example interpolated forward rate – 0.380 – ( – 0.190 ) F = 137.9 + ( – 0.190 ) + ----------------------------------------- ( 121 – 90 ) = 137.9 – 0.254 = 137.65 181 – 90 2.3 Key-figures The following section describes the available key-figures for basic fixed cashflows. For key figures for dual currency cashflows, see 2.3.5 Dual currency on page 147. 2.3.1 Valuation Detailed calculations are available in the instrument-specific sections. 112 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures 2.3.1.1 Interest Rate The interest rate is the rate that is used in the calculation of IR exposure for the period between the cashflow's risk date and spot date. The interest rate is based on the Present Value Discount Factor (Dv) and Present Value Spot Discount Factor (Ds): where R[] is the rate type defined in the Instrument Editor's IR Exposure page (Base IR Exposure Setup feature), and t is the time between the spot date and risk date, calculated using the Date Basis defined in the Instrument Editor's IR Exposure page. Note: If the risk calculation is based on the risk yield, the yield type and date basis are derived from the setup in the Risk Yield page (Risk Yield feature) of the Instrument Editor. Depending on the setup, the Interest Rate key figure displays: • The zero coupon rates of the valuation curve (by default) • The same rate (yield-to-maturity), when the instrument's risk yield is set with Method = Yield-to-Maturity in the Risk Setup page (the Risk Setup page is available when the Feature Risk Setup (Bond) is selected). 2.3.1.2 Market Value The market value of the transaction (cashflow) calculated using the valuation method specified for the instrument, given in the figure currency. 2.3.1.3 Market Value Local The market value of the transaction (cashflow) calculated using the valuation method specified for the instrument, given in the currency of the transaction (cashflow). 2.3.2 Profit and Loss 2.3.2.1 Accrued Interest Accrued interest of the coupon converted into figure currency. 2.3.2.2 Accrued Interest Local Accrued interest in the coupon/cashflow currency. 2.3.2.3 Accrued Profit Non-interest accrued profit, for example, accrued discount premium for bonds, or amortized fees and option premiums, converted into figure currency. 2.3.2.3.1 Accrued Profit (BVC) The Accrued Profit (BVC) component of accrued profit is a Closing the Books figure which is calculated separately for each BVC adjustment, as follows: Accrued Profit (BVC) = BVC Amount (D_left - D_total) / (1 - D_total) Where: – D_total = discount factor for the period from adjustment to maturity using all-in yield as of the adjustment date. – D_left = discount factor for the period from valuation to maturity using all-in yield as of the adjustment date. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 113 2 Market standards and calculations 2.3 Key-figures 2.3.2.3.2 Accrued Profit (Costs) This is a Closing the Books figure and is the part of Accrued Profit directly related to costs (for example, fees), which is calculated separately for each fee, as follows: Accrued Fee Profit = Fee Amount (D_left - D_total) / (1 - D_total) Where: – D_total = discount factor for the period from adjustment to maturity using all-in yield as of the adjustment date. – D_left = discount factor for the period from valuation to maturity using all-in yield as of the adjustment date. 2.3.2.3.3 Accrued Profit (Discount) This is a Closing the Books figure and is the part of Accrued Profit directly related to Discount Premium (for example, fees), which is calculated for the Discount (Premium) of a Bond, as follows: Accrued Discount Profit = Discount/Premium Amount (D_left - D_total) / (1 - D_total) Where: – D_total = discount factor for the period from adjustment to maturity using all-in yield as of the adjustment date. – D_left = discount factor for the period from valuation to maturity using all-in yield as of the adjustment date. 2.3.2.3.4 Accrued Profit (Residual) The Accrued Profit (Residual) figure (that is, the discount/premium component) is then the difference between the total Accrued Profit figure and the Accrued Profit (Costs) and Accrued Profit (BVC) figures. 2.3.2.4 Accrued Profit Local Non-interest accrued profit, for example, accrued discount premium for bonds, or amortized fees and option premiums, in the currency of the transaction (cashflow). 2.3.2.5 FX Profit The part of the difference between the market value and the book value of the transaction (cashflow) due to changes in FX Spot rates. 2.3.2.6 Accrued Margin Profit Accrued Margin Profit Local converted to figure currency. 2.3.2.7 Accrued Margin Profit Local Accrued part of the margin amount. The margin profit is calculated by accruing the margin amount calculated linearly throughout the life of the transaction. 2.3.2.8 Margin Profit Margin Profit Local converted to figure currency. 2.3.2.9 Margin Profit Local The residual margin profit, i.e. Total Margin Profit Local - Accrued Margin Profit Local. 2.3.2.10 Total Margin Profit Margin Profit Local converted to figure currency. 114 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures 2.3.2.11 Total Margin Profit Local Profit resulting from transaction margins, i.e. the discounted margin amount, expressed in the currency of the transaction/margin. Margins are currently supported for short-term loans (3.8 Short term loan on page 305) and FX spots and FX forwards (6.1 FX spot and FX forward on page 383 and FX swaps (6.4 FX swap on page 416.) 2.3.2.12 MtoM Profit The part of the Profit due to changes in market variables other than FX rates, converted into figure currency. 2.3.2.13 MtoM Profit Local The part of the Local Profit due to changes in market variables other than FX rates, expressed in the currency of the transaction (cashflow). 2.3.2.14 Other Profit The part of the Profit not attributable to the other profit types (MtoM, FX, or Accrued), converted into the figure currency. 2.3.2.15 Other Profit Local The part of the Local Profit not attributable to the other profit types (MtoM, FX, or Accrued), expressed in the currency of the transaction (cashflow). 2.3.2.16 Total Profit The difference between the market value and the book value of the transaction (cashflow), converted into figure currency. 2.3.2.17 Total Profit Local The difference between the market value and the book value of the transaction (cashflow), expressed in the currency of the transaction (cashflow). 2.3.3 Option figures FX option key figures are calculated using the valuation model set up by the user: Note: For more information about option valuation models, see section 10.8.6.2.2 on page 611. Equation 2-191 where – S is the FX Spot Rate – X is the FX Strike Rate – Γa is the Asset currency continuous rate – Γc is the Cash currency continuous rate – τe is the time to expiry date – dρ is the time delay between expiry and payment date – σ is the volatility Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 115 2 Market standards and calculations 2.3 Key-figures The valuation formula may use other transaction parameters, such as gap, barrier, or exercise schedule, or model parameters, such as Quality, but these will be considered implied and not shown in the formulas. 2.3.3.1 Asset and cash currencies The values of some key figures will depend on the choice of asset and cash currencies. The asset currency is by default the currency with the higher priority (as defined in Currency Priority Editor), or the base currency in case the traded currencies have no priorities defined. For more information about setting currency priorities, see TRM User Guide, Client Priorities. You can change the (defaulted) asset currency in Transaction Manager. This impacts the option figures displayed in Transaction Manager. 2.3.3.2 Greeks Greeks are sensitivities of option price to changes in the variables determining the price. These are calculated numerically using: Equation 2-192 Greeks - sensitivities of option price where ε is a small number. TRM calculates the Greeks described in the following sections: Basic sensitivities Formula Cross sensitivities Delta Asset Rho Speed Gamma Cash Rho Speed Strike Delta Vega Speed (Vanna, Wega) Strike Gamma Theta Speed Asset Rho Delta Bleed Asset Yield Gamma Gamma Bleed 116 Formula © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures Basic sensitivities Formula Cross sensitivities Cash Rho Asset Rho Bleed Cash Yield Gamma Cash Rho Bleed Vega Vega Bleed Formula Sigma Gamma (Volga) Theta Time Gamma For barrier options, TRM offers some additional key figures, which describe the behavior of the option’s value near the barrier. These figures replicate the standard sensitivity calculations, except that the valuation is done at the barrier, without crossing it. Upper barrier sensitivities Formula Lower barrier sensitivities Upper Barrier Delta Gap Lower Barrier Delta Gap Upper Barrier Gamma Gap Lower Barrier Gamma Gap Upper Barrier Strike Delta Gap Lower Barrier Strike Delta Gap Upper Barrier Strike Gamma Gap Lower Barrier Strike Gamma Gap Upper Barrier Asset Rho Gap Lower Barrier Asset Rho Gap Upper Barrier Asset Yield Gamma Gap Lower Barrier Asset Yield Gamma Gap Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations Formula 117 2 Market standards and calculations 2.3 Key-figures Upper barrier sensitivities Formula Lower barrier sensitivities Upper Barrier Cash Rho Gap Lower Barrier Cash Rho Gap Upper Barrier Cash Yield Gamma Gap Lower Barrier Cash Yield Gamma Gap Upper Barrier Vega Gap Lower Barrier Vega Gap Upper Barrier Sigma Gamma Gap Lower Barrier Sigma Gamma Gap Upper Barrier Theta Gap Lower Barrier Theta Gap Formula 2.3.3.3 Intrinsic and time value There are three methods for intrinsic value calculation: Method Formula Description Zero Volatility Calculate option price assuming volatility zero. Forward Calculate option price assuming volatility zero, and substituting zero for cash rate and IR difference for asset rate. Spot Calculate option price assuming volatility zero, and substituting zero for cash and asset rates. For barrier options intrinsic value calculated at upper and lower barriers is called Upper Barrier Digital and Lower Barrier Digital respectively. 2.3.3.4 Risk figures Sensitivity figures are calculated for one unit of asset currency and expressed in cash currency. To convert them into risk key figures they are multiplied by cash amount (including the sign of the transaction) and FX rate between the cash currency and the figure currency. In addition, theta figures, which are originally calculated for one unit of time (year), are divided by 365 so that they will correspond to a daily change in option value. Similarly, volatility figures (vega, vanna, wega) are calculated for one unit change in volatility (100%). They are divided by 100 so that they will correspond to a change of one percentage unit in volatility. 118 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures 2.3.4 Risk Note: For Theoretical valuation, present value is equal to market value in all cases except for bond futures in IR risk figures calculation. 2.3.4.1 Exposures Exposures in general measure sensitivity of the present value to a change in a market rate. 2.3.4.1.1 FX Exposure The sensitivity of the present value of the cashflow to a change in the FX Spot rate. The magnitude of the change is defined for each currency in Currency Editor (as a percentage). FX exposures are netted within each currency (in Currency Editor), as well as within each class currency (in Currency Class Editor), see TRM User Guide. Totals that include different currencies or different currency classes are taken from the absolute values of the currency or the total exposures of the currency class. 2.3.4.1.2 IR Exposure 1 The sensitivity of the present value of the cashflow to a parallel shift of 1 basis point (1bp) in the yield curve. The value of a position can be seen as a function of a number of discount factors for different maturities: V = V [ D1, D2, ... , Dn] where other dependencies, such as FX rates, have been suppressed since they are immaterial to the issue under consideration. Alternatively, since each discount factor depends on the interest rate for the period in question, it is possible to write: V = Vr [ r1, r2, ... , rn] However, the interest rates in the second formula depend on the definition of the date basis as well as on the type of interest rate (periodic, compounded, and so on). Therefore, the first formula is more fundamental, and IR exposure calculations are based on that one. Based on the first equation, the sensitivities on discount factors can be calculated as: ∂V V i = --------∂D i For fixed cashflows, Vi is simply the amount of the cashflow, while for floating-rate instruments and derivatives, the formula will be more complex. Once the sensitivity with respect to the discount factor is found, the corresponding sensitivity with respect to an interest rate can be derived, given the type of interest rate and date basis. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 119 2 Market standards and calculations 2.3 Key-figures For example, for a yearly compounded rate: D [ t ,r ] = ( 1 + r ) –t ∂D ------- = – t ( 1 + r ) – t – 1 = – tD ( t + 1 ) ⁄ t ∂r Di ∂V ∂V- ∂------∂V- ( ti + 1 ) ⁄ ti ------- = ------- = – ------tD ∂r i ∂D i ∂r i ∂D i i i ( t + 1 ) ⁄ ti ∂V ∂V E 1bp = ------- × 0.0001 = – -------- t i D i i × 0.0001 ∂r i ∂D i where: – ti is the length of period calculated according to the chosen date basis. For other interest rate types, we get similar formulae. ∂V However, the term V r = --------- does not change with the choice of risk yield type and date basis. ∂D i The value of V r is shown in Transaction Manager as the Figure Risk Value. Note: The date basis and yield type that is used for IR exposure calculations can be defined at instrument level using the feature Base IR Exposure Setup: see A.2.48 Base IR Exposure Setup on page 732. If the instrument uses the feature Risk Yield, the date basis and yield type defined for the risk yield override the IR exposure setup for the period from spot date to risk date: see A.2.291 Risk Yield on page 859. 2.3.4.1.3 Discounting via spot date Often, discounting to the valuation date is done via spot date, with two different yield curves used for the part between the risk date and spot date (Valuation Curve), and the spot date and the valuation date (Discount Curve). In this case, we calculate the discount factor sensitivity separately for each discount factor ( D 2 [ r 2 ] from the risk date to the spot date, D 1 [ r 1 ] from the spot date to the valuation date where interest rate r 2 and discount rate r 1 are the rates over the corresponding periods). The total sensitivity to change in discount factors is then: Equation 2-193 IR exposure 1: total sensitivity of DF 2.3.4.1.4 To spot If the switch To Spot in IR Exposure page of the Instrument Editor is set (see A.2.48 Base IR Exposure Setup on page 732), IR exposure calculation is based on discounting to spot instead of to valuation 120 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures date. That is, D 1 [ r 1 ] ,the discount factor between the spot date and the valuation date is set to 1 (and the corresponding sensitivity to zero): Equation 2-194 IR exposure 1: with To Spot switch 2.3.4.2 Spot IR Exposure 1 Spot IR Exposure 1 only takes into account the part of IR exposure due to a movement of the interest rate between the spot date and the risk date: Equation 2-195 Spot IR Exposure 1 where • D 2 is the discount factor between the spot date and the risk date, • r 2 is the corresponding interest rate, converted from D 2 using the date basis and rate type defined in the IR Exposure page of Instrument Editor. r 2 is shown as Figure Interest Rate. Note: The switch To Spot in IR Exposure page of the Instrument Editor has no effect on Spot IR Exposure 1bp. 2.3.4.3 Present Value The market value of the transaction (cashflow) calculated using the risk method specified for the instrument, given in the figure currency. 2.3.4.4 Present Value Local The market value of the transaction (cashflow) calculated using the risk method specified for the instrument, given in the currency of the transaction (cashflow). 2.3.4.5 Basis Point Value Basis point value is used in the risk calculations of bond instruments and represents the value of 1 basis point. The figure is scaled so that it corresponds to a unit of the instrument, not to the position size, and is calculated as follows: (10,000.0 * (- ir_exp_down + ir_exp_up) / 2.0 / (nominal_amount * fx_convert) Where: – IR Exposure Down and IR Exposure Up are calculated with an offset equal to 0.0001 – The offset returns a value of 10,000.0 (1 / 0.0001) – 2.0 reflects the approximation used for the calculation of the numerical derivative. The individual figures can be found in Transaction Manager (that is, the sum of Figure IR Exposure Down / Up from cashflows, Nominal Amount of the transaction, and Figure FX Convert from the cashflows). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 121 2 Market standards and calculations 2.3 Key-figures 2.3.4.6 Yield Yield is shown at transaction and position levels. It is defined as: Equation 2-196 Yield key figure i y = ri Vp ∑ ----------------i ∑ Vp where • r i is the interest rate used for discounting the i th cashflow in the position • V p is the present value of the cashflow. i If an instrument is set up with the Risk Yield feature (A.2.291 Risk Yield on page 859), the same interest rate (yield to maturity) is used for the discounting of all cashflows and key figure Yield shows the yield to maturity: Equation 2-197 Yield key figure: Yield to Maturity i y = r Vp ∑ ---------------i ∑ Vp i = ∑ Vp r -------------i ∑ Vp = r 2.3.4.7 Spread 2.3.4.7.1 Z-DM (Discount Margin) Z-DM is the (constant) spread that has to be added to the risk-free rate used to discount the future (fixed or estimated) cashflows of a bond in order to have the total of the discounted cashflows equal to the market value of the bond (at spot date). The date basis and interest type used in the Z-DM calculation can be set up by adding feature Z-DM/Spread Setup to the instrument: see A.2.343 Z-DM/Spread Setup on page 882. If there is no setup, then the default values are used: Date Basis: Actual/Actual ISDA, Interest Type: Continuous. Z-DM ( μ ) is calculated by solving: Equation 2-198 Key figures: Spread = Z-DM calculation P = ∑ ci D [ R [ Di ,ti ] + μ ,ti ] + D [ R [ Dmat ,tmat ] + μ ,tmat ] where P is the (dirty) price of the instrument at spot, Di and Dmat are discount factors from the risk free curve between spot and payment dates of cashflows, ti and tmat are the times between spot date and payment dates, and ci are the coupon amounts (fixed or estimated) per unit nominal amount. Functions D[] and R[] convert the interest rate into the discount factor, and vice versa, according to the interest type setup. 2.3.4.7.2 Z-Spread Z-spread is the ratio between the Present Value Discount Factor and the Risk Free Discount Factor, converted into the rate using the date basis and interest type defined for risk free curve's interpolation. The risk free curve can be defined in the Currency Editor: see TRM User Guide. If it is not defined, the default curve of the currency is used. 122 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures The calculation for Z-Spread ( μ z ) is: Equation 2-199 Key figures: Spread: Z-Spread calculation μ z = R [ D p ⁄ D rf ,t ] Where Dp and Drf are Present Value Discount Factor and Risk Free Discount Factor, respectively, and t is time between risk base date and cashflow risk date, and is the function that converts discount factor into rate. Risk method Z-Spread In the risk method Z-Spread, the Present Value Discount Factor is calculated by adding Z-DM to the risk free rate (for the period from the spot to the risk date). Discounting from the spot to the valuation date uses the discount curve defined for the instrument as usual. When Z-DM is added to the risk free rate (rrf), it will be used according to the date basis and interest type defined for the risk free rate. For consistency, the Z-DM/Spread Setup has to use the same date basis and interest type as the risk free rate. The key figures Z-DM and Z-Spread are very similar, but not necessarily the same. Even if Z-DM and risk free curve setups match, there is the difference that Z-DM is calculated for the period between the spot and the payment date, while Z-Spread is calculated for the period between the risk base date and the payment date. If IR Exposure Setup (A.2.48 Base IR Exposure Setup on page 732) uses the To Spot switch, Z-DM and Z-spread will be calculated using the same time period. There is still another difference: While Z-DM is added to the risk free rate, Z-Spread is based on the ratio of discount factors. If the time period used (To Spot), the date basis, and the interest type setups match, we have: Equation 2-200 Key figures: Spread discount factors μ z = R [ D [ r rf + μ ,t ] ⁄ D [ r rf + t ] , t ] If we use Continuous Yield, i.e. D [ r, t ] = exp [ – r × t ] and D [ D, t ] = – log [ D ] ⁄ t then we get: μ z = – log [ exp [ – ( r rf + μ ) × t ] ⁄ exp [ – r rf × t ] ] ⁄ t μ z = – log [ exp [ – μ × t ] ] ⁄ t = μ So, in this case, Z-DM is equal to Z-Spread. If the other interest types are used, there may be some minor differences. 2.3.4.7.3 Spread IR Exposure 1 bp The Spread IR Exposure 1 bp is the sensitivity of the present value of the cashflow to a shift in the yield used for discounting from risk date to risk base date. It is defined for fixed cashflows as: Equation 2-201 Key figures: Spread IR Exposure 1 bp ∂D 2 ∂D 1 E μ = V r ⎛ D 1 --------- + D 2 ---------⎞ × 0.0001 ⎝ ∂r 2 ∂r 1 ⎠ Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 123 2 Market standards and calculations 2.3 Key-figures ∂D 2 ∂D 1 E μ = V r ⎛ D 1 --------- + D 2 ---------⎞ × 0.0001 ⎝ ∂r 2 ∂r 1 ⎠ That is, the formula is the same as for IR Exposure 1 bp: see 2.3.4.1.2 IR Exposure 1 on page 119. For floating cashflows, there is a new (not displayed) key figure, Spread Risk Value, which is equal to Figure Payment Amount for the interest cash flow, and zero for the pseudo risk cash flows. In terms of spread risk value, spread IR exposure 1bp is: Equation 2-202 Key figures: Spread IR Exposure 1 bp ∂D 2 ∂D 1 E μ = V μ ⎛ D 1 --------- + D 2 ---------⎞ × 0.0001 ⎝ ∂r 2 ∂r 1 ⎠ Where is V μ the spread risk value. That is, the exposure formula is the same for both floating and fixed cashflows, the only difference being how the risk value is obtained. The date basis and interest type used in these calculations are determined either by the IR exposure setup (feature Base IR Exposure Setup), if given, or by the interpolation method specified in the curve in the discounting (the valuation curve specified in the risk method Zero-Coupon, and the risk-free curve in the risk method Z-Spread). See A.2.289 Risk Setup (FRN) on page 858 or A.2.288 Risk Setup (BOND) on page 858. For fixed bonds, if the risk method Yield to Maturity is used, then the date basis and interest rate defined for the risk yield are applied, even if there is an IR exposure setup (feature Base IR Exposure Setup). See A.2.48 Base IR Exposure Setup on page 732. 2.3.4.7.4 Beta exposure The beta exposure is simply the Spread IR Exposure 1bp scaled with risk method Z-Spread: Equation 2-203 Key figure: beta exposure Eβ = Eμ × μz Where μ z is the Z-Spread. 2.3.4.8 Risk profiles This section describes each risk profile by explaining which risk dates are created, what market and cashflow data are used, and how calculations are carried out. A risk profile is a method to carry out interest rate risk calculations that are specific to a certain type of instrument. Risk profiles are set up at the instrument level by attaching the feature Floating Valuation Setup (A.2.338 Valuation Setup (Floating) on page 879). Each risk profile generates risk cashflows for the cashflows of the transaction, calculating risk values and convexity matrix in the prescribed manner. Risk values can be viewed in the Cashflow / Event Figure view of Transaction Manager. For more information on how IR exposure is calculated from risk values, see 2.3.4 Risk on page 119. Input A risk profile calculation uses two types of input data: market data and cashflow data. Market data includes estimation curve, valuation curve and discount curve. These are set up in the Instrument Editor, Yield Curves page. Additionally, certain risk profiles use volatility and past quotes for the fixing rate. 124 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures All risk profile calculations are carried out at the cashflow level. Different risk profiles use different properties of the cashflow in the calculations. The following sections provide detailed information about these profiles. Output Each risk profile creates a list of risk dates and a corresponding list of risk values, which together characterize the interest rate exposure of the specific cashflow. In addition, for each cashflow the risk profile estimates the fixing rate and the amount of the coupon. 2.3.4.8.1 Plain Vanilla Plain vanilla risk profile corresponds to the standard floating cashflow, where the coupon period is the same as the fixing period. Risk dates are: payment date, coupon start date (since when), and coupon end date (until when). Input data used in calculations: tc s Dp D1 Dn Coupon period length Spread Discount factor for the payment date (from valuation and discount curves) Discount factor for the start of the coupon period (from estimation curve) Discount factor for the end of the coupon period (from estimation curve) Coupon estimate Equation 2-204 Risk profile: Plain vanilla: Estimated amount A e = D 1 ⁄ D n – 1 + st c Valuation Risk values: Equation 2-205 Plain vanilla: Risk values D1 V p = ------ – 1 + st c Dn Dp V 1 = -----Dn Dp D1 V n = ------------2 Dn Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 125 2 Market standards and calculations 2.3 Key-figures Convexity matrix: Equation 2-206 Plain vanilla: Convexity matrix V pp = 0 1 V p1 = -----Dn D1 V pn = – ------2 Dn V 11 = 0 Dp V 1n = ------2 Dn Dp D1 V nn = 2 ------------3 Dn 2.3.4.8.2 Generic Risk dates are: payment date, fixing period start date, and fixing period end date. Input data used in calculations: t tf tc σ σc s Xc Xf Time to fixing date f D p , D1 , Dn Factor (=-1 for inverse floater) Fixing period length Coupon period length Volatility Convexity adjustment volatility Spread Cap rate Floor rate Discount factors Calculated variables: F R aa ac af Forward rate d1 , d2 Black76 factors Adjusted rate Convexity adjustment Cap adjustment Floor adjustment Normal distribution 126 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures where Equation 2-207 Generic V = t c ( R f + s + a c + a f )D p 2 ⎛ e tσc – 1⎞ t F 2 ⎝ ⎠ f a a = --------------------------------tf F + 1 R = F + aa ⎛ D1 ⎞ – 1⎟ ⎜ -----Dn F = ⎜ ---------------⎟ ⎜ t ⎟ ⎝ f ⎠ ac = N ( d1 ) R – N ( d2 ) X af = N ( –d2 ) X – N ( –d1 ) R 2 R σ t log ⎛ ------------⎞ + -------⎝ X – s⎠ 2 d 1 = ----------------------------------------σ t 2 R σ t log ⎛ ------------⎞ – -------⎝ X – s⎠ 2 d 2 = ----------------------------------------σ t The risk values are calculated numerically. 2.3.4.8.3 Constant Maturity Risk dates are: Payment date, start dates, and coupon dates of the underlying swap. We shall consider an individual constant maturity swap (CMS) coupon, since all unfixed coupons are handled in the same way. A fixed coupon becomes a fixed cashflow and is handled likewise. Input data: tp t1 t2 ts Time to payment date Start date of the coupon period End date of the coupon period Start date of the underlying swap Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 127 2 Market standards and calculations 2.3 Key-figures si ei σ s D p, D 1, D i , Start dates of the underlying swap coupons End dates of the underlying swap coupons Volatility e Di Discount factors corresponding to the previously mentioned dates Calculated variables: y yc ac Forward rate Convexity-adjusted rate Convexity adjustment The fair value of CMS coupon is: Equation 2-208 fair value of CMS coupon V = yc ( t2 – t1 ) where yc, the convexity adjusted forward swap rate, is calculated as shown below. For risk values and convexity matrix, we regard the adjusted swap rate as a function of discount factors, and calculate numerically the following derivatives: Equation 2-209 Constant maturity: derivative calculations ∂y c ∂V V x = ---------- = ( t 2 – t 1 ) ---------∂D x ∂D x 2 V xy 2 ∂ yc ∂ V = -------------------- = ( t 2 – t 1 ) -------------------∂D x ∂D y ∂D x ∂D y Convexity adjusted swap rate First, we calculate the forward swap yield from the underlying discount factors: Equation 2-210 Constant maturity: Forward swap yield D1 – D1 y = ------------------∑ τi Di where D1 and D2 are discount factors at the start and end of the swap, respectively, and τi = ti – t i–1 are the swap coupons’ period lengths (where we set t0 = ts). The convexity adjustment applied to the forward yield y for a swap, starting at time T is given by: Equation 2-211 Constant maturity: convexity adjustment 128 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures where σ is the yield volatility and p[yd;y] is the price of the fixed leg of the swap as function of the yield yd. The price function is given by: Equation 2-212 Constant maturity: price function p [ y d ;y ] = D [ y d, t n ] + y c ∑ τi D [ yd, ti ] i where t i are the payment dates of the fixed leg , τi are the length of the coupon periods and the discount factor D[yd;ti] are calculated using compounding with the swap frequency. The adjusted swap yield is then: Equation 2-213 Constant maturity: adjusted swap yield 2.3.4.8.4 Compound (O/N) The Compound (O/N) risk profile corresponds to a coupon determined by compounding overnight rates over the coupon period. Within the compounding period, the result of the compounding up to the valuation date is known, and the rate compounded over the remaining period is estimated from discount factors at the beginning and end of the remaining period. Therefore, the risk dates are: payment date, valuation date, and the coupon end date (until when). Before the start of the coupon period, valuation date is replaced by coupon start date (since when). Input data used in calculations: Dp D1 Discount factor for the payment date (from valuation and discount curves) Dn Discount factor for the end of the coupon period (from estimation curve) During the coupon period = 1, before coupon period discount factor for the start of the coupon period (from estimation curve) The coupon amount is compounded over the period from d s to d e , typically including only business days: Equation 2-214 Compound (O/N) coupon amount where r d is the overnight rate for day d and l d is the length of the period between two consecutive days using the appropriate day count method. The coupon amount can be estimated by: Equation 2-215 Compound (O/N) estimated coupon amount Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 129 2 Market standards and calculations 2.3 Key-figures where A f is the known part of the compound factor: Equation 2-216 Compound (O/N) compound factor and we use as the estimate for the compounding factor for the rest of the period. Risk values: Equation 2-217 Compound (O/N) risk values Convexity matrix is: Equation 2-218 Compound (O/N) convexity matrix 2.3.4.8.5 Generic Compound (O/N) The Generic Compound risk profile is a generalization of Compound (O/N) risk profile, allowing multiplicative spread as well as an additive one. In addition, the daily rate may be capped. Input data: s Spread h Multiplicative spread c Cap for the daily rate (spread-adjusted). Dp Discount factor for the payment date (from valuation and discount curves) 130 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures D1 During the coupon period = 1, before coupon period discount factor for the start of the coupon period (from estimation curve) Dn Discount factor for the end of the coupon period (from estimation curve) The payment amount of a compound floater with additive and multiplicative spreads and a cap is: Equation 2-219 Generic Compound (O/N) where the product is taken over the compounding period, A is the nominal amount of the transaction (from now on we use A = 1.0, and leave it out from subsequent formulas), s (additive spread), h (multiplicative spread), and c (cap) are constants, d is the length of a day (e.g 1/360 or 1/252, depending on the date basis, and r i is the compounding rate for day i (expressed as annually compounded rate). Valuation On a given valuation day k, we know the historical part of the compounding: Equation 2-220 Generic Compound (O/N) valuation day and in terms of the known part the estimated payment amount becomes: Equation 2-221 Generic Compound (O/N) estimated payment amount Writing A f = A k + 1 , and D p for the discount factor between valuation day k and the payment date, the fair value of the payment becomes: Equation 2-222 Generic Compound (O/N) fair value of payment where E[] is the expectation operator. The fair value (Equation 2-222 on page 131) can be calculated numerically given an interest rate model. However, for practical purposes the non-linearity of this instrument is negligible, and it will be more efficient to ignore the optional features embedded in the min operator, and carry out the valuation in a deterministic world. Also, we shall not consider the effect of rounding, since rounding renders the fair value function non-differentiable, and its effect on valuation is small anyway. Furthermore, in order to get rid of the dependence on the O/N discount factors, we shall apply the following approximation: Assume that either r i ≤ c for all i > k or r i > c for all i > k Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 131 2 Market standards and calculations 2.3 Key-figures That is, if , we shall use the estimate Equation 2-223 Generic Compound (O/N) estimate A 1 Otherwise, Equation 2-224 Generic Compound (O/N) estimate A • Fixed estimate In the first case, the cashflow can be treated as fixed, for which standard cashflow valuation and risk analysis will suffice. That is, let n be the number of days left in the fixing period. Then the estimated amount is: Equation 2-225 Generic Compound (O/N) fixed estimate As we now consider this cashflow fixed, risk values are: Generic Compound (O/N) fixed estimate risk values and the convexity matrix is empty. • Variable estimate In the second case, we shall use the following approximation: Let n be the number of days left in the fixing period and let D 1 and D n be the discount factors for the start and end of the (remaining) fixing period respectively. 132 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures Then we make the approximation: Equation 2-226 Generic Compound (O/N) variable estimate where we have set . That is, we assume that the overnight rates during the remaining fixing period are equal. Finally, let us write: Equation 2-227 Then, the estimated fixing amount becomes: Equation 2-228 The risk profile calculates the following key figures: – Estimated Amount Equation 2-229 Generic Compound (O/N) variable estimate: estimated amount – Present Value Equation 2-230 Generic Compound (O/N) variable estimate: present value Risk Values (Discount Factor Sensitivities): For risk values, it is useful to define the following differentials: Equation 2-231 Generic Compound (O/N) variable estimate: risk value differentials Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 133 2 Market standards and calculations 2.3 Key-figures Then, risk factors become: Equation 2-232 Generic Compound (O/N) variable estimate: risk factors 134 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures – Fixing Period Start Equation 2-233 Generic Compound (O/N) variable estimate: fixing period start – Fixing Period End Equation 2-234 Generic Compound (O/N) variable estimate: fixing period end – Convexity Matrix Equation 2-235 Generic Compound (O/N) variable estimate: convexity matrix Notice that if the multiplicative spread h is zero, we get: Equation 2-236 Generic Compound (O/N) variable estimate: multiplicative spread is zero and if the additive spread s is zero, we get: Equation 2-237 Generic Compound (O/N) variable estimate: additive spread is zero Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 135 2 Market standards and calculations 2.3 Key-figures 2.3.4.8.6 Compound (Simple) The Compound (Simple) risk profile is applicable to coupons based on compounded average interest rate. The actual compounding expression is only used for the estimation of the current coupon amount. Future coupons and risk are calculated using a simple generic approximation. Input data used in calculations: tc Coupon period length tf Fixing period length s Spread r Compounded rate up to the valuation day Dp D1 Discount factor for the payment date (from valuation and discount curves) Dn Discount factor for the end of the coupon period (from estimation curve) 136 During the coupon period = 1, before coupon period discount factor for the start of the coupon period (from estimation curve) © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures Coupon estimation Before the start of the coupon period, the estimated coupon is: Equation 2-238 Compound (Simple) estimated coupon During the coupon period, we use an estimate that combines the currently known compounded rate up to the valuation day (r) with a simple estimate of the discount factor for the rest of the period: Equation 2-239 Compound (Simple) during coupon period: estimate where D[] and R[] are rate to discount and discount to rate conversion functions, respectively, and t r is the length of the remaining fixing period. Valuation Risk values per unit nominal amount are calculated as: Equation 2-240 Compound (Simple) risk values Convexity matrix is: Equation 2-241 Compound (Simple) convexity matrix Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 137 2 Market standards and calculations 2.3 Key-figures 2.3.4.8.7 Average (Simple) The Average (Simple) risk profile is applicable to coupons based on interest rate averaged over a period. The actual averaging expression is only used for the estimation of the current coupon amount. Future coupons and risk are calculated using a simple generic approximation. Input data used in calculations: tc Coupon period length tf Fixing period length s Spread r Compounded rate up to the valuation day Dp D1 Discount factor for the payment date (from valuation and discount curves) Dn Discount factor for the end of the coupon period (from estimation curve) During the coupon period = 1, before coupon period discount factor for the start of the coupon period (from estimation curve) Coupon estimate First, we calculate the estimated forward rate (f) for the remaining fixing period: Equation 2-242 Average (Simple) estimated forward rate where t r is the length of the remaining fixing period, and R[] is the function that converts the discount factor into interest rate according to fixing type. Next, we calculate the expected fixing rate, based on the rate known up to the valuation date (r) and the estimated forward rate f: Equation 2-243 Average (Simple) fixing rate Finally, the estimated amount is: Equation 2-244 Average (Simple) estimated amount where D[] is the function that converts interest rate into discount factor according to fixing type. 138 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures Valuation Risk values per unit nominal amount are calculated as: Equation 2-245 Average (Simple) risk values Convexity matrix is: Equation 2-246 Average (Simple) convexity matrix 2.3.4.8.8 Fed Fund The Fed Fund risk profile corresponds to the coupon calculated from the average overnight rate over the coupon period. This average is estimated by assuming that the overnight discount factor stays constant over the coupon period, in which case, this rate can be calculated as follows: Equation 2-247 Fed funds: Average overnight rate where D 1 and D n are the discount factors for the start and end of the coupon period, and d is the number of days in the period. For the coupon with start date after the valuation date, the risk dates are payment date, coupon start date (Since When), and coupon end date (Until When). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 139 2 Market standards and calculations 2.3 Key-figures Risk values: Equation 2-248 Fed funds: Risk values Convexity matrix Equation 2-249 Fed funds: Convexity matrix Estimated amount: Equation 2-250 Fed Funds: estimated amount where tc Coupon period length Dp D1 Dn Discount factor for the coupon payment (from valuation and discount curves) 140 Discount factor for the start of the coupon period (from estimation curve) Discount factor for the end of the coupon period (from estimation curve) © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures s Spread d Number of days in the coupon period. Running coupon For the running coupon, we already know the average rate up to the valuation date. Let r be that rate, and t0 the length of the known period, te the length of the remaining period, and de the number of days in the remaining coupon period. Risk values: Equation 2-251 Fed Funds - running coupons: risk values Convexity matrix: Equation 2-252 Fed funds - running coupon: Convexity matrix Estimated amount: Equation 2-253 Fed Funds - running coupons: estimated amount Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 141 2 Market standards and calculations 2.3 Key-figures 2.3.4.9 Duration figures 2.3.4.9.1 Duration Duration is the mean maturity of money in a transaction. For a simple cashflow, the duration is simply the maturity t of the cashflow. For transactions containing several cashflows, the duration is considered as the weighted average maturity of each cashflow, with the weights, the present values of the cashflows. Equation 2-254 Key figures: Duration Σt i V i U = ------------ΣV i Where Vi Present value of the cashflow i with t i > 0 . ti Time to maturity of the cashflow i with t i > 0 . 2.3.4.9.2 Duration (Days) Duration (Days) is the Duration expressed in days. The Duration (Days) key figure is calculated as follows: Equation 2-255 Key figures: Duration (Days) calculation U ( Days ) = U × B Where U Duration B The date basis defined at the instrument level, for example, 365, 360, and so on, 2.3.4.9.3 Effective Duration Effective duration is the relative change of the present value of a position with respect to a change to the interest rate. Thus, it can be represented as a relative figure of IR Exposure, based on the IR exposure calculated with 1 bp (basis point): Equation 2-256 Key figures: Effective Duration 10000 × E { i1 } U eff = – ----------------------------------Vp Note: For a single bond evaluated with the par method and continuously compounded yield, the effective duration is the same as the Macauley duration; for yearly compounded yield, the effective duration is the same as the modified duration (see 2.3.4.9.5 Modified Duration on page 145). 142 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures For a position with present value close to zero, the effective duration, as well as Duration and Duration (Days), may be unstable (present value in the denominator). For example, if the present value of the position changes from a small positive number to a small negative number, the effective duration will change from a large positive number to a large negative number. (This happens particularly when a bond has been bought but is still in the pending state: the settlement amount belongs to the position and has a present value very close to the bond's present value.) In fact, when present value is zero, effective duration would be infinite, and will therefore not be shown. 2.3.4.9.4 Effective Convexity Convexity is related to the second order term in the Taylor expansion of the value of an asset as a function of yield: Equation 2-257 Convexity In this case, convexity is defined as C = V''/V If instead of yield, we consider zero coupon valuation, there are several variables, and the second order derivative becomes a matrix: Equation 2-258 where ri are the zero rates taken into account in the valuation of the asset. We want to use derivatives with respect to the discount factors D i [ r i ] , in which case Equation 2-259 for off diagonal elements, and Equation 2-260 Here we have written: Equation 2-261 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 143 2 Market standards and calculations 2.3 Key-figures for the part that is independent of the type of the interest rate and can therefore be calculated just by knowing the discount factors. Once we know the risk values and convexity matrix, we can estimate the change in the market value due to a small change Δ r in the valuation curve by: Equation 2-262 Duration figures - Effective Convexity: change in market value Usually, we are interested only in the parallel shift, in which case Equation 2-263 Duration figures - Effective Convexity: parallel shift where Equation 2-264 Duration figures - Effective Convexity: parallel shift and Equation 2-265 Duration figures - Effective Convexity: parallel shift Effective convexity can now be defined as: Equation 2-266 Duration figures - Effective Convexity and the convexity term corresponding to an individual risk date is: Equation 2-267 Duration figures - Effective Convexity: risk date where Vi is the present value of the ith cashflow. Note that for an asset with fixed cashflows, the cross-derivatives H ij are equal to zero when i ≠ j . 144 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures In this case we get: Equation 2-268 Duration figures - Effective Convexity: asset with fixed cashflows In particular, if the present value is calculated using yield-to-maturity method, i.e. if every cashflow is discounted with the same yield y m , we obtain: Equation 2-269 Duration figures - Effective Convexity: YTM method 2.3.4.9.5 Modified Duration For on-balance instruments modified duration is a relative figure of the IR exposure (1 bp) of the transaction based on the present value of the transaction. For off-balance instruments (as well as for on-balance instruments during the settlement period), where the present value is close to zero and not a good measure of risk taken, we substitute an estimate of the size of the underlying position. This estimate depends on the instrument type: • FRA and MM future: Average of the absolute value of the present values of the risk values at each end of the underlying contract period. • Bond future: Average of the absolute values of the present value of the position cashflows and the settlement cashflows of the underlying CTD bond. • IR Swap: Average of the present values of the legs. Example: Bond - Transaction/instrument grouping If you group by transaction or by instrument in Treasury Monitor, modified duration is calculated as follows: Equation 2-270 Grouping by transaction: modified duration calculation 10000 × E { i1 } U mod = -----------------------------------------------sett pos φ × ( Vp + Vp ) Where E { il } sett The present value of the settlement cashflows after the figure Spot Date. The value date of the settlement cashflows is the same as the transaction’s value date. pos The present value of the position cashflows after the figure Spot Date. Position cashflows correspond to all other cashflows, i.e. not settlement. Vp Vp φ The IR exposure to 1 bp change in the interest rate for the cashflows after the figure Spot Date (i.e. excluding cashflows before or on the figure Spot Date). The average of the present value components. φ = 0.5 or 1 depending on the number of present value components. Note: For example, if you have a spot position, the only component is the present value of the position cashflows and in this case φ = 1. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 145 2 Market standards and calculations 2.3 Key-figures Note: Settlement cashflows are cashflows with the same date as the value; position cashflows are all other cashflows. The IR Exposure 1bp and the Present Value figures are calculated to Valuation Date. Note: In the case of a partial forward sell or purchase of a position, you should group Instrument and Liquidity Type (extended), and monitor the 'Committed' part. This excludes the pending settlement that causes a jump in the present value weight at the instrument level. Example: Bond - Total grouping if you group by total in Treasury Monitor, modified duration is calculated as follows: Equation 2-271 Grouping by total: modified duration calculation – E { i1 } U mod = U eff = ⎛ ---------------⎞ × 10000 ⎝ Vp ⎠ where Vp The present value. E { i1 } The IR exposure to 1 basis point (bp) change in the interest rate. Example: IR Swap - Transaction/instrument grouping If you group by transaction or by instrument in Treasury Monitor, modified duration is calculated as follows: Equation 2-272 Modified Duration: IR Swap 10000 × E { i1 } U mod = --------------------------------------------------leg1 leg2 φ × ( Vp + Vp ) Where E { il } The IR exposure to 1 bp change in the interest rate for the cashflows after the figure Spot Date (i.e. excluding cashflows before or on the figure Spot Date). leg1 The present value of the cashflows of the first leg after the figure Spot Date. Vp leg2 The present value of the cashflows of the second leg after the figure Spot Date. φ The average of the present value components. Vp Note: φ = 0.5, in the case of IR Swap as we have two present value components (one per leg). 2.3.4.9.6 Effective Spread Duration Equation 2-273 Key figures: Effective Spread Duration Eμ U μ = ----------------------------V p × 0.0001 where E μ is the total spread IR exposure of the position and Vp is the total present value of the position. 146 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.3 Key-figures 2.3.4.9.7 Effective Beta Duration Effective beta duration (duration times spread or DTS) is effective spread duration scaled by Z-spread. It gives the sensitivity to a relative change in spread, where spread duration is the sensitivity to an absolute change in spread: Equation 2-274 Key figures: Effective Beta Duration Uβ = Uμ × μz See Risk method Z-Spread on page 123. 2.3.5 Dual currency A dual currency cashflow is a cashflow where the actual payment is in a different currency to the cashflow currency. The FX rate used in calculating the settlement amount may be fixed or floating. The cashflow currency amount may also be fixed or floating. TRM supports the following three cases: • Fixed amount, fixed FX rate, see 2.3.5.1 Fixed amount, fixed FX rate on page 147. • Fixed amount, floating FX rate, see 2.3.5.2 Fixed amount, floating FX rate on page 148. • Floating amount, fixed FX rate, see 2.3.5.3 Floating amount, fixed FX rate on page 148. The following sections describe how dual currency cashflows are valuated. 2.3.5.1 Fixed amount, fixed FX rate In this case the payment amount is known, so that it can be treated the same way as any fixed cashflow. The essential figures are: • Settlement Amount As As = ASs where A is Amount, and Ss is Settlement FX Rate • Figure Market Value V = AsD/(SxS) where Sx is the FX rate between cashflow currency and the settlement currency, S is Figure FX Convert (between the cashflow currency and the figure currency) and D is the Figure Market Value Discount Factor. 2.3.5.1.1 Example: Fixed amount, fixed FX rate Let us consider the following cashflow and market data: Name Symbol Value Amount A 7500.0 Settlement FX Rate Ss 10.0 FX Rate Sx 9.799 Figure FX Convert S 1.2 Figure Market Value Discount Factor D 0.9948283718493263 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 147 2 Market standards and calculations 2.3 Key-figures Key figures are: Name Symbol Value Settlement Amount Market Value As 7500.0 × 10.0 = 75000.0 Market Value V 75000.0 x 0.9948 / (9.799 x 1.2) = 6345:22 2.3.5.2 Fixed amount, floating FX rate This case is a risk-wise equivalent to an ordinary single currency cashflow, except that Figure Payment Amount has to be estimated: Payment Amount Apay • Apay = ASx where A is Amount, and Sx is FX Rate between cashflow and settlement currencies (not shown in Transaction Admin). Figure Market Value • Since the FX rate is floating, the market value (and risks) are the same as for a fixed cashflow in the cashflow currency. V = AD/S where D is Figure Market Value Discount Factor (in the cashflow currency). 2.3.5.2.1 Example: Fixed amount, floating FX rate Market data: Name Symbol Value Amount A 1000000.0 FX Rate Sx 9.799 Figure FX Convert S 1.2 Figure Market Value Discount Factor D 0.993433829648000 Name Symbol Value Payment Amount Apay 1000000.0 × 9.799 = 9799000.0 Market Value V 1000000.0 x 0.9934 / 1.2 = 827861.52 Key figures are: 2.3.5.3 Floating amount, fixed FX rate In this case IR exposure is divided between the settlement and cashflow currencies, while FX exxposure is in the cashflow currency. • Payment Amount Ap is estimated using the risk profile defined for the instrument: Ap = A[D1,D2,s]Ss where D1 and D2 are the discount factors (in cashflow currency) for the start and end dates of the interest period, s is the spread, and Ss is the Settlement FX Rate. Function A[] is the payment amount estimation method provided by the risk profile. • 148 Figure Market Value is the estimated payment amount discounted and converted to the figure currency. © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations V = ApayDpay/(SxS) where Dp is the discount factor for payment date (in settlement currency). 2.3.5.3.1 Example: Floating amount, fixed FX rate This example shows calculations with plain vanilla risk profile without spread. Name Symbol Value Amount A 1000000.0 FX Rate Sx 9.799 Settlement FX Rate Ss 10.0 Figure FX Convert S 1.2 Figure Market Value Discount Factor D 0.996858127940000 Figure Present Value Discount Factor (1) D1 0.999053805572000 Figure Present Value Discount Factor (2) D2 0.996858127940000 Figure Present Value Discount Factor (p) Dp 0.996858127940000 Name Symbol Value Payment Amount Apay 1000000.0 x (0.9991 / 0.9969 - 1) x 10.0 = 22025.98 Market Value V 22025.98 x 0.9969 / (9.799 x 1.2) = 1867.26 Key figures are: 2.4 Performance calculations Performance measurement is an area that has become increasingly important as clients of asset managers have become more sophisticated and demanding. Portfolio managers are expected to meet or beat a specified benchmark on a regular basis. In order to facilitate calculations and comparisons of traded and benchmark portfolios, common standards have evolved, such as the Performance Presentation Standards set up by the Association of Investment Management and Research (AIMR-PPS). The performance measurement implemented in TRM in Performance Monitor is based on these standards. One objective of the performance measurement process is to calculate the performance of traded portfolios and then compare it to the performance of selected benchmarks. In principle it is possible to outperform the benchmark by (i) stock (bond) picking, in other words being over or under exposed in a specific security relative to the benchmark and (ii) using leveraged instruments that have different payoff profiles than the underlying cash (spot) instruments. Examples of leveraged instruments include forwards, futures, and options. The benchmark portfolios used for comparison against the traded portfolios consist of transactions created from index compositions which represent the target performance for a portfolio. Risk, for performance measurement, is the amount of deviation from the benchmark rather than absolute changes in the portfolio market value. Treasury Monitor can be used to produce a key-figure level analysis of the traded portfolio versus the benchmark. Performance is measured by the time-weighted rate of return (TWR). TWR measures the change in the value of a portfolio as a percentage of the capital that has actually been invested. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 149 2 Market standards and calculations 2.4 Performance calculations 2.4.1 Actual basis and all cash basis The AIMR-PPS standards require that performance is measured on both an actual basis and an all cash basis. Actual basis and all cash basis can be defined as follows: • Actual basis measures the growth of the actual invested capital, in other words it is a combination of both stock picking and leverage. • All cash basis attempts to eliminate the effects of leverage by restating the position into an equivalent cash position having the same market exposure (the spot equivalent position, SEP). The all cash basis performance is then the performance measured on the restated cash equivalent position. If a fund is using leverage, the AIMR-PPS standards require the presentation of both actual and all cash basis performance. Since the benchmark is normally non-levered, the comparison between the benchmark and all cash basis show the stock picking ability of the fund manager whereas the difference between the actual and the all cash basis performance indicate timely and efficient use of leverage in managing the fund. 2.4.2 Trade date and value date based performance Typically a cash (spot) transaction is committed on the trade date but physically delivered and paid some days later on the value date. Clearly, a bought position is exposed to the market from trade date but the market value during the period until value date depends on whether the trade or value date approach is adopted. The two methods are defined as follows: • With the trade date method, the market value on the trade date is equal to the value of the position side of the transaction, and consequently, the cashflow term on the trade date is equal to the settlement payment. Thus, the trade date method can be seen as trading with immediately delivery and payment. • With the value date method, the market value during the period between trade and value date is the net value of the position and the settlement payment. On the value day the cashflow term is equal to the settlement payment and the market value is equal to the value of the position side. Traditional investment management has adopted the trade date approach, whereas the value date approach is more prevalent among corporate treasuries. TRM supports both approaches. The default is the trade date method. The AIMR-PPS standards stated that trade date valuation was required after 1/1/2005. 2.4.2.1 Bank accounts If the position includes bank accounts then buying a cash (spot) instrument is just a reallocation of the needed cash from the bank account into the bought instrument. This should of course not cause any jumps in the total market value of the position, neither should there be any cashflows in or out of the aggregated position. In value date based performance, the total market value does not show any jumps since the money is physically drawn on the bank account the same day as the bought instrument takes on the full un-netted market value. The cashflow into the instrument is balanced by the negative cashflow at the bank account and thus on the aggregated level there are no cashflows in or out of the position. Using trade date based performance the cashflows do not cancel each other out since the flow into the instrument happens on the trade date whereas the physical out flow on the bank account is at value date. Also the total market value jumps as an effect of the trade; at trade date the total value increases due to the mismatch between the un-netted market value of the bought instrument and the fact that the money is still in the bank account balance (and will earn interest) until the value date. The observed problem can be solved by including a fictitious bank account in the position. On the calculated fictive account the settlements of bought (sold) instruments are drawn (deposited) at trade date and subsequently reversed at value date. In this way, when buying (selling) an instrument we get a negative (positive) cashflow at trade date in the fictitious bank account balancing the cashflow into (out of) the instrument, and one positive (negative) cashflow at value date in the fictitious account balancing the flow out of (into) the real bank account. The increase (decrease) in the market value at instrument level is balanced by the negative (positive) balance in 150 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations the fictitious account. On the aggregated position level, there are no cashflows and no jumps in the market value, either at the trade date or the value date. 2.4.3 Time-weighted rate of return (TWR) The ideal TWR index for the period 0 to T, with valuation whenever cashflows occur, is given by: Equation 2-275 MV 1 MV l + 1 MV L MV T P TWRT, 0 = ------------------------- × .... × ----------------------- × .... × --------------------------------------- × -------------------------MV 0 + C 0 MV l + C l MV L – 1 + C L – 1 MV L + C L where – l = {0, ..., L} is the time, in the period 0 to T, at which the cashflows occur – MVl is the market value including accrued income but before any deposits/withdrawals to/from the portfolio at time l – Cl represents the cashflows (deposits, positive flow / withdrawals, negative flow) to/from the portfolio at time l. The definitions of the market values and the cashflow terms will depend on: (i) whether performance is measured on the actual basis or the all cash basis, (ii) whether the trade date or value date approach is used and (iii) the transaction type, for example whether it is a spot, forward/future, option or composite instruments such as a swap. The major drawback with the ideal TWR index is that it requires re-valuing the portfolio each time there is a cash inflow or outflow. If the portfolio does not include the cash position then every buy/sell creates a cashflow in/out of the portfolio. Thus, the portfolio has to be re-valued every time a transaction takes place. This is neither feasible nor practical and thus the ideal TWR index is normally approximated with the TWR daily sampled index: Equation 2-276 MV 1 MV t + 1 MV T P DailyT, 0 = ------------------------- × .... × ----------------------- × .... × --------------------------------------MV 0 + C 0 MV t + C t MV T – 1 + C T – 1 where – MVt is the market value including accrued income but before any deposits/withdrawals to/from the portfolio on day t, – Ct represents the sum of all cashflows (deposits, positive flow / withdrawals, negative flow) to/from the portfolio during day t: Ct = ∑ C l̃ l̃ ∈ {t – 1, t } The Dietz method overcomes the need to know the valuation of the portfolio on the date of each cashflow by assuming a constant rate of return on the portfolio during the period. The original Dietz method assumed that all cashflows occurred at the midpoint of the period. The modified Dietz Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 151 2 Market standards and calculations 2.4 Performance calculations method weights each cashflow by the amount of time it is held in the portfolio. The modified Dietz method for the period from 0 to T is given by: Equation 2-277 L MV T + ∑ ( Wl – 1 )Cl l=0 P Dietz T, 0 = ------------------------------------------------------L MV 0 + ∑ Wl Cl l=0 where the weight factor Wl is the proportion of the period (from 0 to T) that the cashflow Cl has been in/out of the portfolio: T–l W l = ----------T The original Dietz method is obtained by setting the weight Wl = 1/2, for all l. The AIMR-PPS standards currently require that portfolio performance is evaluated using TWR calculations at least quarterly and these interim returns are geometrically linked. From 1/1/2001 (periods from that date), monthly valuations are required. The AIMR accept approximation methods such as the modified Dietz method. 2.4.3.1 Percentage growth from the TWR index Assuming positive market values, the percentage growth (return) during day t is given by: Equation 2-278 % P TWRt, t – 1 = ( P TWRt, t – 1 – 1 ) × 100 Similarly for the whole period from 0 to T the percentage growth is: Equation 2-279 % P TWR T, 0 = ( P TWRT, 0 – 1 ) × 100 2.4.3.2 TWR calculations in TRM In order to calculate daily return in TRM, the intraday Dietz returns are first calculated. Then, the intraday Dietz returns are geometrically linked as a Time-Weighted Return Index: the product of the Dietz returns allows for transitions from a short/long position to a long/short position in period 0 to T. Finally, the daily return in TRM is derived as the growth from the TWR Index between time t and t-1. 152 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations 2.4.3.2.1 Intraday Dietz returns Due to the problems of determining the exact time of each intra-day cashflow to calculate the intra-day performance, we assume a constant cashflow weighted by factor W. The intraday Dietz return is then given by: Equation 2-280 ∑ MV t ( u ) + ∑ ( W – 1 )C t ( u ) u∈U u∈U P Dietzt, t – 1 = ---------------------------------------------------------------------------------∑ MVt – 1 ( u ) + ∑ WCt ( u ) u∈U u∈U where – U is the position and u an instrument in that position, – MVt(u) is the market value of the instrument u at time t including cashflows during the period t-1 to t (one day), – Ct(u) is the sum of all cashflows in (positive flow) / out (negative flow) to/from the instrument u during the period t-1 to t: Ct ( u ) = ∑ C (u) l̃ l̃ ∈ {t-1, t } – W is the constant weight factor applied to the sum of the cashflows (not the individual cashflows) giving the proportion of the day the intra-day cashflows are assumed to have been in or out of the position. With w = 1, 1/2, or 0, all cashflows are assumed to take place at the beginning, middle or end of the day, respectively. 2.4.3.2.2 Geometric linking of intraday Dietz returns These intraday returns can then be geometrically linked as a Time-Weighted Return Index to provide PDietzT,0 for the period from 0 to T. This method allows for transitions from a short/long position to a long/short position in the period 0 to T. With this method, each transition is assumed to occur at the end of a day. The M (end day) transition points are collected in the set A: Equation 2-281 ⎛ ⎞ ⎛ ⎞ A = {t: sign ⎜ ∑ MV t ( u ) + ∑ ( W – 1 )C t – 1 ( u )⎟ ≠ sign ⎜ ∑ MV t ( u ) + ∑ WC t ( u )⎟, t=1,..,T} ⎝u ∈ U ⎠ ⎝u ∈ U ⎠ u∈U u∈U where the variables are as described for Equation 2-280 on page 153 and A(m) is the mth transition from long/short to short/long (m=1,...,M). The return for a long sub-period [A(m), A(m+1)] is given by: Equation 2-282 A ( m+1 ) P FK_TWR [A ( m ),A ( m + 1 )] ( U ) = ∏ P Dietzt, t – 1 ( U ) t = A ( m )+1 and for a short sub-period: Equation 2-283 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 153 2 Market standards and calculations 2.4 Performance calculations A ( m+1 ) P shortFK_TWR [A ( m ),A ( m + 1 )] ( U ) = 2 – ∏ P Dietz t, t – 1 ( U ) t = A ( m )+1 The combined return index for the whole period from 0 to T, assuming A(0)=0 and A(M+1)=T, is given by the following: Equation 2-284 M P FK_TWR [T,0] ( U ) = ∏ P̃FK_TWR [A( m ),A( m + 1 )] ( U ) m=0 where P̃ FK_TWR [A ( m ),A ( m + 1 )] ( U ) is given by either P FK_TWR [A ( m ),A ( m + 1 )] ( U ) if ⎛ ⎞ sign ( P FK_TWR [A ( m ),0] ( U ) ) = sign ⎜ ∑ MV A ( m ) ( u ) + ∑ WC A ( m ) ( u )⎟ ⎝u ∈ U ⎠ u∈U or P shortFK_TWR [A ( m ),A ( m + 1 )] ( U ) if ⎛ ⎞ sign ( P FK_TWR [A ( m ),0] ( U ) ) ≠ sign ⎜ ∑ MV A ( m ) ( u ) + ∑ WC A ( m ) ( u )⎟ ⎝u ∈ U ⎠ u∈U 2.4.3.2.3 TRM Return as the percentage growth of the TWR Index Finally, the return during day t is given by: Equation 2-285 TRM Return as the percentage growth of the TWR Index % P TWRt, t – 1 = ( P TWRt, t – 1 – 1 ) × 100 2.4.4 Money-weighted return Given a portfolio with initial market value V0, cashflows ci on dates ti, and final market value VT at time T, money weighted return, or internal rate of return (y), is defined as the constant interest rate 154 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations such that the total of the initial value and all cashflows prolonged to time T with y is equal to the final value: Equation 2-286 ci V0 ----------------- + ∑ ------------------------- – VT = 0 D ( y ,T ) D (y,T – t i) i If the type of the interest rate is compounded (at any frequency), it is possible to choose to discount all cashflows to the start date, or any other date for that matter, and obtain the same result. Periodic rate and discount rate will usually provide different results depending on the valuation date. 2.4.4.1 Periodic Rate If we use interest type Periodic Rate and prolong to the end date of the observation period, the above equation can be solved without iteration: Equation 2-287 V 0 ( 1 + yT ) + ∑ c i ( 1 + y ( T – t i ) ) – V T = 0 i ⎛ ⎞ V T – V 0 – Σc i = y ⎜ V 0 T + ∑ c i ( T – t i ) ⎟ ⎝ ⎠ i V T – V 0 – Σc i y = --------------------------------------------V0 T + Σi ci ( T – ti ) 2.4.5 Instrument market values for third currency The saved Performance Data (Market Value) of a Portfolio is based on Treasury Monitor's market value calculation. This performance data is saved by running the Performance Data Calculation activity. The Performance Data Calculation activity saves the home currency market value and the local market value as they are calculated by Treasury Monitor. Equation 2-288 Home currency market value and local currency market value V HomeCCY = V LocalCCY × S v { LocalCCY ⁄ HomeCCY } where V HomeCCY The saved performance data (market value) Sv The FX conversion from the transaction's Trading Currency (for example GBP) into the chosen Figure Currency (for example, EUR or USD) depends on the FX method that is defined at the instrument level (Instrument Editor - Base Valuation page). See A.2.50 Base Valuation Setup on page 734. FX method calculations are described in section 2.1.6.3 FX rate calculation on page 79. LocalCCY The transaction currency HomeCCY The currency in which the Performance Data Calculation activity was run. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 155 2 Market standards and calculations 2.4 Performance calculations 2.4.5.1 Converting the portfolio home currency into figure currency By default, the Performance Monitor's market value is calculated and stored in the portfolio trading currency. Therefore, in order to display the market value in a third currency (i.e. in a figure currency other than the portfolio trading currency) the Performance Monitor converts the home currency market value into the third currency using the FX spot rate. Note: If you want to avoid the FX spot conversion and use the figure currency data that is calculated in the same way as in the Treasury Monitor, see 2.4.5.2 Figure currency based on Treasury Monitor's market value calculation on page 156. To convert the portfolio home currency into the figure currency you use the Performance Data Calculation activity as follows: Field Description Top Portfolio To Process Name of the top portfolio. The activity saves the home currency market value in the portfolio base currency. This is the default behavior if nothing is set in the Figure Currency field. Figure Currency Leave this field empty to save the home currency market value in the portfolio base currency. To display the market value in a third currency in the FX Spot Rate figure, the Performance Monitor converts the home currency market value to the third currency. Equation 2-289 Home currency market value and local currency market value V ThirdCCY = V HomeCCY × S { HomeCCY ⁄ ThirdCCY } where S The FX Spot. Note: Only one home currency market value is saved at a time. When you run the activity again, the previous market value is replaced with the new one. 2.4.5.2 Figure currency based on Treasury Monitor's market value calculation The Performance Monitor's market value can also be directly expressed (i.e. without an FX spot conversion as detailed in 2.4.5.1 Converting the portfolio home currency into figure currency on page 156) in a third currency i.e. in a figure currency other than the portfolio trading currency. In this case, like in the Treasury Monitor, the FX conversion of the transaction's cashflow currency (for example GBP) into the chosen figure currency (for example, EUR or USD) depends on the FX Method set up in the Instrument Editor in the Base Valuation page (Base Valuation Setup feature). The FX methods can be: • Spot Rate • Today's Rate (Forward points) • Today's Rate (IR Differential) See A.2.50 Base Valuation Setup on page 734 for more information. 156 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations To convert the portfolio home currency directly into the figure currency you use the Performance Data Calculation activity as follows: Field Description Top Portfolio To Process Name of the top portfolio. The activity saves the home currency market value in the portfolio base currency. This is the default behavior if nothing is set in the Figure Currency field. Figure Currency The activity saves the home currency market value in the selected figure currency. For example, if you run the Performance Data Calculation activity with a top portfolio base currency of USD and nothing in the Figure Currency field, and then you run the activity again with Figure Currency = EUR, the activity will store both the USD home currency market value and the EUR home currency market value in the database. 2.4.5.3 Examples The following the examples illustrate the different FX method calculations for a transaction of 100000000 GBP using the following data: Data Example Top Portfolio base currency USD Trading Portfolio base currency EUR Transaction currency GBP 2.4.5.3.1 FX Method = Spot Rate (Default) This example illustrates two scenarios, one with the Top Portfolio and one with the Portfolio using the Spot Rate method. The Today' s Rate (Forward Points) method is very similar to the Spot Rate method and is not described separately. Note: For the trading of futures, you need to specify a cost of carry instrument at the portfolio level. Scenario 1: The activity is run for the Top Portfolio in USD When the Performance Data Calculation activity is run on the Top Portfolio with a different base currency to the Trading Portfolio's, the Market Value is saved in the Top Portfolio currency and over the previously saved market value for the trading currency is overridden. Equation 2-290 Example - Spot Rate equation 1 V HomeCCY = V LocalCCY × -----------------------------------------------------S { LocalCCY ⁄ HomeCCY } Equation 2-291 Example - Spot Rate S { GBP ⁄ USD } = 1.50 Equation 2-292 Example - Spot Rate: Top Currency calculation V TopHomeCCY = 100000000 × 1.50 = USD150000000 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 157 2 Market standards and calculations 2.4 Performance calculations Furthermore, in Performance Monitor, when the user selects both the Top and the Trading Portfolios, the stored Market Value in the Top Portfolio currency (USD) is converted to the Trading Portfolio currency (EUR) using the FX Spot Rate. The third currency is calculated as follows: Equation 2-293 Example - Spot Rate: Third Currency equation 1 V ThirdCCY = V HomeCCY × -----------------------------------------------------S { ThirdCCY ⁄ HomeCCY } Equation 2-294 Example - Spot Rate S { EUR ⁄ USD } = 1.20 Equation 2-295 Example - Spot Rate: Third Currency conversion 1 V ThirdCCY = 150000000 × ---------- = EUR125000000 1.20 Scenario 2 The activity is run for the trading portfolio in EUR When the activity is run for the Trading Portfolio the following calculations are done: Equation 2-296 Example - Spot Rate: Trading Portfolio equation V HomeCCY = V LocalCCY × S v { LocalCCY ⁄ HomeCCY } Equation 2-297 Example - Spot Rate: Trading Portfolio FX Spot S { GBP ⁄ EUR } = 1.25 Equation 2-298 Example - Spot Rate: Trading Portfolio Currency conversion V TopHomeCCY = 100000000 × 1.25 = EUR125000000 Furthermore, in Performance Monitor, when the user selects both the Top and the Trading Portfolios, the stored Market Value in the Trading Portfolio currency (EUR) is converted to the Top Portfolio currency (USD) using the FX Spot Rate. The third currency is calculated as follows: Equation 2-299 Example - Spot Rate: Trading Portfolio Third Currency equation V ThirdCCY = V HomeCCY × S { HomeCCY ⁄ ThirdCCY } Equation 2-300 Example - Spot Rate: Trading Portfolio S { EUR ⁄ USD } = 1.20 Equation 2-301 Example - Spot Rate: Trading Portfolio Third Currency conversion V ThirdCCY = 125000000 × 1.20 = USD150000000 158 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations 2.4.5.3.2 FX Method = Today' s Rate (IR Differential) Scenario 1: The activity is run for the Top Portfolio in USD Equation 2-302 Example - Today' s Rate (IR Differential) Top Portfolio equation V HomeCCY = V LocalCCY × S v { LocalCCY ⁄ HomeCCY } Equation 2-303 Example - Today' s Rate (IR Differential) Top Portfolio currency conversion S v { GBP ⁄ USD } = 1.49983775759643 Equation 2-304 Example - Today' s Rate (IR Differential) Top Portfolio V TopHomeCCY = 100000000 × 1.49983775759 = USD149983775.76 Furthermore, in Performance Monitor, when the user selects both the Top and the Trading Portfolios, the stored Market Value in the Top Portfolio currency (USD) is converted to the Trading Portfolio currency (EUR) using the FX Spot Rate. The third currency is calculated as follows: Equation 2-305 Example - Today' s Rate (IR Differential) Top Portfolio: Third Currency equation 1 V ThirdCCY = V HomeCCY × -----------------------------------------------------S { ThirdCCY ⁄ HomeCCY } Equation 2-306 Example - Today' s Rate (IR Differential) Top Portfolio: FX Spot S { EUR ⁄ USD } = 1.20 Equation 2-307 Example - Today' s Rate (IR Differential) Top Portfolio: Third Currency conversion 1 V ThirdCCY = 149983775.76 × ------- = EUR124986479.80 1.2 Scenario 2: The activity is run for the Trading Portfolio in EUR Equation 2-308 Example - Today' s Rate (IR Differential): Trading Portfolio equation V HomeCCY = V LocalCCY × S v { LocalCCY ⁄ HomeCCY } Equation 2-309 Example - Today' s Rate (IR Differential): Trading Portfolio FX Spot S v { GBP ⁄ EUR } = 1.24988909927463 Equation 2-310 Example - Today' s Rate (IR Differential): Trading Portfolio Currency conversion V TradingCCY = 100000000 × 1.24988909927 = EUR124988909.93 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 159 2 Market standards and calculations 2.4 Performance calculations Furthermore, in Performance Monitor, when the user selects both the Top and the Trading Portfolios, the stored Market Value in the Trading Portfolio currency (EUR) is converted to the Top Portfolio currency (USD) using the FX Spot Rate. The third currency is calculated as follows: Equation 2-311 Example - Spot Rate: Trading Portfolio Third Currency equation V ThirdCCY = V HomeCCY × S { HomeCCY ⁄ ThirdCCY } Equation 2-312 Example - Spot Rate: Trading Portfolio S { EUR ⁄ USD } = 1.20 Equation 2-313 Example - Spot Rate: Trading Portfolio Third Currency conversion V ThirdCCY = 124988909.93 × 1.20 = USD149986691.91 2.4.6 Instrument market values and cashflows 2.4.6.1 Spot instruments Spot instruments are un-leveraged instruments and therefore performance measurement based on actual basis and all cash basis will be identical for those instruments. For the actual basis approach, the selected trade or value date method defined for the instrument will determine the market values and cashflows terms. For the all cash basis approach, the trade date values are used. 2.4.6.2 Forward/future instruments For forward and future instruments the delivery price is typically set such that the contract cost nothing to enter. The payoff function is linear since a 1 unit increase (decrease) in the unit forward price implies a 1 unit increase (decrease) in the market value of the (long) forward/future contract. However, since no initial investment is required the instrument has a leveraged percentage payoff compared with an equivalent spot position. As an example, consider a forward contract with delivery price 90, forward price 100 and thus a market value of 10. If the forward price increases by 1 unit to 101 then the market value of the forward also increases by 1 unit to 11 leading to a percentages return of (11/10 -1) 10%. The percentages return on the spot position is around (101/100 - 1) 1% and thus the forward position can be regarded as geared 10 times compared to the spot position. The market value at time t of a forward contract is given by: Equation 2-314 MV t = F t × #unit – K × #unit where Ft is the forward price at time t, K is the delivery price and #unit is the contract size. The sensitivity with respect to the spot rate St is given by: Equation 2-315 ∂MV t ∂( F t × # unit ) ∂( S t × D (t,T) × #unit ) -------------- = ------------------------------- = ------------------------------------------------------ = D (t,T) × #unit ∂S t ∂S t ∂S t where we have used the arbitrage free relation between the spot and forward rates expressed by the discount factor D(t,T) for the period between t and the maturity of the contract T. 160 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations The spot equivalent position, SEP (used for the all cash basis approach to performance measurement) should have the same market exposure as the forward. Therefore: Equation 2-316 ∂MV SEPt ----------------------- = D (t,T) × #unit → MV SEPt = S t × D (t,T) × #unit = F t × ( #unit ) ∂S t The market value of the spot equivalent position MVSEPt is given by the value of the position side of the forward/future transaction. The market values and cashflow terms for the two performance methods are: • Actual basis: The performance should measure the growth of the actual invested capital, in other words the market value is MVt given by Equation 2-314 on page 161. If the transaction has a cash settlement then the cashflow term at value date is equal to the settled cash amount. If the transaction results in delivery of the underlying, then this is handled as a spot transaction committed at the notification date. • All cash basis: The effect of the used leveraged should be eliminated by restating the position into a spot equivalent one, in other words the market value is given by MVSEPt in Equation 2-316 on page 161. The cashflow term at trade date should be equal to the cash needed to buy the spot equivalent position: Equation 2-317 C 0 = MV SEP0 = F 0 × # unit = K × # unit The periodical fixing of futures will cause the period market value change to be realized. From a performance perspective this is equivalent to selling/buying market value and thus the cashflow term will balance the change in market value such that the performance is unaffected by the mark-to-market process. 2.4.6.3 Option instruments There is a large variety of different option contracts in the market which have a non-linear payoff function with respect to the price of some underlying instrument. One option position and one spot position requiring the same initial investment will certainly have very different percentages returns. Typically, the return of the option position will have larger volatility than the return of the spot position. In this sense the option position is a leveraged position. First we assume an option valuation model, in TRM it is the Black-Scholes model, linking the theoretical unit value of the option f and the spot rate of the underlying instrument St: Equation 2-318 MV t = f ( S t, t, .... ) The sensitivity of the option position is then given by: Equation 2-319 ∂MV t ∂( f ( S t, t, .... ) ) -------------- = -------------------------------- × #unit = Δ ( S t, t, .... ) × #unit ∂S t ∂S t where the partial derivative using the Black-Scholes model is delta, a risk key-figure. The spot equivalent position (SEP) should have the same instantaneous market exposure as the option position. Therefore: Equation 2-320 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 161 2 Market standards and calculations 2.4 Performance calculations ∂MV SEPt ----------------------- = Δ ( S t, t, .... ) × #unit → MV SEPt = S t × Δ ( S t, t, .... ) × #unit ∂S t Thus, the SEP position is equal to: Δ ( S t, t, .... ) × #unit units of the underlying instrument. The delta typically varies over the life of the option and thus the unit size of the SEP position is not constant over time. From the above analysis the following definitions follow: • Actual basis: The performance should measure the growth of the actual invested capital, in other words the market value is MVt given by Equation 2-318 on page 162. If the transaction has a cash settlement then the cashflow term at value date is equal to the settled cash amount. If the transaction results in delivery of the underlying, then this is handled as a spot transaction committed at the exercise date. • All cash basis: The effect of the used leveraged should be eliminated by restating the position into a spot equivalent one, in other words the market value is given by MVSEPt in Equation 2-320 on page 162. The cashflow term at trade date should be equal to the cash needed to buy the spot equivalent position: Equation 2-321 C 0 = MV SEP0 = S 0 × Δ ( S 0, 0, .... ) × #unit where S0 and Δ ( S 0, 0, .... ) are the spot rate and delta, respectively, at the time the position was committed. The unit size of the SEP position may vary with time: increases can be regarded as more units being bought and decreases as some units being sold. Thus, from a performance perspective the result is a re-balancing cashflow of: Equation 2-322 C t = S t × ( Δ ( S t, t, .... ) – Δ ( S t – 1, t – 1, .... ) ) × #unit 2.4.6.4 Swaps and other composite instruments Swaps and composite instruments such as buy/sell back repos are essentially a combination of other instruments. In general the actual basis approach treats the composite as a separate instrument whereas the all cash basis approach handles the components of the composite as separate transactions. For example, when using the actual basis the market value of a regular interest rate swap is the net value of the receiving and the paying leg. For the all cash basis however the swap is regarded as one long spot position in the receiving leg and one short spot position in the paying leg. 2.4.7 Example portfolio As an example portfolio we will use a cash position together with a spot and forward position in the same instrument. The initial cash position is 100. On day 1 we first commit one spot transaction of 1 unit at the price 50 for delivery at day 3. Secondly we commit a one month forward transaction of 1 unit at the delivery price 50.5. The market rates used are given in the table below. The overnight balance on the bank account will earn the constant O/N interest rate of 0.1%. Day Spot Rate Forward Rate O/N Interest Rate 0 50 50.5 0.1% 1 51 51.5 0.1% 162 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations Day Spot Rate Forward Rate O/N Interest Rate 2 52 52.5 0.1% 3 53 53.5 0.1% 4 54 54.5 0.1% 5 55 55.5 0.1% 6 56 56.5 0.1% 7 57 57.5 0.1% 8 58 58.5 0.1% 9 59 59.5 0.1% 2.4.7.1 Actual basis performance with value date method The market values and the cashflow terms have been calculated according to the value date version of the actual basis performance method (see table below). Day 3 is the value date of the spot transaction and it can be seen that the instrument level cashflow of 50 is balanced by the bank account cashflow of -50 such that no cashflows occur at the aggregated (portfolio) level. Day Spot Forward Bank Account Portfolio Market Value Cash flow Market Value Cash flow Market Value Cash flow Market Value Cash flow 0 0 0 0 0 100 0 100 0 1 1 0 1 0 100.10 0 102.1 0 2 2 0 2 0 100.20 0 104.2 0 3 53 50 3 0 50.30 -50 106.3 0 4 54 0 4 0 50.35 0 108.35 0 5 55 0 5 0 50.40 0 110.40 0 6 56 0 6 0 50.45 0 112.45 0 7 57 0 7 0 50.50 0 114.50 0 8 58 0 8 0 50.55 0 116.55 0 9 59 0 9 0 50.60 0 118.60 0 On the portfolio level the performance (see Equation 2-280 on page 153 and Equation 2-279 on page 152) is given by: 102.1 104.2 106.3 108.35 110.40 112.45 114.50 116.55 118.60 P Dietz 9, 0 = ------------- × ------------- × ------------- × ---------------- × ---------------- × ---------------- × ---------------- × ---------------- × ---------------100 102.1 104.2 106.3 108.35 110.40 112.45 114.50 116.55 118.60 % = ---------------- = 1.1860 → P Dietz 9, 0 = ( P Dietz9, 0 – 1 ) × 100 = 18.60% 100 Thus the growth of the invested capital has been 18.60% over the period. The spot instrument level performance with the weight factor W set to 1 is given by: The high period performance is more or less due only to the 100% return of day 2 (the infinite performance of the first day is skipped by setting 1/0 = 1). The high return on day 2 is a consequence of using the value date method - the market value of the position side and the Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 163 2 Market standards and calculations 2.4 Performance calculations 1 2 53 54 55 56 57 58 59 P Dietz9, 0 = --- × --- × --------------- × ------ × ------ × ------ × ------ × ------ × ------ = 2.2692 0 1 2 + 50 53 54 55 56 57 58 % → P Dietz 9, 0 = ( P Dietz9, 0 – 1 ) × 100 = 126.92% payment side of the transaction is netted between trade date and value date. This gives a distorted instrument level performance that is not easily interpreted. 2.4.7.2 Actual Basis Performance with Trade Date Method The market values and the cashflow terms have been calculated according to the trade date version of the actual basis performance method (see table below). On day 1 the spot transaction is committed and thus we have a cashflow of 50 at the instrument level. In the table we can see that this cashflow is balanced by the negative cashflow of -50 in the calculated fictive bank account called Settlement. We also notice that the market value at spot instrument level from trade to value date is matched by the negative balance in the fictive bank account, such that the market value at portfolio level is the same as for the value date version of actual basis shown above. Day Spot Forward Bank Account Settlement Portfolio Market Value Cash flow Market Value Cash flow Market Value Cash flow Market Value Cash flow Market Value Cash flow 0 0 0 0 0 100 0 0 0 100 0 1 51 50 1 0 100.10 0 -50 -50 102.1 0 2 52 0 2 0 100.20 0 -50 0 104.2 0 3 53 0 3 0 50.30 -50 0 50 106.3 0 4 54 0 4 0 50.35 0 0 0 108.35 0 5 55 0 5 0 50.40 0 0 0 110.40 0 6 56 0 6 0 50.45 0 0 0 112.45 0 7 57 0 7 0 50.50 0 0 0 114.50 0 8 58 0 8 0 50.55 0 0 0 116.55 0 9 59 0 9 0 50.60 0 0 0 118.60 0 On the portfolio level the performance is the same as calculated for the value date method, 18.60%. The performance at the spot instrument level with the weight factor W set to 1 is now given by: 51 52 53 54 55 56 57 58 59 % P Dietz 9, 0 = --------------- × ------ × ------ × ------ × ------ × ------ × ------ × ------ × ------ = 1.18 → P Dietz9, 0 = 18% 0 + 50 51 52 53 54 55 56 57 58 showing that the instrument level performance is both stable and connected to the underlying rate change. In this example the spot rate percentages return is also 18% and thus the match is exact. With more buys and sells creating more cashflows in and out the match will not be 100%, still the connection is very strong. The performance attribution analysis of the selection effect have to be based on the trade date version and not on the value date version since the latter one is distorted by the trading in the instrument. The performance of the forward instrument is given by: 1 2 3 4 5 6 7 8 9 % P Dietz 9, 0 = --- × --- × --- × --- × --- × --- × --- × --- × --- = 9.00 → P Dietz9, 0 = 800% 0 1 2 3 4 5 6 7 8 164 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations Skipping day 0 (setting 1/0 = 1), the return of the forward was 800%. In comparison to the return on the spot position of 18%, the forward is clearly a leveraged instrument. 2.4.7.3 All cash basis performance (trade date only) The market values and the cashflow terms have been calculated according to the all cash basis performance method (see table below). With this method, all spot transactions are handled according to the trade date version. The figures for the spot transaction in the table below are therefore the same as for the actual basis performance with trade date method (previous page). The differences in the rest of the table are due to the fact that the forward position has been restated into the spot equivalent position (SEP) using the definition in 2.4.6.2 Forward/future instruments on page 160 (Equation 2-316 on page 161). Day Spot Forward Bank Account Settlement Portfolio Market Value Cash flow Market Value Cash flow Market Value Cash flow Market Value Cash flow Market Value Cash flow 0 0 0 0 0 100 0 0 0 100 0 1 51 50 51.50 50.5 100.10 0 -50 -50 152.60 50.5 2 52 0 52.50 0 100.20 0 -50 0 154.70 0 3 53 0 53.50 0 50.30 -50 0 50 156.80 0 4 54 0 54.50 0 50.35 0 0 0 158.85 0 5 55 0 55.50 0 50.40 0 0 0 160.90 0 6 56 0 56.50 0 50.45 0 0 0 162.95 0 7 57 0 57.50 0 50.50 0 0 0 165.00 0 8 58 0 58.50 0 50.55 0 0 0 167.05 0 9 59 0 59.50 0 50.60 0 0 0 169.10 0 On the forward instrument level the performance (W = 1) is now given by: · 51 52.5 53.5 54.5 55.5 56.5 57.5 58.5 59.5 P Dietz 9, 0 = ------------------- × ---------- × ---------- × ---------- × ---------- × ---------- × ---------- × ---------- × ---------- = 1.1782 0 + 50.5 51.5 52.5 53.5 54.5 55.5 56.5 57.5 58.5 % → P Dietz9, 0 = 17.82% It can be seen that the all cash basis performance for the forward instrument is very similar to the 18% return on the spot position. The use of forwards and futures gives the fund manager the possibility to gear the portfolio. In other words, they can take on more market exposure than there is cash in the portfolio to buy. In this sense the fund manager borrows money from the market. This implicit borrowing of the fund is represented at the aggregated portfolio level by a cashflow into the fund at the trade date of the forward / future. In the table above this can be seen as a cashflow of 50.5 on day 1 at the portfolio level. The all cash basis performance on the total portfolio level is given by: Note that the capital base of the fund was not fully invested; there was about 50 money that could have been invested in the spot instrument for example. If so, the all cash basis performance at the portfolio level would have been around 18%. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 165 2 Market standards and calculations 2.4 Performance calculations P Dietz9, 0 = 152.6 154.7 156.8 158.85 160.9 162.95 165 167.05 169.1 ------------------------× ------------- × ------------- × ---------------- × ---------------- × ---------------- × ---------------- × ---------------- × ---------------165 167.05 100 + 50.5 152.6 154.7 156.8 158.85 160.9 162.95 % = 1.1236 → P Dietz9, 0 = 12.36% 2.4.8 Risk-adjusted returns TRM produces risk-adjusted return figures in Performance Monitor. This allows you to measure the performance of your portfolio in relation to the amount of risk taken. Throughout this section a simplified notation for the time weighted rate of return (TWR) is used. The linked intraday Dietz returns used as TWR figures in TRM, defined in Equation 2-284 on page 154 as: P FK_TWR [T,0] ( U ) will here be denoted simply as: TWR T, 0 ( P ) 2.4.8.1 Sampling frequency As described in 2.4.3.2 TWR calculations in TRM on page 152, the time-weighted rate of return (TWR) in TRM is calculated from the intraday Dietz returns, based on daily market values and cashflows. These returns are then geometrically linked to calculate the TWR for longer periods. Due to the method of linking, it is generally not possible to calculate the TWR of a sub-period directly from the sub-period market values and cashflows. The sub-period (from b to a, b ≥ a) TWR of a portfolio P is instead given by the following equation: Equation 2-323 TWR b, 0 ( P ) TWR b, a ( P ) = ----------------------------TWR a, 0 ( P ) where TWRx,0(P) is the cumulative performance, from time 0 to x (a or b) of the portfolio P based on intraday Dietz returns. 2.4.8.1.1 Sub-period return The periodic return (%) of the sub-period is: Equation 2-324 R periodic ( b, a ) ( P ) = 100 × ( TWR b, a ( P ) – 1 ) The continuously compounded return (%) for the sub-period is: Equation 2-325 R cont ( b, a ) ( P ) = 100 × ln ( TWR b, a ( P ) ) 166 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations where ln() is the natural logarithm. Research has shown that the periodic return data tend to be skewed whereas the continuously compounded return data are more normally distributed. This is a tendency which becomes more pronounced with longer sub-periods. The measures of risk-adjusted return implemented in TRM assume normally distributed returns. The following sampling frequencies T, or sub-periods, expressed in calendar days are supported in TRM: T (sampling frequency) Calendar Days 1 1 day 1W 7 days 1M 30 days 3M 90 days During non-business days, the portfolio is assumed to have zero return and will therefore only accrue interest. For business days, the return for the sub-period, expressed in calendar days from d-T to d is therefore: Equation 2-326 TWR d, 0 ( P ) R d, d – T ( P ) = 100 × ln ⎛⎝ ------------------------------------⎞⎠ TWR d – T, 0 ( P ) (continuous yield) Equation 2-327 TWR d, 0 ( P ) R d, d – T ( P ) = 100 × ⎛ ------------------------------------ – 1⎞ ⎝ TWR d – T, 0 ( P ) ⎠ (periodic) 2.4.8.2 Aggregation periods Statistical measures (mean, variance and standard deviation) of the return given by Equation 2-326 on page 167 or Equation 2-327 on page 167 above can be calculated for either fixed or moving aggregation periods. Each measure will be associated with (and displayed at) the end date of the aggregation period. The aggregation period is expressed in terms of the sampling frequency, or T-periods (1 day, 1 week etc.). The total aggregation period length is given as N T-periods, where N is an integer. The return calculations, and hence the statistical measures, are based on the daily linked TWR series. If the length of the TWR series (which is in days) is not an integer multiple of N*T for fixed periods, or simply T for the moving periods, then the first period will be a short period. For example, assume that we have daily returns for one and a half years from 31/12/96 to 30/6/98, monthly sampling (T =1M) and a 12-month fixed aggregation period (N=12). The set of end dates would then be given by: Datesfixed = {30/6/98, 30/6/97} where the first period, to 30/6/97, would be a short period (only 6 months data available, from 31/12/96). For a 12-month moving aggregation period the set of end dates would be given by: Datesmoving = {30/6/98, 31/5/98, 30/4/98, 31/3/98, 28/2/98, 31/1/98, 31/12/97} and the first period, to 31/12/97, would be a full 12-month period. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 167 2 Market standards and calculations 2.4 Performance calculations 2.4.8.3 Portfolio returns The cumulative return of portfolio P for the aggregation period consisting of N T-periods and with an end date d is denoted by Rd,d-NT(P) and is calculated in the same way as for the sub-period return (Equation 2-326 on page 167 or Equation 2-327 on page 167): Equation 2-328 TWR d, 0 ( P ) R d, d – NT ( P ) = 100 × ln ⎛ ----------------------------------------⎞ ⎝ TWR d – NT, 0 ( P )⎠ (continuous yield) Equation 2-329 TWR d, 0 ( P ) R d, d – NT ( P ) = 100 × ⎛ ---------------------------------------- – 1⎞ ⎝ TWR d – NT, 0 ( P ) ⎠ (periodic) The annualized return is then given by: Equation 2-330 K(T) R annual, d, d – NT ( P ) = ⎛ -------------⎞ R (P) ⎝ N ⎠ d, d – NT (continuous yield) Equation 2-331 K(T) ------------⎛ ⎞ R d, d – NT ( P )⎞ N ⎛ ⎜ – 1⎟ R annual, d, d – NT ( P ) = 100 × 1 + -----------------------------⎜⎝ ⎠ ⎟ 100 ⎝ ⎠ (periodic) where K(T) is the number of T-periods making up a business year. The number of days, weeks and so on of a business year will differ from year to year. In order to simplify the calculations K(T) is fixed according to the sampling frequency T as follows: T (Sampling frequency) K(T) (no. of T-periods in business year) 1 (non-business days included) 365 1 (non-business days excluded) 260 1W 52 1M 12 3M 4 Annualizing the returns in this way makes the returns for different period lengths and sampling frequencies more comparable. Fund reports typically present return and risk adjusted return figures on an annualized basis. 168 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations 2.4.8.3.1 Statistics of the portfolio return The mean, variance and standard deviation of the portfolio return for portfolio P over the aggregation period are given as key-figures in Performance Monitor. Zero returns (from non-business days) are not included in these calculations and so these are estimates of the underlying market. A slightly different notation to that used for the return figures is employed for statistical figures. Mean Equation 2-332 T, N Rd ( P ) 1 = ---Ñ N–1 ∑ Rd – nT,d – ( n + 1 )T ( P ) n=0 Variance Equation 2-333 T, N Var ( R d ( P ) ) 1 = ------------Ñ – 1 N–1 T, N ∑ ( Rd – nT,d – ( n + 1 )T ( P ) – Rd (P)) 2 n=0 Standard Deviation Equation 2-334 T, N σ ( Rd (P)) = T, N Var ( R d (P)) where d is a period end date (as defined in 2.4.8.2 Aggregation periods on page 168), T is one of the supported sampling frequencies, N is the length of the period, expressed in T-periods and Ñ is the number of T-periodic returns that are non-null (business days). To clarify the notation used here for the statistical figures, we shall calculate the mean and variance for the last period ending 30/6/98 from the example given above in 2.4.8.2 Aggregation periods on page 168. (Daily returns for one and a half years from 31/12/96 to 30/6/98, monthly sampling (T =1M) and a 12-month aggregation period (N=12). The last period is the same for both the fixed and moving aggregation periods. Mean 11 1M,12 R 30/6/98 ( P ) 1 = ------ ∑ R 30/6/98-n × 1M, 30/6/98- ( n + 1 ) × 1M ( P ) 12 n=0 1 = ------ ( R 30/6/98, 31/5/98 ( P ) + ........ + R 31/7/97, 30/6/97 ( P ) ) 12 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 169 2 Market standards and calculations 2.4 Performance calculations Variance 11 1M,12 Var ( R 30/6/98 ( P ) ) 2 1M,12 1 = ------ ∑ ( R 30/6/98-n × 1M, 30/6/98- ( n + 1 ) × 1M ( P ) – R 30/6/98 ( P ) ) 11 n=0 2 2 1M,12 1M,12 1 = ------ ( ( R 30/6/98, 31/5/98 ( P ) – R 30/6/98 ( P ) ) + ( R 31/7/97, 30/6/97 ( P ) – R 30/6/98 ( P ) ) ) 11 The volatility is the annualized standard deviation of the cumulative return. Volatility Equation 2-335 T, N σ annual ( R d (P))= T, N K ( T ) × σ ( Rd (P)) where K(T) is the number of T-periods making up the business year. This scaling makes the volatility from one sampling frequency comparable with the volatility calculated from a different sampling frequency. The covariance between two portfolios describes the association between them. For example if a positive (negative) return in the portfolio P is associated with a positive (negative) return in the benchmark portfolio B, then the covariance between the portfolios will be positive. If a positive return in one of them is associated with a negative return in the other, then the covariance between them will be negative. Given that the returns are normally distributed then a covariance of zero implies that the returns are totally independent; if you observe the return of one portfolio it gives you no additional information about the likely return of the other portfolio. The covariance calculations in TRM exclude the null returns (the returns for non-business days) and so the covariance estimates are based on the underlying market. Covariance Equation 2-336 T, N Cov ( R d 1 -----------Ñ – 1 T, N ( P ), R d ( B ) )= N–1 T, N ∑ ( Rd – nT,d – ( n + 1)T ( P ) – Rd T, N ( P ) ) × ( R d – nT,d – ( n + 1 )T ( B ) – R d (B)) n=0 The standardized covariance is called the correlation coefficient and can have values ranging from -1 to +1. A correlation coefficient of +1 implies perfect positive correlation and -1 implies perfect negative correlation. Perfect positive (negative) correlation means that there is a positive (negative) linear relation between the returns of the two portfolios. For example if you observe a positive return in the benchmark portfolio B then you also know the positive (negative) return of the portfolio P. 170 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations Correlation Coefficient Equation 2-337 T, N ρ ( R d ( P ), T, N Rd ( B ) ) = T, N T, N Cov ( R d ( P ), R d ( B ) ) -------------------------------------------------------------------------------------T, N T, N Var ( R d ( P ) ) × Var ( R d ( B ) ) 2.4.8.3.2 TRM variables The following key-figures related to portfolio return are available in Performance Monitor. The statistics are provided for user analysis. Standard risk adjusted return measures (for example the Sharpe Ratio and the Treynor Ratio) are also provided, and are described in 2.4.9 Risk-adjusted return measures on page 175. • The return, cumulative return and annualized return figures: Return, Return (Cumulative) and Return (Annualized) key-figures, respectively. • The statistics of the portfolio (cumulative) return: Return Mean, Return Variance, Return Standard Deviation, Return Volatility, Covariance, Correlation Coefficient. 2.4.8.4 Excess returns In performance analysis the fund manager is more interested in the return relative to the benchmark portfolio than the return of the portfolio itself. The cumulative excess return of portfolio P relative to the benchmark portfolio B is the difference in returns: Equation 2-338 R d, d – NT ( P – B ) = R d, d – NT ( P ) – R d, d – NT ( B ) The annualized excess return is then calculated in a similar way to the annualized return as shown above: Equation 2-339 K(T) R annual, d, d – NT ( P – B ) = ⎛⎝ -------------⎞⎠ R (P – B) N d, d – NT (continuous yield) Equation 2-340 K(T) ------------⎛ ⎞ R d, d – NT ( P – B )⎞ N ⎜ ⎛ – 1⎟ R annual, d, d – NT ( P – B ) = 100 × 1 + ---------------------------------------⎜⎝ ⎠ ⎟ 100 ⎝ ⎠ (periodic) 2.4.8.4.1 Statistics of the excess return The mean, variance, and standard deviation of the excess return of the portfolio P relative to the benchmark B are given as key-figures in Performance Monitor. Tracking error is the same as the standard deviation. The annualized tracking error is calculated in the same way as the volatility figure above. Zero returns (from non-business days) are not included in these calculations. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 171 2 Market standards and calculations 2.4 Performance calculations Mean Equation 2-341 T, N Rd ( P 1 – B ) = ---Ñ N–1 ∑ Rd – nT,d – ( n + 1 )T ( P ) – Rd – nT,d – ( n + 1 )T ( B ) n=0 Variance Equation 2-342 T, N Var ( R d 1 -----------Ñ – 1 (P – B)) = N–1 T, N ∑ ( ( R d – nT,d – ( n + 1 )T ( P ) – R d – nT,d – ( n + 1 )T ( B ) ) – R d (P – B)) 2 n=0 Standard Deviation Equation 2-343 T, N σ ( Rd (P – B)) = T, N Var ( R d (P – B)) Tracking Error Equation 2-344 T, N TE ( R d T, N ( P – B ) ) = σ ( Rd (P – B)) Tracking Error (Annualized) Equation 2-345 T, N TE annual ( R d (P – B)) = T, N K ( T ) × TE ( R d (P – B)) where – d is a period end date (as defined in 2.4.8.2 Aggregation periods on page 168) – T is one of the supported sampling frequencies – N is the length of the period, expressed in T-periods – Ñ is the number of T-periodic returns that are non-null (business days) and – K(T) is the number of T-periods making up the business year. 2.4.8.4.2 TRM variables The following key-figures are available in Performance Monitor. The statistics are provided for user analysis. Standard risk adjusted return measures (for example Alpha, Beta, the Information Ratio) are also provided, and are described in 2.4.9 Risk-adjusted return measures on page 175. • 172 The excess return, cumulative excess return and annualized excess return: Excess Return, Excess Return (Cumulative) and Excess Return (Annualized) key-figures, respectively. © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations • The statistics of the excess return: Excess Return Mean, Excess Return Variance, Excess Return Standard Deviation, Tracking Error, Tracking Error (Annualized), Excess Return Volatility (same as Tracking Error (Annualized)). 2.4.8.5 Linear regression The figure below shows concurrent portfolio and benchmark returns together with the estimated best-fit linear regression (least squares method). If we assume that we have the following set of concurrent portfolio returns: { R d – nT,d – ( n + 1 )T ( P ), ( R d – nT,d – ( n + 1 )T ( B ) ), n = 0, ..... , N -1 } where n represents each ‘pair’ of concurrent portfolio R(P) and benchmark R(B) returns, then the linear regression function for each pair is then given by the following straight-line equation: Equation 2-346 R d – nT,d – ( n + 1 )T ( P ) = α + β × R d – nT,d – ( n + 1 )T ( B ) α (alpha) and β (beta) are selected such that the sum of the squared differences between each pair of concurrent returns (estimation error) is minimized. The estimation error is given by: Equation 2-347 N–1 T, N Err d ( α, β) = ∑ [ Rd – nT,d – ( n + 1 )T ( P ) – (α + β × Rd – nT,d – ( n + 1)T ( B )) ] 2 n=0 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 173 2 Market standards and calculations 2.4 Performance calculations Minimizing the estimation error gives the following relationships: Equation 2-348 T, N α* = R d T, N ( P ) – β* × R d (B) Equation 2-349 T, N T, N Cov ( R d ( P ), R d ( B ) ) β* = ------------------------------------------------------------T, N Var ( R d ( B ) ) Equation 2-350 T, N Err d T, N ( α*, β* ) = ( N – 1 ) × Var ( R d 2 (P)) × (1 – R ) where R2 is given by: Equation 2-351 T, N T, N ⎛ ⎞2 Cov ( R ( P ), R ( B ) ) 2 T, N T, N d d R ( R d ( P ), R d ( B ) ) = ⎜⎜ ---------------------------------------------------------------------------------------⎟⎟ T, N T, N ⎝ Var ( R d ( P ) ) × Var ( R d ( B ) )⎠ α* and β* are the best fit values of the alpha α and beta β. Alpha is the intercept on the y-axis and beta is the slope of the linear regression function. Alpha represents the part of the return from portfolio P which is independent of the benchmark movement and beta is the sensitivity of the return with respect to the benchmark. The variable R2, a least squares measure (the correlation coefficient given by Equation 2-337 on page 171 squared), is an indication of the goodness of fit of the linear regression to the data. The higher the value of R2, the better the fit of the linear function to the data - in other words, the more the portfolio returns are determined by the benchmark returns. 2.4.9 Risk-adjusted return measures In all risk-adjusted return measures the return is related to the risk taken. Therefore we need to quantify the risk. The most common measures are the portfolio return standard deviation, beta and the tracking error. The standard deviation can be seen as the risk from the perspective of the end investor in the fund whereas beta and the tracking error represent more the risk taken by the fund manager. Other risk figures, described below, are also provided for user risk analysis. 2.4.9.1 TRM variables The following risk adjusted return measures are provided. These are described in more detail below. General statistics (mean, variance, standard deviation) of the portfolio and excess returns are also provided (see 2.4.8.3 Portfolio returns on page 168 and 2.4.8.4 Excess returns on page 171). • 174 Risk adjusted return measures: Return Standard Deviation (standard deviation of the portfolio return), Return Volatility (annualized standard deviation of the portfolio return), Beta, Tracking Error, Tracking Error (Annualized), Alpha, Alpha (Annualized), Information Ratio, Sharpe Ratio, Modigliani-Modigliani, Treynor Ratio, Jensen’s Alpha. © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations 2.4.9.2 Return standard deviation The end investor’s main concern is typically the absolute level of the portfolio returns. For the investor the risk is therefore the uncertainty of the future portfolio returns. The historical risk is often measured as the N period standard deviation of the T-periodic returns of the portfolio P, as shown in Equation 2-334 on page 169 (square root of the variance). If we assume that the portfolio returns are normally distributed then we can calculate confidence intervals for the future returns, based on the historical standard deviation (SD) and mean. For example, we can say that the future returns will be in the interval mean +/- 1SD with 68% confidence and in the interval mean +/- 2SD with 95% confidence. 2.4.9.3 Return volatility The volatility is the annualized standard deviation of the cumulative portfolio return -standard deviation scaled by √K(T), where K(T) is, as shown above, the number of T-periods making up the business year (Equation 2-335 on page 170). This scaling makes the volatility from one sampling frequency comparable with the volatility calculated from a different sampling frequency. 2.4.9.4 Beta The risk for the fund manager is more the uncertainty of the future returns relative to the benchmark portfolio than the return of the portfolio itself; the risk-less portfolio for a fund manager is a portfolio that is guaranteed the same future returns as the benchmark. The historical risk relative to the benchmark can be measured by beta which, as shown in the previous section, is a measure of the sensitivity of the portfolio P with respect to changes in the benchmark portfolio B: Equation 2-352 T, N β ( R d ( P ), T, N Rd ( B ) ) = T, N T, N Cov ( R d ( P ), R d ( B ) ) ------------------------------------------------------------T, N Var ( R d ( B ) ) where the covariance is given by Equation 2-336 on page 171 and the variance by Equation 2-333 on page 169. A beta of 1 implies that the portfolio will tend to move with the benchmark, and thus the fund manager has zero risk relative to the benchmark. A beta greater (less) than 1 means that the portfolio will fluctuates more (less) than the benchmark and therefore the fund manager has taken a position relative to the benchmark. 2.4.9.5 Tracking error Tracking error is another benchmark related risk measure defined as the N period standard deviation of the T-periodic excess return of the portfolio P relative to the benchmark B (Equation 2-344 on page 172). The annualized tracking error for excess returns is calculated in the same way as the annualized volatility for portfolio returns above; tracking error scaled by √K(T), where K(T) is the number of T-periods making up the business year. This scaling, as before, means that annualized tracking errors calculated with different sampling frequencies (T-periods) can be compared. If we assume that the excess returns are normally distributed and that the historical tracking error is a good prediction of the future then, as for the portfolio return itself above, we can predict confidence intervals for the future excess returns (mean +/- 1SD with 68% confidence and mean +/- 2SD with 95% confidence). 2.4.9.6 Alpha This is the alpha term in the linear regression presented in 2.4.8.5 Linear regression on page 173. This figure can be written in terms of T-period return: Equation 2-353 where as before, the covariance is given by Equation 2-336 on page 171, the variance by Equation 2-333 on page 169, and the means by Equation 2-332 on page 169. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 175 2 Market standards and calculations 2.4 Performance calculations T, N α ( R d ( P ), T, N Rd ( B ) ) = T, N Rd ( P ) T, N T, N Cov ( R d ( P ), R d ( B ) ) T, N - × Rd ( B ) - ------------------------------------------------------------T, N Var ( R d ( B ) ) The annualized alpha is then given by: Equation 2-354 T, N α annual ( R d T, N ( P ), R d T, N ( B ) ) = K ( T ) × α ( Rd T, N ( P ), R d (B)) (continuous yield) Equation 2-355 T, N α annual ( R d ( P ), T, N Rd ( B ) ) T, N T, N α ( R d ( P ), R d ( B ) )⎞ ⎛⎛ = 100 × ⎜ ⎜ 1 + -------------------------------------------------------⎟ 100 ⎠ ⎝⎝ K(T) ⎞ – 1⎟ ⎠ (periodic) where K(T) is, as before, the number of T-periods making up a business year. The alpha is the part of the return from portfolio P that can’t be attributed to the risk taken in terms of beta. A positive alpha can be obtained by stock picking and/or market timing. With stock picking the fund manager tries to be overexposed or underexposed in securities having a mean return above or below the benchmark return, respectively. With market timing the manager tries to fine-tune the beta of the fund such that it is less or greater than 1 when the benchmark return is negative or positive, respectively. A fund tracking the benchmark will, by definition, have an alpha value of zero. The alpha value can therefore be seen as the contribution to the portfolio’s return coming from active fund management. 2.4.9.7 R squared The R2 figure is a measure of how much information alpha and beta provide about the portfolio. It is a least squares variable (see 2.4.8.5 Linear regression on page 173), an indication of the goodness of fit of the linear regression to the data. The higher the value of R2, the better the fit of the linear function to the data - in other words, the more the portfolio returns can be described in relation to the benchmark returns. Figures over 0.75 or under 0.25 are considered to indicate that the explanatory power is high or low, respectively. In other words, R2 provides an indication of how well the behavior of the portfolio returns is described by the alpha and beta values. 2.4.9.8 Information ratio The information ratio is the annualized period excess return of the portfolio P relative to the benchmark B, divided by the annualized tracking error: Equation 2-356 T, N IR d R annual, d, d – NT ( P – B ) ( P, B ) = -------------------------------------------------------T, N TE annual ( R d ( P – B ) ) where the annualized excess return is given by Equation 2-339 on page 171 (continuously compounded returns) or Equation 2-340 on page 172 (periodic returns), and the annualized tracking error by Equation 2-341 on page 172. 176 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations For example: 1M, 12 IR 30/6/98 ( P, B ) is the information ratio calculated from the monthly excess returns during the 12-month period starting at 970630 (980630 - 12*1M) and ending at 980630. A positive information ratio indicates that the investment decision to deviate from the benchmark was a good decision since it resulted in a higher return. The higher the information ratio the more excess return was obtained by the same risk taken. An information ratio of +0.5 is considered to be an acceptable result, a ratio of +0.75 a good result and a figure of +1.0 is typically seen as an excellent result. 2.4.9.9 Sharpe ratio The figure below shows the risks and returns of some portfolios - the benchmark B, example portfolios and a risk-free portfolio. The return is measured as the annualized period return, Rannual, and the risk as the annualized standard deviation of the T-periodic returns (the volatility σannual). 2.4.9.9.1 Risk-return characteristics (risk measured by volatility) It is clear that the benchmark B is preferable to portfolio P2 since the return is higher and the risk is less. The comparison against P1 is not so clear cut; the return of P1 is lower but so is the risk. In portfolio theory the existence of a risk-free portfolio is usually assumed. The return of the risk-free portfolio is fixed (in other words the volatility is zero) and known in advance. Furthermore the investor is allowed to buy the portfolio (invest money at the risk-free interest rate), or sell short the portfolio (borrow money at the risk-free interest rate, and invest the proceeds in the risky portfolio). All combinations of the risk-free portfolio and a risky portfolio lie along the straight line connecting them (line 1 for P1 and line 3 for P2) in the risk-return diagram above. By borrowing at the risk-free interest rate and investing the proceeds in portfolio P1, the investor can construct the portfolio P′1 that has the same risk as the benchmark B but a higher return. Given the existence of the risk-free portfolio a rational investor will prefer portfolio P1 to B and P2(and B to P2). The preferred portfolio is the one with the greatest slope, that is to say with the largest Sharpe ratio: Equation 2-357 T, N Sharpe d R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree ) ( P, P riskfree ) = ----------------------------------------------------------------------------------------------------------------T, N σ annual ( R d ( P ) ) Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 177 2 Market standards and calculations 2.4 Performance calculations where the annualized returns are given by Equation 2-330 on page 168 (continuously compounded returns) or Equation 2-331 on page 169 (periodic returns), and the volatility by Equation 2-335 on page 170. A high Sharpe Ratio is therefore an indication of high returns relative to the risk taken. 2.4.9.10 Modigliani-Modigliani (M2) This is a version of the Sharpe ratio analysis that ranks portfolios in exactly the same order as the Sharpe analysis but gives the result in terms of return and not as a ratio. The risk-adjusted return measure is called Modigliani-Modigliani, or M2 for short. Given a portfolio P, M2 is the return of the combination of the risk-free portfolio and P that has the same risk (in terms of volatility) as the benchmark B. Thus, for portfolio P1 in the figure above (Risk-return characteristics (risk measured by volatility)), M2 is equal to the return of portfolio P′1. A high value of M2 is therefore an indication of high returns relative to the risk taken. Mathematically, M2 of portfolio P is given by: Equation 2-358 M 2 T, N d ( P, B, P riskfree ) T, N = R annual, d, d – NT ( P riskfree ) + σ annual ( R d T, N ( B ) ) × Sharpe d ( P, P riskfree ) = R annual, d, d – NT ( P riskfree ) + T, N σ annual ( R d ( B ) ) -------------------------------------------- × R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree ) T, N σ annual ( R d ( P ) ) The annualized returns are given by Equation 2-330 on page 168 (continuously compounded returns) or Equation 2-331 on page 169 (periodic returns), and the volatility by Equation 2-335 on page 170. 178 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations 2.4.9.11 Treynor ratio The Treynor ratio is similar to the Sharpe ratio but with beta as the risk measure. The figure below shows the risk and return characteristics for some portfolios where the risk measure is beta. Note that the benchmark B has a beta of 1 and the risk free portfolio is assumed to have a beta of zero. 2.4.9.11.1 Risk-return characteristics (risk measured by beta) The Treynor ratio measures the slope of the line connecting the risk-free portfolio and the risky portfolio: Equation 2-359 T, N Treynor d R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree ) ( P, B, P riskfree ) = ----------------------------------------------------------------------------------------------------------------T, N T, N β ( R d ( P ), R d ( B ) ) where the annualized returns are, as before, given by Equation 2-330 on page 168 (continuously compounded returns) or Equation 2-331 on page 169 (periodic returns), and the beta by Equation 2-352 on page 175. As for both the Sharpe Ratio and M2, a high value of this ratio is an indication of high returns relative to the risk taken. The fund manager has outperformed the benchmark if the fund has a higher Treynor ratio than the benchmark. In the figure above, portfolio P1 has outperformed the benchmark in terms of Treynor ratio (but not P2). 2.4.9.12 Jensen’s Alpha If the benchmark consists of all securities the fund can invest in (for example the issued equities in all listed companies besides the tobacco related ones), we make the assumption that the line connecting the risk-free portfolio and the benchmark (line 2) represents the set of risk-return effective portfolios. So for every risk level the largest expected return is obtained by investing in a combination of the risk-free portfolio and the benchmark that has the wanted risk level. If the wanted risk level in beta terms is β̃ then the expected annualized period return of the effective portfolio is given by: Equation 2-360 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 179 2 Market standards and calculations 2.4 Performance calculations R annual, d, d – NT ( P ( β̃ ) ) = R annual, d, d – NT ( P riskfree ) + β̃ × R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree ) Jensen’s Alpha is calculated as the actual return of the portfolio P less the return of the effective portfolio (Equation 2-360 on page 179) with identical beta: Equation 2-361 T, N Jensen d T, N – β ( Rd ( P, B, P riskfree ) = R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree ) T, N ( P ), R d ( B ) ) × ( R annual, d, d – NT ( P ) – R annual, d, d – NT ( P riskfree ) ) where the annualized returns are, as for the Treynor ratio, given by Equation 2-330 on page 168 (continuously compounded returns) or Equation 2-331 on page 169 (periodic returns), and the beta by Equation 2-352 on page 175. A positive value of Jensen’s Alpha indicates that the portfolio has a higher return than the effective portfolio (a benchmark with the same level of risk) and a negative value implies a lower return. In the figure above (Risk-return characteristics (risk measured by beta)), we have a positive value of Jensen’s alpha for portfolio P1 (the return is higher than for B′) and a negative value for portfolio P2 (the return is less than for B′′). Therefore portfolio P1 is a more risk-return effective portfolio than the benchmark (but not P2). 2.4.10 Performance attribution The goal of performance attribution is to quantify the contribution of the various investment decisions to the final overall portfolio (excess) return. The investment decision variables supported are the ones expressed via the Performance Monitor grouping dimensions, for example, Market, Currency, Branch Codes, Issuer, Maturity Period, and so on. The attribution models split the excess return into Allocation, Selection and Interaction effects: • Allocation is the investment decision between the selected grouping • Selection measures the investment decision within the selected grouping • Interaction is the interaction between the allocation and selection term The benchmark is represented as a portfolio with transactions. 2.4.10.1 Performance attribution methods The following attribution methods are used in TRM: • Single currency portfolios The Brinson framework. • Multi currency portfolios The Karnosky and Singer framework. • Combining attribution effects over time The Cariño method. The calculations used in each of these methods are described in the next section. 180 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations 2.4.10.1.1 Base currency performance attribution Here are the calculations used for the Brinson attribution of excess return: Equation 2-362 R – R = Σ wi Ri – Σ wi Ri = A + S + I i i Allocation Equation 2-363 A = Σ ( wi – wi ) ( Ri – R ) i Selection Equation 2-364 S = Σ wi ( Ri – Ri ) i Interaction Equation 2-365 I = Σ ( wi – wi ) ( Ri – Ri ) i where wi is the fraction of the market value invested in the i-th sector, and Ri is the return. The corresponding benchmark values are denoted by wi and Ri . 2.4.10.1.2 Multi- currency performance attribution The return of the multi-currency portfolio is given by: Equation 2-366 R base = Σ w i ( R i – C̃ ccy ( i ) ) + Σ ( w i ( ccy ) + h ccy ) ( C̃ ccy + ε base, ccy ) i ccy + Σ h ccy ( C ccy – C̃ ccy ) ccy where: – wi is the fraction of the market value invested in the i-th asset. – Ri is the return of the assets in the i-th segment expressed in the local currency. – Cccy is the local currency risk free return. – hccy is the currency weight of FX overlay hedge transactions. – εccy is the change in the spot FX rate (common to all investments in each currency). – Cccy is the local currency return of FX overlay hedge transactions. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 181 2 Market standards and calculations 2.4 Performance calculations 2.4.10.1.3 Asset-related performance attribution Brinson style factors: Equation 2-367 A asset = Σ ( w i – w i ) ( ( R i – C̃ ccy ( i ) ) – BRP ) i Equation 2-368 S asset = Σ w i ( R i – R i ) i Equation 2-369 I asset = Σ ( w i – w i ) ( R i – R i ) i where BRP is the benchmark local return premium: Equation 2-370 BRP = Σ w i ( R i – C̃ ccy ( i ) ) i Asset leverage: Equation 2-371 L asset = ( – BRP ) ( Σ w i – Σ w i ) i i Equation 2-372 ( Σ wi + Σ i ccy h ccy = 1 ) 2.4.10.1.4 Currency related performance attribution Brinson style factors: Equation 2-373 A hedge = Σ ccy ( ( w i ( ccy ) + h ccy ) – ( w i ( ccy ) + h ccy ) ) ( ( C̃ ccy + ε base, ccy ) – BCR ) Equation 2-374 S hedge = Σ ccy h ccy ( C ccy – C̃ ccy ) Equation 2-375 I hedge = Σ ccy ( h ccy – h ccy ) ( C ccy – C̃ ccy ) where CRP is the benchmark currency return: Equation 2-376 182 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations BCR = Σ ( w i ( ccy ) + h ccy ) ( C ccy + ε base, ccy ) ccy Assumed common FX return might imply a small unexplained residual: Equation 2-377 R base – R base = A asset + S asset + I asset + L asset + A hedge + S hedge + I hedge 2.4.10.1.5 Linking attribution factors over time Daily attribution is preferable as weight factors wi are time dependent. Excess return and arithmetical factors are not additive over time: Equation 2-378 R – R = ( 1 + R1 ) ( 1 + R 2 ) – ( 1 + R 1 ) ( 1 + R2 ) ≠ ( R1 – R1 ) + ( R2 – R2 ) The error can be distributed over time such that: Equation 2-379 1 R – R = ---- Σ k t ( R t – R t ) Kt where Equation 2-380 ln ( 1 + R ) – ln ( 1 + R ) K = ----------------------------------------------------R–R and Equation 2-381 ln ( 1 + R t ) – ln ( 1 + R t ) k t = -------------------------------------------------------Rt – Rt 2.4.10.2 Example of single currency performance attribution This example is based on four equities grouped into two sectors by branch code: Automobiles-sector (BMW and General Motors) and Telecom-sector (Motorola and Nokia). There are two portfolios: a managed trading portfolio and a benchmark portfolio. The performance of the managed trading portfolio is measured against the benchmark, where each stock has an equal 25% weight at the beginning of the period. For the sake of simplification, the performance measurement period is only one day, 23rd of April 2003. The market rates used in this example are fictitious and are set to illustrate the mechanism of performance attribution. In the managed trading portfolio, the Telecom-sector is over weighted and, respectively, the Automobiles-sector is under weighted in comparison to the benchmark with equal weights. The weights, amounts and returns for equities, sectors, managed portfolio and benchmark are presented in the Performance Monitor view below. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 183 2 Market standards and calculations 2.4 Performance calculations The benchmark portfolio has a return of 8.57 % and the managed portfolio has a return of 12.86 %. The investment decisions of the managed portfolio have created a 4.29% excess return, which can be further analyzed by Performance Attribution Key-Figures in Performance Monitor. The Key-Figures Allocation, Selection and Interaction for Automobiles and Telecom sector are calculated as shown in the following sections. 184 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations 2.4.10.2.1 Automobiles 2.4.10.2.2 Telecoms sector Allocation = (66.00% - 50.00%) * (27.21% - 8.57%) = 2.999677 %. Selection = 50.00% * (26.26% - 27.21%) = -0.471547 %. Interaction = (66.10% - 50.00%) * (26.26% - 27.21%) = -0.151837 %. The Allocation Figure expresses how successful the asset manager has been in allocating funds between sectors. In this example, it is the decision to overweight the Telecom sector and to underweight the Automobiles sector. The Telecom sector return is considerably higher than the negative one of the Automobiles sector. The positive Allocation Figure of the Telecom sector is intuitively straightforward, since the sector performed well and it was over weighted in the managed portfolio. The positive Allocation Figure of the Automobiles sector is due to the fact that this lower return sector was under weighted in the managed portfolio in comparison to the benchmark. The Selection Figure expresses how successful the asset manager has been in stock picking (to select equities within a certain group) here within a sector. The negative Figure Selection means that within the sector, higher return equity was underweighted and lower return equity was overweighted, in comparison to the benchmark portfolio. The Figure Intersection represents the part of the excess return that cannot be attributed either to allocation or selection decisions. The sum of the Allocation, Selection and Interaction figures equals the difference between managed portfolio and benchmark portfolio returns, that is, the excess return. 2.4.10.3 Example of multi-currency performance attribution The following example is based on four equities, which are grouped according to currency denomination; EUR for BMW and NOKIA and USD for GENERAL MOTORS and MOTOROLA. The benchmark portfolio consists of these four stocks which have an initial weight of 25 % each. Therefore, the benchmark portfolio has initially equivalent exposures in both currencies. The managed trading portfolio consists of the investments in these four stocks, but with different weights than in the benchmark portfolio. In comparison with the benchmark, USD assets are Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 185 2 Market standards and calculations 2.4 Performance calculations over-weighted: USD denominated stocks total 72% and EUR stocks 28% of the initial market value of the managed portfolio. In order to bring currency exposure of the managed portfolio in line with the benchmark, USD dollars are sold against EUR by FX-Forward transaction. As a result of the hedge, the managed portfolio has 49.60 % exposure in EUR and 50.40 % exposure in USD. For the sake of simplification, the performance measurement period is only one day, 23rd of April 2003. During the day, USD is set to depreciate 10 % against the EUR. The market rates used in this example are fictitious and are set to illustrate the mechanism of multi-currency attribution. All market values are expressed in EUR. The following image displays asset market values at the beginning and end of the period: This image illustrates the portfolio structure: 186 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations These are the intermediate results used to calculate attribution figures: The Key-Figures Asset Allocation, Asset Selection, Asset Interaction and Asset Leverage for EUR denominated investments is calculated as follows: 2.4.10.3.1 Asset allocation The value added by the decision to deviate from the benchmark’s asset allocation is indicated by the asset allocation key figure. For multicurrency investments, the relevant benchmark to be used to analyze the value added of local currency allocation decisions is the average local currency return premium, known as BRP. Equation 2-382 A asset where Wi Asset Weight of the ith group in the Portfolio Asset Weight of the ith group in the Benchmark Return of the ith group in the Benchmark local currency risk free rate of return BRP is the benchmark local return premium: Equation 2-383 BRP Asset Allocation = (27.62%-50.00%) * (12.97%-8.38%) = -1.028916306% Equation 2-384 S asset Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 187 2 Market standards and calculations 2.4 Performance calculations Asset Selection = 50.00% * (19.06% - 12.98%) = 3.0397352% Asset Interaction = (27.62% - 50.00%) * (19.06% - 12.98%) = -1.36075776% Equation 2-385 Asset Leverage = 8.38% * (99.99% - 100.00%) = -0.000836592% Equation 2-386 The Key-Figures Hedge Allocation, Hedge Selection and Hedge Interaction for EUR denominated investments are calculated as follows: 2.4.10.3.2 Hedge allocation The value added by the decision to deviate from the benchmark’s currency allocation is indicated by the hedge allocation key figure. When determining the amount allocated to a certain currency, both the underlying investments and currency overlays are taken into account. When determining currency returns, both the risk-free return of a currency and change in the FX rate against the portfolio's base currency are taken into account. Equation 2-387 A hedge where CRP is the benchmark currency return. It expresses the currency return (risk free rate + change in FX rate against the portfolio's base currency) of the benchmark. 188 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations Currency weight of portfolio FX overlay hedge transactions. Currency weight of Benchmark FX overlay hedge transactions. Change in the spot FX rate (common to all investments in a particular currency) Hedge Allocation = (49.60%-50.00%)*(0.01% - (-4.54%)) = -0.018016123% Hedge Selection Equation 2-388 Hedge selection where Local currency return of FX overlay hedge transactions. In this example, the hedge selection figure is zero, since there are no hedges in the benchmark portfolio. Hedge Interaction = (21.99% - 0.00%) * (0.01% - 0.009722%) = -0.000038688%. Equation 2-389 Hedge interaction 2.4.11 Performance measurement key-figures The key-figures available in Performance Monitor are described in the following table. These figures include the risk adjusted return measures, for example the Information Ratio and Modigliani-Modigliani (see 2.4.8 Risk-adjusted returns on page 166). More details about these key-figures and how they are calculated are given in the section 2.4 Performance calculations on page 149. Figure Definition Allocation The Brinson performance attribution factor measuring how well money has been allocated (relative benchmark) between the selected groups (such as Branch Code), given by: Allocation_i (T) = (w_it - W_it)*(R_it - R_i) where w_it is the Attribution Weight of the ith group in the portfolio W_it is the Attribution Weight of the ith group in the Benchmark R_it is the Return of the ith group in the Benchmark R_t is the Benchmark total return at time T Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 189 2 Market standards and calculations 2.4 Performance calculations Figure Definition Allocation (Cumulative) The allocation factor (A) that is additive over time: where R = cumulative total Portfolio Return R = cumulative total Benchmark Return and Rt = total Portfolio return on day t Rt = total Benchmark Return on day t Allocation (cumulative) T = sum t=1 to T Excess Return Factor (t) * Allocation (t) / Excess Return Factor (Cumulative) Alpha The part of the return on a portfolio that cannot be attributed to the risk taken (the risk taken in terms of beta). It is the intercept of the y-axis of the linear regression function between the portfolio and the benchmark portfolio. Alpha (Annualized) The alpha of the portfolio, converted into an annualized figure. Asset Allocation The multi-currency performance attribution is based on Karnosky and Singer framework. The Allocation, Selection, and Interaction terms follow Brinson et al. framework, similar to the single currency performance attribution. The Asset Allocation is the performance attribution factor measuring how successfully funds have been allocated relative to the benchmark between the selected groups (such as Branch Code) given by: where Asset Weight of the ith group in the Portfolio Asset Weight of the ith group in the Benchmark Return of the ith group in the Benchmark Local currency risk free rate of return BRP is the benchmark local return premium: 190 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations Figure Definition Asset Allocation (Cumulative) Since Excess Return and arithmetical factors are not directly additive over time, the following methodology ("Combining Attribution Effects over Time" by D.R . Carino) is applied to link attribution effects over time: where R = cumulative total Portfolio Return R = cumulative total Benchmark Return and R = cumulative total Portfolio Return Rt = cumulative total Benchmark Return AAsset is the portfolio's cumulative Asset Allocation AAssett is the portfolio's Asset Allocation effect at time point t. Asset Interaction Performance attribution factor measuring the interaction between Asset Allocation and Asset Selection. It is part of the Excess Return that cannot be divided to either Allocation or Selection. Asset Interaction (Cumulative) See Key-Figure Asset Allocation (Cumulative), where methodology to link effects over time is described. Asset Leverage The return contribution from leveraged market investment in respect to the total portfolio market value due to unrealized result of FX hedge transactions. For example, you buy US bonds worth 100 M Euro and hedge the currency exposure into Euro using FX forwards. If the dollar goes up 10% the bonds are worth around 110M Euro and you have an offsetting unrealized loss of 10M from the FX forwards. In this case your bond position is leveraged since you have 110M of a portfolio total of 100M invested into it. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 191 2 Market standards and calculations 2.4 Performance calculations Figure Definition Asset Leverage (Cumulative) See Key-Figure Asset Allocation (Cumulative), where methodology to link effects over time is described. Asset Selection Performance attribution factor measuring how successful you have been at selecting securities relative to the benchmark within the selected groups (such as Branch Code), given by: where Asset Weight of the ith group in the Benchmark Return of the ith group in the Portfolio Return of the ith group in the Benchmark Asset Selection (Cumulative) See Key-Figure Asset Allocation (Cumulative), where methodology to link effects over time is described. Asset Selection/Interaction The combined Asset Selection and Asset Interaction factors given by: Note: As a difference to the pure Asset Selection, Portfolio Weight is used here. Asset Selection/ Interaction (Cumulative) See Key-Figure Asset Allocation (Cumulative), where the methodology to link effects over time is described. Asset Weight Fraction of the market value invested in ith asset. Attribution Amount The market value allocated to the selected cell i at beginning of day t, given by: Attribution Amount (T) = Market Value Start (T) + Weight Factor * Cashflows (T) Attribution Weight The percentage of total Attribution Amount allocated into cell i at time t: Attribution Weight (T) = Attribution Amount (T) / Total Attribution Amount (T) (The Total level is defined by the user in the X,Y axis selection lists as in Treasury Monitor.) Beta The gradient of the linear regression function between the portfolio and the benchmark portfolio. This is a measure of the sensitivity of the portfolio with respect to changes in the benchmark portfolio. A value of beta greater than 1 means that the portfolio returns will be more than the benchmark returns (less than 1 means the returns will vary less). Correlation The correlation coefficient between the portfolio and the benchmark portfolio (standardized covariance). A positive (negative) value indicates that if there is a positive return for the benchmark portfolio, then there will also be a positive (negative) return for the portfolio. Covariance The covariance between the portfolio and the benchmark portfolio. A positive (negative) value indicates that if there is a positive return for the benchmark portfolio, then there will also be a positive (negative) return for the portfolio. 192 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations Figure Definition Difference Result The difference of the monetary returns between a trading portfolio and a benchmark portfolio, expressed as daily Monetary P/L Excess Return and calculated as follows: RE t = RE P, t – RE B, t where REt is the Monetary P/L Excess Return for day t REP,t is the Monetary Portfolio Return for day t REB,t is the Monetary Benchmark Return for day t This key-figure behaves like Excess Return, except that money amounts are used. Note: In Treasury Monitor, the key-figures Market Value and Market Value Start are used. Monetary P/L Excess Return is the difference between the trading portfolio’s Market Value Change and that of the benchmark portfolio. Difference Result (Cumulative) The sum of daily Monetary P/L Excess Returns during a period of n days. Difference Return Contribution Displayed under the benchmark, this figure is the line-by-line difference between the Return Contribution of the portfolio and the Return Contribution of the benchmark. Difference Return Contribution (Cumulative) measures the same difference over time. Excess Return This is the portfolio return relative to the benchmark return for the specified interval. Excess Return (Annualized) The difference between the Return (Cumulative) of the portfolio and the Return (Cumulative) of the benchmark portfolio, converted into an annual figure. Excess Return Asset Contribution This is the difference between local portfolio return premium and base currency benchmark return premium. Alternatively, this is the sum of the Asset attribution factors at time point t: Excess Return Asset Contribution (Cumulative) This is the sum of cumulative Asset attribution factors. Excess Return Contribution This is the sum of the attribution factors at time T: Excess Return Contribution (Cumulative) This is the sum of the cumulative attribution factors: Excess Return (Cumulative) The difference between the Return (Cumulative) of the portfolio and the Return (Cumulative) of the benchmark portfolio. Excess Return Factor Daily factor used for linking attribution effects over time. Excess Return Factor (Cumulative) Total period factor used for linking attribution effects over time. Excess Return Hedge Contribution Excess return contribution from the hedge strategy, which is the sum of the Hedge attribution factors at time t: Excess Return Contribution (T) = Allocation (T) + Selection (T) + Interaction (T) Excess Return Contribution (Cumulative) = Allocation (Cumulative) + Selection (Cumulative) + Interaction (Cumulative) Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 193 2 Market standards and calculations 2.4 Performance calculations Figure Definition Excess Return Hedge Contribution (Cumulative) This is the sum of the cumulative Hedge attribution factors. See Key-Figure Asset Allocation (Cumulative), where the methodology to link effects over time is described. Excess Return (N Samples) This is the portfolio return relative to the benchmark return over N sub-periods (T-periods) of sampling frequency T. Excess Return (Sample) This is the portfolio return relative to the benchmark return over one sub-period (T-period) of sampling frequency T. Excess Return Mean The mean value of excess returns over the aggregation period (aggregation period length expressed as N T-periods). Excess Return Semideviation Key-figures: σ ep Excess Return Semideviation (Negative) σ en Excess Return Semideviation (Positive) measure the semideviation of excess return over a benchmark. If the sample returns of the benchmark are ri, then Excess Return Standard Deviation The standard deviation of excess returns over the aggregation period (aggregation period length expressed as N T-periods). Excess Return Variance The variance of excess returns over the aggregation period (aggregation period length expressed as N T-periods). Excess Return Volatility The standard deviation of excess returns over the aggregation period (aggregation period length expressed as N T-periods), converted into an annualized figure. Hedge Allocation The performance attribution factor measuring how successful we have been in our currency strategy in comparison to the benchmark given by: where CRP is the benchmark currency return currency weight of portfolio FX overlay hedge transactions currency weight of Benchmark FX overlay hedge transactions change in the spot FX rate (common to all investments in each currency) Hedge Allocation (Cumulative) 194 See Key-Figure Asset Allocation (Cumulative), where methodology to link effects over time is described. © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations Figure Definition Hedge Interaction The performance attribution factor measuring the interaction between Hedge Allocation and Hedge Selection is given by: Hedge Interaction (Cumulative) See Key-Figure Asset Allocation (Cumulative), where the methodology to link effects over time is described. Hedge Selection The performance attribution factor measuring how successful you have been in hedging the selection of optimal maturity of the hedge transactions is given by: Local currency return of FX overlay hedge transactions. Hedge Selection (Cumulative) See Key-Figure Asset Allocation (Cumulative), where the methodology to link effects over time is described. Hedge Selection/Interaction The combined Hedge Selection and Hedge Interaction factors are given by: Hedge Selection/Interaction (Cumulative) See Key-Figure Asset Allocation (Cumulative), where the methodology to link effects over time is described. Hedge Weight The currency weight of FX overlay hedge transaction. Information Ratio A measurement of the return of the portfolio in terms of the risk taken (risk adjusted return measure). The Excess Return (Annualized) divided by the Tracking Error (Annualized). A positive value indicates that the decision to deviate from the benchmark was a good one since it resulted in a higher return. The higher the value of the Information Ratio, the more excess return was obtained by the same risk taken. Interaction The Brinson performance attribution factor measuring the interaction between allocation and selection, given by: Interaction_i (T) = (w_it – W_it)*(r_it-R_it) where W_it is the Attribution Weight of the ith group in the Benchmark w_it is the Attribution Weight of the ith group in the portfolio r_it is the Return of the ith group in the Portfolio R_it is the Return of the ith group in the Benchmark Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 195 2 Market standards and calculations 2.4 Performance calculations Figure Definition Interaction (Cumulative) Interaction factors (I) that are additive over time. where R = cumulative total Portfolio Return R = cumulative total Benchmark Return and Rt = total Portfolio return on day t Rt = total Benchmark Return on day t Interaction (cumulative) T = sum t=1 to T Excess Return Factor (t) * Interaction (t) / Excess Return Factor (Cumulative) Jensen's Alpha A measurement of the return of the portfolio in terms of the risk taken (risk adjusted return measure). Jensen’s Alpha is defined as the difference between the return on the portfolio and the return on the ‘effective’ benchmark portfolio with the same beta. A positive (negative) value implies that the portfolio has a higher (lower) return than the effective benchmark with the same level of risk. Market Value Movements Movements between buckets/branches are considered to happen between the dates, that is, at midnight. Thus, for an instrument worth X moving from bucket B to A at date T, the market value start at date T will be equal to the market value end at day T-1 plus the amount X. The Market Value Movements key-figure is equal to X. In general: Market Value Start (T) = Market Value End (T-1) + Market Value Movements (T) ModiglianiModigliani A measurement of the return of the portfolio in terms of the risk taken (risk adjusted return measure). Defined as the return of a combination of the portfolio and the risk-free portfolio that has the same risk (volatility) as the benchmark portfolio. A high Modigliani-Modigliani value indicates high returns relative to the risk taken. R2 R squared, is the fit of the linear regression function between the portfolio and the benchmark portfolio. A measure of how well the behavior of the portfolio returns is described by the Alpha and Beta values. Figures over 0.75 or under 0.25 are considered to indicate that the explanatory power is high or low, respectively. Return The rate of return (percentage growth) of the portfolio over a specified interval. Return (Annualized) The return on the portfolio over the aggregation period (length of this period expressed as N T-periods), converted into an annualized figure. Return Contribution The contribution of the selected cell to the total absolute performance, given by: Return Contribution (T) = Attribution Weight (T) * Return (T) = Result (T) / Total Attribution Amount (T) 196 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations Figure Definition Return Contribution (Cumulative) The cumulative value of Return Contribution. Rt, Cumulative Return Contribution for cell i over period from 1 to T is: Here, R is the cumulative total performance, Rt is the total performance for period t, and is the performance of cell i for period t. Return (Cumulative) The return on the portfolio over the aggregation period (length of this period expressed as N T-periods). Return (N Samples) The portfolio return over N sub-periods (T-periods) of sampling frequency T. Return (Sample) The portfolio return over one sub-period (T-period) of sampling frequency T. Return Mean The mean of the cumulative returns over the aggregation period (length of this period expressed as N T-periods). Return Semideviation Displays the standard deviations of returns which are below (above) the average returns, respectively. Key-figures: Return Semideviation (Upside) ( σ u ) Return Semideviation (Downside) ( σ d ) Return Semideviation (Positive) ( σ p ) Return Semideviation (Negative) ( σ n ) are based an sample returns Ri. Let sample count (the number of consecutive samples used in averaging) be n. Then for the kth sample: where Ri is the sample mean return. Return Standard Deviation The standard deviation of the cumulative returns over the aggregation period (length of this period expressed as N T-periods). Return Variance The variance of the cumulative returns over the aggregation period (length of this period expressed as N T-periods). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 197 2 Market standards and calculations 2.4 Performance calculations Figure Definition Return Volatility The standard deviation of the cumulative returns over the aggregation period (length of this period expressed as N T-periods), converted into an annualized figure. Selection The Brinson performance attribution factor measuring how good you have been at selecting securities (relative benchmark) within the selected groups (such as Branch code), given by: Selection_i (T) = W_it*(r_it-R_it) where W_it is the Attribution Weight of the ith group in the Benchmark r_it is the Return of the ith group in the Portfolio R_it is the Return of the ith group in the Benchmark Selection (Cumulative) The selection factors (S) that are additive over time. where R = cumulative total Portfolio Return R = cumulative total Benchmark Return and Rt = total Portfolio return on day t Rt = total Benchmark Return on day t Selection (cumulative) T = sum t=1 to T Excess Return Factor (t) * Selection (t) / Excess Return Factor (Cumulative) Selection/ Interaction 198 The combined Selection and Interaction factors given by: © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.4 Performance calculations Figure Definition Selection/ Interaction (Cumulative) Since Excess Return and arithmetical factors are not directly additive over time, the following methodology is applied in order to link attribution effects over time: where R = cumulative total Portfolio Return R = cumulative total Benchmark Return and Rt = total Portfolio return on day t Rt = total Benchmark Return on day t Sharpe Ratio A measurement of the return of the portfolio in terms of the risk taken (risk adjusted return measure). Defined as the difference between the annualized return of the portfolio and the annualized return of a risk-free portfolio, expressed as a ratio of the annual standard deviation (volatility) of the portfolio. A high Sharpe Ratio indicates high returns relative to the risk taken. Tracking Error The standard deviation of excess returns over the aggregation period (length of this period expressed as N T-periods). Tracking Error (Annualized) The standard deviation of excess returns over the aggregation period (length of this period expressed as N T-periods), converted into an annualized figure. Treynor Ratio A measurement of the return of the portfolio in terms of the risk taken (risk adjusted return measure). Defined as the difference between the annualized return of the portfolio and the annualized return of a risk-free portfolio, expressed as a ratio of the beta between the portfolio and the benchmark portfolio. A high Treynor Ratio indicates high returns relative to the risk taken. 2.4.11.1 Performance measurement (debug) key-figures Debug key-figures in Performance Monitor are intermediate results for multi-currency performance attribution. The return for the multi-currency portfolio is given by the following equation: R base = ∑ wi ( Ri – Cccy( i ) ) + ∑ ( wi( ccy) + hccy ) ( Cccy + εbase, ccy ) + ∑ hccy ( Cccy – Cccy ) i ccy ccy Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 199 2 Market standards and calculations 2.5 Value-at-Risk calculations The following key-figures are found in the Debug key-figure folder: Figure Definition FX Rate FX rate between the base currency and the currency in question (for example, Instrument Currency). Multi-currency attribution uses an implied FX rate (from all transactions except FX) because, under the multi-currency framework, only one common FX rate for all transaction types is accepted. Combinations of, for example, O/N, T/N, and Spot rates, as they are applied elsewhere in TRM valuation depending on the cashflow value date, are not accepted. FX Return Return of the currency with respect to the base currency during the period. This is basically the return that is the result of the changes in the (implied) FX rate. In the return formula for multi-currency attribution, this term is marked with εbase,ccy. IR Return The currency risk-free rate of return for the period (the shortest maturity rate from the yield curve defined for the currency). This rate is taken from the risk-free curve defined for the currency. This yield curve should only have the O/N-period defined; the rate set for that period will define the risk-free return of the currency. In the return formula for multi-currency attribution, this term is marked with: C ccy ( i ) Adjusted Asset Return Local rate of return for the assets within the respective group. In the return formula for multi-currency attribution, this term is marked with Ri (or Ri if the key-figure is displayed under the Benchmark). Adjusted Hedge Return The currency return of the legs of the hedge transaction within the respective group. In the return formula for multi-currency attribution, this term is marked with hi (or hi if the key-figure is displayed under the Benchmark). Return Premium Local return premium BRP = ∑ wi ( Ri – Cccy( i ) ) i Deposit Return This is the currency exposure return: ( w i ( ccy ) + h ccy ) ( C ccy + ε base, ccy ) Note: The configuration of implicitly matched instruments in TRM should lead to identical FX valuations. Any differences will cause the sum of the attribution terms to not sum exactly to the portfolio excess return. Given the extensive instrument coverage and the flexibility in valuation techniques in TRM, it is likely that the user will have to accept same degree of mismatch between the attribution figures and the excess return. 2.5 Value-at-Risk calculations Value-at-risk (VaR) is a measure of the potential change in value of a portfolio or position with a defined level of confidence over a selected risk horizon (one day, one month, and so on). For example, you could measure your maximum potential loss with a 95% confidence level on an FX deal due to an unfavorable change in the FX rate over one day. (A 95% confidence level means that your maximum potential loss will not exceed the change in value predicted by this method 95% of the time, i.e. 5% of the time you risk losing more than this value.) 200 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.5 Value-at-Risk calculations The value-at-risk (VaR) calculations in TRM are performed in an integrated real-time module that allows the full functionality of Treasury Monitor to be used with the VaR key-figures produced. In order to perform these calculations, certain statistical data (volatility and correlation) of the market variables are required. These data can be imported from RiskMetrics or any other source with a similar file interface. The data source can be augmented with proprietary data on market variables which it doesn't cover. Mapping between TRM market variables and the imported statistical data is carried out in VaR Mapping Editor. The flexibility of this board allows instruments such as bonds to be mapped to their own volatility and correlation data instead of using a zero-coupon curve. VaR Data Board provides the possibility for extensive stress testing by simulating changes in the market conditions. User-defined scenarios can be created and the correlation and volatility data can be edited. The required confidence level and risk horizon can be defined for each portfolio. In order to do so, the properties VAR-CONFIDENCE-LEVEL and VAR-HORIZON-ID should be added to the Properties page in Portfolio Editor. See TRM User Guide for more information about TRM VaR related applications and portfolio properties. The rest of this section assumes that RiskMetrics is the source of the statistical data. 2.5.1 TRM approach to VaR calculations In order to calculate the VaR figures for a position, an estimate of the probability distribution for that position is required. This is created from the imported statistical data (the volatilities and correlations of the market variables) and the sensitivity of the position to changes in those market variables (deltas). To use the statistical data to assess the value-at-risk of a position, you need to first perform the following steps: • Import the statistical data into the system (see 2.5.3.1 RiskMetrics data on page 203). • Calculate any missing data (see 2.5.4 Transforming RiskMetrics data on page 204). • Map the cashflows of the position to the RiskMetrics maturity vertices (see 2.5.4.3 Cashflow mapping on page 205. • Calculate the VaR deltas of the position (see 2.5.5.1 Calculating VaR deltas on page 207). 2.5.2 RiskMetrics data In RiskMetrics, the basic underlying assumption is that the relative change in each market variable X, from one period to another, is normally distributed with a mean of zero and standard deviation σ: Xt – Xt – 1 ------------------------ ∼ N ( 0, σ x ) Xt – 1 Equation 2-390 VaR: RiskMetrics data Furthermore, the joint distribution of the relative changes in all market variables is assumed to follow a multivariate normal distribution with the correlations between the market variables given in the correlation matrix C. RiskMetrics provides the correlation matrix C and the volatilities of the different market variables. The volatility V of market variable X is defined as 1.65 σ x . A detailed description of the creation of these data and the format in which they are available is given in the RiskMetrics Technical Document. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 201 2 Market standards and calculations 2.5 Value-at-Risk calculations 2.5.2.1 Variance-covariance matrix It is simple to reconstruct the standard deviations of the market variables, σ x , from the volatility data supplied by RiskMetrics (volatility is defined as 1.65 times standard deviation). If other data sets are used (not RiskMetrics) then the measure of volatility may be different, in which case the multiplier I0, (1.65 in the case of RiskMetrics) will be given in the data file and stored with the volatility data. TRM works with the variance-covariance matrix Σ : Equation 2-391 variance-covariance matrix Σ = σCσ where C is the correlation matrix, σ is a diagonal matrix of the standard deviations of the market variables and the elements are given by Equation 2-392 VaR: Correlation-diagonal matrix Σ ij = σ i C ij σ j This matrix contains both the volatility and correlation information. Note that since the diagonal elements of the correlation matrix are equal to one (Cii = 1), the diagonal elements of Σ are the variances (standard deviations squared: Σ ii = σ i2 ). Also (Cji = Cij). 2.5.2.2 Risk horizons The range of values within which a market variable is likely to move depends on the time horizon used. RiskMetrics provide data for two horizons: one day and one month. The maximum potential loss is sometimes referred to as DEaR, Daily Earnings at Risk, for the one day time horizon whereas the risk measure for the one month horizon is referred to as VaR, Value at Risk. The data in the RiskMetrics files are given for the period in question, not as yearly rates. Theoretically, the volatilities for different time horizons should be obtained from the one day volatility by multiplying by the square root of time. For example, if σ 1 is the one day volatility and σ 5 the five day volatility, the following equation should hold: Equation 2-393 VaR: Risk horizons σ5 = 5σ 1 However, there is evidence that long term volatilities differ from the values obtained using this equation. Therefore the one month horizon is also needed for calculating long term risk measures. For risk horizons beyond one month we use the formula above, replacing the one day volatility with the one month volatility. Risk horizons between one day and one month are interpolated from these two figures as described in 2.5.4.2 Interpolating volatilities and correlations on page 204. 2.5.3 Market variables A market variable is any variable for which there is a market quote (for example rate, yield or price) which affects the value of a cashflow. The market variables recognized by RiskMetrics differ from those used by TRM. The RiskMetrics market variables are mapped to the correct TRM market variables in VaR Mapping Editor. The RiskMetrics data may also have to be transformed in one way or another before it can be used for calculations in TRM. 202 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.5 Value-at-Risk calculations This section describes these different types of data. The section 2.5.4 Transforming RiskMetrics data on page 204 describes how the RiskMetrics data are transformed into data suitable for TRM. 2.5.3.1 RiskMetrics data The RiskMetrics data provided are the volatilities and correlations for the market variables given below. The data are provided for certain periods, the RiskMetrics vertices (for example, 1 month, 2 months, and so on) since providing data for all periods would be unfeasible. Data for periods in-between these vertices are calculated using cashflow mapping (see 2.5.4.3 Cashflow mapping on page 205). • Foreign exchange (FX) spot rates for certain currencies. The data are always calculated with US dollar (USD) as the quote currency, for example SEK/USD. The volatility of an FX rate does not depend on the direction in which it is quoted (SEK/USD or USD/SEK), but the sign of the correlation between the two rates will change if the direction is changed. The symbol for spot quotes is XS (for example, the Swedish krona spot quote is SEK.XS). • Money market (MM) rates for the same set of currencies. These rates are for the periods (vertices) O/N, 1 week, and 1, 2, 3, 6, and 12 months. The symbols for these rates are of the form R001, R007, R030, and so on (for example, SEK.R001, SEK.R007). • Government bond zero rates for different currencies. Periods (vertices) included are 2, 3, 4, 5, 7, 9 10, 15, 20, and 30 years. The symbols for government zero rates are of the form Z02, Z03, Z04 and so on (for example, for Swedish bonds SEK.Z02, SEK.Z03, SEK.Z04). • Swap zero rates for different currencies. Periods (vertices) included are 2, 3, 4, 5, 7, and 10 years. The symbols for these rates are of the form S02,S03 and so on (for example, SEK.S02,SEK.S03). • Equity indexes. The symbol for a stock index is SE (for example Swedish stock index is SEK.SE). 2.5.3.2 TRM market data The market data for TRM falls into the following categories: • Foreign Exchange (FX) spot rates for any currency involved in trading. Since the present value of a position is expressed in the portfolio base currency or the monitoring currency selected in Treasury Monitor, the VaR key-figures should also be expressed in the same currency. The original data from RiskMetrics are always expressed in terms of US dollars and so they have to be converted into correlations and volatilities in terms of the base currency (see 2.5.4.1 Reference currency on page 204). • Interest rate (IR) reference rates In TRM, there are several ways to derive an IR reference rate (see 2.2 Yield curves on page 81). A reference rate is taken from a defined yield curve. The simplest way to define a yield curve is to use direct market quotes. It is also possible to derive a zero-coupon yield curve from a set of instruments or other reference rate yield curves, for example, by using a depo curve for the short end and a swap curve for the long end. Offsets can be added to previously defined rates in the yield curve to derive new rates. Due to the possible complexity of this rate derivation, it is not feasible to derive the correlations for the derived yield curve from the correlations of the underlying yield curve. Therefore, each IR reference curve has to be mapped separately to its correlation vertices on the Interest Rate Mapping page of VaR Mapping Editor. • IR instruments An IR instrument, such as a bond and a bond future can be either mapped to volatilities and correlations of a yield curve, or directly to its individual volatility and correlation data, if such is available. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 203 2 Market standards and calculations 2.5 Value-at-Risk calculations In the former case, the default is to use the VaR mapping specified for the instrument's currency, but it is also possible to choose a different mapping by bringing in the feature VaR Mapping Type, see A.2.336 VaR Mapping Type on page 878. To use instrument-specific volatility and correlation data, the instrument has to be given its own mapping in VaR Mapping Editor (Instrument Mapping page). • Equities Equities can either be mapped onto their individual volatility and correlation data or onto a common index. In the latter case, the beta of the equity is used to obtain the equity's volatility from the volatility of the index. The beta defined in Rate Monitor can be overridden for VaR calculations. 2.5.4 Transforming RiskMetrics data This section describes how the RiskMetrics data are transformed into data suitable for TRM. 2.5.4.1 Reference currency In RiskMetrics all currencies are quoted against the US dollar. This means that when value-at-risk is calculated in a different currency, typically the portfolio base currency, or the figure currency of Treasury Monitor, the variance-covariance matrix has to undergo a transformation. To get covariances for the cross rates X=A/B and Y=C/D we use the following equation: Equation 2-394 VaR: Covariances cross rates Cov ( X, Y ) = Σ AC + Σ BD – Σ AD – Σ BC If X and Y are the same rate, in other words A=C and B=D, then Equation 2-395 VaR: Covariances same rate 2 2 2 σ x = Cov ( X, X ) = σ A + σ B – 2Σ AB If one of the rates is not a cross rate, for example if Y=C, then Equation 2-396 VaR: Covariances one of the rates is not a cross rate Cov ( X, C ) = Σ AC – Σ BC 2.5.4.2 Interpolating volatilities and correlations RiskMetrics provide volatility and correlation data for risk horizons of one day and one month. Whenever risk horizons differing from these are used, the data have to be interpolated. 2.5.4.2.1 Volatility It is appropriate to use quadratic interpolation to calculate volatilities for risk horizons (maturities) other than one day and one month. • Case 1: Risk horizon t between t1 (one day) and t2 (one month). If t is the risk horizon for which the standard deviation is needed and t1 < t < t2, let Equation 2-397 VaR: Case 1 - Volatility t – t1 τ = -------------t2 – t1 204 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.5 Value-at-Risk calculations then the volatility σ is given by: Equation 2-398 VaR: Case 1 - Volatility calculation 2 σt = • 2 σ1 σ2 τt ------ + ( 1 – τ )t -----t2 t1 Case 2: For t outside the range [t1, t2], the volatility is scaled by the square root of time. – For t < t1: Equation 2-399 VaR: Case 2 - Volatility σt = – ( t ⁄ t 1 )σ 1 For t > t2: Equation 2-400 VaR: Case 2 - Volatility calculation σt = ( t ⁄ t 2 )σ 2 2.5.4.2.2 Correlation data For correlations, linear interpolation is used. That is, if the two known correlations for the risk horizons t1 (one day) and t2 (one month) are ρ 1 and ρ 2 , then the correlation ρ t for the risk horizon t can be calculated using one of the following methods: • Case 1: Risk horizon t between t1 and t2. Equation 2-401 VaR: Correlation data ρ t = τρ 2 + ( 1 – τ )ρ 1 • Case 2: Risk horizon t outside the range [t1, t2]. – For t < t1: ρ t = ρ 1 – For t > t2: ρ t = ρ 2 2.5.4.3 Cashflow mapping A financial position is made up of one or more cashflows which need to be marked-to-market (present value) using current market rates for the VaR calculations. The present value of most cashflows depends on two variables: • The spot rate of the cashflow currency • The interest rate for the maturity of the cashflow. This means that the number of market variables is of the same order as the number of cashflow dates in the portfolio that is under scrutiny. The volatilities and correlations for all these variables could be derived from the original data set leading to a very large correlation matrix. An alternative approach is to restrict the set of market variables to consist of only the spot rates and interest rates for a given set of periods (the RiskMetrics' vertex periods - 2.5.2 RiskMetrics data on page 201 gives details of the vertices for the different market variables in RiskMetrics). The Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 205 2 Market standards and calculations 2.5 Value-at-Risk calculations cashflows that fall between the vertex periods have to be mapped (redistributed) onto a standard grid of maturity vertices. This is illustrated as follows. In this way, the market variables of the cashflows are mapped onto the market variables of the RiskMetrics vertices. For example, if the interest rate of the second cashflow in the previous figure (at 5 months) is rc and r3m and r6m are the interest rates of the 3 month and 6 month RiskMetrics vertices respectively, then the present value of the cashflow, Vp(rc) will become Vp(r3m, r6m). The next step in the VaR approach is to calculate the vector δ (see 2.5.5.1 Calculating VaR deltas on page 207). This vector contains the VaR deltas (sensitivity of the position to a change in a market variable) for every market variable. The goal of the cashflow mapping is to transform this vector δ into another one, δ m , which contains the sensitivities to changes in the market variables at the maturity vertices used in the VaR calculations. This transformation takes the form of a matrix M where the elements Mij provide the mapping from the ith TRM market variable to the jth VaR market variable. Equation 2-402 VaR: Cashflow mapping δ m = Mδ 2.5.4.3.1 Risk equivalent method The mapping of a cashflow that falls between RiskMetrics vertices is based on the idea that the interest rate for such a cashflow can be considered as a result of an interpolation from the adjacent vertices. More precisely, consider a cashflow whose present value is a function Vp(rd) of the interest rate rd with maturity d. We can regard rd as a linear function of the two closest vertex interest rates r1 and r2. Equation 2-403 VaR: Risk equivalent method r d = ar 1 + br 2 where a and b are interpolation coefficients. Now, we can consider the present value of our cashflow to be a function Vp(ar1+br2) of r1 and r2 instead of rd. Using the risk equivalent method, we do not need to calculate the mapped cashflows as previously described to transform the VaR delta vector δ into δ m , but can simply calculate δ m from the IR exposure (delta) of the original cashflow. This is particularly convenient for derivative instruments where the IR exposure is not calculated directly from the cashflows. 206 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.5 Value-at-Risk calculations To be more specific, we have: Equation 2-404 VaR: Risk equivalent method ∂V ∂V ∂r d ------= ------- ------∂r 1 ∂r d ∂r 1 ∂V p = a ---------∂r d and Equation 2-405 VaR: Risk equivalent method ∂V ∂r d ∂V ------= ------- ------∂r d ∂r 2 ∂r 2 ∂V p = b ---------∂r d Also since a+b=1, the total IR sensitivity is Equation 2-406 VaR: Total IR sensitivity ∂V p ∂V ∂V ---------- = ---------p- + ---------p∂r d ∂r 1 ∂r 2 It can therefore be seen that in this risk equivalent method, the cashflow itself does not get mapped, but the IR risk (exposure) does. 2.5.5 VaR calculations The method used in TRM to calculate value-at-risk is the linear (delta) method. The function V() of the value of the position is approximated with a linear function via a Taylor series expansion: Equation 2-407 VaR: Linear (delta) method (Taylor series expansion) V ( x 1, x 2, …, x n ) ≈ V p + δ 1 ( x 1 – X 1 ) + δ 2 ( x 2 – X 2 ) + … + δ n ( x n – X n ) = V p + δ x where Vp is the current present value, the xi represent the market variables and Xi the current values of those market variables, the δ i (elements of the VaR delta vector δ ) are the partial derivatives of the value function V() with respect to each xi (see 2.5.5.1 Calculating VaR deltas on page 207). In order to produce an estimate of the value-at-risk, first of all the VaR deltas need to be calculated (shown in next section). The standard deviation of the position in question can then be calculated using these VaR deltas and the variance-covariance matrix (see 2.5.2.1 Variance-covariance matrix on page 202). From the standard deviation we know the probability function of the position and this is then used to estimate the value-at-risk at a certain confidence level (probability). 2.5.5.1 Calculating VaR deltas In order to be able to calculate the overall risk for our position, we shall need the vector δ = ( δ 1, δ 2, …, δ n )′ Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 207 2 Market standards and calculations 2.5 Value-at-Risk calculations defined by Equation 2-408 VaR: Vector ∂V p δ i = ---------∂x i where δ i is the sensitivity of the present value Vp to a change in the market variable xi 2.5.5.1.1 Simple cashflows The present value of a simple cashflow of amount A is Equation 2-409 VaR: Present value (simple cashflows) A l V p = ---------------- S = V p × S D ( r, t ) A l V p = ---------------D ( r, t ) where S is the spot rate between the cashflow currency and the portfolio currency and D(r,t) is the discount factor calculated with interest rate r and period t. There is therefore dependency on two market variables, S and r, the spot rate and the interest rate for the cashflow date. Note: Strictly speaking, due to the complicated method of calculating the discount factor, it may depend on the interest rate on more than one date. The error made in ignoring this fact is, however, insignificant. The corresponding VaR deltas are: • FX Delta Equation 2-410 VaR: FX delta δ FX • ∂V p A = = ---------------∂S D ( r, t ) IR Delta Depending on the value of the configuration parameter called var yield volatility, the IR deltas will not be calculated in the same way. The var yield volatility parameter is described in more detail in the TRM System Admin Guide. 208 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.5 Value-at-Risk calculations When the value is true, TRM considers the volatilities stored in the VaR scenarios to be yield volatilities and calculates the IR deltas as follows: Equation 2-411 VaR: IR delta calculations l Vp = Vp × S l l ΔV p = S × Δ V p + V p × ΔS l ∂V p l ΔV p = S × ---------- × Δr + V p × ΔS ∂r ∂V p l ΔV p = ---------- × Δr + V p × ΔS ∂r ∂V p Δr l ΔV p = r × ---------- × ------ + V p × ΔS ∂r r so that ∂V p δ IR = r × ---------∂r In TRM terms: IR Delta = 1000 x IR Exposure (1bp) x Interest Rate with IR Exposure (1bp): Sensitivity of your cashflow Present Value to a change of 1 basis point in the interest rate. Interest Rate: Zero-coupon rate used in the Present Value and IR Exposure (1bp) calculation. When the parameter - var yield volatility is set to false, TRM considers that the volatilities stored in the VaR scenarios are price volatilities and calculates the IR deltas as follows: Equation 2-412 VaR: IR delta calculations (in TRM) l Vp = Vp × S l l ΔV p = S × Δ V p + V p × ΔS l ∂V p l ΔV p = S × ---------- × ΔD + V p × ΔS ∂D ∂V p l ΔV p = ---------- × ΔD + V p × ΔS ∂D ∂V p ΔD l ΔV p = D × ---------- × -------- + V p × ΔS ∂D D so that ∂V p δ IR = D × ---------∂D In TRM terms: IR Delta = Discounted Risk Value Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 209 2 Market standards and calculations 2.5 Value-at-Risk calculations 2.5.5.1.2 Par method If Quoted method is used for the value-at-risk of an instrument (see 2.5.3.2 TRM market data on page 203) then delta is the present value of the instrument itself. 2.5.5.1.3 FX options For FX options, we have option deltas for both the asset and cash currencies, δ a and δ c which are calculated with the normal FX option formulas. Similarly the VaR deltas with respect to the interest rates are obtained by multiplying the IR exposures of the corresponding FX forward deal by the delta of the option. 2.5.5.1.4 IR options From cashflows associated with IR options the VaR currency delta is obtained by dividing the FX exposure by the FX risk offset, and the VaR IR delta by dividing the IR exposure by the IR risk offset (as shown in 2.5.5.1.1 Simple cashflows on page 208). 2.5.5.1.5 Equities An equity transaction creates FX, IR, and Price (equity) exposures. The FX and IR exposures are used to calculate the VaR FX and IR deltas in the normal manner: the FX or IR exposure is divided by the corresponding risk offset (as in 2.5.5.1.1 Simple cashflows on page 208). For Price exposure there are two alternatives. The first is that each equity is mapped to its own market variable. This approach requires that there is volatility and correlation data for each equity dealt with. However, it is more realistic to assume that the volatility and correlation data only exist for each equity index. Each equity can then be mapped to the index it belongs to. With this approach, the variation between the volatilities of the various equities can be determined via the betas. Each equity is assigned its own beta factor β which describes how strong the link between the movement of the stock and the index is. (The betas for individual stocks are calculated outside TRM and are fed in through Rate Monitor.) If beta is equal to one, the volatility of the equity is the same as the index volatility (the price of the stock is directly proportional to the value of the index). If beta is two, the equity's volatility is double the index's volatility and so on. A negative beta means that the price of the stock varies inversely to the value of the index; for example a beta of -2 means that the value of the stock decreases by 20% if there is an increase of 10% in the value of the index. The VaR equity delta of an equity is calculated by: Equation 2-413 VaR: Equities δ EQ = βN where N is the number of equities in the position. 2.5.5.1.6 Equity options The equity exposure of an equity option is based on the delta of the option. Therefore, the VaR equity delta of an equity option is calculated from: Equation 2-414 VaR: Equity options δ EQ = βδN where N is the number of underlying shares in the contract and δ is the option's delta. 2.5.5.2 Mapped deltas The VaR IR deltas described above may need to be mapped to RiskMetrics vertices as described in the 2.5.4.3.1 Risk equivalent method on page 206. 210 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.5 Value-at-Risk calculations If the VaR IR delta δ is with respect to an interest rate r for a period t which is not VaR vertex, then if the closest VaR vertices to t are t1 and t2, δ is mapped to corresponding deltas δ 1 and δ 2 so that Equation 2-415 VaR: Mapped deltas δ 1 = aδ r δ 2 = bδ r where t2 – t a = -------------t2 – t1 t – t1 b = -------------t2 – t1 2.5.5.3 Proportional deltas The correlation and volatility data from RiskMetrics are given as relative values. To get the actual values, we have to multiply these relative values by the current values of the market variables. In order to do this, we use the vector Δ , defined below, instead of the VaR delta vector δ in the VaR calculations (Equation 2-408 on page 208). Equation 2-416 VaR: Proportional deltas Δ = ( δ 1 X 1, δ 2 X 2, …, δ n X n ) where δ 1 is the VaR delta corresponding to the present value in question, and Xi is the current value of the market variable. 2.5.5.4 Value-at-Risk Once we know the delta vector for the position (which is then converted into the vector Δ as shown in Equation 2-416 on page 211) and the appropriate covariances (the variance-covariance matrix Σ as defined in Equation 2-392 on page 202), we can obtain the standard deviation σ of the total position: Equation 2-417 VaR: standard deviation of the total position 2 σ p = Δ′ΣΔ = ∑ Δi ∑ Σij Δj i j From σ , we can construct various risk measures, the most common of which is the (two-sided) confidence interval I 90 = 1.65σ p . The probability that the value of our position changes under the risk horizon less than I90 is 90%. Other confidence intervals can be derived, for example, the probability that the value of the position changes less than I 95 = 1.96σ p is 95%. Even if the value does not remain within the interval, it is not necessary that the position's value diminish, since the value could move up instead of down. Since the tails of the distribution are symmetric, the probability of moving up beyond the confidence interval is 5% for the 1.65σ p interval and 2.5% for the 1.96σ p interval. Thus, the probability of losing more than 1.65σ p is, in fact, only 5% and the probability of losing more than 1.96σ p just 2.5%. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 211 2 Market standards and calculations 2.5 Value-at-Risk calculations In the following figure, the shaded area represents the probability that the value of the position will move below the value-at-risk figure 1.65σ . This probability is 5%. The VaR key-figures which can be selected in Treasury Monitor are described in more detail in the TRM User Guide. 2.5.6 Incremental VaR Incremental VaR is a statistic providing information on the sensitivity of VaR to changes in portfolio holdings. Let wi be the i component of the delta vector of the portfolio and VaR the total value at risk of the portfolio, with the i component of the incremental VAR defined as: Equation 2-418 VaR: Incremental VaR definition ∂VAR IVAR i = w i ---------------∂w i As a consequence of the definition, Equation 2-419 VaR: Incremental VaR calculation ∑ I VARi = VAR i 2.5.6.1 Calculation of incremental VaR Let Cij denote the covariance matrix, w the delta vector and wT the transpose of the delta vector. Since Equation 2-420 VaR: Incremental VaR calculation VAR = T w Cw the i component of the incremental VaR (IVAR) is defined as Equation 2-421 Incremental VaR (IVAR) Incremental VaR can then be interpreted as the product of the exposures of the position with respect to each risk factor wi and the sensitivity of the VaR of the portfolio with respect to changes in each of those risk factors. 212 © Wall Street Systems IPH AB - Confidential 2 Market standards and calculations 2.5 Value-at-Risk calculations ∑ Cij wj j IVAR i = w i ------------------VAR Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 213 2 Market standards and calculations 2.5 Value-at-Risk calculations 214 © Wall Street Systems IPH AB - Confidential Chapter 3 Debt instruments 3.1 Bond Bonds are negotiable issues, which means that their cashflows are known (in terms of structure and dates) when the bond is issued. They can be traded in the market. In TRM, there is a clear distinction between loans and bonds. Loan agreements are set up mostly at deal entry, while bond issues must be completely defined at instrument level (notably in terms of cashflows). As is the case for loans, the definition of cashflows relies completely on the schedule concept (or cashflow structure). See Appendix B Schedules on page 883. Several schedules must be attached to a bond and they drive the generation of the cashflow structure for the deal. For the simplest bond, two schedules are associated with the deal: one schedule for interest flows; and one schedule for principal flows. It is possible to have additional interest schedules in the case of parallel interest flows. Bond instruments must be based on an instrument type derived from the class BOND. 3.1.1 Fixed-rate bond This is the simplest type of bond. Fixed-rate bonds are usually managed as described in the following sections. 3.1.1.1 Instrument setup • Bond main characteristics This information may be relevant to any kind of fixed-rate bond. Information Description Issuer Issuer of the bond. Currency Currency in which the bond is issued. Amount Rounding Specify with how many decimals and with which method the amounts will be rounded. Default Price Denom. For fractional prices, defines the default denominator. If a default price denominator is specified, the Deal Price can be entered as a fraction at deal entry. For example, if you enter 32 in this field, a Deal Price entered as 100-5 is displayed as 100 5/32. See the TRM User Guide. Accrued Interest Method How the system computes settlement accrued interest. For most bonds, the Linear method can be used, but some bonds require a specific method. For bonds traded at dirty price (i.e. price that includes accrued interest), it is also possible to specify an accrued interest method. In this case, the accrued interest is calculated for accounting purposes only (as settlement principal based on dirty price already includes accrued interest). If this field is left blank, no settlement AI is calculated See 2.1.6.1 Accrued interest calculations on page 67 for details of accrued interest methods. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 215 3 Debt instruments 3.1 Bond Information Description Settlement Switches If the bond is traded in dirty price it has to be specified here. Coupon Rate The interest rate of the fixed-rate bond. It is also possible to define whether rounding of the settlement principal is per trading unit, that is, the rounding is done for one unit and then the amount is multiplied by the number of units to obtain the settlement principal and accrued interest. See A.2.51 Bond on page 734. – Dates details The issue date and the maturity date must be specified for the bond. – Trading unit details It is possible to define a minimum bid size or trading units of a bond. If a minimum denomination is defined, deal entry is available either in units or amount and TRM ensures that the amount is a multiple of the denomination size. • Schedules Select the cashflow structure template you want for the instrument. For each set of cashflows defined in the template, select the generation parameters. One system template is provided for fixed-rate plain vanilla bonds (see B.2.1.1.21 Fixed, Bullet Repayment on page 894); you can choose this template or any other template derived from it. Once the template is applied to the instrument, the schedules are created and it is then possible to define their characteristics, such as, date basis, payment convention, calendars, and so on. See Appendix B Schedules on page 883. • Cashflows As the cashflows are an intrinsic characteristic of an issue, they must be defined at instrument level. Generation of the cashflows is automatically done in the instrument setup and takes into account all the information specified in the schedule. Some fields can be manually modified at cashflow level if necessary. The cashflows are saved in the database along with the instrument, and they will be used directly to generate the cashflows of the deal when the bond is sold or purchased. • Trading yield Specify how the yield/price conversion will be made when dealing the instrument. Information Description Yield Convention The convention defines how the yield/price conversion will be made. TRM supports the standard conventions. See 2.1.4 Yield/price conversions on page 38. Price and Rate rounding Defines how the system should round prices and rates. See A.2.323 Trading Yield on page 872. • Quoted It is necessary to specify how a bond is quoted on the market. 216 Information Description Price Type Price % or Yield for a bond. Quote Handling If the Bond quote handling is used, the system will notify Rate Monitor that it is a fixed-rate bond. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond Information Description Currency This quoted notion is time dependant (price type and/or currency may change over the life of a bond). See A.2.274 Quoted on page 849. It is also possible to set up: • Spot day calculations • Cashflow and transaction charge rules • Collateral • Branch Codes • Security Identifiers • Delivery. See Appendix A Features on page 713. 3.1.1.2 Deal capture 3.1.1.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a deal on a fixed-rate bond. Information Description Deal Price or Deal Rate If there is a yield/price convention set on the instrument, it is possible to enter either a rate or a price. The conversion will be made automatically. If there is no convention set, the deal must be entered in price. If a default price denominator is specified at instrument setup, Deal Price can be entered as a fraction. For more information about fractional prices, see the TRM User Guide. By default, Deal Price is considered as clean (i.e. does not include accrued interest). Deal Price is considered dirty if so defined at instrument level (in Settlement Switches) or if you set the Force Dirty Price transaction column value to Yes when entering the transaction. Nominal Amount Face Amount Value Date Enter either the nominal amount or face amount, and the system will compute the other automatically. Official date when money is transferred. This defaults to the spot date of the transaction. In addition, the following optional information can be captured: Information Description Units If the denomination of a bond instrument is specified at instrument setup, the deal can be input in units, and the nominal and face amounts are computed by the system. Trading Unit Size Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 217 3 Debt instruments 3.1 Bond 3.1.1.2.2 Generated data • Transaction Book Value (BV) = NA * price / 100 where: NA = nominal amount price = deal price • Cashflows TRM copies all the future cashflows of the bond and scales them according to the nominal amount engaged (using rounding). Additionally, the system generates a settlement cashflow with amount = BV (see above) and an accrued interest cashflow according to the AI Method. The following cashflow structure is generated for a fixed-rate bond: 3.1.1.3 Processing This section describes the actions that can be done throughout the life of a bond. 3.1.1.3.1 Asset swap You can easily create an asset swap from a bond transaction by executing the Asset Swap action. The asset swap is an interest rate swap where the cashflow structure of one leg (the asset leg) is similar but opposite to the cashflow structure of the bond, and the other leg corresponds to what you have specified (e.g. quarterly floating). • Setup To enable this action, the Allow Swap feature must be associated with the instrument. See A.2.23 Allow Swap on page 722. • Execution Right-click a bond transaction that uses an instrument with the Allow Swap feature, and select Asset Swap action in Transaction Manager. When you execute this action, use the following table to specify the parameters. Information Description Swap Instrument Select the instrument for the asset swap transaction. See 11.1.2 Asset swap on page 656 for information about setting up the Swap Instrument. 218 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond Information Description Opening Date The opening date and value date of the asset swap transaction. Value Date Swap Amount The nominal amount being swapped, which defaults to the nominal amount of the underlying bond transaction. This can be changed in order to swap a fraction of the bond. Asset Amount Read-only. The nominal amount of the underlying bond. Swap Units Read-only. The number of units being swapped (if the underlying bond is traded by units). Asset Units Read-only. The number of units of the underlying bond (if the underlying bond is traded by units). Leg Leg of the swap that will reflect the asset leg, i.e. which reverses the cashflows of the bond. Zero-Coupon Style Switch on so that the nominal amount of the other leg (i.e. the non-asset leg) of the asset swap is adjusted with the deal price of the underlying bond. The system automatically defaults to the zero-coupon style when there are no interest cashflows found in the bond transaction. Include Fees after Value Date Switch on so that fees that are to be settled after the value date of the bond are also copied and reversed asset swap. If this switch is not on, the fees after the value date are ignored. Price/Fee Method Method for reflecting the deal price and the fees of the bond in the asset swap transaction. As for all swaps, a price that is different from par (100) will result in upfront payments in the swap. Choose from: • All-In Price - All-In Price of the underlying bond is used as the price of the asset leg • Deal Price - Deal Price of the underlying bond is used as the price of the asset leg of of the swap. the swap. • Deal Price with Fees - Deal Price of the underlying bond is used as the price of the asset leg of the swap. In addition, the fees of the bond transaction can be reflected (copied and reversed) as upfront payments in the asset swap transaction. The Copied Fees field is used for determining which fees are to be reflected in the swap. • Par - Price of the asset leg of the swap is Par, i.e. 100. • Par with Discount/Premium and Fees - Price of the asset leg of the swap is Par, i.e. 100, but in addition discount/premium and fees of the bond transaction can be reflected (copied and reversed) as upfront payments in the asset swap transaction. The Copied Fees field is used for determining which fees are to be reflected in the swap. • Re-Offer Price - Re-Offer Price of the underlying bond is used as the price of the asset leg of the swap. Copied Fees Fees () Select which fees are to be copied (as reversed) from the bond transaction to the swap transaction as upfront payments: • None - No fees are copied. • All Fees - All fees are copied. • All-In Fees - Only All-In fees are copied (i.e. fees with the All-In attribute). • Re-Offer Fees - Only Re-Offer fees are copied (i.e. fees with the Re-Offer attribute). The fee amounts (in the relevant currency) copied/reversed from the underlying bond transaction and considered as upfront payments in the asset swap transaction. The values are defaulted from the bond transaction according to the selections in Price/Fee Method and Copied Fees fields. You can modify the amounts if needed. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 219 3 Debt instruments 3.1 Bond Information Description Adjust Leg 2 Price With Up-Fronts Switch on so that the Deal Price of the other leg (i.e. the non-asset leg) of the asset swap is adjusted with the upfront payments on the asset leg. By Nominal Amount If the underlying bond is traded in units, you can 'force' the swap transaction to be based on the nominal amount rather than units by setting this switch. If the swap is based on units, the interest amounts are calculated by one unit and multiplied by the number of units. The execution of the action generates a swap transaction. • Cancellation Cancellation of the action is done by canceling the swap transaction. 3.1.1.3.2 Pricing Pricing of bond transactions can be performed at transaction level using a right-click processing action. • Setup A choice of two types of Pricing action are available on the transaction if the Bond Pricing feature is associated with the instrument: Swap Spread or Yield/Price to Maturity. See A.2.79 Bond Pricing on page 746. • Execution – Swap Spread This Pricing action calculates the spread to be add to the floating leg of an asset swap generated from a given bond so that the market value of the asset swap is zero. – Information Description Swap Instrument ID of the Asset Swap instrument. Floating Leg Currency Currency of the floating leg. Floating Leg Frequency Frequency of the floating coupon. Swap Deal Price Deal price of the swap. Swap Spread Calculated spread after pricing. Yield/Price to Maturity This Pricing action calculates a yield (Price) using a given price (Yield) and vice versa. The calculation assumes the Yield Convention (*ISMA-30E360-ANNUAL or other) as defined in the Trading Yield page of the Instrument. 220 Information Description Interest Rate Rate type of the yield. Date Basis Date basis used to convert the time. Pricing Date Opening date of the bond transaction. Pricing Variable Yield (or the price). Pricing Target Variable (Information only) Price (or the yield). © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond Information Description Pricing Target (in %) Target value that you want to achieve. Pricing Result (Information only) Calculated value of the variable after pricing. 3.1.1.3.3 Benchmarking It is possible to analyze and compare a bond issue against those of another bond (the benchmark) or a swap curve, in terms of yields, swap spreads, or par swap rates. See 3.2 Structured bonds on page 244. 3.1.1.3.4 Transaction conversion It is possible to allow schedule conversion at predefined dates during a bond's life. • Setup (at instrument level) This process is available on the transaction if the Transaction Conversion feature is associated with the instrument. See A.2.325 Transaction Conversion on page 873. Then, the user can attach conversion schedules (at the instrument level) in the Schedule page of the Instrument Editor. • Execution – At instrument level: To execute the conversion at a predefined date, in the Instrument Editor, Cashflow page, the user selects the conversion flow and performs Convert action. After this conversion, when capturing a transaction, cashflows are generated according to the converted schedules. – At transaction level: When capturing a transaction before the conversion date, conversion events are also generated in the transaction. To execute the conversion, the user right-clicks the row of the corresponding transaction event and selects Transaction Conversion. The conversion inputs are displayed. See A.2.325 Transaction Conversion on page 873. The execution generates a conversion transaction with the following attributes: – Kind: Conversion – Opening Date: Conversion opening date – Value Date: Conversion value date. The remaining attributes are inherited from the initial transaction. The conversion transaction generates closing cashflows for the initial transaction; and future cashflows are reopened according to the conversion schedules defined at instrument level. 3.1.1.4 Position monitoring 3.1.1.4.1 Setup The cashflow discounting method used in IR risk calculation depends on the instrument set up: • Risk setup: The default risk method is Zero-Coupon or you can select Z-Spread or Yield to Maturity. For more information about these methods, see A.2.288 Risk Setup (BOND) on page 858. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 221 3 Debt instruments 3.1 Bond IR exposure setup: • – By default, TRM uses the valuation curve interpolation settings (IR Quote and Yield Curve Editor - Interpolation page). For example, if the interpolation settings are set up with Interest Type Continuous Yield, then risk calculations use continuously compounding discounting of the cashflows. – If IR Exposure is set up at the instrument level, then TRM uses these settings. For example, if IR exposure is set up with yield type Periodic Rate, then risk calculations use periodic discounting of the cashflows. See A.2.48 Base IR Exposure Setup on page 732. – If the risk method Yield to Maturity is used, then the date basis and interest rate defined for the risk yield are applied, even if there is an IR exposure setup. For more information about these calculations, see 2.3 Key-figures on page 112. 3.1.1.4.2 Calculations In this section, numerical examples demonstrate how the different figures are calculated for fixed-rate bonds. If you need more theoretical information about the method used in these calculations, see Chapter 2 Market standards and calculations on page 33. This example shows a fixed-rate bond with the following deal data: Setup data Instrument Date Basis Act/360 Currency EUR Valuation Method Theoretical Risk Method Theoretical Valuation Date Figure Date Risk Date Figure Date Risk Yield Type Continuous AI Method Linear Schedule Fixed, Bullet Repayment Result IR: Accrued Interest Linear Result IR: Accrual Method Linear Accrual Accrual Yield: Interest Type Periodic Rate Accrual Yield: Date Basis Actual/360 Unless otherwise stated, the figure date used in the calculations is 2001-05-15. On this date, the market data is as follows: Market data on 2001-05-15 Figure Date d_f 2001-05-15 Days to Spot d_fs 2 Discount Rate r_d 3.048771% Other figures calculated by the system are as follows: • 222 Time to Spot t_s = d_fs / B 0.005555556 = 2 / 360 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond • MV Spot Discount Factor D_s = EXP (-t_s * r_d) = 0.9998306382 Transaction data specific to the principal cashflow is as follows: Transaction data Opening Date 2001-02-16 Nominal Amount A 1,000,000 Value Date dt_v.p 2004-01-01 Payment Date dt_p.p 2004-01-02 Issue Date dt_i 2001-01-01 Book Value V_b.p = A 1,000,000 On the figure date, the market data specific to the principal amount is as follows: Market data on 2001-05-15 Interest Rate r.p 4.56933049% Other market data and figures specific to the principal amount are calculated by the system as follows: • Time to Payment t_p.p = (dt_p.p - d_f) / B 2.67222222 = (2004/01/02 – 2001/05/15) / 360 • MV Discount Factor D_V.p = D_s * D_f.p = 0.8851322685 • PV Discount Factor D_P.p = D_s * D_f.p = 0.8851322685 • Discount Factor From Spot D_f.p = EXP (-(t_p.p - t_s) * r.p) = 0.8852822015 On the figure date, the market data specific to the coupons is as follows: Market data Coupon 1 Interest Rate r.c1 Coupon 2 3.5485079% r.c2 Coupon 3 4.145317% r.c3 4.56933049% Transaction data specific to the coupon cashflows is as follows: Transaction data Coupon 1 Coupon 2 Coupon 3 Amount A.c1 50,000 A.c2 50,000 A.c3 50,000 Value Date dt_v.c1 2002-01-01 dt_v.c2 2003-01-01 dt_v.c3 2004-01-01 Payment Date dt_p.c1 2002-01-02 dt_p.c2 2003-01-02 dt_p.c3 2004-01-02 Other market data and figures specific to the coupons are calculated by the system as follows: • Coupon 1 Time to Payment t_p.c1 = (dt_p.c1 - d_f) / B 0.644444444 = (2002/01/02– 2001/05/15) / 360 MV Discount Factor D_V.c1 = D_s * D_f.c1 = 0.977418468 PV Discount Factor D_P.c1 = D_s * D_f.c1 = 0.977418468 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 223 3 Debt instruments 3.1 Bond Discount Factor from Spot D_f.c1 = EXP (- (t_p.c1 - t_s) * r.c1) = 0.977584034 • Coupon 2 Time to Payment t_p.c2 = (dt_p.c2 - d_f) / B 1.658333333 = (2003/01/02 – 2001/05/15) / 360 MV Discount Factor D_V.c2 = D_s * D_f.c2 = 0.933623285 PV Discount Factor D_P.c2 = D_s * D_f.c2 = 0.933623285 Discount Factor from Spot D_f.c2 = EXP (- (t_p.c2 - t_s) * r.c2) = 0.933781432 • Coupon 3 Time to Payment t_p.c3 = (dt_p.c3 - d_f) / B 2.672222222 = (2004/01/02 – 2001/05/15) / 360 MV Discount Factor D_V.c3 = D_s * D_f.c3 = 0.885132268 PV Discount Factor D_P.c3 = D_s * D_f.c3 = 0.885132268 Discount Factor from Spot D_f.c3 = EXP (- (t_p.c3 - t_s) * r.c3) = 0.885282201 3.1.1.4.3 Valuation figures The valuation method commonly used for a fixed-rate bond is the Theoretical method. • Principal flow figures Market Value V.p = A * D_V.p 885,132.27 = 1,000,000 * 0.8851322685 Clean Market Value CMV.p = A * D_f.p 885,282.20 = 1,000,000 * 0.8852822015 • Coupon 1 figures Market Value V.c1 = A.c1 * D_V.c1 48,870.92 = 50,000 * 0.977418468 Clean Market Value CMV.c1 = A.c1 * D_f.c1 - Accrued_Interest_Spot 29,990.31 = 50,000 * 0.977584034 - 18,888.89 • Coupon 2 figures Market Value V.c2 = A.c2 * D_V.c2 46,681.16 = 50,000 * 0.933623285 Clean Market Value CMV.c2 = A.c2 * D_f.c2 46,689.07 = 50,000 * 0.933781432 • Coupon 3 figures Market Value V.c3 = A.c3 * D_V.c3 44,256.61 = 50,000 * 0.885132280 Clean Market Value CMVc3 = A.c3 * D_f.c3 44,264.11 = 50,000 * 0.885282201 • Total transaction figures Market Value = V.p +V.c1 + V.c2 + V.c3 = 1,024,940.97 224 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond Clean Market Value = CMV.p + CMV.c1 + CMV.c2 + CMV.c3 =1,006,225.70 3.1.1.4.4 Result figures The setup of the instrument impacts the way result figures are computed. • Principal flow figures Total Profit Total_Profit.p = V.p - V_b.p -114,867.73 = 885,132.27 – 1,000,000 MtoM Profit MtoM_Profit.p = A * D_f.p - V_b.p -114,717.80 = 1,000,000 * 0.8852822015 – 1,000,000 Other Profit Other_Profit.p = Total_Profit.p - MtoM_Profit.p -149.93 = -114,867.73 – (-114,717.80) • Coupon 1 figures Total Profit Total_Profit.c1 = = V.c1 - V_b.c1 48,870.92 = 48,870.92 - 0 MtoM Profit MtoM_Profit.c1 = A.c1 * D_f.c1 - V_b.c1 - Accrued_Interest.Spot 29,990.31 = 50,000 * 0.977584034 – 0 – 18,888.89 Accrued Interest Accrued_Interest.c1 = A.c1 * (d_f - dt_i) / B 18,611.11 = 50,000 * (2001/05/15 – 2001/01/01) / 360 Other Profit Other_Profit.c1 = Total_Profit.c1 - MtoM_Profit.c1 - Accrued_Interest.c1 269.50 = 48,870.92 - 29,990.31 - 18,611.11 • Coupon 2 figures Total Profit Total_Profit.c2 = V.c2 - V_b.c2 46,681.16 = 46,681.16 - 0 MtoM Profit MtoM_Profit.c2 = A.c2 * D_f.c2 - V_b.c2 46,689.07 = 50,000 * 0.933781432 - 0 Other Profit Other_Profit.c2 = Total_Profit.c2 - MtoM_Profit.c2 -7.91 = 46,681.16 - 46,689.07 • Coupon 3 figures Total Profit Total_Profit.c3 = V.c3 - V_b.c3 44,256.61 = 44,256.61 - 0 MtoM Profit MtoM_Profit.c3 = A.c3 * D_f.c3 - V_b.c3 44,264.11 = 50,000 * 0.885282201 - 0 Other Profit Other_Profit.c3 = Total_Profit.c3 - MtoM_Profit.c3 -7.50 = 44,256.61 - 44,264.11 • Total transaction figures Total Profit = Total_Profit.p + Total_Profit.c1 +Total_Profit.c2 + Total_Profit.c3 = 24,940.97 MtoM Profit = MtoM_Profit.p + MtoM_Profit.c1 + MtoM_Profit.c2 + MtoM_Profit.c3 = 6,225.70 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 225 3 Debt instruments 3.1 Bond Accrued Interest = Accrued_Interest.c1 = 18,611.11 Other Profit = Total_Profit.total - MtoM_Profit.total - Accrued_Interest.total = 104.16 3.1.1.4.5 Risk figures The risk method commonly used for a bond is the Theoretical method. • Principal flow figures IR Exposure 1bp E_i.p = A * (- (t_p.p - t_s) * D_f.p * D_s - t_s * D_f.p * D_s) * 0.0001 -236.53 = 1,000,000*(-(2.6722222-0.005555556)*0.8852822015*0.9998306382-t_s*D_f.p*D_s)*0.0001 Effective Duration U_eff.p = -E_i.p / V.p / 0.0001 2.672222 = -(-236.53) / 885,132.27 / 0.0001 • Coupon 1 figures IR Exposure 1bp E_i.c1 = A.c1 * (- (t_p.c1 - t_s) * D_f.c1 * D_s - t_s * D_f.c1 * D_s) * 0.0001 -3.15 = 50,000 * (-(0.64444444–0.005555556)*0.977584034*0.9998306382–t_s*D_f.c1*D_s)*0.0001 Effective Duration U_eff.c1 = -E_i.c1 / V.c1 / 0.0001 0.64444 = -3.15 / 48,870.92 / 0.0001 • Coupon 2 figures IR Exposure 1bp E_i.c2 = A.c2 * (- (t_p.c2 - t_s) * D_f.c2 * D_s - t_s * D_f.c2 * D_s) * 0.0001 -7.74 = 50,000 * (-(1.658333333-0.005555556)*0.933781432*0.9998306382-t_s*D_f.c2* D_s)*0.0001 Effective Duration U_eff.c2 = -E_i.c2 / V.c2 / 0.0001 1.65833 = -7.74 / 46,681.16 / 0.0001 • Coupon 3 figures IR Exposure 1bp E_i.c3 = A.c3 * (-(t_p.c3 - t_s) * D_f.c3 * D_s - t_s * D_f.c3 * D_s) * 0.0001 -11.83 = 50.000*(-(2.672222222-0.005555556)*0.885282201*0.9998306382-t_s*D_f.c3* D_s)*0.0001 Effective Duration U_eff.c3 = -E_i.c3 / V.c3 / 0.0001 2.672222222 = -11.83 / 44,256.61 / 0.0001 • Total transaction figures IR Exposure 1bp = E_i.p +E_i.c1 + E_i.c2 + E_i.c3 = -259.24 Effective Duration = -E_i.total / V.total / 0.0001 = 2.529357 226 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond 3.1.1.5 Norwegian government bond Norwegian government bonds are based on annual coupon and Actual/365 accrual date basis. The ex-coupon period starts 14 calendar days prior to the interest payment. Accrued interest is calculated as shown in Equation 2-51 Accrued Interest: Norwegian on page 55. 3.1.1.5.1 Instrument setup Norwegian bond instruments must be based on an instrument type derived from the class BOND. • Main characteristics They are set up in a similar way to bonds (3.1.1 Fixed-rate bond on page 215), except for the following. Information Description Currency NOK AI Method Norwegian. See Norwegian on page 77. – Schedule Select a cashflow structure based on the Fixed, Bullet Repayment system template, (FIXED-BULLET). See B.2.1.1.21 Fixed, Bullet Repayment on page 894. • Trading Yield Information Description Yield Convention GOVT-NO-ACT365 (Norwegian Government Actual365) See A.2.323 Trading Yield on page 872. • Quoted parameters Information Description Price Type Yield Quote Handling Bond Currency NOK See A.2.274 Quoted on page 849. • Result parameters Information Description AI Method Coupon % See A.2.49 Base IR Setup on page 733. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 227 3 Debt instruments 3.1 Bond 3.1.2 Floating rate note Floating Rate Notes (FRNs) have interest payments linked to a reference rate which has to be fixed for each coupon. 3.1.2.1 Instrument setup Instrument setup for a floating rate note is similar to that of a fixed-rate bond (see 3.1.1 Fixed-rate bond on page 215), except for the following: • Bond main characteristics The coupon rate needs to be null. • Schedules Select the cashflow structure template you want for the instrument and, for each set of cashflows defined in the template, select the generation parameters. One system template is provided for floating rate bonds (B.2.1.1.22 Floating, Bullet Repayment on page 894); you can choose this template or any other template derived from it. Once the template is applied to the instrument, the schedules are created and it is then possible to define their characteristics. One important set of characteristics in the case of a floating rate note are the fixing parameters: – Fixing Rate (the yield curve) optionally * by a factor and + a spread – Fixing period (3M, 6M, 1Y, and so on) – Price Scenario used to retrieve the price which will be used for fixing – Fixing offset and type (in advance or in arrears). If in advance, the rate of the first cashflow is required. See Appendix B Schedules on page 883. • Discount margin calculation Most FRNs have a known first/next coupon payment, while subsequent coupons will usually be set in terms of a margin over a specific reference rate (such as, LIBOR). As a result, a current margin relative to the reference rate is often calculated. – Discount margin setup Define the parameters used to calculate the discount margin if you want to take it into account in the estimation of the instrument’s future flows. See A.2.343 Z-DM/Spread Setup on page 882. – Quoted It is necessary to specify how the FRN is quoted on the market. Information Description Quote Handling FRN It will then be possible to use the Bid Z-DM/Spread and Ask Z-DM/Spread figures to convert Price into Discount Margin in Rate Monitor. See A.2.274 Quoted on page 849. 228 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond – Risk parameters After the calculation of the discount margin, the payment discount factor of each flow is adjusted. The derived risk structure is achieved by setting the following parameter: Information Description Risk Profile Plain Vanilla See A.2.338 Valuation Setup (Floating) on page 879. 3.1.2.2 Deal capture 3.1.2.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a deal on a floating-rate bond. Information Description Deal Price Price paid for the FRN as a percentage of the Nominal Amount. Nominal Amount Enter either the nominal amount or face amount, and the system will compute the other automatically. Face Amount Value Date Official date when money is transferred. This defaults to the spot date of the transaction. In addition, the following optional information can be captured: Information Description Units If the denomination of a bond instrument is specified at instrument setup, the deal can be input in units, and the nominal and face amounts are computed by the system. Trading Unit Size Nominal/Spot Rate Current "running" coupon can be entered in this field (if fixing of the first coupon has not been carried out in Instrument Editor: see 3.1.2.3.1 Fixing on page 230). 3.1.2.2.2 Generated data • Transaction Book Value (BV) = NA * price / 100 where: NA = nominal amount price = deal price • Cashflows The system copies all the future cashflows of the bond and scales them according to the nominal amount engaged (using rounding). Additionally the system generates a settlement cashflow with amount = BV (see above) and an accrued interest cashflow according to the AI Method. Note: The bond must be fixed at instrument level in order for the accrued interest flow to be generated (see 3.1.2.3.1 Fixing on page 230). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 229 3 Debt instruments 3.1 Bond The following cashflow structure is generated for a floating-rate bond: 3.1.2.3 Processing This section describes the actions that can be done throughout the life of a floating-rate bond. 3.1.2.3.1 Fixing The major process for a floating-rate note is the fixing of the flows. • Setup Depending on the instrument setup (schedules) the fixing can be done in advance (the standard case, at the beginning of each coupon period) or in arrears (at the end of each coupon period). In both cases there can be an offset of n days (before the beginning or end of the coupon period). • Execution When fixing is executed, the rate is retrieved for the specified fixing rate and period according to the designated fixing scenario. The scenario to be used for fixing is configured at the system level, see TRM System Admin Guide. The fixing subscenario is specified at the cashflow level. The following information is stored on the fixed cashflow: The fixing date The rate of the yield curve The coupon rate which is the rate of the yield curve (and optionally * factor + spread) The amount of the coupon. The fixing process can be performed in two ways in TRM: the process itself is exactly the same in each case: the coupon is fixed at both instrument and transaction level. The methods of fixing are as follows: – Directly on the cashflow (in Instrument Editor’s Cashflow page) using the Fix Price action: the fixing affects all deals on this instrument. – Using the Fixing Bond Cashflow activity: all instruments and their deals that need to be fixed for a particular date are affected. See the TRM User Guide for information on the activity parameters. Note: The bond issue must be fixed at instrument level in order for the accrued interest flow to be generated (for transactions captured between coupon fixing date and fixing value date). 230 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond • Cancellation It is possible to cancel the cashflow fixing either manually, using the Undo Fixing action in Instrument Editor; or automatically, using the Fixing Bond Cashflow - Undo activity. See the TRM User Guide for information on the activity parameters. 3.1.2.4 Position monitoring 3.1.2.4.1 Setup The cashflow discounting method used in IR risk calculation depends on the instrument set up: • • Risk setup: – The default risk method is Zero-Coupon or you can select risk method Zero Discount Margin (Z-DM). For more information about these methods, see A.2.289 Risk Setup (FRN) on page 858. – If discount margin is set up at the instrument level (see A.2.164 FRN Valuation on page 791), then the discount margin is used in the valuation and is added to the valuation curve specified for the instrument, and the day count method and yield type used are taken from the interpolation method of this valuation curve. For more information about Discount Margin calculations, see 2.1.5 Discount Margin on page 66. IR exposure setup: – By default, TRM uses the valuation curve interpolation settings (IR Quote and Yield Curve Editor - Interpolation page). For example, if the interpolation settings are set up with Interest Type Continuous Yield, then risk calculations use continuously compounding discounting of the cashflows. – If IR Exposure is set up at the instrument level, then TRM uses these settings. For example, if IR exposure is set up with yield type Periodic Rate, then risk calculations use periodic discounting of the cashflows. See A.2.48 Base IR Exposure Setup on page 732. For more information about these calculations, see 2.3 Key-figures on page 112. 3.1.2.4.2 Calculations - Discount Margin example Let us consider a floating rate note with two coupons remaining, where the next coupon is fixed: • Input data Data Symbol Example Next coupon (fixed) c1 0.0556111111111111 Last coupon (estimated) c2 0.0232101439796721 Time from spot to next coupon (Act/365) t1 13/365 = 0.035616438356164383 Time from spot to last coupon (Act/365) t2 196/365 = 0.53698630136986303 Discount factor from spot to next coupon D1 0.999066136779281 Discount factor from spot to last coupon D2 0.981278683885205 Clean price from market quote P 0.98 Accrued interest Ia 0.05163888888888888 Dirty price Pd P + Ia = 1.0316388888888888 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 231 3 Debt instruments 3.1 Bond Choosing continuous compounded rate as the discount margin yield type, we get the following results: Data Calculation Underlying rate to next coupon r1 = - log[D1] / t1 = - log[0.999] / 0.0356 = 0.026232256389534768 Underlying rate to last coupon r2 = - log[D2] / t2 = - log[0.981] / 0.0537 = 0.035194153518686676 Discount margin must satisfy the following equation: from which we can solve numerically: m = 0.052423976963667664. 3.1.2.4.3 Calculations - FRN example The numerical example in this section demonstrates how the different figures are calculated for a floating-rate note. Instrument data • • Schedule page (Floating Coupon) Interest Type Periodic Rate Date Basis (B) Actual/360 Base Valuation page (Valuation) Method • • 360 Theoretical IR Exposure page Date Basis (B_r) Actual/360 Yield Type Continuous Yield 360 Floating Valuation page Risk Profile Plain Vanilla Transaction data • Nominal Amount A = 1,000,000.00 Deal Price p = 98.00% Spot Date d_v = 2002-02-26 Rate r_c = 0.05 Calculated transaction data Book Value 232 V_b = p*A = 980000 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond Market data Coupon Period (_p_c) Time to Value Date (_t_v) Risk Date (_d_r) Time to Risk Date (_t_r) Principal 1.713888889 2/22/2004 1.713888889 Coupon 1 0.188888889 8/22/2002 0.188888889 Coupon 2 0.7 Risk Cash Flow Start 2 177 8/22/2002 0.188888889 Risk Cash Flow End 2 184 2/22/2003 0.7 2/22/2003 0.7 8/22/2003 1.202777778 8/22/2003 1.202777778 2/22/2004 1.713888889 Coupon 3 1.202777778 Risk Cash Flow Start 3 Risk Cash Flow End 3 181 Coupon 4 1.713888889 Risk Cash Flow Start 4 Risk Cash Flow End 4 184 Valuation data Figure or Valuation Date d_f = 2002-06-15 Figure Market Value Spot Discount Factor D_s = 0.999746283358179 Valuation figures • • • Figure Market Value (_V_) Principal =_A_e*_D_p = 930990.3649 Coupon 1 =_A_e*_D_p = 24432.46813 Coupon 2 =_A_e*_D_p = 18638.33299 Coupon 3 =_A_e*_D_p = 20688.99262 Coupon 4 =_A_e*_D_p = 23545.42006 Transaction V_Tr = SUM(_V) = 1018295.579 Figure Fixing Rate (_r_x) Coupon 1 =r_c = 0.05 Coupon 2 =(INDEX(_D_p,A28,1)/(_D_p)-1)/(_p_c/360) = 0.037392717 Coupon 3 =(INDEX(_D_p,A29,1)/(_D_p)-1)/(_p_c/360) = 0.043109308 Coupon 4 =(INDEX(_D_p,A32,1)/(_D_p)-1)/(_p_c/360) = 0.049481851 Figure Amount (_A_e) Principal =A = 1000000 Coupon 1 =A*_r_x*_p_c/B = 24583.33333 Coupon 2 =A*_r_x*_p_c/B = 19111.8329 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 233 3 Debt instruments 3.1 Bond • Coupon 3 =A*_r_x*_p_c/B = 21674.4023 Coupon 4 =A*_r_x*_p_c/B = 25290.72367 Figure IR Exposure 1bp (_E_i1) Principal =_V_r*(-_t_r*_D_p)*0.0001 = -159.5614042 Coupon 1 =_V_r*(-_t_r*_D_p)*0.0001 = -0.461502176 Coupon 2 Risk Cash Flow Start 2 =_V_r*(-_t_r*_D_p)*0.0001 = -18.77296987 Risk Cash Flow End 2 =_V_r*(-_t_r*_D_p)*0.0001 = 68.26573443 Coupon 3 Risk Cash Flow Start 3 =_V_r*(-_t_r*_D_p)*0.0001 = -68.26573443 Risk Cash Flow End 3 =_V_r*(-_t_r*_D_p)*0.0001 = 114.809443 Coupon 4 Risk Cash Flow Start 4 =_V_r*(-_t_r*_D_p)*0.0001 = -114.809443 Risk Cash Flow End 4 =_V_r*(-_t_r*_D_p)*0.0001 = 159.5614042 Transaction • E_i1_Tr = SUM(_E_i1) = -19.23447204 Figure Risk Value (_V_r) Principal = A = 1000000 Coupon 1 = _A_e = 24583.33333 Coupon 2 Risk Cash Flow Start 2 = A = 1000000 Risk Cash Flow End 2 = -A = -1000000 Coupon 3 Risk Cash Flow Start 3 = A = 1000000 Risk Cash Flow End 3 = -A = -1000000 Coupon 4 Risk Cash Flow Start 4 = A = 1000000 Risk Cash Flow End 4 = -A = -1000000 Transaction • Figure Present Value (_V_p) Principal = _V_r*_D_p = 930990.3649 Coupon 1 = _V_r*_D_p = 24432.46813 Coupon 2 Risk Cash Flow Start 2 = _V_r*_D_p = 993863.1105 Risk Cash Flow End 2 = _V_r*_D_p = -975224.7775 Coupon 3 234 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond Risk Cash Flow Start 3 = _V_r*_D_p = 975224.7775 Risk Cash Flow End 3 = _V_r*_D_p = -954535.7849 Coupon 4 Risk Cash Flow Start 4 = _V_r*_D_p = 954535.7849 Risk Cash Flow End 4 = _V_r*_D_p = -930990.3649 Transaction V_p_Tr = SUM(_V_p) = 1018295.579 Result figures • • • • • Figure MtoM Profit (_P_m) Principal =A*_D_p/D_s-V_b-_P_a = -51776.12227 Coupon 1 =_A_e*_D_p/D_s-_AI = 9299.779742 Coupon 2 =_A_e*_D_p/D_s-_AI = 18643.06305 Coupon 3 =_A_e*_D_p/D_s-_AI = 20694.24309 Coupon 4 =_A_e*_D_p/D_s-_AI = 23551.39544 Transaction P_m_Tr = SUM(_P_m) = 20412.35905 Figure Accrued Interest (_AI) Coupon 1 = (d_f-d_v)/(_d_v-d_v)*_A_e = 15138.88889 Transaction AI_Tr = SUM(_AI) = 15138.88889 Figure Accrued Profit (_P_a) Principal = (d_f-d_v)/(_d_v-d_v)*(A-V_b) = 3002.754821 Transaction P_a_Tr = SUM(_P_a) = 3002.754821 Figure Other Profit (_P_o) Principal = _P_T-_P_m-_P_a-_AI = -236.267694 Coupon 1 = _P_T-_P_m-_P_a-_AI = -6.200496936 Coupon 2 = _P_T-_P_m-_P_a-_AI = -4.73005535 Coupon 3 = _P_T-_P_m-_P_a-_AI = -5.250473862 Coupon 4 = _P_T-_P_m-_P_a-_AI = -5.975380961 Transaction P_o_Tr = SUM(_P_o) = -258.4241011 Total Profit (_P_T) Principal =_V-V_b = -49009.63514 Coupon 1 =_V = 24432.46813 Coupon 2 =_V = 18638.33299 Coupon 3 =_V = 20688.99262 Coupon 4 =_V = 23545.42006 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 235 3 Debt instruments 3.1 Bond Risk figures Figure Effective Duration • Transaction U_eff_Tr = E_i1_Tr/V_Tr/0.0001 = -0.188888889 3.1.3 Australian floating rate note An Australian floating rate note (FRN) is a medium-term bond that provides investors with the ability to achieve returns at a fixed margin above a floating benchmark, usually the 90-day Bank Bill Swap Rate (BBSW). BBSW rates are compiled daily by the Australian Financial Markets Association using the mid-rates of 14 banks. Australian floating rate notes are traded at a trading margin and swap rate, not at a price or yield. The interest margin is determined on the issue date by the credit rating of the issuer, the term to maturity and the market perception of the issuer. The official Treasury Adjustable Rate Bond Pricing Formula is as follows: Price per $100 face value: Equation 3-1 Official Treasury Adjustable Rate Bond Pricing formula where: C 0 if the next interest is not fixed at instrument level, otherwise 1. b The Index (as a percentage) from the last interest reset date to the next interest payment date defined as the average three month Australian bank bill swap reference mid-rate (BBSW) as indicated by Reuters, rounded to four decimal places. IM Spread% defined at schedule level. d The number of days in the current interest period. TM Trading Margin (expressed as a percentage) to express the yield margin to the Index. an v n 236 The number of complete interest periods to maturity at the next interest payment date. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond i s The quarterly swap rate for the period starting on the settlement date and ending on the maturity date. If the frequency of the swap rate is not quarterly, the swap rate is converted to a quarterly compounding rate before it is used. The conversion formula is given as follows: Equation 3-2 Swap Rate Conversion where: • r_in is the swap rate to be converted. • r_out is the resultant compounding rate, num_in and num_out are the number of periods in a year for the frequencies related to r_in and r_out respectively. For example, the number of periods in a year for a quarterly frequency is 4. • r is the discount rate (expressed as a percentage) as determined on the offering date for the period from the settlement date to the next interest payment date, and rounded to four decimal places. • f is the number of days from the settlement date to the next interest payment date. 3.1.3.1 Instrument setup Australian FRN instruments must be based on an instrument type derived from the class BOND. They are set up in a similar way to bonds, but require a different primary feature. • Main characteristics Same set up as for a usual FRN, see 3.1.2 Floating rate note on page 228. See A.2.30 Australian FRN on page 724. • Quotation information Information Description Price Type Select Trading Margin to trade Australian FRN instruments at a trading margin. Quote Handling Select FRN Australian to convert the quotation (trading margin) to the price of the instrument. See Equation 3-1 on page 236. See A.2.274 Quoted on page 849. • Yield Curve Default The setup of the feature Quote Default (Australian FRN) is similar to the usual Quote Default feature, except that it adds the Yield Curve Default page to select the Par rate yield curve to be used for reference rate defaulting. Information Description Currency The currency that you want to specify. Select AUD. Yield Curve Select corresponding yield curve to be used instead of the yield curve defined at the currency level (Currency Editor). A.2.267 Quote Default (Australian FRN) on page 846. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 237 3 Debt instruments 3.1 Bond Valuation approach • To use the quoted valuation method, i.e. market value calculation using the trading margin to price formula (Equation 3-1 on page 236). A.2.31 Australian FRN Method on page 725. 3.1.3.2 Deal capture 3.1.3.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a deal on an Australian FRN: Information Description Trading Margin Instrument quotation. In addition, the following defaulted information can be modified: Information Description Reference Rate Quarterly swap rate for the period from settlement date to maturity date (from the yield curve specified in Yield Curve Default page when provided, otherwise uses the default yield curve defined at currency level). Discount Rate Computed from the settlement date and the next coupon date of the instrument (from the default yield curve defined at currency level). AU Rate Scenario Scenario used to calculate the reference and discount rates. This scenario defaults to the scenario defined at the instrument level (Quote Default page). You can change the default scenario by selecting Quote Default Configuration from the Options menu. See TRM User Guide for more information about changing this configuration. Deal Price Computed using the trading margin to the price formula (Equation 3-1 on page 236). 3.1.3.2.2 Generated data Same as for usual FRN, see 3.1.2.2.2 Generated data on page 229. 3.1.3.3 Processing The actions that can be done throughout the life of an Australian FRN are the same ones as for a usual FRN, see 3.1.2.3 Processing on page 230. 3.1.3.4 Position monitoring There are two basic methods for valuation of Australian FRN instruments: Quoted or Theoretical. When the Theoretical valuation method is used, the Australian FRN is valuated in the same way as a usual FRN instruments. On the other hand, if you want to use the pricing formula (Equation 3-1 on page 236) to compute the market value with the reference rate and discount rate taken on the valuation date as described previously, then you need to attach feature Australian FRN Method (A.2.31 Australian FRN Method on page 725) and use the Quoted valuation method. Swap and discount rates used in the pricing formula are retrieved as follows: • Reference Rate: The quarterly swap rate for the period from valuation date to maturity date is computed from the yield curve specified in the Yield Curves page (Valuation Curve Setup feature) with Usage set to Valuation when provided, otherwise uses the valuation yield curve defined at the currency level. • Discount Rate: Computed between valuation date and next coupon date of the instrument (computed from the yield curve specified in the Yield Curves page (Valuation Curve Setup feature) 238 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond with Usage set to Discount when provided, otherwise uses the valuation yield curve defined at currency level). Note: For the valuation when the next coupon is not fixed, the estimation curve is used to compute the next fixing rate and the discount rate in the pricing formula. If the estimation curve is not defined at the instrument level, then the currency estimation curve is used instead. If no currency estimation curve is defined, then the currency valuation curve will be used. See feature A.2.337 Valuation Curve Setup on page 878. 3.1.4 Zero-coupon bond A zero-coupon bond does not pay any interest during its life, but is instead paid at a significant discount and repays its entire face value at maturity. 3.1.4.1 Instrument setup Instrument setup for a zero-coupon bond resembles a fixed-rate bond except for the following: • Bond main characteristics The coupon rate needs to be null. • Schedules Select the cashflow structure template you want for the instrument and, for each set of cashflow defined in the template, select the generation parameters. One system template is provided for zero-coupon bonds (B.2.1.1.46 Zero-Coupon on page 899); you can choose this template or any other template derived from it. Once the template is applied to the instrument, the schedules are created and it is then possible to define their characteristics. See Appendix B Schedules on page 883. • Trading yield Specify how the yield/price conversion will be made when dealing the instrument. Information Yield Convention Description Select *ISMA-30E360-ANNUAL. For more information about these conventions, see 2.1.4 Yield/price conversions on page 38. Note: *U.S.STREET can also be used when applicable. For example, use *U.S.STREET-ACTACT-SEMIANNUAL for U.S. and UK STRIPS. See A.2.323 Trading Yield on page 872. 3.1.4.2 Deal capture 3.1.4.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a deal on a zero-coupon bond. Information Description Deal Price or If there is a yield/price convention set on the instrument, it is possible to enter either a rate or a price and conversion is made automatically. If there is no convention set, the deal must be entered in price. Deal Rate Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 239 3 Debt instruments 3.1 Bond Information Description Nominal Amount Enter either the nominal amount or face amount, and the system will compute the other automatically. Face Amount Value Date Official date when money is transferred. This defaults to the spot date of the transaction. In addition, the following optional information can be captured: Information Description Units If the denomination of a bond instrument is specified at instrument setup, the deal can be input in units, and the nominal and face amounts are computed by the system. Trading Unit Size 3.1.4.2.2 Generated data • Transaction Book Value (BV) = NA * price / 100 where: NA = nominal amount price = deal price • Cashflows TRM generates a settlement cashflow with amount = BV (see above) and a principal payback cashflow for the nominal amount. The following cashflow structure is generated for a Zero-Coupon bond (bought): 3.1.4.3 Processing This section describes the actions that can be done throughout the life of a zero-coupon bond. 3.1.4.3.1 Asset swap It is possible to carry out the Asset Swap action on a zero-coupon bond (see 3.1.1.3.1 Asset swap on page 218). In this case, the Zero-Coupon Style switch is on by default (no interest flows) and the Book Value instead of the Nominal Amount is used for the second leg of the swap. 3.1.4.3.2 Transaction conversion It is possible to allow schedule conversion at predefined dates during a bond's life. • Setup (at instrument level) This process is available on the transaction if the Transaction Conversion feature is associated with the instrument. 240 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond See A.2.325 Transaction Conversion on page 873. Then, the user can attach conversion schedules (at the instrument level) in the Schedule page of the Instrument Editor. • Execution – At instrument level: To execute the conversion at a predefined date, in the Instrument Editor, Cashflow page, the user selects the conversion flow and performs Convert action. After this conversion, when capturing a transaction, cashflows are generated according to the converted schedules. – At transaction level: When capturing a transaction before the conversion date, conversion events are also generated in the transaction. To execute the conversion, the user right-clicks the row of the corresponding transaction event and selects Transaction Conversion. The conversion inputs are displayed. See A.2.325 Transaction Conversion on page 873. The execution generates a conversion transaction with the following attributes: – Kind: Conversion – Opening Date: Conversion opening date – Value Date: Conversion value date. The remaining attributes are inherited from the initial transaction. The conversion transaction generates closing cashflows for the initial transaction; and future cashflows are reopened according to the conversion schedules defined at instrument level. If the conversion price is different to the original deal price, then a P/L flow is generated, showing the differences between the conversion price and the original deal price. 3.1.5 Amortizing bond An amortizing bond repays the principal according to a pre-defined schedule. Amortizing bonds can be fixed-rate or floaters. A special case of an amortizing bond is the constant annuity. In this case, the rate is fixed and the repayments, occurring at each coupon payment, are calculated so that the sum of the interest + the repayment is constant during the life of the bond. In simple terms, this means that the interest payments are decreasing, while the principal payments are increasing. Note: TRM does not support repayments in the middle of a coupon period but only at coupon payment dates. 3.1.5.1 Instrument setup Most of the characteristics of an amortizing bond are the same as for a fixed/floating rate bond with the following differences. • Schedules Select the cashflow structure template you want for the instrument and, for each set of cashflow defined in the template, select the generation parameters. Depending on whether the rate is floating or fixed, you need to apply either the Floating, Bullet Repayment template (see B.2.1.1.22 Floating, Bullet Repayment on page 894), or the Fixed, Bullet Repayment template (see B.2.1.1.21 Fixed, Bullet Repayment on page 894), or any other template derived from them. Then, for the principal schedule you have to specify the repayment frequency, the method used for repayment calculation, and how much is repaid at each amortization. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 241 3 Debt instruments 3.1 Bond The most common methods are: linear, percentage, and amount. For the interest schedule, the parameters are the same as those for fixed or floating rate bonds. See Appendix B Schedules on page 883. Note that for an annuity repayment, you have to select the Fixed, Annuity Repayment template (see B.2.1.1.20 Fixed, Annuity Repayment on page 894). 3.1.5.2 Deal capture 3.1.5.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a deal on an amortizing fixed-rate bond. Information Description Deal Price or If there is a yield/price convention set on the instrument, it is possible to enter either a rate or a price, and conversion is made automatically. If there is no convention set, the deal must be entered in price. Deal Rate Nominal Amount Nominal amount of the deal. Value Date Official date when money is transferred. This defaults to the spot date of the transaction. In addition, the following optional information can be captured: Information Description Trading Units If the denomination of a bond instrument is specified at instrument setup, the deal can be input in face amount/units and the Nominal Amount will be computed by the system. Face Amount 3.1.5.2.2 Generated data • Transaction Book Value (BV) = NA * price / 100 where: NA = nominal amount price = deal price • Cashflows The system copies all the future cashflows of the bond and scales them according to the nominal amount engaged (using rounding). Additionally, TRM generates a settlement cashflow with amount = BV (see above) and an accrued interest cashflow according to the AI Method. 242 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.1 Bond The following cashflow structure is generated for an amortizing fixed-rate bond: For a fixed annuity they are as follows: 3.1.6 Step-up bond Step-up bonds have interest payments which increase during the life of the bond. 3.1.6.1 Instrument setup Instrument setup for a step-up bond is similar to that of a fixed-rate bond, except for the following: • Schedules The cashflow structure template assigned to the instrument can be the same one used for a fixed-rate bond. However, you also have to specify the rate offset to be applied for each coupon. See Appendix B Schedules on page 883. 3.1.6.2 Deal capture 3.1.6.2.1 Input data The data required is the same as for a fixed-rate bond (see 3.1.1 Fixed-rate bond on page 215). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 243 3 Debt instruments 3.2 Structured bonds 3.1.6.2.2 Generated data • Transaction Book Value (BV) = NA * price / 100 where: NA = nominal amount price = deal price • Cashflows The following cashflow structure is generated for a step-up bond: 3.2 Structured bonds 3.2.1 Callable bond A callable (or puttable) bond is modeled by adding a call or put event to an ordinary bond cashflow structure template. 3.2.1.1 Instrument setup Instrument setup for a callable bond is similar to that of a standard bond (see 3.1.1 Fixed-rate bond on page 215 or 3.1.2 Floating rate note on page 228), except for the following: • Schedule Select the cashflow structure template you want for the instrument. For each set of cashflows defined in the template, select the generation parameters. Call or put events are added to a cashflow structure using a secondary template. Several system-defined secondary templates are provided for use with callable bonds: see B.2.1.2 Secondary templates on page 900; you can choose one of these templates or a user-defined template derived from one of them. Once the template is applied to the instrument, the schedules are created and it is then possible to define their characteristics. The call or put event should specify the following information: 244 – Call/put periods or dates – Call/put price © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.2 Structured bonds – Any other characteristics, for example, whether the call/put option gives the issuer of the bond the right to terminate (call: Transaction Sign = "+") or the holder (put: Transaction Sign = "-"). – If a call/put event has the attribute Special, the original call/put price can be overwritten at call execution. 3.2.1.2 Processing This section describes the processing actions that are specific to transactions on callable bonds. 3.2.1.2.1 Call/Put • Setup To add call or put events to a cashflow structure, you need to select a system-defined secondary template or a user-defined template derived from one of them. • Execution The Execute Call/Put action performed in Transaction Manager's Event view allows you to specify the following information: Information Description Settlement Date The settlement date of the selected event. Amount to Call Defaults to the amount left. Should be less than or equal to the amount left. Counterparty Defaults to the bond issuer. The counterparty of the call transaction. Match with Parent at Apply Automatically matches the call transaction with the original transaction when applied. Executing the Call/Put action on a bond creates a transaction similar to a normal buyback or sell transaction. In other words, the resulting transaction is generated with settlement and position cashflows. Call/Put transactions can be identified as follows: Transaction Kind = Call/Put (Bond) Closing and P/L cashflows are created as part of the end-of-day processing according to the selling method (average balance, FIFO selling, or by manual matching). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 245 3 Debt instruments 3.2 Structured bonds 3.2.2 Dual-currency bond Bond issues can be structured to involve several different currencies. With a dual-currency bond, the currency in which the bond is issued (principal currency) differs from the currency in which the principal is repaid (redemption currency). The currency of the coupon can be either the principal currency, the redemption currency, or another currency. The FX rate to apply can be known (determined on the date of issue) or unknown (determined a number of days before the payment date of the interest cashflow or period start of the coupon). Setting up a dual-currency bond in TRM involves specifying the Dual Currency feature in the instrument definition. Schedule templates for known FX rates or unknown rates (whose rates will be fixed at a defined date) are also applied at instrument level. 3.2.2.1 Instrument setup Instrument setup for a dual-currency bond is similar to that of a standard bond (see 3.1.1 Fixed-rate bond on page 215 or 3.1.2 Floating rate note on page 228), except for the following: • Bond main characteristics Information Description AI Method The method used by the system to compute settlement accrued interests. The usual AI Methods (e.g. linear, and so on) are relevant. See 2.1.6.1 Accrued interest calculations on page 67 for more information. Note: The AI Settlement is generated when the fixing date method is set to In Advance. However, when the fixing date method is set to In Arrears, the accrued interest settlement is unknown and so no AI is calculated. • Dual-currency attributes This information defines the characteristics of the principal cashflow. Information Description Settlement Currency Currency in which the principal cashflow is settled. Settlement FX Rate Rate used to calculate the settlement amount of the principal cashflow. Need Fixing Specify whether the FX rate needs to be fixed: • Select No when the FX rate is known • Select Yes, Unmarked when the FX rate is unknown. Fixing Offset Number of days’ offset allowed, that is, the difference in days between the fixing date and the due date (default = 0). Fixing Max. Offset Maximum number of days’ offset allowed. See A.2.125 Dual Currency on page 771. • Schedules Select a suitable Dual Currency cashflow structure template for the instrument. For each set of cashflows defined in the template, specify the generation parameters. The following system templates are provided for dual-currency structures: – Dual-Currency Known FX This is a fixed bullet structure used for dual currency instruments when the FX rate is known when the deal is entered. For both interest and redemption schedules you can choose a different settlement currency and specify the settlement FX rate. 246 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.2 Structured bonds See B.2.1.1.15 Dual Currency, Known FX Rate on page 893. – Dual-Currency Known FX Floating This is a floating bullet structure used for dual currency instruments when the FX rate is known when the deal is entered. For both interest and redemption schedules you can choose a different settlement currency and specify the settlement FX rate. See B.2.1.1.16 Dual Currency, Known FX Rate, Floating on page 893. – Dual-Currency Unknown FX This is a fixed bullet structure used for dual currency instruments when the settlement FX rate is not known beforehand. For both interest and principal schedules you can choose a different settlement currency. See B.2.1.1.17 Dual Currency, Unknown FX Rate on page 893. Note: This template covers fixed interest rates only. For floating rate issues, you also have to use the Fixing Dates secondary template (see B.2.1.2.15 Fixing Dates on page 903). You can choose one of these templates or any other template derived from them. After the template is applied to the instrument, the schedules are created, it is then possible to define the settlement currency characteristics, as well as other characteristics, such as date basis, payment convention, calendars, and so on. See Appendix A Features on page 713. • FX fixing If the settlement FX rate is unknown when the deal is entered, then this feature needs to be included in the instrument definition. See A.2.174 FX Fixing on page 797. 3.2.2.2 Deal capture 3.2.2.2.1 Input data Deals on dual-currency bonds are captured in the same way as a standard bond (see 3.1.1 Fixed-rate bond on page 215 or 3.1.2 Floating rate note on page 228). 3.2.2.2.2 Generated data • Cashflows Settlement Currency = Settlement Currency (as defined in the schedule) Settlement FX Rate = Settlement FX Rate (as defined in the schedule) Settlement Amount = Amount * Settlement FX Rate 3.2.2.3 Processing This section describes the actions that can be done throughout the life of a dual-currency bond. 3.2.2.3.1 FX fixing When the settlement FX rate of a dual-currency bond is not known beforehand, the FX rates need to be fixed at the agreed fixing date. • Setup Depending on the instrument setup, the fixing can be done in advance (at the beginning of each coupon period) or in arrears (the standard case, at the end of each coupon period). In both cases there can be an offset of n days (before the beginning or end of the coupon period). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 247 3 Debt instruments 3.2 Structured bonds Execution • There are two ways to execute the FX Fixing action, one in the Instrument Editor, the other in Transaction Manager as described further on. – The FX Fixing action performed in Instrument Editor's Cashflow page allows you to set the FX rate. The following values can be input: Information Description Settlement FX Rate Fixing market quote to be entered manually. After the manual entry, the Fix Fx Rate action is available and should be performed to fix the specified FX rate. The fixing process is performed directly on an individual cashflow in the Cashflow page. It is possible to modify the fixing values. – Alternatively, the FX Fixing action performed in Transaction Manager’s Cashflow view on the cashflow allows you to set the FX rate. The following values can be input: Information Description Fixing Date Day the cashflow is fixed. Reference FX Rate Fixing market quote. This is defaulted by the system to the FX cross rate between the actual currency and the currency on the fixing date and can be changed by the user. The fixing process is performed directly on an individual cashflow in the Cashflow view. It is possible to modify the fixing values. Cancellation • It is possible to undo the FX fixing using the Undo FX Fixing action. 3.2.2.3.2 Asset swap It is possible to carry out the Asset Swap action on a dual-currency bond (see 3.1.1.3.1 Asset swap on page 218). 3.2.2.4 Position monitoring For the valuation of the dual-currency bond, an estimation of the future accrued interests can be defined by setting up the feature Generic IR Valuation with the following parameters (see A.2.201 Generic IR Valuation on page 811 for more details): Information Description AI Method The method used by the system to compute accrued interests in the calculation of the market value. For dual-currency bonds, there are two types of dual-currency methods: • Dual Currency Estimated - The estimated accrued interest is calculated using the • Dual Currency Last - The accrued interest is calculated using the FX rate of the forward FX rates. previous FX fixing. Note: Both methods round the figure value in the cashflow currency before converting it into the settlement currency. See 2.1.6.1 Accrued interest calculations on page 67 for more information. 248 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.2 Structured bonds Information Description Settlement Switches Activate the switches that apply to this instrument: • Dirty Price - determines whether price used for valuation includes accrued interest (dirty price) or not. Note: If it is on, the market value for accrued interest is not calculated, even if the AI Method has been configured. Method For dual-currency bond, leave empty. Valuation Modes Valuation mode: Default, Benchmark, or Theoretical. For information about dual currency calculations, see 2.3.5 Dual currency on page 147. 3.2.3 Credit step-up bond Credit step-up bonds are corporate bonds that contain a provision stating that the coupon payment increases as the credit rating of the issuer declines. When the credit rating of the issuer goes up again, the coupon payment goes back down but is floored by the initial rate. A credit-linked note usually offers a higher yield compared to a vanilla bond with a similar credit rating. A Collateralized Debt Obligation (CDO), a common type of credit-linked note, represents a leveraged position in a portfolio of credit risk and enables investors to gain exposure to a large diversified pool of underlying credit risk. 3.2.3.1 Instrument setup Credit step-up bonds are based on an instrument type derived from the class CREDIT-STEP-UP. Instrument setup for a credit step-up bond is similar to that of a fixed-rate or floating-rate bond (see 3.1.1 Fixed-rate bond on page 215 and 3.1.2 Floating rate note on page 228), except for the following additional attributes. • Credit step-up characteristics You set the credit event information at instrument level. Information Credit event type Description Select from Downgrade or Upgrade: • Downgrade when the credit rating deteriorates • Upgrade when the credit rating improves. Date information Date the step up/down action comes into effect and the date after which the coupons are affected by the change in credit rating. Offset parameters Offset that applies to fixed rate or floating rate flows. When the credit event information is saved, the coupon flows at transaction level are updated. See A.2.115 Credit-Step-Up on page 765. • Schedule The cashflow structure template assigned to the instrument can be the same one used for a fixed-rate or floating-rate bond. However, you also have to specify the rate offset or spread offset to be applied for each coupon. See Appendix B Schedules on page 883. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 249 3 Debt instruments 3.3 Schuldscheindarlehen 3.2.3.2 Deal capture 3.2.3.2.1 Input data Deals on credit step-up bonds are captured in the same way as a standard bond (see 3.1.1 Fixed-rate bond on page 215 and 3.1.2 Floating rate note on page 228). 3.2.3.2.2 Generated data Credit events (downgrade/upgrade) saved at instrument level trigger the recalculation of the yield-to-maturity used for accruing discount (or amortizing premium) on transactions on credit step-up bonds. 3.2.3.3 Processing The processing actions that are available on credit step-up bonds are the same as those on standard bonds (see 3.1.1 Fixed-rate bond on page 215 and 3.1.2 Floating rate note on page 228), except for the following. 3.2.3.3.1 Credit event Adding or removing a credit event on the instrument triggers the invalidation of the future cashflows on all the existing deals. It also triggers the regeneration of a new set of cashflows with the new rate or spread defined in the instrument setup. 3.3 Schuldscheindarlehen Schuldscheindarlehen is a bond security representing collateralized ownership in a German loan, with the lending bank participating in the underlying group of banks. Schuldscheindarlehen is a special type of Bond and differs from a plain vanilla bond in the following manner: • The Schuldscheindarlehen is traded without any accrued interest settlement by the buyer. Instead, the issuer pays at the end of the coupon period the exact portion of the coupon that the buyer is entitled to, on a pro-rata-temporis basis (e.g. if the owner buys the Schuldschein at half year and the coupon is due at the end of the year, the owner will only receive half of the coupon amount). • The issuer also pays any previous owners within the coupon period the interest amount on a pro-rata-temporis basis to compensate them for holding the Schuldscheindarlehen for a given period. The coupon amount is split between the different owners during the coupon period according to their holding period. 3.3.1 Instrument setup Schuldschein bonds are based on an instrument type derived from the class BOND. Instrument setup for a Schuldscheindarlehen is similar to that of a fixed-rate bond (see 3.1.1 Fixed-rate bond on page 215), except for the following: • Schuldschein This feature indicates that no accrued interest is settled, but the first coupon is adjusted to the pro-rata-temporis ownership of the coupon, and is settled on the coupon payment date directly by the issuer. A.2.294 Schuldschein on page 860. 250 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.3 Schuldscheindarlehen 3.3.2 Deal capture 3.3.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a Schuldscheindarlehen (both primary and secondary markets): Information Description Nominal Amount Enter either the nominal amount or face amount, and the system will compute the other automatically. Face Amount Value Date Official date when money is transferred. This defaults to the spot date of the transaction. Deal Price Price paid for the bond (expressed as a percentage of the nominal amount). Note: If you need to monitor the ownership transfer, you must record and maintain the subsequent transactions in the secondary market. You can then use standard TRM monitoring and reporting tools to monitor the identity of the holders, the volume of the bonds held by each holder, and the date of purchase and sale of the bonds by the holders. 3.3.2.2 Generated data • Transaction Yields are calculated from the reduced coupon. • Cashflows – The first coupon is reduced and settled on the pro-rata-temporis of the ownership from the transaction's value date to the coupon value date. No accrued interest is generated. – On the coupon payment date, the Issuer of the Schuldschein calculates the interest for each holder of the bond according to their holding period (from the purchase value date to the sale value date). 3.3.3 Processing The actions that can be done throughout the life of a Schuldschein bond are the same ones as for a fixed-rate bond (see 3.1.1.3 Processing on page 218). 3.3.4 Position monitoring This section describes how the Schuldschein bonds are calculated and provides a numerical example that demonstrates the calculations of a Schuldschein bond instrument. 3.3.4.1 Setup There are two basic methods for valuation of Schuldschein bond instruments: Quoted or Theoretical. When the Theoretical method is used, the valuation is similar to the one used to calculate a fixed-rate bond (3.1.1.4 Position monitoring on page 221). When the Quoted method is used, the calculations are processed as described in section 3.3.4.2 Calculations on page 251. 3.3.4.2 Calculations This section describes the model and calculations of Schuldschein bond instruments. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 251 3 Debt instruments 3.3 Schuldscheindarlehen 3.3.4.2.1 Valuation model The market value of a quoted Schuldschein (Quoted valuation method) is calculated as follows: Equation 3-3 Quoted Schuldschein bond where P The price of the deal. A The nominal amount. Ia The accrued interest is calculated according to the generic formula described in 2.1.6.1 Accrued interest calculations on page 67. where: D_f • C is the coupon • t is the length of the accrual period (in years), calculated as follows: • T is the length of the coupon period (in years, calculated with the appropriate date basis) The Discount Factor from figure spot to figure valuation date. 3.3.4.2.2 Numerical example This section demonstrates how the different figures are calculated for a quoted Schuldscheindarlehen. This example shows a Schuldscheindarlehen EUR 1,000,000.00, 5%, issued on 2008-01-01, and due on 2012-01-01. Setup: • Data Symbol Example Instrument Date Basis (30E/360) B 360 Valuation Method Quoted First Coupon Payment 2009-01-01 Issue Date dt_i 2008-01-01 Maturity Date d_m 2012-01-01 Coupon Rate c 5% Coupon Frequency 1 Spot Days 3 Currency EUR AI Method Linear Schedule Fixed, Bullet Repayment • 252 Transaction data (Schuldschein issue - primary market): © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.3 Schuldscheindarlehen On 2008-01-01, Bank1 issues 100,000,000.00 to Bank2. Data Symbol Example Opening Date dt_o_1 2008-01-01 Nominal Amount A_1 100,000,000.00 Issuer Bank1 Counterparty Bank2 Price P 100% Value Date dt_v.p 2008-01-04 Issue Date Formula 2008-01-01 Book Value V_b.p 100,000,000.00 Coupon 1 Amount A_1.c1 5,000,000.00 Coupon 1 Time to Value Date t_v.c1 360 =A Transaction data (transfer of ownership - secondary market): • On 2008-01-02, Bank2 sells its position EUR 30,000,000 and EUR 70,000,000 to two different holders: Holder1 and Holder2 respectively. Data Symbol Example Seller Bank2 Counterparty Holder1 Formula Opening Date dt_o_2 2008-01-02 Nominal Amount A_2 30,000,000.00 Value Date dt_v.p 2008-01-07 Book Value V_b.p 30,000,000.00 =A_2 Symbol Example Formula and Data • Seller Bank2 Counterparty Holder2 Opening Date dt_o_2 2008-01-02 Nominal Amount A_3 70,000,000.00 Value Date dt_v.p 2008-01-07 Book Value V_b.p 70,000,000.00 =A_3 Data Symbol Example Formula Figure Date d_f 2008-01-02 Time to Spot d_s 2008-01-07 Valuation Figure: Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 253 3 Debt instruments 3.4 Denominated bond Data Symbol Example Principal A_1.P 100,000,000.00 Accrued Interest (Coupon 1) 69,444.44 Formula A_1.c1 * (d_s - d_f) / B Calculated transaction data (first coupon payment): • 2009-01-01, the issuer Bank1 pays the coupon amount pro-rata-temporis of the ownership to each holder. Data Symbol Example Formula Amount (Coupon 1) A.c1 5,000,000.00 Value Date (Coupon 1) dt_v.c1 2009-01-01 First coupon to Bank2 1c.p 13,888.89 A_1.c * (dt_0_2 – dt_0_1)/B First coupon to Holder1 2c.p 1,495,833.33 A_2.c * (t_v.c1 -dt_0_2)/B First coupon to Holder2 3c.p 3,490,277.77 A_3.c * (t_v.c1 -dt_0_2)/B 3.4 Denominated bond Bonds (and swaps) with multiple denominations are traditionally a spin off from markets where physical bonds or certificates were used. Some markets still trade bonds or certificates, and these are physically delivered between parties. These certificates were used for secondary trading and made it easier for traders to break down a large issue tranche, facilitating smaller value trades on the back of the original issue. The denominations are aggregated into a single transaction but denomination details are maintained and recorded. In case of physical presentation of coupons, clearing houses and/or paying agents have to pay investors (retail) the exact coupon amounts. However, with the advent of settlement houses the practice of physical delivery is now the exception rather than the rule. The settlement agents merely move electronic representations of the bonds or certificates between accounts. 3.4.1 Instrument setup Denominated bonds must be based on an instrument type derived from the class BOND or SWAP. The setup for multiple-denomination bonds and swaps is similar to that of a fixed-rate bond (see 3.1.1 Fixed-rate bond on page 215), except that you can define the denominations that can be used when capturing transactions at the instrument or hedging swap leg level: • Bond main characteristics Information Description Amount Rounding Nearest number to which the coupon amount is rounded. By default, it is set to 2 decimals (0.01). Note: The rounding step applies to the accrued interest when the Settlement Switch, Round Per Unit is activated (see below). Rounding Method Up, Down or Nearest. The amount is rounded up, down, or to the nearest figure as calculated using the specified Amount Rounding number. Settlement Switches Round Per Unit If the switch Round per Unit is activated, Accrued Interest is based on rounding per denomination (see 3.4.4.2 Calculations on page 256). 254 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.4 Denominated bond • Denominated bond If the denomination of a bond instrument is specified at instrument level using feature Denominated Bond, the deal can be input in units and the Nominal Amount is computed by the system. A.2.120 Denominated Bond on page 767. • Bond Denominations Setup The valid denominations can be defined at the instrument level. Only those denominations will be allowed at deal capture. A.2.60 Bond Denominations Setup on page 739. Note: For monitoring purposes, you can view the positions by Trading Unit in Treasury Monitor, Transaction grouping. For more information, see TRM User Guide. 3.4.2 Deal capture 3.4.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a denominated bond: • Transaction view: Information Description New Denomination The deal is captured by selecting the denominations defined at the instrument level. To select a denomination, right-click the transaction, select the action New Denomination from the drop-down list, and then select the relevant denomination from the list. A new row is added to the Denomination view. You need to populate the Unit column. Note: To delete a denomination, simply right-click the row you want to delete and select Delete Denomination. • Denomination view: Information Description Trading Unit Displays the selected denomination. Units The deal can be input in units and the Nominal Amount is calculated by the system. Leg Group Displays the number of the (Swap) leg group where the denomination applies. 3.4.2.2 Generated data • Transaction Book Value (BV) = NA * price / 100 where: NA = Nominal Amount price = Deal Price • Cashflows Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 255 3 Debt instruments 3.4 Denominated bond When denominations are used at deal capture, the interest (coupon) payments are calculated separately for each denomination according to the following formula: Ic = Units * round[Denomination * Period Length * Coupon Rate,Amount Rounding] where: Ic = interest (coupon) payments Amount Rounding = number of decimals to be used when rounding amounts. 3.4.3 Processing This section describes the actions that can be done throughout the life of a denominated bond. 3.4.3.1 Buyback (sale) and Unwinding (early expiration) When an issue is bought back (or a long position is sold), or when a swap is unwound (early-expired), you enter the denominations and units in the same way as when entering a new transaction. See 3.4.2.1 Input data on page 255 for more information about capturing denominations and units. This information is used the same way as for new transactions, to 'close' (offset) the future interest and redemption payments accordingly. For a swap, a net amount (amount to be settled between the parties) is entered in the same way as in a swap without denominations. See 11.1.2 Asset swap on page 656. Note: For accounting purposes: The fact that buybacks or corresponding issues may have multiple denominations has no impact on realized results. The reason for this is that buybacks are booked at par, and the difference between par and buyback price is recorded directly into P/L. So, there is no linking between the issue price and the buyback price per denomination. 3.4.4 Position monitoring There are two basic methods for valuation of denominated bond instruments: Quoted or Theoretical. 3.4.4.1 Setup The valuation setup for denominated is the same as for usual bonds. 3.1.1.4 Position monitoring on page 221. 3.4.4.2 Calculations The numerical example in this section demonstrates how the different figures are calculated for a multiple denominated bond using the Theoretical method. This example shows a multiple denominated bond with the following data: Setup • Data Symbol Example Issue Date dt_i 2008-01-01 Maturity Date 2012-01-01 Currency EUR Valuation Method Theoretical Coupon 5.6333% AI Method Actual/Actual Annually 256 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.4 Denominated bond Data • Symbol Example Amount Rounding 0.01 Rounding Method Nearest Schedule Fixed, Bullet Repayment Denominations Trading Units 1000 and 5000 Transaction data: Note: When entering a transaction the coupon amount will be different in the two denominations. • Data Symbol Example Formula Opening Data dt_o 2008-01-23 Value Date dt_v 2008-01-25 Interest Rate r 5.6333% First Denomination de_1 1000 Trading Units (First Denomination) n_m_1 100 Nominal Amount (First Denomination) A_1 100 000 de_1 * n_m_1 Coupon Amount (First Denomination) Ic_1 5633 (rounding to 2 decimals) r* de_1=56.333 = 56.33 * n_m_1 Second Denomination de_2 5000 Trading Units (Second Denomination) n_m_2 20 Nominal Amount (Second Denomination) A_2 = 100 000 de_1 * n_m_1 Coupon Amount (Second Denomination) Ic_2 5633.4 (rounding to 2 decimals) r* de_2=281.665 = 281.67 * n_m_2 Accrued interest may be based on rounding per denomination or not depending on whether the settlement switch Round Per Unit (Instrument Editor - Bond page) is activated at the instrument level. – If the switch Round Per Unit is not activated, the accrued interest is calculated like any other bond (Equation 2-71 Accrued interest (generic formula) on page 67): Data Symbol Example Date Basis B 366 Time to Accrued Interest Formula 2008-01-25 2008-01-01 = 24 dt_v - dt_i Accrued Interest (First Denomination) Ia _1 = 369.38 (rounded to 2 decimal places) Ic_1*(dt_v - dt_i)/B= 369.377 Accrued Interest (Second Denomination) Ia _2 = 369.40 (rounded to 2 decimal places) Ic_2*( dt_v - dt_i)/B= 369.4033 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 257 3 Debt instruments 3.5 Convertible bond – "If the switch Round Per Unit is activated, the accrued interest is calculated using the denomination rounding calculation: Equation 3-4 Denomination rounding equation Ia = Unit × round [ Denomination × Periodlength × CouponRate, AmountRounding ] Data Symbol Example Date Basis B 366 Time to Accrued Interest Formula 2008-01-25 2008-01-01 = 24 dt_v - dt_i Accrued Interest (First Denomination) Ia _1 = 369 (rounded to 2 decimal places) r* de_1*(dt_v - dt_i)/B= 3.693967 = 3.69* n_m_1 Accrued Interest (Second Denomination) Ia _2 = 369.40 (rounded to 2 decimal places) r* de_2*(dt_v - dt_i)/B= 18.46984 = 18.47 * n_m_2 Note: Accrued interest at settlement, and 'clean' settlement (principal) amount (i.e. the full settlement amount minus accrued interest and fees/taxes) is calculated directly from the total interest (coupon) amount and total nominal amount respectively, i.e. they are not calculated separately for each denomination. 3.5 Convertible bond Convertible bonds are fixed rate bonds that can be converted to equity, typically to shares of the issuer. The bond can be converted on certain dates or during certain periods. Usually the holder of the bond can decide to convert the bond but sometimes the issuer also has the right to force the conversion. Some convertibles are also callable. The conversion price (and ratio) may depend on time. Usually corporate actions (splits and dividends) also affect the conversion price. 3.5.1 Instrument setup Convertible bond instruments must be based on an instrument type derived from the class CONVERTIBLE-BOND. They are set up in a similar way to fixed-rate bonds (see 3.1.1 Fixed-rate bond on page 215), except for the following characteristics. • Schedules Select a suitable schedule template that includes coupons, redemptions, call events (if the bond is callable), and conversion events. To define the conversion events, TRM provides a pre-defined secondary template designed for this purpose (see B.2.1.2.11 Convertible Conversion on page 902). See Appendix B Schedules on page 883. 258 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.5 Convertible bond • Convertible Bond The conversion price (or ratio) is defined using this feature. Initially one entry is needed. If the conversion price changes due to corporate actions, a new entry must be added each time. Information Description Active From Period during which this conversion price is applicable. Active To Type Defines whether the user can enter conversion price or conversion ratio. Par Value If the convertible bond is traded using units, enter the par value of one unit. Conversion Price If Type = Conversion Price, you can enter the conversion ratio. Otherwise, it is calculated using the conversion price and par value: Conversion Price = Par Value/Conversion Ratio Conversion Ratio If Type = Conversion Ratio, you can enter the conversion price. Otherwise it is calculated using the conversion ratio and par value: Conversion Ratio = Par Value/Conversion Price Underlying The instrument into which the convertible can be converted. Comment Any comment you want to add about the instrument. See A.2.103 Convertible Bond on page 759. 3.5.2 Deal capture 3.5.2.1 Input data The data required is the same as for a fixed-rate bond (see 3.1.1 Fixed-rate bond on page 215). 3.5.2.2 Generated data • Cashflows The following cashflow structure is generated for a convertible bond: Interest flows Accrued interest Nominal Book value Spot Opening date Value date Maturity Maturity date 3.5.3 Processing This section describes the actions that can be done throughout the life of a convertible bond. 3.5.3.1 Conversion The convertible bond is converted to the underlying instrument using the Conversion action. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 259 3 Debt instruments 3.6 Index-linked bond • Setup Conversion parameters are defined in the instrument setup. • Execution Conversion can be executed in Transaction Manager. The following parameters are used: Information Description Conversion Date Date on which the conversion is done. Amount to Convert Nominal amount of the convertible to convert. Delivery Type Usually Delivery Type = Physical Delivery. If the underlying is not delivered, but the profit/loss is settled instead, select Delivery Type = Cash Settlement. Scenario Scenario from which you want to retrieve the market price of the underlying. This parameter is used for cash settlement only. Price Price of the underlying. This parameter is used for cash settlement only. Cash to Receive Amount of cash to receive. This parameter is used for cash settlement or settling the residual if the number of units to be delivered is rounded. This field can be modified. The execution of the action generates a conversion transaction which closes the existing convertible position and replaces it with the appropriate number of units of the underlying instrument. • Cancellation Cancellation of the action is done by canceling the conversion transaction. 3.6 Index-linked bond Index-linked bonds are linked in some way to a standard index. The bond’s cashflows vary according to an underlying index. For example, in inflation index-linked bonds, the coupon and principal payments are adjusted to compensate for changes in inflation. These payments are adjusted in relation to a Consumer Price Index (CPI) value or a Retail Prices Index (RPI) value for a country. A period of time usually elapses between the measurement of price levels and the publication of an index, therefore the index value associated with a given cashflow will be the index as published for a time in the past. This time difference is called the indexation lag. The way in which the index-linked bonds are traded and valued varies according to market conventions. Index-linked bonds must be based on an instrument type derived from the class INDEX-LINKED-BOND. 3.6.1 Instrument setup The following information is relevant to any kind of index-linked bond. Index-linked bonds are set up in a similar way to fixed-rate bonds (see 3.1.1 Fixed-rate bond on page 215) or zero-coupon bonds (see 3.1.4 Zero-coupon bond on page 239), depending on whether there are any coupon payments. The additional values required to set up index-linked bonds are described in the following sections. 260 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond • Index-linked bond main characteristics – • The primary feature A.2.210 Index-Linked Bond on page 818. Trading characteristics Each index-linked bond type has its own specific trading feature. Special risk characteristics • Special risk characteristics Interest sensitivity of index-linked bonds is, by default, calculated in the same way as for similar fixed rate bonds. However, you can capture a factor (e.g. yield beta, a number between 0 and 1) for scaling the IR sensitivity of the instrument, which is then used as a multiplier for scaling IR exposure and duration figures. Effective convexity is scaled by the factor squared. This factor can be entered either as a static sensitivity scaling factor at instrument level using the instrument feature Base IR Exposure Setup, or as Beta for the instrument in Rate Monitor allowing time-dependent scaling factors. For more information relating to the setup and structure of specific types of index-linked bond, see: • – 3.6.4 Australian index-linked annuity bond on page 263 – 3.6.5 Australian index-linked bond on page 267 – 3.6.6 Brazilian (LFT) selic-linked security on page 270 – 3.6.7 Brazilian FX-linked NBC-E/NTN-D on page 271 – 3.6.8 Brazilian inflation-linked NTN on page 272 – 3.6.9 Canadian real return bond on page 273 – 3.6.10 French OAT€i on page 274 – 3.6.11 Greek index-linked bond on page 277 – 3.6.12 Israeli index-linked bond on page 279 – 3.6.13 Italian BTP €i on page 281 – 3.6.14 Japanese index-linked bond on page 282 – 3.6.15 Swedish index-linked bond on page 283 – 3.6.16 UK index-linked gilt on page 287 – 3.6.17 US Tips on page 292. Schedules Select the cashflow structure template that is appropriate for the instrument. System templates are provided for several types of index-linked bonds; you can choose one of these templates or any other template derived from them. Once a template is applied to the instrument, the schedules are created and it is then possible to define their characteristics, such as, date basis, payment convention, calendars, and so on. See Appendix B Schedules on page 883. • Quoted It is necessary to specify how the index-linked bond is quoted on the market. Each index-linked bond type has its own specific quote handler. See A.2.274 Quoted on page 849. • Valuation approach Each index-linked bond type has its own specific valuation approach feature. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 261 3 Debt instruments 3.6 Index-linked bond 3.6.2 Deal capture 3.6.2.1 Input data In addition to the standard deal parameters, the information required to enter a deal on an index-linked bond is similar to the data required for a fixed-rate bond (see 3.1.1 Fixed-rate bond on page 215). Information Description Deal Price or If there is a yield/price convention set on the instrument, it is possible to enter either a rate or a price and conversion is made automatically. If there is no convention set, the deal must be entered in price. Deal Rate Nominal Amount Face Amount Enter either the nominal amount or face amount, and the system will compute the other automatically. Value Date Official date when money is transferred. This defaults to the spot date of the transaction. Index Value of the index (to which the instrument is index-linked) at trade date. In addition, the following optional information can be captured: Information Description Units If the denomination of a bond instrument is specified at instrument setup, the deal can be input in units, and the nominal and face amounts are computed by the system. Trading Unit Size Index Prolong Rate (For UK index-linked bonds only) Interest rate by which the index rate is prolonged into the future. Index Ratio Index ratio used to adjust the coupon and redemption flows of the bond. Note: If this is defined at instrument level, this is used as the default in the transaction and cannot be modified: for example, see 3.6.7 Brazilian FX-linked NBC-E/NTN-D on page 271. 3.6.2.2 Generated data • Cashflows The following cashflows are generated: – Principal – Interest (unless it is a zero-coupon index-linked bond) – Redemption. 3.6.3 Processing This section describes the actions that can be done throughout the life of an index-linked bond. 3.6.3.1 Fixing The major process for an index-linked bond is the fixing of the coupon and the redemption flows. These need to be adjusted to account for changes in the index. • Setup Depending on the instrument setup (schedules) the fixing can be done in advance or in arrears. In both cases there can be an offset of n days (before the beginning or end of the coupon period). The fixing parameters that define how the fixing rate is calculated are defined in the schedule. 262 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond • Execution When fixing is executed, the rate is retrieved for the specified fixing rate and period according to the designated fixing scenario. The fixing scenario is configured at the system level, see TRM System Admin Guide. The fixing subscenario is specified at the cashflow level. The expression value gives the current value of the expression and is used to calculate the index value. The following information is stored on the fixed cashflow: The The The The fixing date fixing quote expression and expression value amount of the coupon or redemption flow. The fixing process can be performed in two ways in TRM: the process is exactly the same in each case: the coupon is fixed at both instrument and transaction level. The methods of fixing are as follows: – Directly on the cashflow (in Instrument Editor’s Cashflow page) using the Fix Price action: the fixing affects all deals on this instrument. – Using an activity (Fixing Bond Cashflow): all instruments and their deals which need to be fixed for a particular date are affected. Note: The bond issue must be fixed at instrument level in order for the accrued interest flow to be generated (for transactions captured between coupon fixing date and fixing value date). • Cancellation It is possible to cancel the cashflow fixing either manually, using the Undo Fixing action in Instrument Editor; or automatically, using the Fixing Bond Cashflow - Undo activity. 3.6.4 Australian index-linked annuity bond The following sections describe the characteristics that are specific to Australian index-linked annuity bonds. 3.6.4.1 Instrument setup Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following: • Trading characteristics - issue index parameters The Australian CPI is published quarterly and is applied to settlement calculations and valuations starting from the publication date. The index is set up similarly to other indexes. Information Index Description Select the Instrument ID of the underlying index you previously defined. See 7.1 Index types on page 425. Issue Index Enter the value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. See A.2.32 Australian IAB on page 725 or A.2.34 Australian IAB (Round to 3) on page 725. • Bond characteristics Information Description Currency AUD Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 263 3 Debt instruments 3.6 Index-linked bond • Information Description AI Method Australian Index Linked (IAB), or for three decimal places rounding, Australian Index Linked (IAB) (3 dec). Settlement Switches Dirty Price. Coupon Rate Coupon rate of the bond. Schedule parameters Select the cashflow structure template BOND-AU-IAB (Australian Indexed Annuity Bond). See B.2.1.1.4 Australian Indexed Annuity Bond on page 890. In the Interest Adjustment schedule, set the parameter Factor equal to the rounded value of the annuity payment. Note: For rounding to three decimal places, change the expression in the Interest Adjustment schedule to: round((ixau/divider)*factor,0.001)*100 - 100 * factor Set the required fixing characteristics as follows: Information Description Factor Enter the annuity payment percentage. Note: The Fixing Rate and Divider fields default to the values you selected in the Issue Index page. Method Select 4th Wednesday (M) as the index is published (and index adjustment cashflows fixed) on the 4th Wednesday of the publishing month. Frequency Enter 3. First Date Enter the first publishing (fixing) date applicable to this instrument. The subsequent publishing dates are calculated from this date onwards using the monthly frequency specified in the Frequency field. After you have generated the cashflows, remove the default value from the field Amount Rounding in the Schedule page and leave the field Amount Rounding empty for all Interest Adjustment cashflows in the Cashflow page. • • Trading yield parameters Information Description Yield Convention Australian Government Index Annuity - GOVT-AU-IX-ANNUITY Quoted Information Description Price Type Yield (w/o rounding) Quote Handling Depending on how you want to round the adjusted annuity, select one of the following: Currency 264 • Index-Linked Annuity Bond (Australian): six decimal places rounding • Index-Linked Annuity Bond (Australian 3 Digits Rounding): three decimal places rounding AUD © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond • • Result parameters Information Description AI Method Australian Index Linked (IAB), or for three decimal places rounding, Australian Index Linked (IAB) (3 dec). Valuation approach Australian Indexed Annuity Bonds can be valuated either using a direct (yield) quote, or taken from the yield curve. – For a direct quote, see A.2.33 Australian IAB Valuation on page 725), or if adjusted annuities are to be rounded to 3 decimal places, see A.2.35 Australian IAB Valuation (Round to 3) on page 726. – For a valuation taken from the yield curve (loans only), see A.2.36 Australian IAB Par Curve Valuation on page 726, or if adjusted annuities are to be rounded to 3 decimal places, see A.2.37 Australian IAB Par Curve Valuation (Round to 3) on page 727. Note: To use a yield curve, you must first set one up in the IR Quote and Yield Curve Editor. For general information about setting up yield curves, see TRM User Guide. 3.6.4.2 Deal capture 3.6.4.2.1 Input data In addition to standard deal parameters, the information required to enter a deal on an australian index-linked bond is similar to usual index-linked bonds (see 3.6 Index-linked bond on page 260). Information Description Face Amount Enter the face amount. The Nominal Amount is automatically calculated by the system. Nominal Amount Shows the remaining amount taking into account the annuity payments. In addition, the following optional information can be captured: Information Description Index The system automatically fetches the latest available CPI value for the settlement date. You may change the index value. Note: In Rate Monitor, the index value of a given quarter is associated with the first day of the quarter (Jan. 1, Apr. 1, Jul. 1, Oct. 1). The publication date is given in the field Period From. Deal Rate Enter the trade yield. 3.6.4.2.2 Generated data • Transaction The formula used to calculate the price depends on whether the CPI value that will determine the next coupon is known or not. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 265 3 Debt instruments 3.6 Index-linked bond – If the value is not known, we use the inflation rate (q) for coupon estimation: Equation 3-5 Coupon estimation: CPI value unknown – If the value is known, the formula is: Equation 3-6 Coupon estimation: CPI value known where Br – 1 Previous annuity payment B0 Original unadjusted annuity payment h Rounding precision, 3 or 6, depending on the issue q Quarterly inflation factor Ii CPI for quarter I: where I = 0 corresponds to the quarter before the issue date of the bond, and I = 1 corresponds to the latest quarter for which the CPI has been issued on the settlement date y Trading yield v • n Number of full quarters from the next annuity payment to maturity f Number of days from settlement to the next annuity payment date d Number of days in the full quarter ending on the next annuity payment date Z 1 if there is an annuity payment to the purchaser at the next annuity payment date, otherwise 0. Cashflows The following cashflows are generated: 266 – Principal – Interest – Interest Adjustment – Amortization – Delivery. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond • Fixing In the fixing of Australian index-linked annuity bonds, rounding is carried out at the total annuity payment level. To make sure that the total of the fixed interest and amortization payments are correct, one of the cashflows takes into account the rounding of the other. Note: In Rate Monitor, the index value of a given quarter is associated with the first day of the quarter (Jan. 1, Apr. 1, Jul. 1, Oct. 1). The publication date is given in the field Period From. 3.6.4.3 Processing 3.6.4.3.1 Fixing The fixing of the inflation adjustment (Interest Adjustment cashflow) is carried out at the instrument level in Instrument Editor - Cashflow page. • Execution Information Description Fixing Quote Select action Fix Price. The appropriate CPI value is displayed and the amount of the inflation adjustment is automatically calculated. You can also first set the relevant CPI value, and then select the action Fix Price. Update the cashflows (click Update) and save the instrument. 3.6.5 Australian index-linked bond The following sections describe the characteristics that are specific to Australian index-linked bonds. 3.6.5.1 Instrument setup Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following: • Trading characteristics See A.2.29 Australian CIB on page 724. – Issue Index parameters Information Description Index Instrument ID of the underlying index. See 7.1 Index types on page 425. Issue Index (Not used for Australian index-linked bonds) However, a value must be entered as 100.00 for calculation purposes only. • Bond characteristics Information Description Currency AUD Settlement parameters Dirty Price. Coupon Rate Coupon rate of the bond. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 267 3 Debt instruments 3.6 Index-linked bond Schedule parameters • Select the cashflow structure template BOND-AU-CIB (Australian Capital Indexed Bond). See B.2.1.1.3 Australian Capital Indexed Bond on page 890. Trading yield • Information Description Yield Convention Australian Government Index - GOVT-AU-IX Quoted • Information Description Price Type Yield (w/o rounding) Quote Handling Index-Linked Bond (Australian) Currency AUD Valuation approach • See A.2.38 Australian Index-Linked Bond Valuation on page 727. 3.6.5.2 Position monitoring In this section, numerical examples demonstrate how the different figures are calculated for Australian Treasury index-linked bonds. If you need more theoretical information about the method used in these calculations, see Chapter 2 Market standards and calculations on page 33. This example shows an Australian Treasury index-linked bond, with the following deal data: Setup data First interest payment date 1994-08-20 (Q3 / 1994) First reference quarter Q4 / 1993 Maturity date dt_m 2015-08-20 Interest r 4.00% Face amount 1,000.00 Transaction data Settlement date dt_s 2007-01-23 Next coupon date dt_c 2007-02-20 (Q1 / 2007) Yield y 2.76% Current quarter length dp 92 Index factor p 1.25 Adjustment factor K_t 141.270 (Q3 / 2006) 268 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond Other important deal data is calculated by the system as follows: • Quarters left n = FLOOR(YEARFRAC(dt_s, st_m, 0) * 4, 1) = 34 • Reference index v = ROUND (1 / (1 + y / 4), 9) = 99.31% • Days to next coupon dc = dt_c - dt_s 28 = 2007/02/20 - 2007/01/23 • Time to next coupon t_n = dc / dp 0.3043478 = 28 / 92 • Unadjusted dirty price Pdu =ROUND (POWER (v, t_n) * (ROUND (r / 4,9) * (1 + ROUND ((1 - POWER (v., n)) / (y / 4), 9)) + POWER (v, n)) * POWER (1 + p / 100, -t_n.), 9) = 109.71994% • Adjusted dirty price P_d = ROUND (K_t. * Pdu / 100,5) = 155.001% • Accrued interest I_a = ROUND ((r / 4) * K_t / 100 * (dp - dc) / dp, 5) = 0.98300000000% • Clean price P_c = P_d - I_a = 154.018% 3.6.5.2.1 Settlement figures Settlement flows for the transaction are calculated as follows: • Nominal amount A.s = 10,000,000.00 • Clean price P_c.s = A * P_c 15,401,800.00 = 10,000,000.00 * 1.54018 • Accrued interest I_a.s = A * I_a 98,300.00 • Total = 15,500,100.00 3.6.5.2.2 Fixing figures Fixing flows for the transaction are calculated using the following data: Fixing data Coupon date 2007-05-20 Fixing date 2007-02-20 Reference quarter 141.82 (Q4 / 2006) Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 269 3 Debt instruments 3.6 Index-linked bond • Index adjustment factor cf = 141.82 / 100 = 1.41820 • Nominal coupon cn = r / 4 0.0100000 = 0.04 /4 • Adjusted amount Ap = A * cn *cf 141,820.00 = 10,000,000 * 0.010000 * 1.41820 3.6.5.2.3 Valuation figures Unless otherwise stated, the figure date used in the calculations is 2007-01-20. On this date, the market data is as follows: Market data on 2007-01-20 Market quote (dirty, adjusted) p_q 155.00 Figure D D_s 0.99960191 • Market value = p_q / 100 * A * D_s 15,493,829.60 = 155.00 / 100 * 10,000,000 * 0.99960191 3.6.6 Brazilian (LFT) selic-linked security Brazilian LFT (Letra Financeira do Tesouro) instruments are zero-coupon bonds linked to the O/N SELIC interest rate. The maturities can be over two years. These instruments are traded and quoted in 1000’s (Date Basis = BRL/252) and have a unique security ID (ISIN number), issue and maturity date. 3.6.6.1 Instrument setup Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics See A.2.52 Bond - Brazilian LFT on page 737. • • Bond characteristics Information Description Currency BRL Schedule parameters The Brazilian LFT Bond system-defined primary template is provided for this type of index-linked bond, where: – Fixing parameters Need Fixing = Yes Fixing Date Method = In Arrears Expression = iix/trading unit where: iix = instrument-specific index entered in Rate Monitor together with Bid and Ask (select the Rate Monitor figure Index Value). See B.2.1.1.7 Brazilian LFT Bond on page 891. 270 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond • • • Trading yield Information Description Yield Convention Brazilian LFT - BOND-BR-LFT Quoted Information Description Price Type Yield Quote Handling Index-Link Bond (LFT) Currency BRL Valuation approach See A.2.53 Bond - Brazilian LFT Valuation on page 737. 3.6.7 Brazilian FX-linked NBC-E/NTN-D NBC-E/NTN-D instruments are fixed-rate bonds linked to the PTAX-index (FX rate). The maturities are 2Y, 3Y, and 5Y. The fixed rate is 12% pa. These instruments are traded and quoted in 1000’s and have a unique security ID (ISIN number), issue date, and maturity date. The coupons and redemption cashflows are adjusted by the index ratio, and the fixing dates are the coupon/redemption value dates. 3.6.7.1 Instrument setup Instrument setup for these index-linked bonds is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics See A.2.54 Bond - Brazilian FX-Linked NBC on page 737. – Issue index parameters Information Description Index Instrument ID of the underlying index: PTAX-index (FX rate). See 7.1 Index types on page 425. Issue Index • • Value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. Bond characteristics Information Description Currency BRL Settlement parameters Dirty Price Coupon Rate Coupon rate is 12% and the coupon is paid semi-annually. Schedule The Brazilian FX-Linked Bond (NBC) system-defined primary template is provided for these index-linked bonds, where: Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 271 3 Debt instruments 3.6 Index-linked bond – Fixing parameters Need Fixing = Yes Fixing Date Method = In Arrears Expression = ixlag_d/divider*price where: ixlag_d = lagged index value of one day divider = index value on the transaction’s opening date inserted on deal capture price = quoted bond price See B.2.1.1.5 Brazilian FX-Linked Bond (NBC) on page 890. • • • Trading yield Information Description Yield Convention Brazilian NBC - BOND-BR-NBC Quoted Information Description Price Type Yield Quote Handling Index-Link Bond (NBC) Currency BRL Valuation approach See A.2.55 Bond - Brazilian FX-Linked NBC Valuation on page 737. 3.6.8 Brazilian inflation-linked NTN Brazilian NTN-B/NTN-C (Nota do Tesouro Nacional) instruments are inflation-linked securities, setup as fixed-rate bonds, linked to the IGPM-index (NTN-C) or the ICPA-index (NTN-B). The maturities are 2Y, 3Y, and 5Y. The fixed rate is 12% p.a. or 6% p.a. These instruments are traded and quoted in 1000’s and have a unique security ID (ISIN number), issue date, and maturity date. The coupons and redemption cashflow are adjusted by the index ratio and the fixing dates are the coupon/redemption value dates. 3.6.8.1 Instrument setup Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics See A.2.56 Bond - Brazilian Inflation-Linked NTN on page 738. – Issue Index parameters Information Description Index Instrument ID of the underlying index: IGPM-index (NTN-C) or the ICPA-index (NTN-B). See 7.1 Index types on page 425. Issue Index 272 Value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond • Schedule Information Description Fixing parameters • • • • • Need Fixing = Yes • Fixing Date Method = In Arrears • Expression = ix/divider*price Bond characteristics Information Description Currency BRL Settlement parameters Dirty Price Coupon Rate Coupon rate is 6% or 12% and the coupon is paid semi-annually. Trading yield Information Description Yield Convention Brazilian NTN - BOND-BR-NTN Quoted Information Description Price Type Yield Quote Handling Bond Currency BRL Valuation approach See A.2.57 Bond - Brazilian Inflation-Linked NTN Valuation on page 738. 3.6.9 Canadian real return bond The following sections describe the characteristics that are specific to Canadian real return bonds. 3.6.9.1 Instrument setup Instrument setup for Canadian real return bonds is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics – Issue Index parameters Information Index Description Instrument ID of the underlying index. See 7.1 Index types on page 425. Issue Index Value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. See A.2.58 Bond - Canadian RRB on page 738. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 273 3 Debt instruments 3.6 Index-linked bond • Bond characteristics Information Description AI Method Canadian See Canadian on page 73. Currency CAD Coupon Rate Coupon rate of the bond. See A.2.210 Index-Linked Bond on page 818. • Schedule parameters The Canadian real return bonds system-defined primary template is provided for these index-linked bonds, where: Information Description Fixing parameters • Need Fixing = Yes • Fixing Date Method = In Arrears • Expression = ixratio*price See B.2.1.1.8 Canadian Real Return Bond on page 891. • Trading yield Information Description Yield Convention Canadian Government See 2.1.4.2.18 GOVT-CA (financial/instrument/canadian@price) on page 51. • • Quoted Information Description Price Type Price % Quote Handling Index-Linked Bond (Canadian) Currency CAD Valuation approach See A.2.59 Bond - Canadian Index-Linked Bond Valuation on page 738. 3.6.10 French OAT€i The following sections describe the characteristics that are specific to French OAT€i bonds. 3.6.10.1 Instrument setup Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics See A.2.65 Bond - French OAT€i on page 741. 274 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond – Issue Index parameters Information Description Index Instrument ID of the underlying index. See 7.1 Index types on page 425. Issue Index • • Value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. Bond characteristics Information Description Currency EUR Coupon Rate Coupon rate of the bond. Schedule parameters – The French Index-Linked Bond (OAT) system-defined primary template is provided for this type of index-linked bond, where: Information Description Fixing parameters • Need Fixing = Yes • Fixing Date Method = In Arrears • Expression = max (ixratio, 1) * price See B.2.1.1.24 French Index-Linked Bond (OAT) on page 895. • • • Trading yield Information Description Yield Convention French Government OAT - GOVT-FR-OAT Quoted Information Description Price Type Price % Quote Handling Index-Linked Bond (French) Currency EUR Valuation approach See A.2.66 Bond - French Index-Linked Bond Valuation on page 742. 3.6.10.2 Position monitoring In this section, numerical examples demonstrate how the different figures are calculated for French OAT€i linked bonds. If you need more theoretical information about the method used in these calculations, see Chapter 2 Market standards and calculations on page 33. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 275 3 Debt instruments 3.6 Index-linked bond This example shows a French OAT€i linked bond, with the following deal data: Setup data Index at issue v_0 92.98393 Maturity date dt_m 2012-07-25 Interest c_m 3.00% Rounding decimals 5 Yield rounding y_round 6 Settlement date dt_s 2007-06-20 Next coupon date dt_c 2007-07-25 Yield y 2.40% (= round(2.396461364098%, 2)) Last index (2007-03) v_1 103.39 Current index (2007-04) v_2 104.05 Day of month d_1 20 Transaction data Other important deal data is calculated by the system as follows: • Coupons left n_c = FLOOR (YEARFRAC (dt_s, dt_m, 4), 1) +1 =6 • Reference index v = ROUND (v_1 + (d_1 - 1) / DAY (EOMONTH (dt_s, 0)) * (v_2 - v_1), decimals) = 103.80800 • Dirty price p_d_n = (POWER (1 + y, -n_c. + 1) + c_m * ((1 + y) * (1 - POWER (1 + y, -n_c))) / (y)) * POWER (1 + y, -d_c / 365) = 105.57230% • Accrued interest unadjusted I_a_n = c_m * (365 - d_c) / 365 2.7123288% = 0.03 * (365 - 35) / 365 • Accrued interest I_a = g_i * I_a_n 3.0280710% = 1.1164100000 * 0.027123288 • Clean price unadjusted p_c_n = p_d_n - ROUND (I_a_n, y_round) = 102.8600% • Clean price p_c = p_c_n * g_i 114.83393259% = 1.028600 * 1.1164100000 • Days to next coupon dcv = DAYS360 (dt_s, dt_c) = 35 • Index adjustment factor g_i = ROUND (v / v_0, decimals) = 1.1164100000 3.6.10.2.1 Settlement figures Settlement flows for the transaction are calculated as follows: • 276 Nominal amount A = 1,000,000.00 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond • Clean price p_c.s = A * p_c 1,148,339.33 = 1,000,000.00 * 1.1483393259 • Accrued interest I_a.s = A * I_a 30,280.71 = 1,000,000.00 * 0.03280710 • Total = 1,178,620.04 3.6.10.2.2 Fixing figures Fixing flows for the transaction are calculated using the following data: Fixing data Fixing date Index on 2007-04-25 2007-07-25 vf • Index adjustment factor gf = ROUND (vf / v_0, decimals) 1.12923 = 105 / 92.98393 • Nominal coupon cn = ROUND(c_m * gf, 7) 0.033876900 = ROUND (0.03 * 1.12923, 7) • Adjusted amount Ap = A * cn 33,876.00 = 1,000,000 * 0.033876900 105 3.6.10.2.3 Valuation figures Unless otherwise stated, the figure date used in the calculations is 2007-06-18. On this date, the market data is as follows: Market data on 2007-06-18 Figure date 2007-06-18 Figure spot date d_s.f 2007-06-20 Market quote (clean unadjusted) p_q 102.86% Index adjustment factor gv 1.11641 Spot discount factor Ds 0.9998027 Days to next coupon dcv 35 • Accrued interest ai.f = A * c_m * (365 - dcv) / 365 * gv * Ds 30,274.73 = 1,000,000 * 0.03 * (365 / 35) / 365 * 1.11641 * 0.9998027 • Clean price = A * p_q * gv * Ds 1,148,112.72 = 1,000,000 * 1.0286 * 1.11641 * 0.9998027 3.6.11 Greek index-linked bond The following sections describe the characteristics that are specific to Greek index-linked bonds. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 277 3 Debt instruments 3.6 Index-linked bond 3.6.11.1 Instrument setup Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics See A.2.71 Bond - Greek Index-Linked Bond on page 744. – Issue Index parameters Information Description Index Instrument ID of the underlying index. See 7.2.1 Simple Index on page 426. Issue Index • • Value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. Bond characteristics Information Description Currency EUR AI Method Greek (3 decimals). See Greek (3 decimals) on page 74. Coupon Rate Coupon rate of the bond. Schedule parameters – The Greek Index-Linked Bond system-defined primary template is provided for this type of index-linked bond, where: Information Description Fixing parameters • Need Fixing = Yes • Expression = ixratio*price See B.2.1.1.25 Greek Index-Linked Bond on page 895. • • • Trading yield Information Description Yield Convention GOVT-EUROZONE Quoted Information Description Price Type Price % Quote Handling Index-Linked Bond (Greek) Currency EUR Valuation approach See A.2.72 Bond - Greek Index-linked Bond Valuation on page 744. 278 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond 3.6.12 Israeli index-linked bond Israeli index-linked bond instruments must be based on an instrument type derived from the class INDEX-LINKED-BOND. The following sections describe the characteristics that are specific to Israeli index-linked bonds. 3.6.12.1 Instrument setup Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics - Issue Index parameters Information Index Description Instrument ID of the underlying index. See 7.1 Index types on page 425. Issue Index Value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. See A.2.73 Bond - Israeli Index-Linked Bond on page 744. • Bond characteristics Information Description Currency ILS AI Method Israeli (Linear, 5 decimals) See Israeli (Linear, 5 decimals) on page 76. • Settlement Switches Dirty Price. Coupon Rate Coupon rate of the bond. Note: According to the market convention, the deal price of Israeli index-linked bonds is treated not just as Dirty Price but as an inflation-adjusted dirty price. At deal entry, this means that you should capture the dirty price as well as the index ratio. The settlement amount is equal to the deal price times the nominal amount. Schedule parameters The Israeli Index-Linked Bond system-defined primary template (BOND-IL-IX) is provided for this type of index-linked bond, where: Information Description Fixing parameters • Need Fixing = Yes • Fixing Date Method = In Arrears • Expression = round(ixratio*price,0.0000001) See B.2.1.1.28 Israeli Index-Linked Bond on page 895. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 279 3 Debt instruments 3.6 Index-linked bond For Israeli GALIL Index-Linked Bond, the system-defined primary template (BOND-IL-IX-GALIL) is provided for this type of index-linked bond, where: Information Description Fixing parameters • Need Fixing = Yes • Fixing Date Method = In Arrears • Expression = round((max(ixratio,1)*((1+price/100)^(years)-1)),0.0000001)*nom inal • Fixing rate Type = Amount See B.2.1.1.29 Israeli Index-Linked Bond Galil on page 896. • Trading yield Information Description Yield Convention *U.S.STREET-ACTACT-SEMIANNUAL See 2.1.4.2.12 *U.S.STREET-ACTACT-ANNUAL (financial/instrument/us-street@price-1) on page 45. • • Quoted Information Description Price Type Price % Quote Handling Index-Linked Bond (Israeli) Currency ILS Optionally, time-dependent index value Complete the following parameters: Information Description Date Date when rebasing is done. Type Choices are: Value or Factor • Value - When you select this option, the New / Old Value fields are available for editing, the Factor field is no longer available. • Factor - When you select this option, only the Factor field is available for editing, the New / Old Value fields are no longer available. Old Value Index value before the rebase. Defaults to the same value as specified in the Factor field when type Factor is selected. New Value Index Value after the rebase. Defaults to 1 when type Factor is selected. Factor Rebase factor. When type Value is selected, this field displays Old Value / New Value, rounded to 9 decimals (i.e. trailing zeros are not displayed). See A.2.214 Index Rebase (Index-Linked Bond) on page 820. • Valuation approach See A.2.74 Bond - Israeli Index-Linked Bond Valuation on page 745. 280 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond 3.6.12.2 Deal capture In addition to standard deal parameters, the information required to enter a deal on an Israeli index-linked bond is similar to usual index-linked bonds (see 3.6 Index-linked bond on page 260). 3.6.12.2.1 Input data Index at Issue and Index Ratio columns (take into account all the rebases that took place from the bond's issue date until (and including) the transaction's opening date). Information Description Index at Issue The Index at Issue column is calculated according to the issue index value defined at instrument level (Issue Index page), divided by each published rebase factor between the bond's issue date and the transaction's opening date: Equation 3-7 Israel index-linked bonds: Index at Issue calculations Where - V0 is the base index of the bond on the issue day as defined in the Issue Index page of the index-linked bond. - rbti is the rebase factor at time ti between the issue date and the opening date of the transaction, as defined in the Rebase page of the index. Index Ratio The Index Ratio takes into account the rebased index at issue and and the latest index value. For Israeli index-linked bond the Index Ratio is rounded to 7 decimals. For information about this calculation, see D.4.3.4.3 Calculation for Israeli index-linked bonds on page 925. 3.6.12.3 Processing The processing of an Israeli index-linked bond is the same as for a standard index-linked bond, see 3.6 Index-linked bond on page 260. 3.6.13 Italian BTP €i The following sections describe the characteristics that are specific to Italian BTP€i bonds. 3.6.13.1 Instrument setup Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics See A.2.75 Bond - Italian BTP€i on page 745. – Issue Index parameters Information Description Index Instrument ID of the underlying index. See 7.2.1 Simple Index on page 426. Issue Index Value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 281 3 Debt instruments 3.6 Index-linked bond • • Bond characteristics Information Description Currency EUR AI Method Italian (5 decimals). See Italian (5 decimals) on page 77. Coupon Rate Coupon rate of the bond. Schedule parameters – The Italian Index-Linked Bond (BTP) system-defined primary template is provided for this type of index-linked bond, where: Information Description Fixing parameters • Need Fixing = Yes • Expression = max (ixratio, 1) * price See B.2.1.1.30 Italian Index-Linked Bond (BTP) on page 896. • • • Trading yield Information Description Yield Convention Italian Government - GOVT-IT Quoted Information Description Price Type Price % Quote Handling Index-Linked Bond (Italian) Currency EUR Valuation approach See A.2.76 Bond - Italian Index-Linked Bond Valuation on page 745. 3.6.14 Japanese index-linked bond The following sections describe the characteristics that are specific to Japanese index-linked bonds. 3.6.14.1 Instrument setup Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics – Issue Index parameters Information Index Description Instrument ID of the underlying index. See 7.1 Index types on page 425. Issue Index Value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. See A.2.225 Japanese JGBi on page 825. 282 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond • Bond characteristics Information Description Currency JPY AI Method Japanese Yield (7 decimals) See Japanese Yield (7 decimals) on page 77. Coupon Rate • Coupon rate of the bond. Schedule parameters The Japanese Index-Linked Bond system-defined primary template is provided for this type of index-linked bond, where: Information Description Fixing parameters • Need Fixing = Yes • Fixing Date Method = In Arrears • Expression = ixratio*price See B.2.1.1.31 Japanese Index-Linked Bond on page 896. • Trading yield Information Description Yield Convention Japanese Government See 2.1.4.2.29 GOVT-JP (financial/instrument/simple-yield@price) on page 59. • • Quoted Information Description Price Type Price % Quote Handling Index-Linked Bond (Japanese) Currency JPY Valuation approach See A.2.226 Japanese Index-Linked Bond Valuation on page 826. 3.6.15 Swedish index-linked bond The following sections describe the characteristics that are specific to Swedish index-linked bonds. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 283 3 Debt instruments 3.6 Index-linked bond 3.6.15.1 Instrument setup Instrument setup for this type of index-linked bond is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics – Issue Index parameters Information Description Index Instrument ID of the underlying index. See 7.1 Index types on page 425. Issue Index Value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. See A.2.317 Swedish Index-Linked Treasury Bond on page 869. • • Bond characteristics Information Description Currency SEK Coupon Rate Coupon rate of the bond (unless it is a zero-coupon bond). Schedule parameters – The Swedish Index-Linked Bond system-defined primary template is provided for this type of index-linked bond, where: Information Description Fixing parameters • Need Fixing = Yes • Fixing Date Method = In Arrears • Expression = round (ixse / divider * price, 0.0000001) ixse = expression specific to Swedish index-linked bonds, see D.4.3.6 Swedish CPI market reference - ixse on page 926. See B.2.1.1.38 Swedish Index-Linked Bond on page 898. – For zero-coupon bonds, the Swedish Index-Linked Zero-Coupon Bond system-defined primary template is provided, where: Information Description Fixing parameters • Need Fixing = Yes • Fixing Date Method = In Arrears • Expression = max (ixse / divider, 1) * price ixse = expression specific to Swedish index-linked bonds. See B.2.1.1.39 Swedish Index-Linked ZC Bond on page 898. • 284 Trading yield Information Description Yield Convention Swedish Government - GOVT-SE © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond Quoted • Information Description Price Type Yield Quote Handling Index-Linked Bond (Swedish) Currency SEK Valuation approach • See A.2.318 Swedish Index-Linked Bond Valuation on page 870. 3.6.15.2 Position monitoring In this section, numerical examples demonstrate how the different figures are calculated for Swedish index-linked bonds. If you need more theoretical information about the method used in these calculations, see Chapter 2 Market standards and calculations on page 33. This example shows a Swedish index-linked bond, with the following deal data: Setup data Index at issue v_0 245.1 Maturity date dt_m 2008-12-01 Interest c_m 4.00% Settlement date dt_s 2003-04-30 Next coupon date dt_c 2003-12-01 Yield y 2.30% Nominal amount A 1,000,000.00 Last index (2003-01-01) v_1 276.0 Current index (2003-02-01) v_2 278.4 Day of month d_1 30 Transaction data Other important deal data is calculated by the system as follows: • Coupons left n_c = FLOOR (YEARFRAC (dt_s, dt_m, 4), 1) + 1 =6 • Dirty price p_d = (POWER (1 + y, -n_c + 1) + c_m * ((1 + y) * (1 - POWER (1 + y, -n_c))) / (y)) * Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 285 3 Debt instruments 3.6 Index-linked bond POWER (1 + y, -d_c / 360) * g_i = 125.43308% • Accrued interest I_a = g_i * (360 - d_c) / 360 * c_m = 0.018799437871 • Clean price p_c = p_d - I_a = 123.55313963% • Reference index v = v_1 + (MIN(d_1, 30) -1) / 30 *(v_2 - v_1) = 278.32 • Days to next coupon d_c = DAYS360 (dt_s, dt_c) = 211 • Index adjustment factor g_i = v / v_0 = 1.1355365157 3.6.15.2.1 Settlement figures Settlement flows for the transaction are calculated as follows: • Principal flow P = A * P_c 1,235,531.40 = 1,000,000 * 1.2355313963 • Accrued interest flow AI = A * I_a 18,799.44 = 1,000,000 * 0.018799437871 3.6.15.2.2 Fixing figures Fixing flows for the transaction are calculated using the following data: Fixing data Fixing date Index on 2002-09-01 2002-12-01 vf • Index adjustment factor gf = vf / v_0 1.11995104 = 274.50 / 245.1 • Nominal coupon cn = ROUND(c_m * gf, 7) 0.0447980 = ROUND (0.04 * 1.11995104, 7) • Adjusted amount Ap = A * cn 44,798.00 = 1,000,000 * 0.0447980 274.50 3.6.15.2.3 Valuation figures Unless otherwise stated, the figure date used in the calculations is 2003-04-28. On this date, the market data is as follows: Market data on 2003-04-28 Figure date 2003-04-28 Figure spot date d_s.f 2003-04-30 Market quote (real yield) y_f 2.30% Index adjustment factor g_f 1.135536516 286 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond Market data on 2003-04-28 Spot discount factor D_s.f 1.00 • Days to next coupon d_c.f = DAYS360 (d_s.f, dt_c) = 211.00 • Dirty price d_p.f = (POWER(1 + y_f, -n_c. + 1) + c_m * ((1 + y_f) * (1 - POWER (1 + y_f, -n_c))) / (y_f.)) * POWER (1 + y_f,- d_c.f / 360) * g_f 1.254330834 • Accrued interest ai.f = g_f * (360 - d_c.f) / 360 * c_m = 0.018799438 • Clean price = p_d.f - ai.f = 1.235531396 • Market value = A * ai.f * D_s.f + A * p_c.f * D_s.f = 1,254,330.83 3.6.16 UK index-linked gilt The following sections describe the characteristics that are specific to UK (3 month and 8 month) index-linked gilts. 3.6.16.1 Instrument setup Instrument setup for UK index-linked gilts is the same as for index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics See A.2.329 UK ILG (3M) on page 876 and A.2.330 UK ILG (8M) on page 876. – Issue Index parameters Information Description Index Instrument ID of the underlying index. See 7.1 Index types on page 425. Issue Index • • Value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. Bond characteristics Information Description Currency GBP Coupon Rate Coupon rate of the bond. Schedule parameters Select the appropriate cashflow structure template, BOND-UK-IG-3M or BOND-UK-IG-8M. See B.2.1.1.42 United Kingdom Index-Linked Gilt (3M) on page 898 or B.2.1.1.43 United Kingdom Index-Linked Gilt (8M) on page 899. Note: These templates correspond to rounding down to 4 decimal places. Some issues (both 8M and 3M) use different rounding conventions. To round down to 2 decimal places, replace Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 287 3 Debt instruments 3.6 Index-linked bond the function round ( , 0.000001, -1) by round ( ,0.0001, -1). To round to nearest 6 decimal places, use round ( , 0.00000001). Trading yield • Information Description Yield Convention UK Government - GOVT-UK Quoted • Information Description Price Type Price % Quote Handling Index-Linked Bond (UK 3M) or Index-Linked Bond (UK 8M) Currency GBP Valuation approach • See A.2.331 UK Index-Linked Bond (3M) Valuation on page 876 and A.2.332 UK Index-Linked Bond (8M) Valuation on page 877. 3.6.16.2 Position monitoring In the following sections, numerical examples demonstrate how the different figures are calculated for UK 3 month and 8 month index-linked gilts. If you need more theoretical information about the method used in these calculations, see Chapter 2 Market standards and calculations on page 33. 3.6.16.2.1 Calculations - UK 3 month This example shows a UK 3 month index-linked gilt, with the following deal data: Setup • Data Symbol Example Index at issue v_0 193.725 Maturity date dt_m 2012-11-22 Interest c_m 1.25% Rounding decimals 5 Yield rounding y_round 6 Dividend rounding decimals_div 6 Data Symbol Example Settlement date dt_s 2007-06-18 Previous coupon date dt_p 2007-05-22 Next coupon date dt_c 2007-11-22 Coupons left n_c 21 Yield y 2.19% Transaction data • 288 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond Data Symbol Example Last index (2007-03) v_1 204.40 Current index (2007-04) v_2 205.40 Day of month d_1 18 Other important deal data is calculated by the system as follows: • Dirty price d_p = (POWER (1 + y / 2, -n_c + 1) + c_m / 2 * ((1 + y / 2) * (1 - POWER (1 + y / 2, -n_c))) / (y / 2)) * POWER (1 + y / 2, -d_c / 183) = 91.37171% • Accrued interest unadjusted I_u = c_m / 2 * (p_c - d_c) / p_c = 0.0917120% • Accrued interest I_ a = g_i * I_u = 0.0970340% • Clean price unadjusted p_cu = d_p - I_u = 91.2800% • Clean price Pca =p_cu * g_i = 96.57697839% • Reference index v = ROUND (v_1 + (d_1 - 1) / DAY(EOMONTH (dt_s, 0)) * (v_2 - v_1), decimals) = 204.96667 • Coupon period p_c = dt_c - dt_p = 184 • Days to next coupon d_c = dt_c - dt_s = 157 • Index adjustment factor g_i = ROUND (v / v_0, decimals) = 1.0580300000 Settlement figures Settlement flows for the transaction are calculated as follows: • Nominal amount A = 1,000,000.00 • Clean price Pca.s = A * Pca = 965,769.78 • Accrued Interest I_a.s = A * I_a = 970.34 • Total = 966,740.12 Fixing figures Fixing flows for the transaction are calculated using the following data: Data Symbol Fixing date Index on 2007-08-22 Example 2007-11-22 vf 205.40 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 289 3 Debt instruments 3.6 Index-linked bond • Index adjustment factor gf = ROUND (vf / v_0, decimals) = 1.06027 • Nominal coupon cn = ROUND (c_m / 2 * gf, decimals_div + 2) = 0.006626690 • Adjusted amount Ap = A * cn = 6,626.69 Valuation figures Unless otherwise stated, the figure date used in the calculations is 2007-06-16. On this date, the market data is as follows: Market data on 2007-06-16 • Data Symbol Figure date Example 2007-06-16 Figure spot date d_s.f 2007-06-18 Market quote (clean unadjusted) Pcu 91.28% Index adjustment factor gv 1.05803 Spot discount factor Ds 0.999564 Days to next coupon dnv 157 • Accrued interest = A * (c_m / 2) * (p_c - dnv) / p_c * gv * D_s = 969.92 • Principal = A * Pcu * gv * D_s = 965,348.87 3.6.16.2.2 Calculations - UK 8 month This example shows a UK 8 month index-linked gilt, with the following deal data: Setup data • Data Symbol Example Issue date 1982-01-28 Index at issue (5/1981) 294.10 Rebasing index (2/1983) 394.50 Index at issue rebased v_0 74.55006337136 Maturity date dt_m 20011-08-23 Interest r 2.50% Rounding decimals dec 0.0001000 Symbol Example Transaction data • Data Opening date 2007-03-28 Settlement date d.s 2007-03-29 Previous coupon date d.pc 2007-02-23 Next coupon date dt.c 2007-08-23 290 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond Data Symbol Example Reference index for next coupon v 202.70 Latest published index v_l 203.10 Forecast delay months m_d 2 Next but one coupon date 2008-02-23 Coupons left n 8 Index Prolong Rate pi 3% Note: Index Prolong Rate (for the underlying index) is shown in Rate Monitor under key figure Index Rate. If the index rate is not given, the default value is 3%. Other important deal data is calculated by the system as follows: • Index forecast factor g_f = (v_l / v0) * POWER (u, m_d * 2 / 12) = 2.710955377 • Next but one coupon amount estimate d2 = (r / 2) * g_f / u = 3.4391490% • Days to next coupon d.n = dt.c - d.s = 147 • Current coupon period p = dt.c - d.pc = 181 • Time to next coupon t_n = d.n / p = 0.81215 Price from real yield • Yield (real) y = 2.2656270% • Semi-annual real discount factor) w = 1 / (1 + y. / 2) = 0.988798754 • Semi-annual inflation factor) u = POWER (1 + pi, -0.5) = 0.985329278 • Dirty price P_d = (d1 + d2 * u * w + (g_f * r * w * w) / (2 * (1 - w)) * (1 - POWER (w, n -1))) * POWER (u * w, d.n / p) + g_f * POWER (u, d.n / p) * POWER (w, n + d.n / p) = 271.106796% • Accrued interest (adjusted) I_a = d1 * ((p - d.n) / p) = 0.63679558% • Clean price (adjusted) p_c = P_d - I_a = 270.4700% • Nominal from real = 2 * ((y / 2 + 1) * SQRT(1 + pi) - 1) = 5.2771916% Settlement figures Settlement flows for the transaction are calculated as follows: • Nominal amount A = 10,000,000.00 • Clean price p_c.s = A * p_c = 27,047,000.00 • Accrued interest I_a.s = I_a * A = 63,679.56 • Total = 27,110,679.56 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 291 3 Debt instruments 3.6 Index-linked bond Fixing figures Fixing flows for the transaction are calculated using the following data: Fixing data Coupon date 2007-08-23 Index on 2006-12-01 vf • Index adjustment factor g_i = v / v0 = 2.718978239 • Adjusted coupon d1 = FLOOR ((r / 2) * g_i, dec) = 3.3900% • Adjusted amount Ap = A * d1 = 339,000.00 202.70 Valuation figures Unless otherwise stated, the figure date used in the calculations is 2007-03-28. On this date, the market data is as follows: Market data on 2007-03-28 Figure date 2007-03-28 Figure spot date d_s.f 2007-03-29 Discount factor for spot date Ds 0.999854679 Market quote Pc 270.47% Days to next coupon dvc 147 • Principal market value = A * Pc * Ds = 27,043,069.49 • Accrued interest market value = A * d1 * (p - dvc) / p * Ds = 63,670.30 3.6.17 US Tips The following sections describe the characteristics that are specific to US Treasury index-linked bonds. 3.6.17.1 Instrument setup Instrument setup for US Tips is the same as for other index-linked bonds (see 3.6 Index-linked bond on page 260) except for the following parameters: • Trading characteristics See A.2.334 US TIPS on page 877. – Issue Index parameters Information Index Description Instrument ID of the underlying index. See 7.1 Index types on page 425. Issue Index 292 Value of the underlying index at issue. This value is used to adjust the coupon and redemption flows of the bond. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond • • Bond characteristics Information Description Currency USD Coupon Rate Coupon rate of the bond. Schedule parameters The US Treasury Inflation Protected Security system-defined primary template is provided for these index-linked bonds, where: Information Description Fixing parameters • Need Fixing = Yes • Fixing Date Method = In Arrears • Expression = ixratio*price See B.2.1.1.44 US Treasury Inflation Protected Security on page 899. • • • Trading yield Information Description Yield Convention U.S. Treasury - *U.S.TREASURY Quoted Information Description Price Type Price % Quote Handling Index-Linked Bond (US TIPS) Currency USD Valuation approach See A.2.333 US Index-Linked Bond Valuation on page 877. 3.6.17.2 Position monitoring In the following sections, numerical examples demonstrate how the different figures are calculated for US Treasury index-linked bonds, both at the time of issue and at trading. If you need more theoretical information about the method used in these calculations, see Chapter 2 Market standards and calculations on page 33. 3.6.17.2.1 Calculations - at issue This example shows a US Treasury index-linked bond, with the following deal data (at issue): Setup data Issue date 1998-01-15 Index at issue v_0 161.55484 Maturity date dt_m 2008-01-15 Interest r 3.625% Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 293 3 Debt instruments 3.6 Index-linked bond Transaction data Opening date 1998-10-13 Spot days 2 Settlement date dt_s 1998-10-15 Previous coupon date dt_c0 1998-07-15 Next coupon date dt_c 1999-01-15 Yield y 3.650% Last index v_1 163.20 Current index v_2 163.40 Day of month d_1 (= dt_s) 15 Length of month m_1 31 Other important deal data is calculated by the system as follows: • Coupons left c_n = FLOOR (YEARFRAC (dt_c, dt_m, 0) * 2, 1) = 18 • Yield factor vy = 1 / (1 + y / 2) = 0.9821 • Dirty price unadjusted P_u = (r / 2 + (1 - POWER (vy, c_n)) / (y / 2) * (r / 2) + POWER (vy, c_n)) / (1 + (d / p) * (y / 2)) = 100.7032666% • Accrued interest unadjusted I_u = ROUND ((pn - dn) / pn * r / 2, 8) = 0.00906250 • Accrued interest adjusted I_a = ROUND (I_u * g_i, 8) = 0.0091598300 294 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.6 Index-linked bond • Clean price unadjusted P_cu = ROUND (P_u - I_u, 5) = 99.79700% • Clean price adjusted P_a = ROUND (P_cu * g_i, 5) = 100.86900% • Reference index v = ROUND (v1 + (d_1 - 1) / m_1 * (v2 - v1), 5) = 163.2903200 • Index adjustment factor g_i = ROUND (v / v_0, 5) = 1.0107400000 • Days to next coupon d = dt_c - dt_s = 92 • Current coupon period p = dt_c - dt_c0 = 184 Settlement figures • Nominal amount An = 1,000,000.00 • Clean price = An * P_a = 1,008,690.00 • Accrued interest = An * I_a = 9,159.83 • Total = 1,017,849.83 Fixing figures Fixing flows for the transaction are calculated using the following data: Fixing data Coupon date Index on 2002-09-01 1999-01-15 vf • Index adjustment factor gf = ROUND (vf / v_0, 5) = 1.01514 • Nominal coupon cn = r / 2 * gf = 0.0183994 • Adjusted amount Ap = cn * An = 18,399.41 164 Valuation figures Unless otherwise stated, the figure date used in the calculations is 1998-10-13. On this date, the market data is as follows: Market data on 1998-10-13 Figure date 1998-10-13 Figure spot date d_s.f 1998-10-15 Market quote (clean unadjusted price) Pq 99.7970% Index adjustment factor g_v 1.010740 Spot discount factor D_s 1 Days to next coupon dcv 92 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 295 3 Debt instruments 3.6 Index-linked bond • Accrued interest = An * ROUND ((pn - dcv) / pn * r / 2, 8) * g_v * D_s = 9,159.83 • Principal = An * Pq * g_v = 1,008,688.20 3.6.17.2.2 Calculations - at trading This example shows a US Treasury index-linked bond, with the following deal data (at trading): Setup data Index at issue v_0 198.47742 Maturity date dt_m 2016-01-15 Interest r 2.00% Settlement date dt_s 2007-06-18 Previous coupon date dt_c0 2007-01-15 Next coupon date dt_c 2007-07-15 Yield y 2.783% Last index v_1 205.35200 Current index v_2 206.68600 Day of month d_1 (= dt_s) 18 Length of month m_1 30 Transaction data Other important deal data is calculated by the system as follows: • Coupons left c_n = FLOOR (YEARFRAC (dt_c, dt_m, 0) * 2, 1) = 17 • Yield factor vy = 1 / (1 + y / 2) = 0.9863 • Dirty price unadjusted P_u = (r / 2 + (1 - POWER (vy, c_n)) / (y / 2) * (r / 2) + POWER (vy, c_n)) / (1 + (d_1 / m_1) * (y / 2)) = 94.9133290% • Accrued interest unadjusted I_u = ROUND ((pn - dn) / pn * r / 2, 8) = 0.00850829 • Accrued interest adjusted I_a = I_u * g_i = 0.0088354338 • Clean price unadjusted P_a = P_u - I_u = 94.06250% • Clean price adjusted P_a = P_cu * g_i = 97.67920% • Reference index v = ROUND (v1 + (d_1 - 1) / m_1 * (v2 - v1), 5) = 206.1079300 • Index adjustment factor g_i = ROUND (v / v_0, 5) = 1.0384500000 • Days to next coupon dn = dt_c - dt_s = 27 • Current coupon period pn = dt_c - dt_c0 = 181 296 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.7 Asset backed security Settlement figures • Nominal amount An = 1,000,000.00 • Clean price = An * P_a = 976,792.03 • Accrued Interest = An * I_a = 8,835.43 • Total = 985,627.47 3.7 Asset backed security With normal bonds, the investor is dependent on the creditworthiness of the issuer for payment of the coupons and repayment of the original investment. In contrast, asset-backed securities have a pool of assets that collateralize the bond and generate the cashflows. Asset-backed securities (ABS) are backed by assets such as consumer loans, credit card receivables, royalties, and leases. However, the majority of the market consists of securities backed by residential mortgage loans with mortgage-backed securities (MBS). The main risk for the investor is the risk of repayment. When an individual asset is repaid (repayment), the security is amortized by the principal amount of that mortgage or loan. The structure of the security determines precisely how this amortization is passed on to investors; however it is done, it is impossible to predict the cashflows precisely for fixed or floating-rate instruments. Note: TRM does not support repayments in the middle of a coupon period but only at coupon payment dates. 3.7.1 Instrument setup Asset-backed security instruments must be based on an instrument type derived from the class ABS. They are set up in a similar way to standard bonds (see 3.1 Bond on page 215). The additional values required to set up ABS instruments are described in the following sections. • ABS main characteristics The main characteristics of an ABS are defined in the same way as a Bond instrument, but using the primary feature ABS: see A.2.1 ABS - Asset Backed Security on page 713. • Schedules Select the cashflow structure template that is appropriate for the instrument. System templates are provided for both fixed-rate ABS (see B.2.1.1.1 ABS-MBS, Fixed Rate on page 890) and floating-rate ABS (see B.2.1.1.2 ABS-MBS, Floating Rate on page 890); you can choose one of these templates or any other template derived from them. Note: It is possible to modify the Start Date value for the redemption cashflow to reflect any restrictions on the date when repayments are allowed to begin on the ABS. • Repayment estimation The estimations of future repayments are defined and stored in the Repayment Estimates page. To define a new set of repayments, click Generate to open the resulting dialog and enter the following parameters: Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 297 3 Debt instruments 3.7 Asset backed security Important: Do not use the Add/Remove and Clear buttons in the Repayment Estimates page. Information Description Estimation Date Date from when the estimation is valid. Outstanding Read-only. Percentage of the initial nominal amount which is outstanding (the current repayment included) on the Estimation Date. Legal Maturity Read-only. Legal maturity of the instrument. Expected Maturity Expected maturity of the instrument. The date must be later than the estimation date and earlier or equal to the legal maturity date. Default is the legal maturity date. Method Defines which method to use to generate the estimate: • Annuity does a fixed annuity calculation. • Copy Previous + Fixed % copies the previous estimation, if it exists, and adds % between % From and % To. • Fixed % creates a repayment of % between % From and % To. • Linear performs linear amortization of the outstanding principal until the date specified in the Expected Maturity field. • WAL Date allow the user to enter an expected maturity date different from the coupon date. The selected WAL (Weighted Average Life) date is displayed in WAL Date field of the Repayment Estimates page. When this method is used, two repayments are automatically created from this date, by splitting the redemption amount between previous and next coupon dates (according to the WAL date) as follows: - PrevCD is the first coupon value date immediately before the WAL date: P*OutstandingAmount is prepaid at PrevCD. - NextCD is the first coupon value date immediately after the WAL date: (1-P)* OutstandingAmount is paid at NextCD. where P = (WAL date - PrevCD)/(NextCD - PrevCD) Note: WAL Date is visible in Transaction Manager. Interest Rate The last known fixed rate (only used for annuity calculation). % From Date from when % should apply in Copy Previous + Fixed % and Fixed % methods. % To Date until when % should apply in Copy Previous + Fixed % and Fixed % methods. % Percentage to use in Copy Previous + Fixed % and Fixed % methods. Click OK to display the repayments generated for this date. The information displayed is as follows: 298 Information Description Outstanding Read-only. Percentage of the initial nominal amount which is outstanding (the current repayment included). WAL Date This date is used when the expected maturity date is different to the coupon date, i.e. when the method WAL Date is selected during the generation. Value Date Read-only. Date on which the repayment may occur for the selected row, valid for the specified estimation date. Estimation Date Date from when the estimation is valid. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.7 Asset backed security Information Description Percentage For the selected row, the percentage of the principal which is estimated to be repaid on a specified estimation date. Active From/To Read-only. First and/or last date that the estimation is valid. Each row displayed consists of a repayment estimate, valid for a given period (defined by the fields Active From/Active To). – To refine the repayment estimate for this value date, you can edit the percentage of a row. Click Update to validate the modification. – To generate a new set of estimates for a different date, enter this date in Estimation Date and generate again as described above. – To remove a set of estimations, click Delete. All the estimates with Active From included in the period defined in the Delete dialog are removed. Alternative repayment parameters • Optionally, you can add the feature Alternative Repayment Estimates to override the repayment parameters set up in the Repayment Estimates page. This feature adds two pages, Alternative Repayment Estimate Setup and Alternative Repayment Estimates. The Alternative Repayment Estimates page is set up in the same way as the Repayment Estimates page. A.2.27 Alternative Repayment Estimates on page 723. Note: For accounting: Alternative repayments should not be used for the valuation modes used in accounting. Accounting should use the set of estimates defined in the Repayment Estimates page to ensure that the accrual figures are consistent with the yield calculation. (The yield is calculated based on the estimates defined in the Repayment Estimates page.) 3.7.2 Deal capture A deal involving an asset-backed security is entered in a similar way to a bond deal. 3.7.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a deal on an asset-backed security. Information Description Price or Rate If there is a yield/price convention set on the instrument, it is possible to enter either a rate or a price, and conversion is made automatically. If there is no convention set, the deal must be entered in price. Face Amount The deal can be input in face amount or units, in which case, the Nominal Amount is computed by the system. or Units Amount Nominal amount of the deal. This amount is computed by the system when the face amount or units are entered. 3.7.2.2 Generated data • Cashflows Only definite cashflows are generated on a deal with an ABS instrument: – Position cashflow Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 299 3 Debt instruments 3.7 Asset backed security – Known future amortization flows and corresponding interest flows (no uncertain cashflows are generated) – Accrued interest flow – Delivery flow (pseudo) 3.7.3 Processing This section describes the actions that can be done throughout the life of an ABS. 3.7.3.1 Fixing repayment flows Repayment flows for an ABS are not known in advance and can only be estimated. Therefore, when you know a repayment is definitely going to take place, the cashflow needs to be fixed. The following information is needed to fix a repayment: Fixing Rate = Real percentage of principal • Execution There are two ways to execute fixing of repayment flows. In both cases, the results of the action are identical. The action parameters are defaulted from the repayment percentage specified in the Repayment page. If the WAL (Years) is provided, then it is used to calculate the expected maturity in the subsequent estimate regeneration. The methods of fixing are as follows: – Directly on the cashflow (in Instrument Editor’s Cashflow page) using the Fix Repayment action: the fixing affects all deals on the instrument by updating the cashflows at transaction level when the instrument is saved. – Using the activity Fixing ABS Repayment: all instruments and their deals which need to be fixed for a particular date are affected by the activity. Note: See the TRM User Guide for general information on running activities, and also specific information on the activity parameters. When the fixing of the repayment is done, the cashflows are updated as follows: – The repayment flow and the next interest flow are added to the deal. – The position flow is added to reflect the outstanding principal amount. Additionally, after the fixing of the repayment, the system automatically prompts to re-estimate the repayment estimate based on the result of the fixing. The action parameters are defaulted from the previous estimation. Click OK to accept these defaults. Note: This action can be executed automatically using the Selling Values activity. See the TRM User Guide for information on the activity parameters. In case of Floating Rate ABS, the next interest should be fixed before the repayment can be fixed. This is required to ensure the correct recalculation of yield accrual and regeneration of estimates for a annuity repayment. 3.7.3.2 Full Repayment When an ABS is fully repaid, the current position of the corresponding ABS is closed by creating a Sell transaction with the outstanding amount as the nominal amount. • Execution There are two ways for full repayment of an ABS, in both cases, the results are identical. 300 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.7 Asset backed security Directly on the cashflow at the instrument level (Instrument Editor - Cashflow page) using the Full Repayment action. This closes the current position on the corresponding ABS as follows: – A Sell transaction is generated (consolidated per Portfolio/Counterparty/Result mode) with a nominal amount equal to the amount left at the full repayment date. The Sell transaction has a position flow that closes the current position and a settlement flow to repay the ABS. Note: No delivery flow is generated in this transaction in order to reflect the market practice where the issuer may call back the security, usually after the full repayment date. You can generate the security settlement (delivery flow) at a later date as described in the next section. Using the activity Fixing ABS Repayment (Full Repayment), see TRM User Guide for more information about this activity. – After a full repayment, you can generate the security settlement (delivery flow) by right-clicking the previously generated Sell transaction and selecting ABS Custody Account Clearing. This action also clears the custody balance. Enter the following parameters in the resulting dialog: Information Description Opening Date Defaults to the opening date of the Sell transaction. Value Date Defaults to the opening date plus the spot date. From (Read-only) Defaults to the owner of the original transaction. From Custodian Custody account defined for the owner. Only the accounts with Custody account kind are available for selection. From Account Account from the custody account you selected in the From Custodian field. To Defaults to the issuer of the ABS. You can modify the issuer. To Custodian Custody account defined for the issuer you selected in the To field. Only the accounts with Custody account kind are available for selection. To Account Account from the custody account you selected in the To Custodian field. Click OK. A transfer transaction is created to generate a delivery cashflow between the Owner of the transaction and the Issuer of the ABS. Note: You can cancel the transfer transaction by clicking the Cancel command at the transaction level. • Cancellation You can cancel a full repayment by selecting the Cancel Full Repayment action on the corresponding redemption flow (Instrument Editor - Cashflow page). 3.7.3.3 Fixing coupon flows The unknown interest flows for a floating-rate ABS need to be fixed. The procedure for fixing these flows is the same as the one used for floating-rate notes. See 3.1.2.3.1 Fixing on page 230 for more information. 3.7.3.4 Selling Values activity If yield accrual is used, you can set up an activity (using type Selling Values) to have accrued profit available for the selling process. You must run the activity before processing the selling. This can be Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 301 3 Debt instruments 3.7 Asset backed security done by setting activity to run automatically, for example, at the end of each day, before the end of day accounting processing. Note: See the TRM User Guide for information about how to set up and use activities in general. 3.7.4 Position monitoring 3.7.4.1 Setup The presence of the valuation method feature ABS Valuation in the instrument definition determines that the instrument is valuated as an asset-backed security. See A.2.2 ABS Valuation on page 714. 3.7.4.2 Calculations TRM values an asset-backed security according to the current valid estimates on the valuation dates. It does so by expanding a cashflow structure matching the estimated repayment structure according to the parameters defined at the instrument level. Note: The expanded repayment estimate of an ABS that can be seen in Treasury Monitor corresponds to the cashflow structure of an equivalent bond instrument. Therefore, ABS valuation behaves in exactly the same way as valuation of an equivalent bond. 3.7.5 Australian MBS Australian MBS are similar to other MBS instruments already handled by TRM, except that they are quoted in trading margin, and that the formula used to compute the price is specific. This specific formula is used to convert the trading margin (market quote) to the instrument's price: Equation 3-8 Trading Margin conversion - Australian MBS then MarketValue = Price * Outs tan ding Principal where: C Next coupon amount per $100 FV IM Spread% defined at schedule level. TM Quoted yield in % f Number of days from settlement to next coupon date. d Number of days between previous and next coupon dates. 302 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.7 Asset backed security a Annuity Factor i s Quarterly Swap Rate between settlement date and maturity date, this rate is interpolated on the yield curve defined in the Quote Default page at the instrument level. The corresponding frequency is retrieved from the Yield Type field of the yield curve. Note: If not quarterly, the corresponding rate is converted according to the Equation 3-2 on page 237. r Discount Rate between settlement date and next coupon date (interpolated on the default yield curve defined at currency editor level). n Number of coupon periods between the next coupon date and the Weighted Average Life (WAL) date with the appropriate ’n’ rounding convention applied (see 3.7.5.1 Instrument setup on page 303 for information about this setup): Equation 3-9 Number of coupon periods where: • WAL is calculated as shown in 3.7.5.2.1 Input data on page 304. • 365.25 or 365 corresponds to the Days Divisor selected at the instrument level in the Bond page. 3.7.5.1 Instrument setup Australian MBS must be based on an instrument type derived from the class ABS. They are set up in a similar way to ABS, but require a different primary feature. • Main characteristics Same setup as for usual ABS with the following additional parameter: Information Description N-Periods’ Rounding Nearest number to which the number of coupon periods ’n’ (as calculated in Equation 3-9 on page 303) between the next coupon date and the Weighted Average Life date is rounded. For example, 0 for none, 1 for an integer, or 0.1 for a rounding to the first decimal. N-Periods’ Rounding Method Up, Down or Nearest. The amount is rounded up, down, or to the nearest figure as calculated using the specified N-Periods’ Rounding number. Days Divisor The divisor used in the pricing (valuation) formula . Choices are: • 365 • 365.25. See A.2.39 Australian MBS on page 727. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 303 3 Debt instruments 3.7 Asset backed security Quotation information • Information Description Price Type Select Trading Margin to trade Australian MBS at a trading margin. Quote Handling Select MBS (Australian) to convert the quotation (trading margin) to the price of the instrument. See Equation 3-8 on page 302. See A.2.274 Quoted on page 849. Yield Curve Default • The setup of the feature Quote Default (Australian MBS) is similar to the usual Quote Default feature except that it adds the Yield Curve Default page to select the Par rate yield curve to be used for reference rate defaulting. Information Description Currency The currency that you want to specify. Select AUD. Yield Curve Select corresponding yield curve to be used instead of the yield curve defined at the currency level (Currency Editor). A.2.268 Quote Default (Australian MBS) on page 846. Valuation approach • To allow quoted valuation of market value calculation instead of the usual valuation of ABS. A.2.40 Australian MBS Valuation on page 728. 3.7.5.2 Deal capture 3.7.5.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a deal on an Australian MBS: Information Description Trading Margin Instrument quotation. In addition, the following defaulted information can be modified: Information Description Reference Rate Quarterly swap rate for the period from settlement date to maturity date (from the yield curve specified in Yield Curve Default page when provided, otherwise uses the default yield curve defined at currency level). Discount Rate Computed from the settlement date and the next coupon date of the instrument (from the default yield curve defined at currency level). AU Rate Scenario Scenario used to calculate the reference and discount rates. This scenario defaults to the scenario defined at the instrument level (Quote Default page). You can change the default scenario by selecting Quote Default Configuration from the Options menu. See TRM User Guide for more information about changing this configuration. 304 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.8 Short term loan Information Description WAL Date If repayments were created with the WAL Date method at the instrument level, then the entered date is automatically populated according to that date, otherwise the WAL date is computed as follows for each row of repayments according to the value date to the transaction settlement date: Equation 3-10 WAL Date Deal Price Computed using the trading margin to the price formula (Equation 3-8 on page 302). 3.7.5.3 Processing The actions that can be done throughout the life of an Australian MBS are the same ones as for a usual MBS (see 3.7.3 Processing on page 300). 3.7.5.4 Position monitoring There are two basic methods for valuation of Australian MBS instruments: Quoted or Theoretical. 3.7.5.4.1 Setup When the Theoretical valuation method is used, the Australian MBS is valuated in the same way as a usual MBS. On the other hand, if you want to use the pricing formula (Equation 3-8 on page 302) to compute the market value, then you need to attach the feature Australian MBS Method (A.2.40 Australian MBS Valuation on page 728) and use the Quoted valuation method. Swap and discount rates used in the pricing formula are retrieved as follows: • Reference Rate: The quarterly swap rate for the period from valuation date to maturity date is computed from the yield curve specified in the Yield Curves page (Valuation Curve Setup feature) with Usage set to Valuation, when provided, otherwise uses the valuation yield curve defined at the currency level. • Discount Rate: Computed between valuation date and next coupon date of the instrument (computed from the yield curve specified in the Yield Curves page (Valuation Curve Setup feature) with Usage set to Discount, when provided, otherwise uses the valuation yield curve defined at currency level). Note: For the valuation when the next coupon is not fixed, the estimation curve is used to compute the next fixing rate and the discount rate in the pricing formula. If the estimation curve is not defined at the instrument level, then the currency estimation curve is used instead. If no currency estimation curve is defined, then the currency valuation curve will be used. See feature A.2.337 Valuation Curve Setup on page 878. 3.8 Short term loan Deposits and short-term loans are usually fixed-rate agreements to deposit or borrow a specified amount for a specified period. They are basically the same instrument, with the name simply depending on whether they are seen from the borrower's (loan) or the depositor's (deposit) standpoint. A buy transaction is made by the lender while a sell transaction is made by the borrower. The maturity is usually less than one year and the principal and interest are paid out at expiration. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 305 3 Debt instruments 3.8 Short term loan 3.8.1 Instrument setup Short-term loans must be based on an instrument type derived from the class SHORT-LOAN. • Main characteristics The following basic information may be captured when defining the instrument. This information is relevant to any kind of short term loan/deposit. Information Description Currency Currency of the instrument. If the currency is not defined at instrument level, it needs to be specified separately for each transaction. Date Basis Date basis of the instrument. If the date basis is not defined at instrument level, it can be specified separately for each transaction. Rounding parameters Method and precision used to round cashflow amounts. Interest Type Interest rate type used to calculate the cashflows of the instrument. Transaction Sign Sign of the transaction. If the sign is not defined at instrument level, it needs to be specified separately for each transaction. Principal Subtype Type of repayment and interest cashflows (default values are Redemption and Interest). Interest Subtype See A.2.299 Short Term Loan on page 862. • Maturity definition It is possible to set up maturity information at instrument level. Information Description Calendar parameters Calendars used to calculate the maturity date. Gap Set Gap set used for supplying the available maturity periods. Maturity Date Period If defined, this maturity period is applied to each transaction. See A.2.230 Maturity Date Setup on page 827. • Short loan margin definition It is possible to input margins when entering a loan. See A.2.300 Short Term Loan Margin Result on page 863. For a short-term loan/deposit it is also possible to set up: • Spot date calculation • Value date calculation to enable easy entry of forward deals with this instrument • Cashflow and transaction charge rules • Manual charges • Branch codes • Deal rate defaulting when entering the transaction See Appendix A Features on page 713. 306 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.8 Short term loan 3.8.2 Deal capture 3.8.2.1 Input data Note: For margin loans, make sure that the columns Margin and Margin (bp) are visible in the Transaction view. In addition to the standard deal parameters, the following information is required to enter a short-term loan/deposit: Information Description Currency Currency of the transaction. Value Date Date when the loan/deposit starts, and from which interest starts to accrue. This defaults to the spot date of the transaction. Maturity Date Date when the transaction matures. If you enter a maturity code, the date is calculated automatically; otherwise you can enter the date manually. Maturity Code If the maturity definition parameters are defined at instrument level, these are used by default and cannot be modified. Nominal Amount Amount deposited/lent, that is, the amount exchanged on the value date of the transaction, and the amount on which interest is calculated. Deal Rate Rate at which interest is calculated for the transaction. In addition, the following optional information can be captured: Information Description Value Date Code If the Value Date Setup feature is applied at instrument level, you can enter the value date period you want to use to calculate the value date for the transaction, for example, 3M (3 months). This can be used to compute the value date for a forward purchase of a short-term loan/deposit. Note: If you specify a value date period in the instrument setup, this is used as the default in the transaction and cannot be modified: see A.2.339 Value Date Setup on page 879. Date Basis Date basis of the transaction. If the date basis is not defined at instrument level, it can be specified separately for each transaction. Margin You can enter the margin as a percentage in the Margin column or as basis points in the Margin (bp) column, in which case, the margins are stored as a percentage but displayed as basis points (multiplied by 100). Margin (bp) The margin added or subtracted from the Nominal/Spot Rate to get Deal Rate. Positive margins are always in favor of the portfolio owner and negative margins against the portfolio owner. Thus, for short-term loans placed, the margin will be added to Nominal/Spot Rate to get Deal Rate, and for short-term loans taken, the margin will be subtracted from Nominal/Spot Rate to get Deal Rate. The exact calculation is the following: Deal Rate = Nominal / Spot Rate + Transaction Sign * Margin Nominal Spot / Rate The interest rate excluding margins. 3.8.2.2 Generated data • Transaction – Book value of the transaction is automatically defaulted to the nominal amount. – Issuer is determined by the transaction direction: Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 307 3 Debt instruments 3.8 Short term loan Transaction Sign = Buy, Issuer = Counterparty Transaction Sign = Sell, Issuer = Portfolio Owner • Cashflows The following cashflow structure is generated for a bought transaction (depositor side). The interest amount is calculated as follows: rounder (A * (1 / D - 1)) where: D = discount factor A = nominal amount rounder depends on the instrument’s rounding parameters – Margin cashflows A Margin cashflow is generated if a transaction margin rate is entered and the instrument has the feature Short Term Loan Margin. The Margin cashflow is only used for calculating Margin Profit. The Margin cashflow is calculated in the same way as the interest, using the captured margin rate. This cashflow effectively represents the margin rates contribution in the final interest amount. 3.8.3 Processing This section describes the actions that can be done throughout the life of a short-term loan/deposit. 3.8.3.1 Early expiration Short-term loans/deposits can be matured earlier than their agreed maturity date. This process is referred to as early expiration. However, the action is only enabled for transactions that have reached a certain state in the transaction flow. • Execution Early expiration of short-term deposits/loans can be done in two different ways. In both cases, the following information is needed to process the early-expiration: 308 Information Description Opening Date Date when the early expiration is executed. By default, this is today’s date. Value Date Date when the early expiration is settled. This must be earlier than the original maturity date and later than the original value date of the initial transaction. Amount to Expire Amount to be early expired. This defaults to the amount still available to be early expired, taking into account previous partial early expirations and roll overs. Rate Rate at which the early expiration is done. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.8 Short term loan The execution generates an early expiration transaction with the following attributes: Transaction sign = opposite of initial transaction Nominal amount = amount to expire Rate = early expiration rate Opening date = date when the early expiration is done Value date = date when the early expiration is settled Kind = Early Expiration The remaining attributes are inherited from the initial transaction. • Cancellation You can undo the early expiration by canceling the early expiration transaction. 3.8.3.2 Early expiration with margins You can also specify margins when you early expire short term loans. See A.2.300 Short Term Loan Margin Result on page 863. • Execution When early expiring a short loan with margin, the following information is displayed/ calculated instead of the Rate field: Information Description Nominal Rate Defaulted from the original deal. Margin Defaulted from the original deal and cannot be modified. Margin is added to or subtracted from the Nominal Rate to get the Deal Rate. Deal Rate Rate at which the early expiration is done. Defaulted from the original deal. When a transaction being early expired has margin cashflows (i.e. instrument has feature Short Term Loan Margin), the margin accrued from the value date of the underlying deposit until the settlement date of the early expiration is realized. • Cancellation You can undo the early expiration by canceling the early expiration transaction. 3.8.3.3 Roll over You can defer the maturity of a short-term loan/deposit to a later date. This process is referred to as a roll-over. See A.2.14 Allow Roll Over (Short Loan) on page 719. • Setup It is possible to restrict the use of the roll-over methods at instrument level (see below for methods description). It is also possible to specify the default method for the instrument. • Execution Roll-over of short-term deposits/loans can be done in four different ways. In all cases, the following information is needed to process the roll-over: Information Description Roll Over Date Date when the roll-over is executed. Value Date Date of the roll over transaction. Corresponds to the maturity date of the initial transaction. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 309 3 Debt instruments 3.8 Short term loan Information Description Roll Over Method Method used for the roll over: Settle All, Settle Interest, Delay Interest, Compound Interest, Settle Interest and Allow Increase, Capitalize Interest and Allow Increase. The outcome of the roll over depends on the chosen method, see further on in this section for more information. Nominal Amount Amount of the roll-over. This defaults to the amount left of the initial transaction but you can override this if you want to perform a partial roll-over. Additional Amount Amount to be added to the initial principal amount if you want to increase capital at roll over. This field becomes available when one of the Allow Increase roll over methods has been selected. New Nominal Amount Original nominal amount plus interest (if interest is capitalized) plus the additional amount. This field becomes available when one of the Allow Increase roll over methods has been selected. Gap Maturity Date Gap set used for supplying the available maturity periods. The maturity date for the loan/deposit. The defaulting is defined as follows: • If the parent transaction was defined with a maturity period, the roll over maturity date defaults according to that period, otherwise you have to enter the maturity date. • If the switch No Maturity Defaulting is selected at the instrument level (Roll Over page), then the maturity date of the rollover is never defaulted and you must enter it. Note: If the specified maturity date does not fall on a business day, you can choose to keep the non business day or to change it. Deal Rate (Mandatory) New interest rate for the roll-over, that is, the rate at which interest is calculated from the old maturity date until the new maturity date. By default, the rate is defaulted from the initial transaction however it is possible to disable this defaulting by selecting the switch No Rate Defaulting at the instrument level (Roll Over page). The outcome of the roll-over depends on the method chosen as follows: Method Description Settle All The initial transaction is paid in its entirety at the initial maturity date. The default nominal amount of the roll-over transaction equals the sum of the interest and principal cashflows of the initial transaction. Settle Interest The interest of the initial transaction is paid at the initial maturity date, but the principal payment is deferred. The part of the principal which is rolled over is paid back at the end of the roll-over transaction. The default nominal amount of the roll-over transaction equals the principal cashflow of the initial transaction but can be reduced (partial roll-over). Settle Interest, Allow Increase This method allows the user to provide additional capital (increase the principal) as part of the roll over process. The interest from the underlying deposit/loan is settled, and the original principal amount (plus the additional capital) is rolled over. Capitalize Interest, Allow Increase 310 This method allows the user to provide additional capital (increase the principal) as part of the roll over process. The interest from the underlying deposit/loan is capitalized (that is, realized and added to the initial nominal amount) and included with the additional capital in the roll over. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.8 Short term loan Method Description Delay Interest Nothing is paid at the initial maturity date: both the interest and principal payments are deferred. The parts of the principal and interest cashflows which are rolled over are paid back at the end of the roll-over transaction. The default nominal amount of the roll-over transaction equals the principal cashflow of the initial transaction but can be reduced (partial roll-over). Compound Interest This method is the same as Delay Interest, but the closed interest of the initial transaction is reinvested in the roll-over. New interest accrues on top of the initial transaction’s interest. The default nominal amount of the roll-over transaction equals the principal cashflow of the initial transaction but can be reduced (partial roll-over). The execution generates a new transaction with the following attributes: Nominal amount = amount (can be smaller than the initial transaction) Rate = roll-over rate Opening date = date when the roll-over is done Value date = maturity date of the initial transaction Maturity date = maturity of the roll-over Kind = Roll-over • Cancellation You can undo the roll-over by canceling the roll-over transaction. 3.8.3.4 Roll over with margins You can specify margins in case you roll over short term loans. See A.2.15 Allow Roll Over (Short Loan - Margin Result) on page 719. • Execution This roll over behaves exactly as the roll over without margins, except that instead of just the Deal Rate field, the following fields are available: • Information Description Nominal Rate Defaulted from the original deal. Margin Defaulted from the original deal. Added to or subtracted from the Nominal Rate to get Deal Rate. Cancellation You can undo the roll-over by canceling the roll-over transaction. 3.8.4 Position monitoring 3.8.4.1 Setup The presence of the valuation method feature Short Term Loan Valuation in the instrument definition determines that the instrument is valuated as a short term loan. See A.2.301 Short Term Loan Valuation on page 863. 3.8.4.2 Calculations In this section, numerical examples demonstrate how the different figures are calculated for short-term deposit/loan transactions. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 311 3 Debt instruments 3.8 Short term loan If you need more theoretical information about the method used in these calculations, see Chapter 2 Market standards and calculations on page 33. This example shows a 6 month USD deposit with a 3% Periodic Rate, with the following deal data: Setup data Instrument Date Basis Act/360 Instrument Yield Type Periodic Valuation Method Theoretical Risk Method Theoretical Valuation Date Figure Date Result IR: AI Method Linear Result IR: Accrual Method Linear Accrual Accrual Yield: Interest Type Periodic Rate Accrual Yield: Date Basis Actual/360 Result FX: Profit Method FX Forward FX Exposure Offset e_fx 0.01 IR Risk Rate e_ir 0.0001 Transaction data Opening Date 2004-06-01 Spot Date d_p 2004-06-03 Maturity Date d_m 2004-12-03 Nominal Amount c_m 1,000,000 Deal Rate r_b 3% Base Book FX Rate (EUR/USD) S_b 1.18710 Currency USD Portfolio Currency EUR Other important deal data is calculated by the system as follows: • Period t_p = (d_m - d_p) / B 0.508333333 = (2004/12/03 – 2004/06/03) / 360 • Discount Factor D_b = 1 / (1 + t_p * r_b) 0.984979069 = 1 / (1 + 0.508333333 * 0.03) • Interest Cashflow c_I = c_m * r_b * t_p 15,250.00 = 1,000,000 * 0.03 * 0.508333333 • Book Value (Local) V_b = (c_m + c_I) * D_b 1,000,000.00= (1,000,000 + 15,250) * 0.984979069 • Book Value V_bp = ROUND(V_b / S_b ,2) 842,389.02 = ROUND(1,000,000 / 1.18710 ,2) 312 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.8 Short term loan Unless otherwise stated, the figure date used in the calculations is 2004-08-17. On this date, the market data is as follows: Market data on 2004-08-17 Figure Date d_f 2004-08-17 Days to Spot d_fs 2 Interest Rate r_f 1.105695% Discount Rate r_d 1.044985% FX Spot Rate S 1.20000 FX Spot CCY Base Rate S_p 1.2 Other figures are calculated by the system as follows: • Days to Maturity = d_m - d_f 108 = 2004/12/03 – 2004/08/17 • Time to Maturity t_m = (d_m - d_f) / B 0.30000 = 108 / 360 • Time to Spot t_s = d_fs / B 0.00555556 = 2 / 360 • Market Value Discount Factor D_V = D_s * D_I = 0.9966917723 • Present Value Discount Factor D_P = D_s * D_I = 0.9966917723 • Market Value Spot Discount Factor D_s = EXP(-t_s * r_d) = 0.9999419470 • Discount Factor From Spot D_I =EXP(-(t_m - t_s)* r_f) = 0.9967496366 3.8.4.2.1 Valuation figures The valuation method commonly used for a short-term loan/deposit is the Theoretical method. • Principal flow figures Local Market Value V_lp = c_m * D_V 996,691.77 = 1,000,000 * 0.9966917723 Market Value V_p = V_lp / S 830,576.48 = 996,691.77 / 1.200 Clean Market Value CMV_p = V_p / D_s 830,624.70 = 830,576.48 / 0.9999419470 • Interest flow figures Local Market Value V_li = c_I * D_V 15,199.55 = 15,250 * 0.9966917723 Market Value V_i = V_li / S 12,666.29 = 15,199.55 / 1.200 Clean Market Value CMV_i = (c_I * D_V / D_s - (c_I * (t_p - t_m + t_s)) / t_p) / S 7,319.80 = (15,250 * 0.9966917723 - (c_I * (0.50833333 - 0.3 + 0.00555556)) / t_p) / 1.2 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 313 3 Debt instruments 3.8 Short term loan • Transaction figures Local Market Value = V_lp + V_li 1,011,891.32 = 996,691.77 + 15,199.55 Market Value = V_p + V_i 843,242.77 = 830,576.48 + 12,666.29 Clean Market Value = CMV_p + CMV_i 837,944.50 = 830,624.70 + 7,319.80 3.8.4.2.2 Result figures The setup of the instrument impacts the way result figures are computed. • Principal flow figures Total Profit (Local) P_tlp = V_lp - V_b -3,308.23 = 996,691.77 – 1,000,000 MtoM Profit (Local) P_mlp = c_m * D_V / D_s - V_b -3,250.36 = 1,000,000 * (0.9966917723/0.9999419470) – 1,000,000 Accrued Interest (Local) I_alp = 0 Accrued Profit (Local) P_alp = 0 Other Profit (Local) P_olp = P_tlp - P_mlp -57.86 = (-3,308.23) – (-3,250.36) FX Profit P_fxp = V_b * (1 / S_p) - V_bp -9,055.68 = 1,000,000 * (1 / 1.2000) – 842,389.02 Total Profit P_tp = V_p - V_bp -11,812.54 = 830,576.48 – 842,389.02 MtoM Profit P_mp = P_mlp / S -2,708.64 = -3,250.36 / 1.2 Accrued Interest I_ap = 0 Accrued Profit P_ap = 0 Other Profit P_op = P_tp - P_fxp - P_mp -48.22 = (-11,812.54) – (-9,055.68) – (-2,708.64) • Interest flow figures Total Profit (Local) P_tli = V_li = 15,199.55 MtoM Profit (Local) P_mli = =c_I * D_V / D_s - (c_I * (t_p - t_m + t_s)) / t_p 8,783.77 = 15,250 * (0.9966917723 / 0.9999419470) – (c_I * (0.508333333 - 0.3 + 0.00555556)) / t_p Accrued Interest (Local) I_ali = c_I * (t_p - t_m) / t_p 6,250.00 = 15,250 * (0.508333333 – 0.3) / 0.508333333 Other Profit (Local) P_oli = P_tli - P_mli – I_ali 165.78 = 15,199.55 – 8,783.77 – 6,250.00 314 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.8 Short term loan Total Profit P_ti = V_i = 12,666.29 MtoM Profit P_mi = P_mli / S 7,319.80 = 8,783.77 / 1.2 Accrued Interest I_ai = I_ali / S 5,208.33 = 6,250.00 / 1.2 Other Profit P_oi = P_ti - P_mi – I_ai 138.15 = 12,666.29 -7,319.80 – 5,208.33 • Transaction figures Total Profit (Local) = P_tlp + P_tli 11,891.32 = -3,308.23 + 15,199.55 MtoM Profit (Local) = P_mlp + P_mli 5,533.40 = -3,250.36 + 8,783.77 Accrued Interest (Local) = I_ali = 6,250.00 Other Profit (Local) = P_olp + P_oli -58.75 = (-57.86) + (-0.88) FX Profit = P_fxp = -9,055.69 Total Profit = P_tp + P_ti 853.75 = -11,812.54 + 12,666.29 MtoM Profit = P_mp + P_mi 4,611.17 = -2,708.64 + 7,319.80 Accrued Interest = I_ap + I_ai 5,208.33 = 0 + 5,208.33 Other Profit = P_op + P_oi 89.93 = (-48.22) + 138.15 3.8.4.2.3 Risk figures The risk method commonly used for a short-term loan/deposit is the Theoretical method. • Principal flow figures IR Exposure 1bp E_ip = (c_m) * (-(t_m - t_s)*D_I*D_s - t_s*D_I*D_s) / S * e_ir -24.92 = 1,000,000*(-(0.3-0.005555556)*0.9967496366*0.9999419470-0.005555556*D_I*D_s) /1.2*0.0001 FX Exposure E_fxp = V_p * e_fx 8,305.76 = 830,576.48 * 0.01 Effective Duration U_eff = -E_ip / V_p / 0.0001 0.300000 = -(-24.92) / 830,576.48 / 0.0001 • Interest flow figures IR Exposure 1bp E_ipi = (c_I) * (-(t_m - t_s)* D_I * D_s - t_s * D_I * D_s) / S * e_ir -0.38 = 15,250.00 *(-(0.3 - 0.005555556) * 0.9967496366 * 0.9999419470 - t_s * D_I * D_s) / 1.2 * 0.0001 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 315 3 Debt instruments 3.9 Discount paper FX Exposure E_fxi = V_i * e_fx 126.66 = 12,666.29 * 0.01 Effective Duration U_eff = -E_ipi / V_i / 0.0001 0.300000 = -(-0.38) / 12,666.29 / 0.0001 • Transaction figures IR Exposure 1bp = E_ip + E_ipi -25.30 = (-24.92) + (-0.38) FX Exposure = E_fxp + E_fxi 8432.43 = 8,305.76 + 126.66 Effective Duration U_eff = -(E_ip + E_ipi) / (V_p + V_i) / 0.0001 0.300000 = -((-24.92) + (-0.38)) / (830,576.48 + 12,666.29) / 0.0001 3.9 Discount paper A discount paper is a short-term instrument which pays its face amount at maturity and is purchased at a discount price. Most discount papers are listed instruments. The most commonly traded discount paper is the US Treasury-Bill. 3.9.1 Instrument setup Discount papers are based on an instrument type derived from the class DISCOUNT. • Main characteristics The following basic information may be captured when defining the instrument. This information is relevant to any kind of discount paper. Information Description Currency Currency of the discount paper (that is, if it is a listed discount paper). Leave this field blank if you want to specify the currency when you enter the deal in Transaction Manager when you are defining an OTC discount paper. Date Basis Date basis of the instrument. If the date basis is not defined at instrument level, it needs to be specified separately for each transaction. Rounding parameters Method and precision used to round cashflow amounts. Yield Type Yield type of the discount paper, typically a discount rate. Transaction Sign Sign of the transaction. If the sign is not defined at instrument level, it needs to be specified separately for each transaction. Principal Subtype Type of principal or interest cashflows. Interest Subtype Issuer Issuer of the instrument. See A.2.121 Discount Paper on page 768 or A.2.122 Discount Paper OTC on page 770. – Date details For listed discount papers, you must specify the issue date and maturity date of the instrument. 316 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.9 Discount paper For OTC discount papers, you can set up maturity information. – Information Description Calendar Calendars used to calculate the maturity date. Gap Set Gap set used for supplying the available maturity periods. Maturity Date Period If defined, this maturity period is applied to each transaction. Trading unit details It is possible to define a minimum bid size or trading units of a discount paper. If a minimum denomination is defined, deal entry is available either in units or amount and TRM ensures that the amount is a multiple of the denomination size. • Quoted If you want to enter quotes for a discount paper, this must be specified at instrument level. Information Description Price Type Select Yield. Select Discount Paper to display yields and prices in Rate Monitor. Quote Handling See A.2.274 Quoted on page 849. • Valuation approach Discount papers can be valuated using either Fixed IR Valuation or Discount Valuation features. See A.2.150 Fixed IR Valuation on page 784 or A.2.123 Discount Valuation on page 770. Examples of calculations using these methods are provided in section 3.9.4 Position monitoring on page 320. It is also possible to set up: • Spot date calculation • Value date calculation to enable easy entry of forward deals with this instrument • Cashflow and transaction charge rules • Collateral • Branch codes • Quotation information. See Appendix A Features on page 713. 3.9.2 Deal capture 3.9.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a discount paper: Information Currency Description Currency of the transaction. If you specified the currency in the instrument setup (for example, for a US T-Bill), this is used as the default currency in the transaction and cannot be modified. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 317 3 Debt instruments 3.9 Discount paper Information Description Maturity Date Date for the maturity of the contract. If you enter a maturity code, the date is calculated automatically; otherwise you can enter the date manually. Maturity Code Note: For listed discount papers, the maturity date defaults from the instrument setup and cannot be changed. Value Date Date when the transaction starts. This defaults to the spot date of the transaction. Nominal Amount Amount of the discount paper. This is equal to the principal (the amount on which the interest is calculated). Units For listed discount papers, the nominal amount must be a multiple of the minimum contract size defined in the instrument setup. Deal Rate Rate used to discount the nominal amount (the book rate). In addition, the following optional information can be captured: Information Description Deal Price Deal price of the transaction (expressed as a percentage of the nominal amount) used to calculate the book value and the settlement amount. Value Date Code If the Value Date Setup feature is applied at instrument level, you can enter the value date period you want to use to calculate the value date for the transaction, for example, 3M (3 months). This can be used to compute the value date for a forward purchase of a discount paper. Note: If you specify a value date period in the instrument setup, this is used as the default in the transaction and cannot be modified: see A.2.339 Value Date Setup on page 879. Issuer Issuer of the discount paper. If Issuer is defined at instrument level, this is used by default and cannot be modified. Date Basis Date basis of the transaction. If this value is defined at instrument level, this is used by default and cannot be modified at deal entry. 3.9.2.2 Generated data • Transaction A discount paper is bought or sold at a discount price. This means that the Book Value (BV) is equal to the nominal amount discounted with the deal rate. BV = NA * D • Cashflows The following cashflows are generated: 318 – The principal/settlement cashflow is generated with amount = book value – There is only one payback cashflow (principal/payback) – There is no interest cashflow. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.9 Discount paper The figure below illustrates the cashflows which are established in TRM when a discount paper is purchased. 3.9.3 Processing This section describes the actions that can be done throughout the life of a discount paper. 3.9.3.1 Early expiration Discount papers can be matured earlier than their agreed maturity date. This process is referred to as early expiration. However, the action is only enabled for transactions that have reached a certain state in the transaction flow. • Execution The following information is needed to process the early-expiration: Information Description Opening Date Date when the early expiration is executed. By default, this is today’s date. Value Date Date when the early expiration is settled. This must be earlier than the original maturity date and later than the original value date of the initial transaction. Amount to Expire Amount to be early expired. This defaults to the amount still available to be early expired, taking into account previous partial early expirations and roll overs. Rate Rate at which the early expiration is done. The execution generates an early expiration transaction with the following attributes: Transaction sign = opposite of initial transaction Nominal amount = amount to expire Rate = early expiration rate Opening date = date when the early expiration is done Value date = date when the early expiration is settled Kind = Early Expiration The remaining attributes are inherited from the initial transaction. • Cancellation You can undo the early expiration by canceling the early expiration transaction. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 319 3 Debt instruments 3.9 Discount paper 3.9.4 Position monitoring 3.9.4.1 Setup In addition to the basic valuation setup which can be set up for every instrument (see A.2.50 Base Valuation Setup on page 734) it is possible to set up the following: Information Description AI Method It is possible to override the standard linear method in order to accrue interest differently for the valuation figures (see A.2.49 Base IR Setup on page 733, Chapter 1 Concepts on page 21, A.2.337 Valuation Curve Setup on page 878). Spread Curve It is possible to add spread curves to correspond to the credit risk (see A.2.305 Spread Curve Setup on page 865, Chapter 1 Concepts on page 21, A.2.337 Valuation Curve Setup on page 878). 3.9.4.2 Calculations - Theoretical In this section, numerical examples demonstrate how the different figures are calculated for discount papers. See Chapter 2 Market standards and calculations on page 33. This example shows a US T-Bill, with the following deal data: Setup data Instrument Date Basis Act/360 Instrument Yield Type Discount Valuation Method Theoretical Valuation Date Figure Date Risk Date Figure Date Risk Yield Type Continuous Result IR: Accrued Interest Linear Result IR: Accrual Method Linear Accrual Accrual Yield: Interest Type Periodic Rate Accrual Yield: Date Basis Actual/360 FX Exposure Offset e_fx 0.01 Transaction data Opening Date 2004-02-02 Nominal Amount c_m 1,000,000 Deal Rate r_b 3% Base Book FX Rate (EUR/USD) S_b 1.2 Maturity Date d_m 2004-07-01 Value Date d_a 2004-02-04 Currency USD Portfolio Currency EUR 320 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.9 Discount paper Other important deal data is calculated by the system as follows: • Book Value (Local) V_b = c_m * D_b 987,750.00 = 1,000,000 * 0.98775 • Book Value V_p = V_b / S_b 823,125.00 = 987,750.00 / 1.2 • Period t_p = DAYS360(d_a,d_m,TRUE) / B 0.408333333 = (2004/02/04,2004/07/01,TRUE) / 360 • Discount Factor D_b = 1 – t_p * r_b 0.98775 = 1 – 0.408333333 * 0.03 Unless otherwise stated, the figure date used in the calculations is 2004-03-01. On this date, the market data is as follows: Market data on 2004-03-01 Figure Date d_f 2004-03-01 Interest Rate r_f 1.113119% Days to Spot d_fs 2 Discount Rate r_d 1.044985% FX Conversion Rate S 1.260000 Other figures are calculated by the system as follows: • Days to Maturity = d_m - d_f 122 = 2004/07/01 – 2004/03/01 • Time to Maturity t_m = (d_m - d_f) / B 0.33888889 = 122 / 360 • Time to Spot t_s = d_fs / B 0.005555556 = 2 / 360 • Market Value Discount Factor D_V = D_s * D_I = 0.996238639 • Present Value Discount Factor D_P = D_s * D_I = 0.996238639 • Spot Discount Factor D_s = EXP(-t_s*r_d) = 0.999941947 • Spot-Maturity Discount Factor D_I =EXP(-(t_m-t_s)*r_f) = 0.996296478 Valuation figures The valuation method commonly used for a discount paper is the Theoretical method. • Local Market Value V_l = c_m * D_V 996,238.64 = 1,000,000 * 0.996239 • Market Value V = V_l / S 790,665.59 = 996,238.64 / 1.2600 • Clean Market Value = V / D_s 790,711.49 = 790,665.59 / 0.999941947 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 321 3 Debt instruments 3.9 Discount paper Result figures The setup of the instrument impacts the way result figures are computed. • Total Profit (Local) P_tl = V_l – V_b 8,488.64 = 996,238.64 – 987,750.00 • MtoM Profit (Local) P_ml = -c_m * ((1 - r_b * (t_m - t_s)) - (D_I)) 6,296.48 = 1,000,000*((1 - 0.03 *(0.33888889-0.005555556)) - 0.996296478 • Accrued Profit (Local) P_al = = -c_m * (D_b -(1 - (t_m - t_s) * r_b)) 2,250.00 = -1,000,000*(0.98775-(1-(0.33888889-0.005555556)*0.03)) • Other Profit (Local) P_ol = P_tl - P_ml - P_al -57.84 = 8,488.64 – 6,296.48 – 2,250 • FX Profit P_fx = V_b * (1/S - 1/S_b) -39,196.43 = 987,750.00*(1 / 1.260000 – 1 / 1.20000) • Total Profit P_t = V – V_p -32,459.41 = 790,665.59 – 823,125.00 • MtoM Profit P_m = P_ml / S 4,997.20 = 6,296.48 / 1.260000 • Accrued Profit P_a = P_al / S 1,785.71 = 2,250.00 / 1.260000 • Other Profit P_o = P_t - P_m - P_a - P_fx -45.90 = -32,459.41 - 4,997.20 - 1,785.71 – (-39,196.43) Risk figures The risk method commonly used for a discount paper is the Theoretical method. • IR Exposure 1bp E_ip = c_m * (-(t_m-t_s) * D_I*D_s - t_s *D_I* D_s) /S * 0.0001 -26.79 = 1,000,000*(-(0.33888889-0.005555556)*0.996296478*0.999941947-t_s*(D_I*D_s)/1.26*0.0001 • IR Exposure 1bp from spot E_is = c_m * (-(t_m - t_s) * D_I) / S * 0.0001 -26.357050 = 1,000,000 * (-(0.33888889-0.005555556)*0.996296478 / 1.26 * 0.0001 • FX Exposure E_fx = e_fx * V 7,906.66 = 0.01 * 790,665.59 • Effective Duration U_eff = -E_ip / V / 0.0001 0.338889 = -(-26.79) / 790,665.59 / 0.0001 3.9.4.3 Calculations - Discount Yield Discount yield is calculated from quoted market value at spot, using Yield Type and Date Basis defined in IR Exposure page in the Instrument Editor: Equation 3-11 Discount yield where – 322 V is market value at spot, A is the amount © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.9 Discount paper – t v is time between spot date and value date calculated using the IR Exposure date basis – R[] is the function that converts discount factor into rate, according to the Yield Type defined for IR Exposure . 3.9.4.3.1 Example Instrument data • Discount Paper page Date Basis Actual/365 Interest Type Periodic Rate Price Rounding 0.001 (3 decimal places) pr = 3 • Dates page Maturity Date • • 2009-08-05 Base Valuation page Method Quoted Switches To Spot IR Exposure page Date Basis Actual/365 Yield Type Continuous Yield Switches To Spot Transaction data Nominal Amount A = 100000 Valuation data Valuation Date 2008-08-05 Figure Market Quote rm = 5 d v = 365 ds = 2 Days to Maturity Date Days to Spot Calculated data • Price (P) Let [ X ] k mean rounding to k decimal places. Then Equation 3-12 Discount Yield Price = 95.263 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 323 3 Debt instruments 3.9 Discount paper • Discount Yield (y) Using Equation 3-13 Discount Yield: Discount Yield (y) = 0.994520547945206 The discount yield (Figure Interest Rate) is: Equation 3-14 Discount Yield: Figure Interest Rate = 0.0487960741031 • IR Exposure (E1) Figure Risk Value is: Vr = A = 1000000 Sensitivity of discount factor is (for continuous yield): Equation 3-15 Discount Yield: IR Exposure (E1) = -0.947410109589 Figure IR Exposure 1bp is: Equation 3-16 Discount Yield: IR Exposure (1bp) E 1 = V r D r × 0.0001 = -94.7410109589 3.9.4.4 Calculations - Modified Duration / Effective Duration The following numerical example demonstrates how Modified Duration and Effective Duration figures are calculated for depo/discount papers. For more information about Duration key figures, see 2.3.4.9 Duration figures on page 142. 3.9.4.4.1 Example: Depo/Discount Paper The example in this section shows an overnight paper of 100,000,000 at 0.70 with a price of 99,998,088.89. Transaction data • On November 9th, the Principal cashflow was equal to -99 998 088.89 • On November 10th, the Principal cashflow was equal to 100,000,000.00 324 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.9 Discount paper Valuation data Valuation Date 2009-11-09 Valuation Mode Theoretical Date Basis Actual/365 Risk figures • Principal cashflow (risk date = 2009-11-09) Equation 3-17 Time to maturity of the cashflow dr – dv t i = ---------------- = 0 365 • Present Value Discount Factor Dp = 1 Present Value Vp= -99,998,088.89 IR Exposure E { i1 } = 0 Amortization cashflow (risk date = 2009-11-10) Equation 3-18 Time to maturity of the cashflow dr – dv t i = ---------------- = 1 ⁄ 365 365 Present Value Discount Factor Dp = 0.999964445709 Present Value Vp = -99,996,444.57 IR Exposure E { i1 } = – V p × t i × 0.0001 = 27.39628618 Transaction figures IR Exposure E { i1 } = – V p × t i × 0.0001 = 0 + 27.39628618 = 27.39628618 Present Value Modified Duration Effective Duration Vp = -99,998,088.89+99,996,444.57 = -1644.3 Sett Pos 1000 × [ Ei1 + E i1 ] 10000 × [ 27.39628618 ] U Mod = ------------------------------------------------------= ------------------------------------------------------------------------------------------------------------- = 0.002739704 Sett Pos 0.5 × ( – 99 , 998, 088.89 + 99, 996, 444.57 ) 0.5 × ( V p + Vp ) – E { i1 } – 27.39628618 U eff = ⎛⎝ ----------------⎞⎠ × 10000 = ⎛⎝ ----------------------------------⎞⎠ × 10000 = 166.6117372 Vp – 1644.3191 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 325 3 Debt instruments 3.10 Loan 3.10 Loan In TRM, loans are agreements to lend or borrow money for a medium/long term with multiple interest (and potentially principal) payments occurring during the life of the deal. The key concept concerning loans is that of the cashflow schedule. Several schedules must be attached to a loan deal, and they drive the generation of the cashflow structure for the deal. For the simplest types of loans, two schedules are associated with the deal: one schedule for interest flows; and one schedule for principal flows. For more complex deals, there will be additional schedules for optional events, additional interest cashflows, and so on. Loans belong to the instrument class LOAN. This class covers a diverse set of instruments: from fixed annual interest / bullet repayment loans to more complex, exotic structures. Therefore, this chapter is organized into the following sections: – How TRM handles fixed-rate loans – How TRM deals with floating-rate loans – A list of more exotic deals that can be set up in TRM. 3.10.1 Fixed-rate loan Fixed-rate loans pay interest at a pre-defined (fixed) rate. 3.10.1.1 Instrument setup • Loan main characteristics The following basic information may be captured when defining the instrument. This information is relevant to any kind of fixed-rate loan. Information Currency Description Currency of the loan. Leave this field blank if you want to specify the currency when you enter the deal in Transaction Manager. Transaction Sign Sign of the transaction. If the sign is not defined at instrument level, it needs to be specified separately for each transaction. AI Method Method used to calculate accrued interest if interest starts to accrue before the value date of the transaction. Settlement Switches Dirty Price: Switch on to use the dirty price for the instrument, that is, to include accrued interest in the instrument’s price. Par: Switch on in order to have the deal price defaulted to 100. Rounding Parameters Method and precision used to round cashflow amounts. Structure Schedule template to be used for the loan. If a structure is not defined at instrument level, a schedule needs to be specified for each transaction. Usually the structure is defined at the instrument level. If this is not the case, then you have to define it for each transaction at transaction level. See A.2.202 Generic Loan on page 812. 326 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.10 Loan • Maturity definition It is possible to set up maturity information at instrument level. Information Description Calendar parameters Calendars used to calculate the maturity date. Gap Set Gap set used for supplying the available maturity periods. Maturity Date Period If defined, this maturity period is applied to each transaction. See A.2.230 Maturity Date Setup on page 827. • Selectable cashflow structures With this option, you can limit the choice of schedules available to assign to a loan in Transaction Manager by associating one or several schedule template groups to the instrument. At deal entry, only the templates belonging to these groups will be available for selection. If a cashflow structure is already set up in the instrument’s main characteristics, it will override any schedule groups. See A.2.293 Schedule Template Setup on page 859. It is also possible to set up: • Spot day calculations • Manual charges • Cashflow and transaction charge rules • Branch codes. See Appendix A Features on page 713. 3.10.1.2 Deal capture Depending on the selected cashflow structure, the information needed to deal the instrument and the generated cashflows are very different. The transaction level information is the same. 3.10.1.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a deal on a fixed rate loan: Information Currency Description Currency of the transaction. If you specified the currency in the instrument setup, this is used as the default currency in the transaction and cannot be modified. Maturity Date Date for the maturity of the contract. If you use maturity date setup, the date is calculated automatically from the selected maturity period, otherwise you can enter the date manually. Nominal Amount Amount of the loan. This is equal to the principal (the amount on which the interest is calculated). Deal Price Deal price of the transaction (expressed as a percentage of the nominal amount) used to calculate the book value and the settlement amount. In order to have the deal price defaulted to 100, you should set the settlement switch Par in Instrument Editor. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 327 3 Debt instruments 3.10 Loan These values alone are not sufficient to define the deal. To complete the creation of a fixed-rate loan, the cashflow structure of the deal also needs to be specified, either in the instrument setup, or at deal entry, by applying a schedule template. The following sections explain how the system handles standard fixed-rate cashflow structures. 3.10.1.2.2 Generated data • Book Value (clean price): BV = A * p /100 where: A = Nominal Amount p = deal price • Book Value (dirty price): BV = (A * p /100) - AI where: A = Nominal Amount p = deal price AI = Accrued Interest 3.10.1.2.3 Bullet repayment structure A fixed-rate loan with periodic interest and total repayment of the principal at maturity represents a bullet repayment structure. • Input data To define this kind of structure, a template is required which contains at least one schedule for fixed-rate interest flows, and one schedule for repayment flows. TRM provides a pre-defined system template designed for this: see B.2.1.1.21 Fixed, Bullet Repayment on page 894. For each set of cashflows, the following information must be supplied at deal entry: – – Interest flows Information Description Frequency Method and Period The frequency method/period for the interest cashflows (for example, Years/1 generates one interest flow per year). Interest Rate The fixed interest rate (for example, 5%). Repayment flows No information required. • Generated data – Schedule When a template is selected, one schedule is created for each item in the template. Some of the values are automatically defaulted from the transaction parameters (see Appendix B Schedules on page 883), while others can be modified at deal entry (see above). 328 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.10 Loan – Cashflows For a fixed-rate loan with repayment at maturity, the cashflows generated are as follows: 3.10.1.2.4 Fixed-rate loan - amortizing structure A fixed-rate loan with periodic interest and repayment of the principal in several steps during the deal represents an amortizing structure. • Input data To define this kind of structure, a template which contains at least one schedule for fixed-rate interest cashflows, and one schedule for repayment cashflows is required. TRM provides a pre-defined system template (B.2.1.1.21 Fixed, Bullet Repayment on page 894) designed for this purpose. For each set of cashflows, the following information must be supplied at deal entry: – – Interest flows Information Description Frequency Method and Period The frequency method/period for the interest cashflows (for example, Years/1 generates one interest flow per year). Interest Rate The fixed interest rate (for example, 5%). Repayment flows Information Description Frequency Method and Period The frequency method/period for the repayment cashflow (for example, Times/Year-1 means that one repayment will occur every year). Calculation Method and Repayment % Defines how the repayments have to be generated. Start Date • For example, using percentage 10% as the method means 10% of the initial capital at each repayment, with the remaining capital being repaid at maturity. Start date can be moved forward in order to start amortizing later. Generated data – Schedule When a template is selected, one schedule is created for each item in the template. Some of the values are automatically defaulted from the transaction parameters, while others can be modified at deal entry. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 329 3 Debt instruments 3.10 Loan – Cashflows For an amortizing loan, the cashflows generated are as follows: 3.10.1.2.5 Fixed-rate loan - fixed annuity structure A fixed-rate loan with a fixed amount of principal and interest over the life of the deal represents a fixed annuity structure. • Input data To define this kind of structure, TRM provides a pre-defined system template (B.2.1.1.20 Fixed, Annuity Repayment on page 894) designed for this purpose. For each set of cashflows, the following information must be supplied at deal entry: – – Interest flows Information Description Frequency Method and Period The frequency method/period for the interest cashflows (for example, Years/1 generates one interest flow per year). Interest Rate The fixed interest rate (for example, 5%). Repayment flows No information required. • Generated data – Schedule When a template is selected, one schedule is created for each item in the template. Some of the values are automatically defaulted from the transaction parameters (see Appendix B Schedules on page 883), while others can be modified at deal entry (see above). 330 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.10 Loan – Cashflows For a fixed-annuity loan, the cashflows generated are as follows: 3.10.1.2.6 Fixed-rate loan - irregular annuity With an irregular annuity, the flows are computed equally throughout the life of the loan except for the final payment, which is adjusted according to how much of the loan remains outstanding. • Input data To define this kind of structure, the following information must be supplied at deal entry in the Schedule view: – • Principal schedule Information Description Interest Rate The fixed interest rate (for example, 5%). Generated data – The annuity is computed equally across all flows, except the last one. – The remaining principal is repaid on the final cashflow (100 - rate). 3.10.1.2.7 Fixed-rate loan - margin It is possible to specify a margin when entering a fixed rate loan. As well as the standard fixed-rate loan input data and generated cashflows there are input data and generated cashflows for margins. • Input data For margin loans, you need to attach a secondary schedule Margin to the interest schedule and specify the margin in the Spread schedule field (of the Margin schedule). • Generated data – Margin flows A Margin cashflow is generated if a margin schedule is attached to the transaction and a margin rate is entered (in the Spread field). The Margin cashflow is only used for calculating Margin Profit. The Margin cashflow is calculated in the same way as the interest, using the captured margin rate. This cashflow effectively represents the margin rates contribution in the final interest amount. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 331 3 Debt instruments 3.10 Loan 3.10.1.3 Processing This section describes the actions that can be done throughout the life of a loan. 3.10.1.3.1 Early expiration Loans can be matured earlier than their agreed maturity date. This process is referred to as early expiration. • Execution Early expiration of loans requires the following information: Information Description Opening Date Date when the early expiration is executed. By default, this is today’s date unless a Fixing/Action Date was specified at transaction level. Value Date Date when the early expiration is settled. This must be earlier than the original maturity date and later than the original value date of the initial transaction. Settlement Date Date when early-expiration price is paid. Amount to Expire Amount to be early expired. This defaults to the amount still available to be early expired, taking into account previous partial early expirations and roll overs. Price The premium or discount the early expiration is made at. Settlement Price Method Clean Price: AI is created as Payable cashflow and P/L flow is the difference between early-expiration price and original deal price. Dirty Price: AI is created as Not Payable cashflow, and P/L flow is reduce by the AI amount. Accrued Interest The accrued interest that will be paid in the early expiration transaction. This value can be modified. Options • Amortize P/L Switch on to amortize the P/L from the value date until the original maturity date. If this switch is off, the Sell P/L flow created by the early expiration (arising from Net Amount – Accrued Interest) occurs on the early expiration value date. • No Fee Realization Switch on to continue to amortize fees to maturity. For example, this can be used in the case of an asset swap, which mirrors the issue fees, to keep the fees amortizing even when the asset swap is fully unwound. If this switch is off, at early expiration, the fees that were amortizing until the maturity date are closed. • Delay Interest (only available when the settlement price method is set to Clean Price) Switch on to delay the accrued interest payment to the next interest payment date. The execution generates an early expiration transaction with the following attributes: Transaction sign = opposite of initial transaction Nominal amount = amount to expire Price = early expiration rate Opening date = date when the early expiration is done Value date = date when the early expiration is settled Kind = Early Expiration The remaining attributes are inherited from the initial transaction. The early expiration transaction generates closing cashflows for the initial transaction and P/L cashflows if there is a difference between the early expiration price and the original deal price. 332 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.10 Loan • Cancellation You can undo the early expiration by canceling the early expiration transaction. 3.10.1.3.2 Roll over You can defer the maturity of a loan to a later date. This process is referred to as a roll-over. See A.2.9 Allow Roll Over on page 716. • Setup It is possible to restrict the use of the roll-over methods at instrument level (see below for methods description). It is also possible to specify the default roll over method for the instrument. • Execution Roll-over of loans can be done in four different ways. In all cases, the following information is needed to process the roll over: Information Description Roll Over Date Date when the roll over is executed. Maturity Date New maturity date for the loan. This must be later than the maturity date of the initial transaction. The maturity date is calculated automatically from the maturity period of the initial transaction. Nominal Amount Amount of the roll over. This defaults to the amount left of the initial transaction but you can override this if you want to perform a partial roll over. Additional Amount Amount to be added to the initial principal amount if you want to increase capital at roll over. This field becomes available when one of the Allow Increase roll over methods has been selected. New Nominal Amount Original nominal amount plus interest (if interest is capitalized) plus the additional amount. This field becomes available when one of the Allow Increase roll over methods has been selected. Rate A new interest rate for the roll over, that is, the rate at which interest is calculated from the old maturity date until the new maturity date. By default, the rate displayed is taken from the interest schedule information, and is used to generate the interest schedule of the new roll over transaction. Roll Over Method Method used for the roll over. The outcome of the roll-over depends on the method chosen as follows: Method Description Settle All The initial transaction is paid in its entirety at the initial maturity date. The default nominal amount of the roll over transaction equals the sum of the interest and principal cashflows of the initial transaction. Settle Interest The interest of the initial transaction is paid at the initial maturity date, but the principal payment is deferred. The part of the principal which is rolled over is paid back at the end of the roll over transaction. Settle Interest, Allow Increase This method allows the user to provide additional capital (increase the principal) as part of the roll over process. The interest from the underlying loan is settled, and the original principal amount (plus the additional capital) is rolled over. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 333 3 Debt instruments 3.10 Loan Method Description Capitalize Interest, Allow Increase This method allows the user to provide additional capital (increase the principal) as part of the roll over process. Delay Interest Nothing is paid at the initial maturity date: both the interest and principal payments are deferred. The parts of the principal and interest cashflows which are rolled over are paid back when the first interest payment of the roll over transaction occurs. Compound Interest This method is the same as Delay Interest, but the closed interest of the initial transaction is reinvested in the roll over. New interest accrues on top of the initial transaction’s interest. The interest from the underlying loan is capitalized (that is, realized and added to the initial nominal amount) and included with the additional capital in the roll over. The execution generates a new transaction with the following attributes: Nominal amount = amount (can be smaller than initial one) Rate = roll-over rate Opening date = date when the roll-over is done Value date = maturity date of the initial transaction Maturity date = maturity of the roll-over Kind = Roll-over • Cancellation You can undo the roll over by canceling the roll over transaction. 3.10.1.3.3 Trade assignment Trade assignments are changes of ownership of transactions. • Execution Change of ownership during the life of a transaction can be performed in two steps: – Right-click the existing transaction and choose Assignment(sale) action. This action closes the existing transaction, and when required, exchanges settlement amounts between the old and new owners of the transaction. – Right-click the generated transaction and choose Assignment (purchase) action. This action creates the new transaction with the new owner. Assignment (sale) of a transaction to another client requires the following information: Information Description Opening Date Date when the early expiration is executed. By default, this is today’s date unless a Fixing/Action Date was specified at transaction level. Value Date Date when the early expiration is settled. This must be earlier than the original maturity date and later than the original value date of the initial transaction. Settlement Date Date when assignment price is paid. Amount Left Read-only. Remaining amount of the initial transaction. Assignee New owner of the transaction Settlement Price Method Clean Price: AI is created as Payable cashflow and P/L flow is the difference between assignment price and original deal price. Dirty Price: AI is created as Not Payable cashflow, and P/L flow is reduce by the AI amount. Currency 334 Read-only. Currency of loan. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.10 Loan Information Description Settlement Price The price of the assignment. Accrued Interest Read-only. Interest accrued on specified date. Options • Amortize P/L Switch on Amortize P/L to amortize the P/L from the value date until the original maturity date. If this switch is off, the Sell P/L flow created by the assignment (arising from Net Amount – Accrued Interest) occurs on the assignment value date. • No Fee Realization Switch on No Fee Realization so that fees keep amortizing to maturity. If this switch is off at assignment, the fees that were amortizing until the maturity date are closed. Execution generates an Assignment transaction with following cashflows: – Cashflows to close the future cashflows of the original transactions (closing of cashflows where payment date is after the assignment value date) – Settlement flows between the assignor and the assignee, reflecting the settlement amounts. The generated transaction has the following attributes: Information Description Transaction Sign Opposite of the original transaction sign. Nominal Amount Amount to assign. Opening Date Opening date of action. Value Date Value date of action. Kind Assignment. The original transaction remains unchanged. The assignee can then select the Assignment (purchase) action on the generated closing transaction. Selecting the portfolio from the resulting dialog generates a new transaction, reflecting the future cashflows of the original transaction and settlement flows between assignee and assignor. Note: The Counterparty field is open, to allow Counterparty change if required. • Cancellation You can undo the assignment action by canceling the generated assignment transaction. 3.10.1.3.4 Changing the counterparty of a transaction You can terminate the existing transaction against one counterparty and reopen it against another counterparty. The following information is required: Information Description Opening Date Date when the transfer is executed. By default, this is today’s date unless a Fixing/Action Date was specified at transaction level. Value Date Date when the transfer is settled. This must be earlier than the original maturity date and later than the original value date of the initial transaction. Counterparty New counterparty for the transaction. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 335 3 Debt instruments 3.10 Loan A transaction will be generated whose Kind is Counterparty Conversion. The characteristics of the new transaction will be the same than the old one, except for Counterparty and opening/value date. This action generates closing cashflows for the future cashflows from the original transaction, and futures cashflows between the original owner and the new counterparty. No settlement/result flows will be affected to the generated transaction, as the assignment is between the counterparties only. The generated transaction can be canceled to undo the action. 3.10.1.3.5 Transferring transactions between portfolios You can transfer the transaction from one portfolio to another. This is effectively a sale in one portfolio and a purchase in another. Portfolio transfer of an existing transaction can be performed at transaction level by right-clicking and choosing Transfer. Transfer of a transaction to another portfolio requires the following information: Information Description Opening Date Date when the transfer is executed. By default, this is today’s date unless a Fixing/Action Date was specified at transaction level. Value Date Date when the transfer is settled. This must be earlier than the original maturity date and later than the original value date of the initial transaction. Settlement Date Payment date for settlement flows. New Portfolio New portfolio for the transaction No Settlement switch If On, the generated settlement amount is marked as pseudo (i.e. not bookable, not payable). Settlement Price Method Clean Price: AI is created as Payable cashflow and P/L flow is the difference between transfer price and original deal price. Dirty Price: AI is created as Not Payable cashflow, and P/L flow is reduce by the AI amount. Currency Read-only. Currency of loan. Settlement Price The price of the assignment. Accrued Interest Read-only. Interest accrued on specified date. Options • Amortize P/L • No Fee Realization Two Transfer transactions are generated: 1. A sale is created in the source portfolio of the transfer, i.e. closing cashflows of the original transaction and settlement flows (real or pseudo, depending on inputs). 2. A purchase is then created in the receiving portfolio, with future flows and settlement flows (real or pseudo, depending on inputs). The original transaction remains unchanged. The user can undo the portfolio transfer action by canceling the generated transactions. 3.10.1.3.6 Transaction Conversion To allow schedule conversion at predefined dates during transaction's life. • Setup This process is available on the transaction if the Transaction Conversion feature is associated with the instrument. See A.2.325 Transaction Conversion on page 873. 336 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.10 Loan Then, the user is allowed to attach the Conversion schedule to the existing schedule and to define conversion events and converted schedules. • Execution When conversion schedules are defined, the user is allowed to execute generated conversion events. The conversion inputs are displayed. See A.2.325 Transaction Conversion on page 873. The execution generates a conversion transaction with the following attributes: – Kind: Conversion – Opening Date: Conversion opening date – Value Date: Conversion value date. The conversion transaction generates closing cashflows for the initial transaction. If the conversion price is different to the original deal price, then a P/L flow is generated, showing the differences between the conversion price and the original deal price. 3.10.1.4 Position monitoring 3.10.1.4.1 Setup The cashflow discounting method (periodic, continuously compounded) used in IR risk calculation depends on the instrument set up. By default, TRM uses the valuation curve interpolation settings (IR Quote and Yield Curve Editor Interpolation page). For example, if the interpolation settings are set up with Interest Type Continuous Yield, then risk calculations use continuously compounding discounting of the cashflows. If IR Exposure is set up at the instrument level, then TRM uses these settings. For example, if IR exposure is set up with Yield Type Periodic, then risk calculations use periodic discounting of the cashflows. For more information about risk calculations, see 2.3 Key-figures on page 112. 3.10.2 Floating-rate loan Interest cashflows for a floating-rate loan are linked to a market reference. The market reference has to be observed for each interest period. The fixing of the interest rate can be done before interest starts accruing (classical in-advance fixing), or at the end of the period (in-arrears fixing). 3.10.2.1 Instrument setup Floating-rate loans are set up in a similar way to fixed-rate loans, but refer to a different type of cashflow structure: the structure you choose needs to generate floating interest cashflows. You can pre-define the cashflow structure in the main characteristics of the loan, or restrict the available schedule templates at deal entry using the Schedule Groups option. See A.2.293 Schedule Template Setup on page 859. 3.10.2.2 Deal capture Depending on the selected cashflow structure, the information needed to deal the instrument and the generated cashflows are very different. The transaction level information is always the same. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 337 3 Debt instruments 3.10 Loan 3.10.2.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a deal on a floating-rate loan: Information Description Currency Currency of the transaction. If you specified the currency in the instrument setup, this is used as the default currency in the transaction and cannot be modified. Maturity Date Date for the maturity of the contract. If you use maturity date setup the date is calculated automatically from the selected maturity period, otherwise you can enter the date manually. Nominal Amount Amount of the loan. This is equal to the principal (the amount on which the interest is calculated). Deal Price Deal price of the transaction (expressed as a percentage of the nominal amount) used to calculate the book value and the settlement amount. 3.10.2.2.2 Generated data • Book Value (clean price): BV = A * p /100 where: A = Nominal Amount p = deal price • Book Value (dirty price): BV = (A * p /100) - AI where: A = Nominal Amount p = deal price AI = Accrued Interest These values alone are not sufficient to define the deal. To complete the creation of a floating-rate loan, the cashflow structure of the deal also needs to be specified, either in the instrument setup, or at deal entry. See Appendix B Schedules on page 883. 3.10.2.2.3 Bullet repayment structure For a floating-rate loan, a template which contains at least one schedule for floating-rate interest cashflows and one schedule for repayment flows is required. • Input data For each set of cashflows, the following information must be supplied: – 338 Interest flows Information Description Frequency Method and Period The frequency method/period for the interest cashflows (for example, Years/1 generates one interest flow per year). Interest Rate The first rate of interest (for example, 5%), if known. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.10 Loan Information Description Fixing parameters Formulae used to evaluate the rate. This is known as an "expression" in TRM. Typical expressions would be, for example, "ir", referring to an ir rate market reference (yield curve) or "ir + spread%". See Appendix D Expressions on page 917. Yield curve to be used in the expression. Period (for example, 3M or 6M) and the scenario used to get the rates when fixing the cashflows. Define if the fixing will be done in-advance or in-arrears and enter the offset in days. – Repayment flows Information Description Frequency Method and Period The frequency method/period for the repayment cashflow (for example, Bullet means that the loan will be entirely repaid at maturity). It is also possible to define amortizable or accreting principal cashflows. Some other parameters in the schedule can be adjusted to modify the way the cashflows are generated. See Appendix B Schedules on page 883. • Generated data – Schedule When a template is selected, one schedule is created for each item in the template. Some of the values are automatically defaulted from the transaction parameters (see Appendix B Schedules on page 883), while others can be modified at deal entry (see above). – Cashflows For a floating-rate loan with repayment at maturity, the cashflows generated are as follows: 3.10.2.3 Processing Floating-rate loans are processed in a similar way to fixed-rate loans, but with the following additional process. 3.10.2.3.1 Interest fixing For a floating-rate loan, the amount of each interest flow has to be determined before it is paid: this process is known as fixing. • Execution Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 339 3 Debt instruments 3.10 Loan Each interest cashflow of a floating-rate deal contains some parameters that define how its amount is fixed. – The fixing period determined by a from/to date value pair indicates when the amount of the flow has to be fixed; it can be before the interest starts accruing (in-advance fixing), or before the payment of the interest (in-arrears fixing). – The fixing parameters (expression, rate, spread, and so on) that define how the fixing rate is calculated. – An "expression value" which is informative and gives the current value of the expression. Executing the fixing modifies the cashflow as follows: Marks it as being fixed Sets the fixing date Stores the rate of the market reference used for fixing Stores the effective interest rate (nominal rate) on the cashflow Sets the amount of the cashflow The fixing process can be performed in four ways in TRM: the process which is triggered is exactly the same in the four cases, the only difference being the quantity of deals or cashflows which are affected. The four ways of fixing are as follows: – Directly on the deal: the fixing only affects the deal – Directly on an individual cashflow in the Cashflow view: the fixing affects an individual cashflow – On the instrument (in Instrument Editor): the fixing affects all the deals on this instrument – Using an automated activity (Fixing Transaction Cashflow): potentially all deals which have to be fixed for a particular date may be affected. See the TRM User Guide for general information on running activities, and also specific information on the activity parameters. If the Fixing action is carried out directly on an individual cashflow using the second method, it is possible to modify the fixing values. When the fixing quote is modified, this updates both the nominal rate and the amount accordingly. Similarly, if the nominal rate is modified, the amount is affected (but not the fixing quote). It is also possible to modify the amount independently from the other fixing values. This may be necessary when rounding differences arise, for example. • Cancellation It is possible to cancel the fixing either manually, using the Undo Fixing action; or automatically, using the Fixing Transaction Cashflow - Undo activity. See the TRM User Guide for general information on running activities, and also specific information on the activity parameters. 3.10.3 Other loan structures All the cashflow structures available for bonds are also available for loans (see 3.1 Bond on page 215). You can also find information about all system-defined cashflow structures available in TRM in Appendix B Schedules on page 883. Some of the structures that can be generated for a loan are described in this section. 3.10.3.1 Dual currency structure • Regular dual-currency: The currency in which the instrument is issued (principal currency) differs from the currency in which the principal is repaid (redemption currency). The currency of the interest flow can be either the principal currency or the redemption currency. The FX rate to apply can be known (determined on the date of issue) or fixed later (determined a number of days before the payment date of the interest cashflow). 340 © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.10 Loan • Reverse dual-currency: The principal currency and redemption currency are identical, but interest payments are in a different currency. The FX rate used for the calculation of interest is either known when the loan is agreed or fixed later. 3.10.3.1.1 Instrument setup Instrument setup for a dual-currency loan is similar to that of a standard loan (see 3.10 Loan on page 326), except for the following: • Loan main characteristics Information Description AI Method The method used by the system to compute settlement accrued interests. For dual-currency loans, there are two types of dual-currency methods: • Dual Currency Estimated • Dual Currency Last. See 2.1.6.1 Accrued interest calculations on page 67 for more information. • Dual-currency attributes This information defines the characteristics of the principal cashflow. Leave these fields blank if you want to specify the details when you enter the deal. Information Description Settlement Currency Currency in which the principal cashflow is settled. Settlement FX Rate Rate used to calculate the settlement amount of the principal cashflow. Need Fixing Specify whether the FX rate needs to be fixed: • Select No when the FX rate is known • Select Yes, FX Rate when the FX rate is unknown. The old value "Yes, Unmarked" is not used. Fixing Offset Number of days’ offset allowed, that is, the difference in days between the fixing date and the due date (default = 0). Fixing Max. Offset Maximum number of days’ offset allowed. See A.2.125 Dual Currency on page 771. • FX fixing If the settlement FX rate is unknown when the deal is entered, then this feature needs to be included in the instrument definition. See A.2.174 FX Fixing on page 797. 3.10.3.1.2 Deal capture • Input data Deals on dual-currency loans are captured in a similar way to those on a standard loan. To complete the creation of a dual-currency loan transaction, the cashflow structure of the deal also needs to be specified, either in the instrument setup, or at deal entry, by applying a schedule template. The following system templates are provided for dual-currency structures: Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 341 3 Debt instruments 3.10 Loan – Dual-Currency Known FX This is a fixed bullet structure used for dual currency instruments when the FX rate is known when the deal is entered. For both interest and redemption schedules you can choose a different settlement currency and specify the settlement FX rate. See B.2.1.1.15 Dual Currency, Known FX Rate on page 893. – Dual-Currency Known FX Floating This is a floating bullet structure used for dual currency instruments when the FX rate is known when the deal is entered. For both interest and redemption schedules you can choose a different settlement currency and specify the settlement FX rate. See B.2.1.1.16 Dual Currency, Known FX Rate, Floating on page 893. – Dual-Currency Unknown FX This is a fixed bullet structure used for dual currency instruments when the settlement FX rate is not known beforehand. For both interest and principal schedules you can choose a different settlement currency. See B.2.1.1.17 Dual Currency, Unknown FX Rate on page 893. Note that this template covers fixed interest rates only. For floating rates, you also have to use the Fixing Dates secondary template (see B.2.1.2.15 Fixing Dates on page 903). You can choose one of these templates or any other template derived from them. Once the template is applied to the transaction, the schedules are created and it is then possible to define the settlement currency characteristics, as well as other characteristics such as, date basis, payment convention, calendars, and so on. See Appendix B Schedules on page 883. • Generated data – Cashflows Settlement Currency = Settlement Currency (as defined in the schedule) Settlement FX Rate = Settlement FX Rate (as defined in the schedule) Settlement Amount = Amount * Settlement FX Rate 3.10.3.1.3 Processing • Early expiration The early expiration of a dual currency loan is similar to that of a standard loan, except that you can set the Settlement FX Rate and view the settlement amount. See 3.10.1.3 Processing on page 332. – Execution You perform the Early Expiration action in the Transaction Manager’s Transaction view on the transaction that you want to early expire. You can enter the following information: 342 Information Description Settlement Currency (Read-only) Currency to use for settlement. Settlement FX Rate Rate used to calculate the settlement amount of the principal cashflow. Settlement Accrued Interest Final amount to be settled. © Wall Street Systems IPH AB - Confidential 3 Debt instruments 3.10 Loan • FX fixing When the settlement FX rate of a dual-currency loan is not known beforehand, the FX rates need to be fixed at the agreed fixing date. – Setup Depending on the instrument setup, the fixing can be done in advance or in arrears. In both cases there can be an offset of n days (before the beginning or end of the interest period). – Execution The FX Fixing action performed in Transaction Manager’s Cashflow view on the cashflow allows you to set the FX rate. The following values can be input: Information Description Fixing Date Day the cashflow is fixed. Reference FX Rate Fixing market quote. This is defaulted by the system to the FX cross rate between the actual currency and the currency on the fixing date and can be changed by the user. The fixing process is performed directly on an individual cashflow in the Cashflow view. It is possible to modify the fixing values. – Cancellation It is possible to undo the FX fixing using the Undo FX Fixing action. 3.10.3.1.4 Position monitoring For information about dual currency calculations, see 2.3.5 Dual currency on page 147. 3.10.3.2 Rainbow coupon structure In these structures there is an option on each interest payment to choose the payment in a different currency (a maximum of three currencies can be defined in TRM). 3.10.3.3 Callable structure These structures are used to create callable/puttable loans. Call/Put can be simply optional or triggered by a market event. It is also possible to have a Call/Put with barriers (in or out). 3.10.3.4 Currency transaction option Options for repayment to occur in a different currency: this option can be simple, triggered or linked with a barrier. This option can be applied to a principal repayment or a call option 3.10.3.5 Transaction conversion option Deals with an embedded option to move to a different cashflow structure, for example, an option to move from a fixed to a floating rate, or from an annual to a zero coupon structure. These transaction conversions can also be linked to barriers or triggers. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 343 3 Debt instruments 3.10 Loan 344 © Wall Street Systems IPH AB - Confidential Chapter 4 Equities In TRM, the term equity is used to cover the following instruments: • Common stock Common stock is security that represents ownership in a company that has issued stock. The stockholder has a right to receive dividends and the right to vote in the shareholders’ meeting. • Preferred stock Preferred stock is security that represents ownership in a company that has issued stock. Preferred stock typically has better rights to dividends than common stock, but less voting rights (or even none at all). • Subscription rights A subscription right gives the holder the right to buy the underlying security at a predetermined price. Typically, the rights have a short lifetime: they are detached from stock at a specific date and expire worthless if they are not used to purchase the underlying stock. • Mutual fund shares A mutual fund share represents one unit of ownership in the assets of a mutual fund. 4.1 Equity Equity instruments must be based on an instrument type derived from the class EQUITY. 4.1.1 Instrument setup • Equity main characteristics The following basic information may be captured when defining the instrument. This information is relevant to any kind of equity instrument. Information Description Issuer and Guarantor parameters Issuer and guarantor information for the equity instrument. Currency Currency in which the equity is traded. Rounding parameters Method and precision used to round cashflow amounts. See A.2.127 Equity on page 772. • Equity information The outstanding number of shares and voting rights for the equity may change over time. It is possible to define this information at instrument level. See A.2.132 Equity Info on page 776. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 345 4 Equities 4.1 Equity Quotation • You can specify quotation information for the equity at instrument level. See A.2.274 Quoted on page 849. Trading unit • Equities can be traded in multiples of a minimum bid size. It is possible to define this information in the instrument setup. See A.2.321 Trading Unit (Equity) on page 871. For an equity instrument, it is also possible to set up: • Spot date calculation • Value date calculation • Delivery (custodian) information • Cashflow and transaction charge rules • Manual charges • Branch codes. See Appendix A Features on page 713. 4.1.2 Deal capture 4.1.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a transaction with an equity instrument: Information Description Value Date Official date when money is transferred. This defaults to the spot date as defined for the instrument. Trading Units Number of units bought or sold. The Equity Trading Unit feature is used to define the minimum bid size of shares or fund shares. See A.2.321 Trading Unit (Equity) on page 871. Deal Price Price of one unit. In addition, the following optional information can be captured: Information Description Value Date Code If the Value Date Setup feature is applied at instrument level, you can enter the value date period you want to use to calculate the value date for the transaction, for example, 3M (3 months). This can be used to compute the value date for a forward purchase of equity. Note: If you specify a value date period in the instrument setup, this is used as the default in the transaction and cannot be modified: see A.2.339 Value Date Setup on page 879. 346 © Wall Street Systems IPH AB - Confidential 4 Equities 4.1 Equity 4.1.2.2 Generated data • Cashflows For an equity instrument, the cashflows generated are as follows: Value date Opening date Position cashflow Spot days Delivery cashflow Settlement amount 4.1.3 Processing When managing an equity portfolio, there are various corporate actions that need to be processed. The processing in TRM of the most commonly used corporate actions is described in this section. 4.1.3.1 Cash dividend In most cases, the holders of common stock, preferred stock, or mutual fund shares receive regular cash dividends up to four times each year. In addition, they may receive special dividends. • Setup When the information about the cash dividend is declared by the issuer of the security, the instrument definition needs to be updated with the dividend information. See A.2.128 Equity Cash Dividend on page 773. • Execution On the ex-dividend date, the equity is quoted without the dividend and the market price drops approximately by the amount of the dividend. The exact amount of the dividend is known at the end of the previous business day. It is calculated from the position at the close of business prior to the ex-dividend date. The activity Dividend that creates the dividend transaction(s) needs to be performed at the beginning of the ex-dividend date (or at the end of the previous day). The following information is needed to process the cash dividend: Information Description Portfolio The dividend is calculated for this portfolio and all of its subportfolios. Minimum Transaction State The minimum transaction state that is taken into account when the position is determined for the dividend calculation. Note: See the TRM User Guide for information about this activity and how to set up activities in general. The execution creates the dividend transaction, which has an incoming cashflow on the dividend payment date. From the ex-dividend date onwards, the market value of this transaction is calculated separately from the equity position. The execution processes each portfolio (and owner) separately: a dividend transaction is created in each portfolio (and for each owner) where there is a position on the relevant equity on the day preceding the ex-dividend date. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 347 4 Equities 4.1 Equity • Cancellation In case the dividend transactions are incorrect it is possible to cancel them manually and rerun the dividend activity. 4.1.3.2 Split and reverse split When an equity instrument is split, the number of outstanding shares increases: each share is split into a certain number of shares. For example: Before the split: Buy 5,000 units of equity where the price of each unit = 10 EUR (total book value = 50,000 EUR) split 1 unit into 5 shares After the split: The position is 25,000 units of equity where the price of each unit = 2 EUR (total book value = 50,000 EUR) In a reverse split, the number of outstanding shares decreases with a certain ratio. For example: Before the split: Buy 5,000 units of equity where the price of each unit = 10 EUR (total book value = 50,000 EUR) split 5 units into 1 share After the split: The position is 1,000 units of equity where the price of each unit = 50 EUR (total book value = 50,000 EUR) • Setup The data used to split an equity position is defined in the instrument setup. The following information is required to process the split: Information Description Date Date on which the split was declared or the information was entered in the instrument setup. Split parameters Date of the split, the split ratio, and the action required if an Odd Lot results from the split. See A.2.138 Equity Split on page 779. • Execution If there are no Odd Lots or, if you do not want to create an Odd Lot adjustment transaction, you can perform the split or reverse split simply by defining the split information using the Equity Split feature in the instrument setup (see above). Otherwise, if any Odd Lots do result from the split or reverse split (and you do want to create the corresponding adjustment transactions), the Split activity must be used. Note: See the TRM User Guide for general information on running activities, and also specific information on the activity parameters. 348 © Wall Street Systems IPH AB - Confidential 4 Equities 4.1 Equity Each portfolio is processed separately. Based on the existing position, a new position is created using the following rules: Old units = Number of units in the position at the moment of the split (that is, at the end of the day before the split date) New units = Old units * From/To Units, rounded using the rounding parameters specified in the feature Odd lot = Old units – Used units Factor = Used units / Old units If there is an Odd Lot, a Sell transaction is created to sell the Odd Lot for the specified compensation price (as defined in the instrument definition): Odd lot compensation = Odd lot compensation price * Odd lot The existing position is adjusted so that the Odd Lot compensation amount (the resulting number of units) is now considered as new units. The book value is adjusted by the factor. If the factor = 1, there is no Odd Lot compensation and the book value is not adjusted. • Cancellation If you need to cancel or correct the split or reverse split: – Correct the Equity Split parameters defined in the instrument setup – Cancel the incorrect Odd Lot transactions, if any – Rerun the Split activity, if you wish to create Odd Lot adjustment transactions. 4.1.3.3 Detachment Detachment is a corporate action that takes place typically when a shareholder receives subscription rights in place of equity. The number of subscription rights received by the shareholder is proportional to the number of equity units held. If subscription rights are detached from an equity, it is also possible to transfer part of the book value from the equity to the subscription right (when the value of the equity and the value of the right are specified). For example: Before the detachment: Buy 5,000 units of equity where the price of each unit = 10 EUR (total book value = 50,000 EUR) Detachment of subscription rights: 1 right per 5 shares Market price for 1 share = 8 EUR Market price for subscription right = 2 EUR After the detachment: The book value that is transferred for the original position to the new one: 50,000 EUR * (1/5) * (2/8) = 2,500 EUR Receipt of subscription rights incurs a cost (1 EUR), therefore the following position cashflow is added to the generated detachment transaction: New units * Price per unit = 5,000 * (1/5) * 1 = 1,000 Note: At a later date, subscription rights can also be used to buy equity (either the same as the original equity or different equity) at a certain price (see 4.1.3.4 Conversion on page 351). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 349 4 Equities 4.1 Equity • Setup When the information about the detachment is known, the instrument definition needs to be updated. Information Description Date Date on which the detachment was declared or the information was entered in the instrument setup. Detachment parameters Date of the detachment and the action required if an Odd Lot results from the detachment. Value of the Right Values required to determine how much of the book value is transferred from the original equity to the new one. Value of the Equity See A.2.130 Equity Detachment on page 774. • Execution The Detachment activity is used to calculate what the shareholder gets per share held. Note: See the TRM User Guide for general information on running activities, and also specific information on the Detachment activity parameters. Each portfolio is processed separately. Based on the existing position, a new position is created using the following rules: Old units = Number of units in the position at the moment of detachment (in general, this is the position at the end of the previous day) If, for example, there is a split on the same day as the detachment, you must define whether the detachment is processed before or after the split. New units = Units to receive * Round(Old units / Units to sell) rounded using the rounding parameters specified for the detachment at instrument level Odd units are computed as follows: Odd lot = Old units – Units to sell * Truncate(Old units / Units to sell) Odd lot compensation = Odd lot compensation price * Odd lot If there is an odd lot, the compensation amount is added as a profit/loss cashflow to the detachment transaction. Price to pay = Price to pay per unit * New units The price to pay is added as settlement principal to the detachment transaction. When subscription rights are detached from an equity, it is possible to determine the book value amount that is transferred from the equity to the subscription right, using the following calculation: Book value amount * (Units to receive * Value of right)/(Units to sell * Value of equity) • Cancellation You can cancel the detachment action by cancelling the detachment transactions and also the generated cashflows in the original transaction. 350 © Wall Street Systems IPH AB - Confidential 4 Equities 4.1 Equity 4.1.3.4 Conversion Subscription rights can be used to purchase new shares (either the same as the original equity or different equity) at a certain price. This corporate action is known as Conversion. Conversion can be used, for example, in a merger where shares held in one company are converted to shares in another company. • Setup When the information about the conversion is known, the instrument definition needs to be updated. Information Description Date Date on which the conversion was declared or the information was entered in the instrument setup. Conversion parameters Date of the conversion, the conversion ratio, and the action required if an Odd Lot results from the conversion. See A.2.129 Equity Conversion on page 773. • Execution The Conversion activity is used to convert shares or subscription rights into new equity. The following information is needed to run the activity: Information Description Portfolio Conversion is processed for this portfolio and all of its subportfolios. Minimum Transaction State Minimum transaction state that is taken into account when the position is determined for the conversion. Note: See the TRM User Guide for information about how to set up activities in general. Each portfolio is processed separately. Based on the existing position, a new position is created using the following rules: Old units = Number of units in the position at the moment of conversion New units = Units to receive * Round(Old units / Units to sell), rounded using the rounding parameters specified for the detachment at instrument level The new position is created with the correct number of units with regard to the rounding conventions. Price to pay = Price to pay per unit * New units This amount is added as settlement principal to the conversion transaction. Factor = Units to sell * Truncate(Old units / Units to sell) / Old units This factor determines the part of the book value that is moved from the old position to the new converted position. The old position is closed completely if there is no odd lot (that is, a sell transaction is generated with the whole number of units). The position is closed partially in the case of an odd lot. The odd lot is sold at the compensation price. The odd lot sell transaction has the following characteristics: Odd lot units = Old units - Units to sell * Truncate(Old units / Units to sell) Book value = Odd lot compensation = Odd lot selling price * Odd lot units Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 351 4 Equities 4.1 Equity Cancellation • You can cancel the conversion by cancelling the conversion transactions. 4.1.3.5 Return of capital Return of Capital occurs when the company pays back part of the capital to the shareholders. This corporate action differs from a cash dividend (see 4.1.3.1 Cash dividend on page 347), because the book value of the shares is decreased by the amount of the capital returned. Setup • When the information about the return of capital is known, the instrument definition needs to be updated. Information Description Date Date on which the return of capital was declared or the information was entered in the instrument setup. Return of capital parameters Date of the return of capital, and information required to determine the capital to be returned. See A.2.137 Equity Return of Capital on page 778. Execution • The Return of Capital activity is used to pay back the capital to the shareholders. Running this activity decreases the book value by the amount of capital returned (the number of units multiplied by capital per unit). The returned capital is shown as a principal cashflow. Note: See the TRM User Guide for general information on running activities, and also specific information on the activity parameters. Cancellation • You can cancel the return of capital action by cancelling the return of capital transactions and also the generated cashflows in the original transaction. 4.1.4 Position monitoring In this section, numerical examples demonstrate how the different figures are calculated for an equity instrument. If you need more theoretical information about the method used in these calculations, see Chapter 2 Market standards and calculations on page 33. This example shows a share, with the following deal data: Setup • Data Symbol Valuation Method FX Exposure Offset Example Quoted, to Spot h_fx 0.01 Symbol Example Transaction • Data Opening Date Trading Units 352 2004-02-02 n_m 10,000 © Wall Street Systems IPH AB - Confidential 4 Equities 4.1 Equity Data Symbol Example Deal Price P_b 3.00 Base Book FX Rate (EUR/USD) S_b 1.2 Value Date d_a 2004-02-04 Currency USD Portfolio Currency EUR Other important deal data is calculated by the system as follows: Data Symbol Example Formula Book Value (Local) V_b 30,000.00 = 10,000 * 3.00 = n_m * P_b Book Value V_p 25,000.00 = 30,000.00 / 1.2 = V_b / S_b Unless otherwise stated, the figure date used in the calculations is 2004-03-01. On this date, the market data is as follows: • • Market data on 2004-03-01 Data Symbol Example Figure date d_f 2004-03-01 Market Price P_f 3.20 FX Conversion Rate S 1.260000 Valuation figures The valuation method commonly used for an equity instrument is the Par method. Data Symbol Example Formula Local Market Value V_l 32,000.00 = 10,000 * 3.20 = n_m * P_f Market Value V 25,396.93 = 32,000.00 / 1.2600 = V_l / S Clean Market Value V_clean 32,000 = 10,000 * 3.20 / 1.2600 = n_m * P_f / S Note that if the instrument is not defined as being valued To Spot, Market Value will be discounted from spot to the figure date. However, Clean Market Value will not; therefore, the Clean Market Value figure may be different from the Market Value figure. • Result figures The setup of the instrument impacts the way result figures are computed. Data Symbol Example Formula Total Profit (Local) P_tl 2,000.00 = 32,000.00 – 30,000.00 = V_l – V_b MtoM Profit (Local) P_ml 2,000.00 = 32,000.00 – 30,000.00 = V_l – V_b FX Profit P_fx -1,190.48 = 30,000.00*(1/1.260000 – 1/1.20000) = V_b*(1/S - 1/S_b) Total Profit P_t 396.83 = 25,396.83 – 25,000.00 = V – V_p MtoM Profit P_m 1,587.30 = 2,000.00 / 1.260000 = P_ml / S Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 353 4 Equities 4.1 Equity Risk figures • Data Symbol Example Formula FX Exposure E_fx 253.97 = 0.01 * 25,396.83 = h_fx * V 354 © Wall Street Systems IPH AB - Confidential Chapter 5 Security lending 5.1 Repurchase agreement In a repurchase agreement (repo), one party sells a security to another party with the agreement to repurchase the same security at a fixed future date and at an agreed price. In essence, the seller of the security is borrowing the amount received from the sale and placing the sold securities with the purchaser as collateral. The difference between the sale price of the security and the cost of repurchase is, in effect, interest charged to the borrower. The period of time between the sale and the repurchase is called the repo period. Physical transfer of the security from the custody of the borrower to the custody of the lender usually takes place, but in the case of overnight repos, for example, there may be no transfer. If the security does not physically change hands, the buyer of the security is exposed to a higher credit risk. Underlying a repo transaction is usually a fixed-rate government bond or discount paper. Collateral delivered against the cash in a repo transaction can be in a single (single-collateral repo) or in multiple (multi-collateral repo) underlying instruments. These collateral instruments must be defined with the feature Collateral in order to be available as collateral, see 5.1.4 Collateral on page 365. TRM also allows you to use cash as collateral. To do so, you must define cash collateral account instruments, see 5.1.7 Cash Collateral on page 376. You can use both collateral instruments and cash collateral instruments for margin movement transactions. Margin movements are required when the exposure exceeds the threshold defined in the collateral agreement (Margin page). You must set up specific margin movement instruments to handle this type of situation, see 5.1.6 Margin movement on page 370. In some situations, you may need to substitute a collateral instrument for another during the lifetime of a repo transaction. You must set up specific substitution instruments for this event, see 5.1.5 Substitution on page 366. To enable substitution, you need to set up the conditions for substitution in the collateral agreement (Substitution page). See TRM User Guide for more information about collateral agreements. Repos are driven either by the need to lend or borrow cash, or the need to borrow a specific security. 5.1.1 Repo (classic) The following information is relevant to any kind of repo. If you want to setup a Buy/sell back repo see 5.1.2 Buy/sell back and sell/buy back on page 362. 5.1.1.1 Instrument setup Repo instruments must be based on an instrument type derived from the class REPO. • Repo main characteristics Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 355 5 Security lending 5.1 Repurchase agreement This information may be relevant to any kind of repo instrument. Information Currency Description Currency of the repo deal. Leave this field blank if you want to specify the currency of the repo transaction when you enter the deal. Transaction Sign Interest Type Date Basis Sign to be applied to the transaction: Reverse Repo (Buy/Lend) or Repo (Sell/Borrow). • Select either Repo or Reverse Repo if you want this to be the default direction of the transaction, that is, the direction cannot be modified at deal entry. • Leave this field blank if you want to specify the direction of the repo deal at deal entry. Type of interest rate used to calculate the repo interest amount, for example, Periodic Rate. Date basis used to calculate the interest of the repo. If this is not defined at instrument level, the date basis of the currency is used unless you provide another date basis at deal entry. Amount Rounding parameters Method used to round cashflow amounts of the repo. Principal Cashflow Type Type of repayment cashflow (for example, Principal or Expiration). Interest Cashflow Type Type of interest cashflows. Collateral Calculation Method Calculation method defaulted to transaction column Collateral Calculation Method of new transactions in repo instrument and applied when collateral amount of a collateral entry in a repo transaction is manually updated. • Single: Select Single, if you want the system to keep settlement amount of the collateral and recalculate collateral market price to match the new collateral amount, This method can only be used in single collateral repo transaction. • Multiple: Select Multiple, if you want the system to keep the collateral market price of the collateral and recalculate settlement amount to match the new collateral amount. This method allows you to enter multiple collateral to a repo transaction. Note: The Collateral Calculation Method always defaults to Multiple in substitution and open margin transactions, but can be manually set to Single. Switches • Use Dirty Price: Switch on to define that the Collateral Price/Maturity Collateral Price should be expressed as the dirty price. This information is displayed at transaction level as Dirty Collateral Price. • Use Collateral Price Rounding: Switch on to define that Collateral Price and Maturity Collateral Price are rounded using the rounding parameters of the underlying collateral instrument. If this switch is not on, collateral prices are always calculated exactly. If the feature Repo Rounding is used, the rounding parameters are taken from the rounding setup of the collateral instrument (see A.2.280 Repo Rounding on page 854). Otherwise, the rounding parameters are taken from Trading Yield setup of the collateral instrument (see A.2.323 Trading Yield on page 872). See A.2.283 Repurchase Agreement on page 854. • 356 Maturity definition © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement It is possible to set up maturity information at instrument level. Information Description Calendar parameters Calendars used to calculate the maturity date. Gap Set Gap set used for supplying the available maturity periods. Maturity Date Period If defined, this maturity period is applied to each transaction. See A.2.230 Maturity Date Setup on page 827. • Collateral agreement definition It is possible to set up collateral agreement to be used in transactions at instrument level. Information Description Agreement The collateral agreement you want to use in the repo transactions. • If defined, this collateral agreement is defaulted to all new transactions. The defaulted agreement can be changed to any other valid collateral agreement in Transaction Manager. • If not defined, collateral agreement is defaulted according to collateral agreement setup given in Client Editor for the owner of the transaction. For more information about the setup of a collateral agreement at the client-level, see TRM User Guide. See A.2.95 Collateral Setup on page 756. • Collateral Quote defaulting If feature Quote Default (Collateral) is selected for a repo instrument, the current market price or yield is automatically defaulted according to the setup of the feature to fields collateral market price or collateral market rate of a new collateral entry in a repo transaction as soon as a new collateral instrument has been selected. Information Description Scenario Scenario to use to price the transactions. Mode Pricing mode: Method • Select Automatic if you want to retrieve the quotes automatically in Transaction Manager. • Select Manual if you want to retrieve the quotes manually in Transaction Manager. Defaulting method: Ask, Bid, Buy/Sell, or Mid. If you select Buy/Sell: when the transaction sign is positive the Ask price is used, and when the transaction sign is negative, the Bid price is used. See A.2.270 Quote Default (Collateral) on page 847. • Repo Cash Delivery definition This feature sets all non-delivery cashflows of a repo transaction with the attribute Not Payable and creates a separate cash delivery flow corresponding to a delivery flow for each collateral instrument. Concretely, the total settlement and maturity amounts on value date and maturity date of the repo, respectively, are split by collateral instrument for settlement purposes. As cash delivery flows have corresponding collateral instrument as leg instrument of the flow, these flows can be identified by leg instrument in rules. This enables the setting of cash settlement instructions correctly when they are dependent on collateral instruments. The splitting of settlement amounts by collateral instrument also enables delivery versus payment (DvP) settlements to be generated from multi-collateral repos. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 357 5 Security lending 5.1 Repurchase agreement See A.2.277 Repo Cash Delivery on page 853. It is also possible to set up: • Spot day and value date calculations • Manual charges • Cashflow and transaction charge rules • Branch codes. See Appendix A Features on page 713. 5.1.1.2 Deal capture Repo transactions can be entered in a cash-driven or collateral-driven manner depending on if the transaction is initially agreed with the counterparty for a specific cash amount against any acceptable collateral or for a specific amount of particular collateral. 5.1.1.2.1 Input data – cash amount In addition to the standard deal parameters, the following information is required if you want to trade cash versus general collateral. • Transaction view Information Currency Description Currency of the repo deal. If the currency is not defined at instrument level, it can be specified separately for each transaction. Maturity Date Date when the repo deal matures. Maturity Code • If you enter a maturity code, the date is calculated automatically; otherwise you can enter the date manually. • (Information only.) If the maturity definition parameters are defined at instrument level, these are used by default. Nominal Amount Cash amount of the repo. Deal Rate Repo rate (expressed as a percentage) used to calculate the repo interest (cash). Date Basis Date basis of the repo deal. If the date basis is not defined at instrument level, it can be specified separately for each transaction. Collateral Agreement Collateral Agreement of the repo deal. If the agreement is not defined at instrument level, it defaults according to collateral agreement definition given in Client Editor for the owner of the transaction. You can change the default agreement to any other collateral agreement as long as it is valid for the counterparty of the repo. Collateral agreement specifies various conditions applied for the repo including: • Collateral Valuation Currency • Collateral Requirement calculation • Cover Haircut of the repo • Total Collateral Haircut • Eligible collateral • Collateral Substitution • Margin calls and returns See TRM User Guide for more information about the Collateral Agreement Editor. 358 © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement • Repo view In this view, you can add collateral to the repo transaction by using the New Collateral action. Information Description Collateral Instrument Instrument (bonds, discount papers, and additionally cash collateral account) to be used as collateral. Only instruments with the Collateral feature (A.2.93 Collateral on page 755) attached and not flagged as ineligible in Collateral Haircut definition of the selected collateral agreement are available for selection. For information about the collateral instrument setup, 5.1.4 Collateral on page 365. Collateral Market Price Market price of the collateral instrument. This price can be defaulted by the system when the feature Quote Default (Collateral) is used. See A.2.270 Quote Default (Collateral) on page 847. The system calculates the required amount of collateral automatically based on the above transaction and repo attributes as well as the following: – Cover Haircut of the repo. – Total Collateral Haircut. These are assigned automatically by the system according to the selected collateral agreement. The calculated collateral amount or collateral units is rounded up to the closest deliverable amount/units using minimum bid size or trading units definition of the collateral instrument. If the multiple collateral are delivered against cash, the Collateral Calculation Method must be set to Multiple at the transaction level and the collateral amount or collateral units of the first collateral must be manually adjusted down to the correct amount/units before adding a new collateral in Repo view by using the New Collateral action. If the Collateral Calculation Method is set to Single before adjusting down collateral amount, the system recalculates collateral market price to match settlement amount of the collateral and the new collateral amount, instead of recalculating the settlement amount. Adding new collateral after that will not be possible because the transaction is already fully collateralized. Note: Manually changing the collateral calculation method of the transaction at any time will always affect the calculations of the last collateral of the transaction. When a collateral instrument is selected, the eligibility of the selected instrument is validated against the selected collateral agreement. 5.1.1.2.2 Input data - collateral amount If you want to trade a specific amount of a security against cash, then the nominal amount of the transaction is not given. Unlike a cash-driven scenario where you only have to enter the collateral instrument and collateral market price, in a collateral-driven scenario, you must also give collateral instrument, collateral market price and collateral amount. Based on this information, the system calculates automatically correct nominal amount for the transaction., using collateral price rounding if the repo instrument is set up with switch Use Collateral Price Rounding. As long as nominal amount of the transaction has not been manually given, the system continues to treat the transaction as a collateral-driven one and updates the nominal amount according to collateral attributes that you provided. 5.1.1.3 Processing This section describes the actions that can be done throughout the life of a repo transaction. 5.1.1.3.1 Roll over You can defer the maturity of a repo transaction to a later date. This process is called a rollover. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 359 5 Security lending 5.1 Repurchase agreement • Setup The feature Allow Roll Over (repo) enables repo transactions to be rolled over. Repo transactions can be rolled over in a similar manner to short-term loans. • See A.2.13 Allow Roll Over (repo) on page 719. • Execution Rollover of a repo is always collateral-driven in that any partial rollovers are identified by adjusting down the collateral amount of one or several collaterals of the maturing repo. Rollover transactions are created by executing the Roll Over action from an outstanding repo deal in Transaction Manager or Collateral Valuation Board. Rollover is available if the remaining collateral amount of at least one of the collateral instruments is greater than zero. This action can be triggered from the following places: – Transaction Manager - Transaction view (for all collaterals of the transaction) – Transaction Manager - Repo view (for a specific collateral) – Collateral Valuation Board - Collateral Position view (for all collaterals of the transaction). See TRM User Guide for more information. Rollover transactions are created by executing the Roll Over action from an outstanding repo deal in Transaction Manager or Collateral Valuation Board. Rollover is available if the remaining collateral amount of at least one of the collateral instruments is greater than zero. This action can be triggered from either of the following places: – Transaction Manager - Transaction view (for all collaterals of the transaction) – Transaction Manager - Repo view (for a specific collateral) – Collateral Valuation Board - Collateral Position view (for all collaterals of the transaction) Required input for the rollover is given in the Roll Over dialog but can be modified or completed in Repo view of Transaction Manager in the new row created by the action. When the action is selected from the right-click action, the system opens one of two dialogs depending on whether single or multiple maturing collateral instruments are affected by the rollover. Note, that all previous collateral substitutions are taken into account when the system identifies collateral for the roll-over transaction. This means that the roll-over collateral is not necessarily the same as the original collateral of the repo being rolled over. If the action is executed from Transaction view of Transaction Manager and multiple collateral instruments with remaining collateral amount greater than zero are found, you must capture the following information: Information Description Opening Date Opening date of the rollover transaction. Defaulted to the current date or if given before selecting the action, as fixing/action date of the underlying transaction. Value Date (Information only.) Value date of the rollover transaction. Defaulted to the opening date adjusted with spot days of the repo instrument. Roll over Method (Mandatory) Method used for the rollover. Defaulted according to the select default method at instrument-level, but can be modified to any of the other methods if these are not identified as excluded. Gap Gap used to calculate new maturity date from value date of the rollover. If the maturity gap is identified in the maturing repo, the same gap is defaulted to the rollover as well, but can be modified to any other gap. 360 © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement Information Description Maturity Date Maturity Date of the rollover. The maturity date is calculated by the system based on value date and selected the maturity gap, but can be modified to any other valid date. Deal Rate Repo rate of the rollover. Defaulted to the deal rate of the maturing repo, but can be modified to any other rate. Re-Price Collateral If set the collateral of the repo transaction is re-priced using the market price at the time of the rollover to calculate the cash amount of the rollover. The difference between the maturing cash amount of the repo and new cash amount of the rollover is settled as part of the maturity settlement of the maturing repo and included in the nominal amount of the rollover. This is defaulted according to corresponding setup in the repo instrument but can be manually set/cleared in the dialog. If only one collateral instrument with a remaining collateral amount greater than zero is found, the dialog contains the following additional fields: Information Description Collateral Instrument (Information only.) Collateral instrument of the maturing collateral. Collateral Amount Collateral amount of the maturing collateral. Defaulted to the remaining collateral amount, but can be modified to any amount that does not exceed the remaining amount. Collateral Units Units of the maturing collateral if the collateral instrument is set up with trading units. Collateral Market Rate Current market yield of the collateral instrument, if Re-Price Collateral is used. Collateral Market Price Current market price of the collateral instrument, if Re-Price Collateral is used. All deliveries of rolled-over collateral (as well as settlements of maturing principal) are always deferred to the maturity date of the rollover. The various rollover methods available in the dialog reflect different treatments of maturing interest in the rollover. Each method can be used with or without Re-Price Collateral, resulting in an additional cash settlement that reflects the difference between original and current value of the rolled-over collateral, increasing or decreasing the nominal amount of the rollover transaction accordingly. The following methods are supported: Method Description Settle Interest The interest of the maturing repo transaction is paid at the initial maturity date. The nominal amount of the rolled over transaction is equal to the principal cashflow of the initial transaction according to the collateral amount of the rollover (i.e. if half of the maturing collateral is rolled over, the nominal amount is half of the principal) adjusted up or down when Re-Price Collateral is used. Delay Interest The interest of the maturing repo transaction is deferred to the new maturity date of the rollover. The nominal amount of the rolled over transaction is equal to the principal cashflow of the initial transaction according to the collateral amount of the rollover adjusted up or down when Re-Price Collateral is used. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 361 5 Security lending 5.1 Repurchase agreement Method Description Compound Interest The interest of the maturing repo transaction is deferred to the new maturity date of the rollover, and the new interest of the rollover transaction is calculated based on the total of the nominal amount and deferred interest. The nominal amount of the rolled over transaction is equal to the principal cashflow of the initial transaction according to the collateral amount of the rollover adjusted up or down when Re-Price Collateral is used. Capitalize Interest The interest of the maturing repo transaction is capitalized to the principal of the rollover transaction, and the new interest of the rollover transaction is calculated from the nominal amount including capitalized interest. The nominal amount of the rolled over transaction is equal equal to the total of principal and interest cashflows of the initial transaction according to the collateral amount of the rollover adjusted up or down when Re-Price Collateral is used. Accepting the dialog creates a new rollover transaction, if necessary, you can finalize this rollover transaction in the Repo view of Transaction Manager. If the action was executed from Transaction view of Transaction Manager for more than one maturing collateral instruments, you can modify the defaulted collateral amount or units of each collateral to a smaller value in the event of a partial rollover, or delete one or several of the maturing collaterals to restrict the rollover to a subset of collaterals. If Re-Price Collateral was used, you can also adjust the defaulted collateral market prices. • Cancellation You can undo the roll-over by canceling the roll-over transaction. 5.1.2 Buy/sell back and sell/buy back Sell/buy backs and buy/sell backs are similar to classic repos and reverse repos respectively. With sell/buy backs and buy/sell backs, however, the coupon that is payable during the repo term and received by the buyer of the bond is not immediately transferred to the seller, as in a classic repo or reverse repo, but paid back at the end of the repo term, compounded by the repo rate. 5.1.1 Repo (classic) on page 355. 5.1.2.1 Instrument setup A buy/sell back (and sell/buy back) instrument is set up in the same way as a normal repo instrument (see 5.1.1 Repo (classic) on page 355) with the following additional attributes: • Repo main characteristics Information Description Switches • Reinvest Coupon: Switch on for a buy/sell back where the coupon is received by the buyer of the bond and only paid back at the end of the repo. This information is displayed in the Reinvest Coupon column in Transaction Manager’s Transaction view. See A.2.283 Repurchase Agreement on page 854. 5.1.2.2 Deal capture • Input data Buy/sell back (and sell/buy back) deals are captured in a similar way to collateral-driven repo deals (see 5.1.1.2 Deal capture on page 358). The following additional fields may also be used at deal entry. 362 © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement – Transaction view Information Description Reinvestment Rate Rate used to reinvest the coupon. By default, this is the same as the repo rate (i.e Deal Rate of the transaction) but can be set manually to a different rate. 5.1.3 Floating Repo A floating repo is like a classic repo except that the single interest payment (which is payable at repo maturity) is not agreed up front as with a normal repo but is fixed in arrears at the end of the repo period. In all other aspects, the transaction is like a normal classic repo. 5.1.3.1 Instrument setup The setup for a floating-repo instrument is, for the most part, identical to that of a normal fixed-rate repo instrument. The differences are described below. Floating-repo instruments must be based on an instrument type derived from the class REPO-FLOATING. • Main characteristics In addition to the standard information that applies to any repo instrument (provided in the Repo page), you can define the floating characteristics of the instrument in the Floating Repo page. Information Description Interest Method Interest calculation method that controls which expression is used in the floating interest cashflow of the transaction. The following methods are available: • Average: The expression 'average' is used to support the calculation of the interest rate as an average of daily observations during the interest period. • Average (Business Days): The expression 'average_q' is used to support the calculation of the interest rate as an average of daily observations during the interest period using quotations on business days only. • Compound: The expression 'compound' is used to support the calculation of the interest rate as a compund rate using daily observations during the interest period. • In Arrears: The expression 'ir+spread' is used to support the calculation of the interest rate using a single observation at the end of the interest period. Fixing Rate IR Quote reference used when fixing the cashflow. Fixing Period Tenor from which the quotation is retrieved when fixing the interest rate of the transaction, for example, O/N or 1M. Fixing Subscenario Rate subscenario from which the interest rate is retrieved. Fixing Offset Number of business days before the interest date. Fixing of interest occurs on this date. If the fixing offset is set to anything other than 0 when average/compound interest methods are used, the quotation of the fixing date is used for all dates between the fixing date and the interest date. Fixing Calendar Calendar used for fixing. See A.2.284 Repurchase Agreement (Floating) on page 856. • Repo cash delivery (floating) definition Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 363 5 Security lending 5.1 Repurchase agreement The feature Repo Cash Delivery (Floating), like the feature Repo Cash Delivery for fixed-rate repos, sets all non-delivery cashflows of a repo transaction to Not Payable and creates a separate cash delivery flow corresponding to a delivery flow for each collateral instrument. The difference between the two features is that in floating-rate repos, cash delivery flows are only created for the value date of the repo when the transaction is captured. Corresponding flows for the maturity date are created by the Fixing action executed on the fixing date of the interest cashflow. See A.2.278 Repo Cash Delivery (Floating) on page 853. • Repo valuation (floating) definition The normal valuation setup options used in floating loans are available in floating-repo instruments too. In particular, it is important to select the correct risk profile after selecting the feature Valuation Setup (Floating). For information on risk profiles see 2.3.4.8 Risk profiles on page 124. See A.2.338 Valuation Setup (Floating) on page 879. 5.1.3.2 Deal capture Floating repo transactions are entered in the same way as fixed-rate repos with the few exceptions described below. 5.1.3.2.1 Input data In addition to the standard deal parameters and repo specific parameters described earlier (see 5.1.2.1 Instrument setup on page 362), the following information is required if you want to trade a floating-rate repo. • Transaction view Information Description Deal Rate The Deal Rate of a floating-rate repo is the spread over or under the reference given as basis points. For example, 2.50 is interpreted as a spread of 0.025%. The value given in this field is propagated to the Spread field of the interest cashflow. This field is mandatory. Fixing Rate IR Quote reference used when fixing the cashflow. This field is automatically populated if the Fixing Rate is given at instrument level. If not, any valid IR Quote with usage Fixing can be given for the transaction. This field is mandatory. Fixing Period Tenor from which the quotation is retrieved when fixing the interest rate of the transaction, for example, O/N or 1M. This field is automatically populated if the Fixing Period is given at instrument level. Otherwise, any valid tenor in the identified Fixing Rate can be given for the transaction. This field is mandatory. Fixing Subscenario Rate subscenario from which the interest rate is retrieved. This field is automatically populated if the Fixing Subscenario is given at instrument level. Otherwise, any valid subscenario can be given for the transaction. If nothing is given, the system uses the default subscenario. Fixing Offset Number of business days before the interest date. This field is automatically populated if the Fixing Offset is given at instrument level. Otherwise, any number of business days can be given in the field. If nothing is given, 0 is used by the system and the Fixing To date of the floating interest cashflow is always set to the Maturity Date of the transaction. 364 © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement Information Description Fixing Calendar Calendar used for fixing. This field is automatically populated if Fixing Calendar is given at the instrument level. Otherwise, any valid calendar can be given for the transaction. If nothing is given, the calendar of the currency of the transaction is used when setting the fixing date for the floating interest cashflow. 5.1.3.3 Processing This section describes the different actions that can be done throughout the life of a floating-rate repo transaction as opposed to a fixed-rate repo transaction. 5.1.3.3.1 Interest fixing Like for a floating-rate loan, the amount of each interest flow in a floating repo transaction has to be determined before it is paid: this process is known as fixing. Fixing is done in exactly the same way as for a floating loan transaction. When fixing is executed for a floating repo transaction with an instrument with feature Repo Cash Delivery (Floating), the system also creates Cash Delivery flows required for maturity date settlement. This cannot be done before fixing because the final cash settlement amount on the maturity date is not known. See 3.10.2.3.1 Interest fixing on page 339 for more information. 5.1.3.3.2 Roll over Floating repo transactions can be rolled over in the same way as fixed-rate repos but with two minor differences: 1. The Rollover action is only available for a floating repo transaction after it has been fixed. This is because the final interest payment at the maturity of the original floating-repo transaction must be known before the rollover can be successfully processed. 2. In the same way as in the capture of a new floating repo transaction, the Deal Rate of the rollover given in the Rollover action dialog is interpreted as a spread over or under the fixing reference as basis points and passed to the Spread field of the floating interest cashflow of the new rollover transaction. See 5.1.1.3.1 Roll over on page 359 for more information. 5.1.4 Collateral Some instrument setup affecting repo transactions is made directly in the collateral instruments instead of the repo instrument. You can define the following instruments as collateral instruments available for repo transactions: • Bonds: 3.1 Bond on page 215. • Discount papers: 3.9 Discount paper on page 316. • Floating Rate Notes (FRNs): 3.1.2 Floating rate note on page 228. To use these instruments as collateral, you must ensure that they are properly set up with feature Collateral, see A.2.93 Collateral on page 755. Additionally, you can define the following instruments to support using cash as margin collateral in repo operations: • Cash collateral account: 5.1.7 Cash Collateral on page 376. 5.1.4.1 Instrument setup • Main characteristics – Trading Units definition Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 365 5 Security lending 5.1 Repurchase agreement Smallest possible denomination of the security that can be delivered under a (Repo) transaction in the market can be identified in Trading Unit setup of the collateral instrument. Information Description Trading Units If the instrument is traded in units, the size of one unit is given here (for example, 10,000.00). Units definition should only be used if the instrument is structured in units. This setup should not be made only to indicate the smallest deliverable denomination since trading units definition makes all cashflow calculations (for example, interest amounts) to be first made for one unit of instrument and then multiplied by the number of units of the transaction, instead of calculating the amounts for the full nominal amount of the transaction directly. Minimum Bid Size If the instrument is traded and delivered in nominal amount instead of units, the smallest deliverable denomination can be given as Minimum Bid Size (for example, 10,000.00). Minimum Bid Size has no impact on cashflow calculations, only on rounding of nominal amount (transactions traded directly in the instrument) and collateral amount (repo transactions using the instrument as collateral). Note that only one of the definitions can be given for any given instrument (either Trading Units or Minimum Bid Size). Refer to the relevant primary feature. • Collateral definition This feature identifies the instrument as a valid collateral to be used in repo transactions. See A.2.93 Collateral on page 755. • Repo rounding feature This feature allows you to define the pricing precision to be used in repo transactions for the collateral instrument. If defined, this setup overrides the rounding parameters of the instrument specified with the Trading Yield feature (unless Use Bond Rounding has been set in the repo instrument) when collateral price and collateral maturity price are calculated in repo transactions. Information Description Price rounding parameters Rounding used for collateral price. Maturity price rounding parameters Rounding used for maturity collateral price. This can be specified at deal entry in the Repo view. This can be specified at deal entry in the Repo view. See A.2.280 Repo Rounding on page 854. 5.1.5 Substitution Collateral substitution takes place when existing collateral that is held or given against a repo exposure is partially or fully substituted against new collateral. The return of the existing collateral and receipt of the new collateral can be settled free or versus a cash payment. If delivery versus payment is used, the cash amount to be settled against the delivery of securities can be either the initial amount of cash that was originally settled against the delivery of existing collateral or the value of original collateral at the time of substitution. In both cases, the same amount of cash is used in the delivery of both collateral instruments. The net cash effect is zero but both deliveries take place as DvP (Delivery versus Payment). 366 © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement The value of original collateral to be substituted is used to calculate required amount of new collateral. Either initial value of the substituted collateral in the repo transaction or the current value of it at the time of substitution can be used as a basis for this calculation. The method used is specified at collateral agreement level by identifying the substitution method to be used in the agreement. If no method has been identified in a collateral agreement, substitutions are not allowed for any repos in it. The substitution is modeled with an independent action transaction created from the original repo. The substitution transaction is not created in the original repo instrument but a separate substitution instrument is used instead. 5.1.5.1 Instrument setup Substitution instruments must be based on an instrument type derived from the class SUBSTITUTION. • Main characteristics Substitution features use the primary feature Substitution (see A.2.306 Substitution on page 865). Substitution instruments do not require any specific set up. • Collateral Quote defaulting This feature can also be used in a substitution instrument to make the system automatically default current market price or yield according to the setup of the feature for both old (if substitution method Current Value is used) and new collateral in a substitution transaction. See A.2.270 Quote Default (Collateral) on page 847. • Repo Cash Delivery definition The feature Repo Cash Delivery (Substitution) must be used in substitution instruments when delivery-versus-payment settlements are required on the value date of the substitution. Typically, a substitution instrument with this feature is used if the repo instrument of the transaction from which the substitution transaction is created uses feature Repo Cash Delivery. This feature creates a separate Cash Delivery flow corresponding to a delivery flow in each collateral instrument on the value date of the substitution. As in a repo, the total settlement amount on the value date of the substitution is split by the collateral instrument for settlement purposes. See A.2.277 Repo Cash Delivery on page 853. It is also possible to set up: • Spot day calculations • Manual charges • Cashflow and transaction charge rules • Branch codes. See Appendix A Features on page 713. 5.1.5.2 Deal capture 5.1.5.2.1 Input data Substitution transactions are always created by executing a Substitution action from an outstanding repo or earlier substitution deal. This action can be triggered from one of the following places: • Transaction view of Transaction Manager (for all collaterals of the transaction). • Repo view of Transaction Manager (for a specific collateral). • Collateral view of Collateral Valuation Board (for a specific collateral). When the action is triggered from Transaction view of Transaction Manager, any number of existing collateral holdings can be substituted in the same substitution action from a multi-collateral repo. In Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 367 5 Security lending 5.1 Repurchase agreement the other two views, this action is executed from a specific collateral holding and only that collateral is substituted. In all cases, old collateral can be substituted for new collateral in one or several collateral instruments. 5.1.5.3 Processing This section describes the actions that can be done throughout the life of a repo transaction. 5.1.5.3.1 Substitution Substitution action is available if the remaining collateral amount of at least one of the collateral instruments is greater than zero and if the collateral agreement of the transaction allows substitutions. Required input data for the substitution is given in the action dialog and in the new transaction created by the action in the Repo view of Transaction Manager. • Setup The collateral agreement defines whether the Substitution action is enabled (Collateral Agreement Editor - Substitution page). See the TRM User Guide for more information about collateral agreements. • Execution When the Substitution action is selected from the right-click menu, the system opens one of two dialogs depending on whether single or multiple old collateral instruments are affected by the substitution. If the action is executed from Transaction view of Transaction Manager and multiple collateral instruments with remaining collateral amount greater than zero are found, you must provide the following information. Information Description Opening Date Opening Date of the substitution transaction. This is defaulted as current date or, if given before selecting the action, as fixing/action date of the underlying transaction. Value Date Value Date of the substitution transaction. This is defaulted as opening date adjusted with spot days of the substitution instrument identified in the collateral agreement of the underlying transaction. Substitution Method Method used to calculate the value of substituted collateral. This is defaulted as the method identified in the Collateral Agreement of the underlying transaction as one of the following: • Original Collateral Value Original value of old collateral in the underlying transaction is used to calculate required amount of new collateral • Current Collateral Value Current value of old collateral calculated by using the latest available collateral market price is used to calculate required amount of new collateral. If only one collateral instrument with the remaining collateral amount greater than zero is found, the dialog contains the following additional fields. Information Description Substitution Collateral (Information only.) The collateral instrument of the old collateral. Amount Amount of old collateral. This is defaulted to the full remaining collateral amount but can be modified to any smaller amount. 368 © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement Information Description Units Units of old collateral if collateral instrument has been set up with trading units. Market Rate This field is used to identify current market yield of the collateral instrument if the substitution method Current Collateral Value is used. Market Price This field is used to identify current market price of the collateral instrument if the substitution method Current Collateral Value is used. Accepting the dialog creates a new substitution transaction which must be completed by adding the new collateral delivered against the substituted collateral in Repo view of Transaction Manager. – If the action is executed from Collateral Valuation Board, a Transaction Manager application in which the substitution transaction is created is opened automatically. – If the action is executed from Transaction view of Transaction Manager for more than one old collateral instrument, you can modify defaulted collateral amount/units of each collateral to a smaller value in case of a partial substitution, or delete one or several of the old collaterals to restrict the substitution to a subset of collaterals. If the substitution method Current Collateral Value is used, you can also adjust defaulted collateral market prices of old collaterals. After this, you can add the first new collateral using the New Collateral action. When the first new collateral is added, the old collateral is frozen and can no longer be modified. – If the action was executed for a single old collateral instrument, the system freezes the old collateral and creates the first new collateral automatically. After the first new collateral has been manually or automatically created, you can finalize the transaction by giving the details of new collateral delivered against the substituted collateral as follows: Information Description Collateral Instrument Instrument (bonds, discount papers, and additionally cash collateral account) to be used as collateral. Only instruments with the Collateral feature (A.2.93 Collateral on page 755) attached and not flagged as ineligible in collateral haircut definition of the selected collateral agreement are available for selection. For information about the collateral instrument setup, 5.1.4 Collateral on page 365. Collateral Market Price Market price of the collateral instrument. This price can be defaulted by the system when the feature Quote Default (Collateral) is used. See A.2.269 Quote Default (Collateral) on page 673. Collateral Amount Amount of the collateral. Collateral Units Number of units of the collateral if collateral instrument has been set up with Trading Units. When new collateral is added to a substitution transaction, it behaves like a cash-driven repo transaction. The system sets the nominal amount of the transaction as the value of old collateral and automatically calculates the required collateral amount/units of new collateral based on collateral market price as soon as the collateral instrument has been selected. Note: The Collateral Calculation Method always defaults to Multiple in substitution transactions, but it can be manually set to Single to affect calculations resulting from a manual adjustment of collateral amount in the last new collateral of the substitution transaction in the same manner as in a cash-driven repo transaction. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 369 5 Security lending 5.1 Repurchase agreement 5.1.6 Margin movement A margin movement transaction (a margin call) is required when exposure exceeds the threshold defined in a collateral agreement and an additional deposit of collateral is required. Note: Managing collateral is described in the TRM User Guide. 5.1.6.1 Instrument setup Margin movement instruments must be based on an instrument type derived from the class MARGIN-MOVEMENT. • Main characteristics Margin movement instruments do not require any specific set up. They are simply recognized by the following feature in the Margin Movement instrument class: – • The primary feature Margin-Movement (see A.2.229 Margin Movement on page 827). Collateral Quote defaulting If feature Quote Default (Collateral) is selected for a margin instrument, current market price or yield is automatically defaulted according to the setup of the feature to fields collateral market price or collateral market rate of a new collateral entry in a margin transaction as soon as a new collateral instrument has been selected. See A.2.270 Quote Default (Collateral) on page 847. • Collateral Agreement definition It is possible to set up collateral agreement to be used in transactions at instrument level. Information Description Agreement If defined, this collateral agreement is defaulted to all new transactions. The defaulted agreement can be changed to any other valid collateral agreement in Transaction Manager. If not defined, collateral agreement is defaulted according to collateral agreement setup given in Client Editor for the owner of the transaction. See A.2.95 Collateral Setup on page 756. It is also possible to set up: • Spot day calculations • Manual charges • Cashflow and transaction charge rules • Branch codes. See Appendix A Features on page 713. 5.1.6.2 Deal capture Margin movements can be made for an indefinite maturity against overall exposure of a counterparty under a specific collateral agreement (Open Margin) or for the remaining maturity of a specific repo transaction against the exposure of that particular repo (Margin). 5.1.6.2.1 Input data - Open Margin Open Margin transactions are independent new transactions that can be captured in Transaction Manager or through the Open Margin Movement action in Collateral Position view of Collateral Valuation Board. 370 © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement Capturing an open margin transaction directly in Transaction Manager is very similar to capturing a new repo transaction. Margin movements are normally made to deliver a specific value of collateral required to bring the total value of collateral in balance with the value of underlying exposure it is securing. Consequently, transactions are typically entered in a cash-driven manner where the target value of margin collateral is given as nominal amount of the transaction before identifying the collateral. It is also possible to enter an open margin transaction in a collateral-driven manner. In addition to the standard deal parameters, the following information is required, if you want to capture a margin call directly in Transaction Manager. • Transaction view Information Description Nominal Amount Value of the margin collateral. If the nominal amount is not given, the system automatically calculates it based on collateral amounts and collateral market prices of the selected collateral instruments. Collateral Agreement Collateral agreement of the margin call. If the agreement is not defined at the instrument level, it is defaulted according to collateral agreement definition given in Client Editor for the Owner of the transaction. You can change the default agreement to any other valid collateral agreement for the counterparty of the repo. Collateral agreement specifies various conditions applied for the margin call transaction including: • • Currency • Total Collateral Haircut • Eligible collateral. Repo view In this view, you can add collateral to the open margin transaction by click New Collateral from the right-click menu. Information Description Collateral Instrument Instrument (bonds, discount papers, and additionally cash collateral account) to be used as collateral. Only instruments with the Collateral feature (A.2.93 Collateral on page 755) attached and not flagged as ineligible in Collateral Haircut definition of the selected collateral agreement are available for selection. For information about the collateral instrument setup, 5.1.4 Collateral on page 365. Collateral Market Price Market price of the collateral instrument. This price can be defaulted by the system when the feature Quote Default (Collateral) is used. See A.2.270 Quote Default (Collateral) on page 847. Collateral Amount Amount of collateral If the nominal amount was given in the transaction, the system calculates the required amount of the collateral automatically based on the above transaction and repo attributes, as well as valuation haircut of the collateral instrument assigned automatically by the system according to the setup of the selected collateral agreement. If multiple margin collateral is delivered against a target value identified in nominal amount of transaction, the collateral amount of the first collateral must be manually adjusted down to the correct amount before adding a new collateral in Repo view by clicking New Collateral in the right-click menu. Collateral Units Units of collateral if the collateral instrument is set up with Trading Units. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 371 5 Security lending 5.1 Repurchase agreement Note: As in substitutions, the Collateral Calculation Method always defaults to Multiple, but can be manually set to Single to affect calculations resulting from a manual adjustment of collateral amount in the last new collateral of the margin transaction in the same manner as in a cash-driven repo transaction. 5.1.6.2.2 Generated data • • • Transaction Type = Margin or Open Margin: – If a specific maturity date is specified (maturity date of the underlying repo transaction), Transaction Type = Margin. – If the maturity date is not specified at deal entry, Transaction Type = Open Margin. Collateral Amount – If the amount is input at deal entry, the collateral amount (nominal amount) is calculated from the collateral instrument/market price and valuation haircut. – The calculation of the collateral amount also takes into account the contract size of the collateral. Collateral Amount Rounding – If margin is received, the collateral amount is rounded up. – If margin is given, the collateral amount is rounded down. 5.1.6.3 Processing 5.1.6.3.1 Open Margin Movement • Execution If an open margin transaction is created using Open Margin Movement action from Collateral Position view of Collateral Valuation Board, a dialog with following fields is opened: Information Opening Date Description Opening date of the open margin transaction. Defaulted to the current date but can be modified to any other valid date. Value Date Value date of the open margin transaction. Defaulted to the opening date adjusted with spot days of the margin instrument identified in the collateral agreement of the collateral position but can be modified to any other valid date. Portfolio Portfolio of the open margin transaction. Defaulted to the portfolio of the collateral position but can be modified to any other valid portfolio. Counterparty Counterparty of the open margin transaction. Defaulted to the counterparty of the collateral position and cannot be changed. Collateral Agreement Collateral agreement of the open margin transaction. Defaulted to the collateral agreement of the collateral position and cannot be changed. Sign Transaction sign of the open margin transaction. Default according to the action in the column Collateral Action of the collateral position and cannot be changed. Currency (Information only.) Currency of the open margin transaction. Defaulted to the currency of the collateral position. 372 © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement Information Description Value Target value of the margin collateral. Defaulted based on cover difference of the collateral position and can be modified to any other value larger than minimum movement value of the collateral agreement of the collateral position. When the dialog is accepted, a Transaction Manager application is opened and a new open margin transaction with the first new collateral is automatically created in it. You can then finalize the transaction by giving the details of margin collateral normally in Repo view of Transaction Manager. Since open margin transactions are for an indefinite period of time, return of the margin collateral does not happen automatically, you must create a separate margin return transaction must be created when you want the margin collateral to be returned. Also, all future cashflows of fixed income securities, including both coupons and principal repayments, are created in the open margin transactions to support settlements of these flows both against the issuer or clearing client of the security and against the counterparty of margin transaction. • Cancellation You can undo this action by canceling the open margin movement transaction. 5.1.6.3.2 Margin Movement Margin transactions are always created by using the Margin Movement action from an outstanding repo transaction either in Transaction Manager or in Collateral Position view of Collateral Valuation Board. • Execution If the action is selected directly from an existing repo transaction in Transaction Manager, the action dialog contains the following fields and default values: Information Description Opening Date Opening date of the margin transaction. Defaulted to the current date or, if given before selecting the action, as fixing/action date of the underlying transaction but can be modified to any other valid date Value Date Value date of the margin transaction. Defaulted to the opening date adjusted with spot days of the margin instrument identified in the collateral agreement of the underlying transaction but can be modified to any other valid date Sign Transaction sign of the margin transaction. Defaulted to +1 (i.e. collateral received from margin call). Currency Currency of the margin transaction. Defaulted to the currency of the collateral agreement of the underlying transaction and cannot be changed. Value Target value of the margin collateral. Defaulted to the minimum movement value of the collateral agreement of the underlying transaction but can be modified to any higher value. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 373 5 Security lending 5.1 Repurchase agreement If the action is selected from Collateral Position view (grouped by Collateral Number) of Collateral Valuation Board, the action dialog is slightly different: Information Description Opening Date Opening date of the margin transaction. Defaulted to the current date but can be modified to any other valid date Value Date Value Date of the margin transaction. Defaulted to the opening date adjusted with spot days of the margin instrument identified in the collateral agreement of the collateral position but can be modified to any other valid date. Collateral Number (Information only.) Transaction number of the repo transaction underlying the collateral position. This is defaulted as collateral number of the collateral position. Sign (Information only.) Transaction sign of the margin transaction. Default according to the action in the column Collateral Action of the collateral position. Currency (Information only.) Currency of the margin transaction. Defaulted to the currency of the collateral agreement of the collateral position. Value Target value of the margin collateral. This is defaulted based on cover difference of the collateral position and can be modified to any other value larger than minimum movement value of the collateral agreement of the collateral position. Note: If the action was executed from Collateral Valuation Board, a Transaction Manager application in which the margin call transaction is created is opened automatically. In both cases, a new margin transaction with the first new collateral is automatically created. You can then finalize the transaction by giving the details of margin collateral normally in Repo view of Transaction Manager. Since margin transactions are for the specific remaining maturity of the underlying repo transaction, return of the margin collateral happens automatically on the maturity date of the underlying repo. Also, coupons and principal repayment cashflows of fixed income securities are only created if they are due for payment before the maturity of the underlying repo transaction. • Cancellation You can undo this action by canceling the margin movement transaction. 5.1.6.3.3 Margin Return A separate margin return (of an earlier margin call) transaction is required when margin collateral must be returned in an unscheduled manner. This is always true when returning margin collateral delivered in an earlier open margin transaction and when the collateral received in a margin transaction must be returned before the scheduled return on the maturity date of the underlying repo transaction. Margin return transactions can only be created using a margin return action from Collateral view of Collateral Valuation Board for a margin collateral holding in a specific collateral instrument. The logic for Margin Return is exactly the same as for Open Margin Return. • 374 Execution © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement When an Open Margin Return or Margin Return action is selected in the Collateral view of Collateral Valuation Board, a dialog with following fields is opened: Information Description Opening Date Opening date of the margin return transaction. Defaulted to the current date but can be modified to any other valid date Value Date Value date of the margin return transaction. Defaulted to the opening date adjusted with spot days of the margin instrument identified in the Collateral Agreement of the underlying margin transaction(s) but can be modified to any other valid date Portfolio Portfolio of the margin return transaction. Defaulted to the portfolio of the underlying margin transaction(s) and cannot be changed. Counterparty Counterparty of the margin return transaction. Defaulted to the counterparty of the underlying margin transaction(s) and cannot be changed. Collateral Agreement Collateral agreement of the margin return transaction. Defaulted to the collateral agreement of the underlying margin transaction(s) and cannot be changed. Sign Transaction Sign of the margin return transaction. Defaulted to the opposite of the sign of the underlying margin transaction(s) and cannot be changed. Currency Currency of the margin return transaction. Defaulted to the currency of the collateral agreement of the underlying margin transaction(s) and cannot be changed. Collateral Currency Currency of the margin collateral instrument. Defaulted to the currency of the collateral instrument of the underlying margin transaction(s) and cannot be changed. FX Rate FX Rate used to convert value of collateral instrument from collateral currency to Currency of the collateral agreement. Defaulted to the current FX spot rate between collateral currency and currency but can be modified to any other rate when collateral currency and currency are not the same. Instrument Collateral instrument being returned. Defaulted to the collateral instrument of the underlying margin transaction(s) and cannot be changed. Collateral Amount Amount of collateral to return. Calculated by the system as the smallest deliverable of the collateral amount with adequate collateral value to match total collateral value to return, but can be modified to any other deliverable amount less than total collateral amount of the underlying margin transaction(s). Collateral Units Units of collateral to return when collateral instrument has been set up with trading units. Collateral Market Price Current market price of collateral instrument. Collateral Market Rate Current market yield of collateral instrument. Cover Value Cover value of the identified collateral amount of the collateral instrument. Calculated by the system using collateral amount, collateral market price and valuation haircuts as defined in the collateral agreement. This value can be modified to any other value, in which case the new collateral amount is calculated accordingly. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 375 5 Security lending 5.1 Repurchase agreement Information Description Total Cover Value To Return (Information only.) Total cover value required to be returned to correct over-collateralization of the collateral position. Defaulted to the cover difference of collateral position. Cover Difference The difference between cover value and total cover value to return. This value is informative only and can be used to check whether cover value of selected collateral to be returned is sufficient. A negative value indicates that more collateral must be returned to correct over-collateralization of the collateral position. When the dialog is accepted, a Transaction Manager application is opened, all underlying margin or open margin transactions affected by the margin return are identified and a new margin return transaction is created, returning the given amount of collateral and closing the current margin or open margin transaction. The new transaction is completed with the data given in the dialog and can be applied and accepted forward in the flow directly. • Cancellation You can undo this action by canceling the margin return transaction. 5.1.7 Cash Collateral Cash can also be used as collateral for an underlying exposure in a collateral agreement. Cash collateral is delivered in a similar manner to security collateral in margin movement transactions (margin calls). Cash collateral is managed in the system as balances with ability to accrue interest. The general characteristics of cash collateral account transactions are the same as those of call Account transactions. See 8.2 Call account on page 446. 5.1.7.1 Instrument setup Cash collateral instruments must be based on an instrument type derived from the class CASH-COLLATERAL-ACCOUNT. • Main characteristics The following basic information may be captured when defining a cash collateral account instrument. Information Description Currency Currency of the cash collateral account. Balance Minimum and maximum balance allowed on the cash collateral account. information Notice period information • Required notice period for cash movements. Interest accrual parameters For cash collateral accounts, you can specify the interest rates used, and the method and frequency that interest is accrued on the cash collateral account. • Interest realization parameters You can also specify how the accrued interest is realized on the cash collateral account. See A.2.90 Cash Collateral Account on page 752. It is also possible to set up: 376 © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement • Spot day calculations • Collateral • Manual charges • Cashflow and transaction charge rules • Branch codes. See Appendix A Features on page 713. 5.1.7.2 Deal capture Cash collateral account transactions are made for an indefinite maturity either against overall exposure of a counterparty under a specific collateral agreement (Open Cash Collateral) or against the exposure of a particular repo operation (Cash Collateral). In order to be able to use cash collateral in a collateral agreement, at least one cash collateral instrument must be identified as eligible collateral in the agreement. 5.1.7.2.1 Input data – Open Cash Collateral New Open Cash Collateral (Account) transactions as well as new movements in existing transactions can be captured and managed in Cash Collateral applications in a similar manner to call accounts. New transactions and movements can also be created using actions from the Collateral Position view in Collateral Valuation Board. Capturing an Open Margin transaction directly in a Cash Collateral Account application is almost identical to capturing a call account transaction. The only difference is that a cash collateral transaction must always be attached to a collateral agreement. Open Cash Collateral transactions are not linked to an existing collateral number, but always attached to a collateral agreement. In addition to the standard deal parameters, the following information is required if you want to capture a new cash collateral account in a Cash Collateral Account application. • • Transaction view Information Description Movement / Initial Balance Initial cash movement (inflow or outflow) on the cash collateral account. Collateral Agreement Collateral Agreement of the cash collateral account. This amount can be zero if you want to open a cash collateral account without any initial movement of cash. Movement view In this view, you can add a cash collateral movement to an existing transaction using the New Movement action. Information Description Opening Date Opening date of the new movement. Value Date Value date of the new movement. This is set automatically by the system based on opening date and notice period setup of the instrument but can be manually changed to a different date. Amount Amount of the new movement. 5.1.7.2.2 Input data – Cash Collateral New Cash Collateral Account transactions targeting specific repos as well as new movements in them are always captured using actions either from the repo transaction in Transaction Manager or in the Collateral Valuation Board. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 377 5 Security lending 5.1 Repurchase agreement If the Cash Collateral action is selected directly from an existing repo transaction in Transaction Manager, the action dialog contains the following fields and default values: Information Description Opening Date Opening date of the cash collateral transaction or movement. Defaulted to the current date or, if given before selecting the action, as fixing/action date of the underlying transaction but can be modified to any other valid date. Value Date Value Date of the cash collateral transaction or movement. Defaulted to the opening date adjusted with spot days of the selected cash collateral instrument but can be modified to any other valid date. Margin Instrument Instrument used for the cash collateral transaction or movement. Manually select one of the eligible cash collateral instruments in the collateral agreement of the underlying repo transaction. Sign Transaction sign of the margin transaction. Defaulted to +1 (i.e. cash collateral given from margin call). Currency Currency of the margin transaction. Defaulted to the currency of the collateral agreement of the underlying repo transaction and cannot be changed. Amount Amount of the cash collateral movement. Defaulted to the minimum movement value of the collateral agreement of the underlying repo transaction but can be modified to any higher value. 5.1.7.3 Processing 5.1.7.3.1 Open Cash Collateral • Execution A cash Collateral transaction or movement can be created through the Open Cash Collateral action from Collateral Position view of Collateral Valuation Board. The following dialog is displayed: Information Opening Date Description Opening date of the cash collateral transaction or movement. Defaulted to the current date but can be modified to any other valid date. Value Date Value date of the cash collateral transaction or movement. Defaulted to the opening date adjusted with spot days of the selected cash collateral instrument but can be modified to any other valid date. Portfolio Portfolio of the cash collateral transaction or movement. Defaulted to the portfolio of the collateral position but can be modified to any other valid portfolio. Counterparty Counterparty of the cash collateral transaction or movement. Defaulted to the counterparty of the collateral position and cannot be changed. Collateral Agreement Collateral agreement of the cash collateral transaction or movement. This is defaulted as the collateral agreement of the collateral position and cannot be changed. Margin Instrument Instrument used for the cash collateral transaction or movement. This must be manually selected as one of the eligible cash collateral instruments in the collateral agreement. 378 © Wall Street Systems IPH AB - Confidential 5 Security lending 5.1 Repurchase agreement Information Description Sign Sign of the cash collateral transaction or movement. Default according to the action in the column Collateral Action of the collateral position and cannot be changed. Currency (Information only.) Currency of the cash collateral transaction or movement. Defaulted to the currency of the collateral position. Amount Amount of the cash collateral movement. Defaulted according to the cover difference of the collateral position and can be modified to any other value larger than minimum movement value of the collateral agreement of the collateral position. When the dialog is accepted, a Cash Collateral Account application opens, usually Cash Collateral Account Trading (default setup). If the system cannot find an existing cash collateral transaction that matches the following values with those given in the dialog, a new cash collateral transaction with a first movement is automatically created: – Portfolio – Counterparty – Collateral Agreement – Margin Instrument – Currency. If an existing transaction is found, a new movement is added to the identified cash collateral transaction. There is no separate return of the cash collateral. Instead, both positive and negative movements of cash can be made in the same cash collateral transaction using the same functionality. • Cancellation To undo this action cancel the new movement, or if a new account transaction was created, cancel the whole transaction. 5.1.7.3.2 Cash Collateral • Execution If the Cash Collateral action is selected from Collateral Position view (grouped by Collateral Number) of Collateral Valuation Board, the dialog is the same as the Open Cash Collateral dialog with the following additions: Information Description Return Date Scheduled return date of the cash collateral. Defaulted to the maturity date of the underlying repo transaction and cannot be changed. The field is informative only and indicates the date as of which the underlying exposures is scheduled to expire. Collateral Number Transaction number of the repo transaction underlying the collateral position. Defaulted to the collateral number of the collateral position and cannot be changed. When the dialog is accepted in Transaction Manager or in Collateral Valuation Board, a Cash Collateral Account application opens, usually Cash Collateral Account Trading (default setup). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 379 5 Security lending 5.2 Security loan If the system cannot find an existing cash collateral transaction that matches the following values with those given in the dialog, a new cash collateral transaction with a first movement is automatically created. – Portfolio – Counterparty – Collateral Agreement – Margin Instrument – Currency – Collateral Number. If an existing transaction is found, a new movement is added to the identified cash collateral transaction. There is no automatic return of the cash collateral on the maturity date of the underlying repo transaction, therefore you must create a separate cash collateral movement in the Cash Collateral Account application when the cash is returned. Cancellation • To undo this action cancel the new movement, or if a new account transaction was created, cancel the whole transaction. 5.2 Security loan A security loan is a transaction in which a given interest-bearing or equity security is lent against a financial compensation. The loan is agreed for an open-ended transaction. Security loans impact only custody movements and balances. The actual security positions for purposes of valuation and accounting, for example, are not impacted. Coupons and dividends are also calculated without considering the security loan transactions. 5.2.1 Instrument setup Security loan instruments must be based on an instrument type derived from the class SECURITY-LOAN. The ALLOW-SECURITY-LOAN feature (see A.2.19 Allow Security Loan on page 721) specifies if the instrument can be loaned. 5.2.2 Deal capture 5.2.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a securities loan: Information Description Secondary Instrument The security being lent (bond or equity). Nominal Amount or Trading Unit nominal amount (bond) or trading unit (equity) to be lent out. Nominal Spot/Rate Lending fee. Currency Currency of instrument. 380 © Wall Street Systems IPH AB - Confidential 5 Security lending 5.2 Security loan 5.2.3 Processing This section describes the actions that can be taken throughout the life of a security loan. 5.2.3.1 Entering security loan fees A security loan fee can be entered at any time by selecting the Security Loan Fee action. • Execution The following information is required: • Information Description Direction Fee direction (In or Out). Amount Fee amount. Opening Date Fee opening date. Value Date Fee value date. Payment Date Fee payment date. From When Date Date from which fee payment is based. Cancellation An Undo Security Loan Fee action is available for undoing (deleting) selected fees. 5.2.3.2 Cutting a security loan transaction The security loan can be cut (matured) by selecting the Security Loan Cut action. • Execution The following information is required: • Information Description Opening Date Date of execution, used as opening date. Value Date Closing date of the transaction. Fee Direction In or Out. Fee Amount Amount. Fee Opening Date Fee opening date. Fee Value Date Fee value date. Fee Payment Date Fee payment date. Fee From When Date Date from which fee payment is based. Cancellation An Undo Security Loan Cut action is available to undo (delete) a captured cut. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 381 5 Security lending 5.2 Security loan 382 © Wall Street Systems IPH AB - Confidential Chapter 6 Forex 6.1 FX spot and FX forward In the foreign exchange market, buyers and sellers conduct foreign exchange (FX) transactions. A currency spot or forward transaction is a deal where one currency is exchanged for another (a base currency and a quote currency). If the value date is the spot date, then the transaction is called a spot deal. If the value date is further in the future, the transaction is a forward. Non-deliverable forwards (NDFs) are FX forward deals that can have a net settlement. Spot rates are quoted as one unit of the base currency against a number of units of the quote currency. In international financial markets, the US dollar is used as the base currency in most quotes. A direct quote is a foreign exchange rate quoted as the domestic currency per unit of the foreign currency. For example, in the US, a direct quote for Japanese yen would be USD/JPY. Conversely, in Japan, a direct quote for US dollars would be JPY/USD. An indirect quote is a foreign exchange rate quoted as the foreign currency per unit of the domestic currency. For example, in the US, an indirect quote for Japanese yen would be JPY/USD. Conversely, in Japan, an indirect quote for US dollars would be USD/JPY. In TRM, FX spot and forward transactions belong to the instrument class FX. 6.1.1 Instrument setup FX spot/forward instruments are based on an instrument type derived from the class FX. • Rate defaulting You can specify that you expect the system to default the rates from the market at deal entry. See A.2.272 Quote Default (FX) on page 848. • Currency information You can specify the currencies of the FX transaction either in the instrument setup or at deal entry. See A.2.192 FX Setup on page 806. • Date information It is possible to set up value date information at instrument level. Information Description Calendar parameters Calendars used to calculate the value date. Gap Set Gap set used for supplying the available value periods. Value Date Period If defined, this value period is applied to each transaction. For an FX instrument, it is also possible to set up: • Spot date calculation Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 383 6 Forex 6.1 FX spot and FX forward Note that it is recommended that you do not specify the spot days in the instrument setup as these are taken by default from the spot days of the two currencies at deal entry. • Cashflow and transaction charge rules • Manual charges • Branch codes • FX Margin Result. See Appendix A Features on page 713. The attributes required for the different types of FX instrument are described in the following sections. 6.1.1.1 FX forward FX forward instruments are set up in a similar way to FX spot instruments. To calculate forward points from currency pairs interest rates, you can specify additional parameters such as Absolute IR Difference. See A.2.175 FX Forward on page 797. 6.1.1.2 Non-deliverable forward (NDF) NDFs are FX forward deals that can have a net settlement. NDFs are set up in a similar way to FX forward instruments. NDFs should use the primary feature Non Deliverable Forward FX Instrument. See A.2.248 Non Deliverable Forward FX Instrument on page 837. 6.1.1.3 FX cross deal An FX spot/forward deal where neither currency is the portfolio base currency is called a cross deal. FX cross deals are set up in a similar way to FX spot/forward instruments, with the following additional parameters: • FX cross rate calculation You need to define how the FX rates (Base Spot FX and Base FX Rate) are calculated. See A.2.171 FX Cross Method on page 796. 6.1.2 Market information 6.1.2.1 Currencies Some additional parameters need to be defined for the currencies which are relevant to your FX transactions: see the TRM User Guide. 6.1.2.2 Quotations and market information Quotations for currencies can be viewed and modified in Rate Monitor. It is possible to define market information feeds for each currency (for example, from Reuters): see the TRM User Guide. 6.1.3 Deal capture 6.1.3.1 Input data • 384 FX spot © Wall Street Systems IPH AB - Confidential 6 Forex 6.1 FX spot and FX forward In addition to the standard deal parameters, the following information is required to enter an FX spot transaction: Information Description Base Currency Base currency of the transaction. (Currency) Quote Currency Quote currency of the transaction. (Currency 2nd) FX Base Amount Amount of the FX transaction in the base currency. FX Quote Amount Amount of the FX transaction in the quote currency. Deal Rate Final FX rate of the transaction = Nominal / Spot Rate + FX Forward Points (+ Margins if applicable) • FX forward (input forward points) In addition to the standard deal parameters, the following information is required to enter an FX forward transaction where the forward points are input manually: Information Description Base Currency Base currency of the transaction. (Currency) Quote Currency Quote currency of the transaction. (Currency 2nd) Value Date Official date when money is transferred. FX Base Amount Amount of the FX transaction in the base currency. FX Quote Amount Amount of the FX transaction in the quote currency. Nominal/Spot Rate Final FX spot rate. FX Forward Points Forward points for the transaction. Deal Rate Final FX rate of the transaction = Nominal / Spot Rate + FX Forward Points (+ Margins if applicable) • FX forward (calculated forward points) In addition to the standard deal parameters, the following information is required to enter an FX forward transaction where the forward points are calculated from Base Currency Interest % and Quote Currency Interest %: Information Description Base Currency Base currency of the transaction. (Currency) Quote Currency Quote currency of the transaction. (Currency 2nd) Value Date Official date when money is transferred. FX Base Amount Amount of the FX transaction in the base currency. FX Quote Amount Amount of the FX transaction in the quote currency. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 385 6 Forex 6.1 FX spot and FX forward Information Description Nominal/Spot Rate Final FX spot rate. Base CCY Interest % Interest rate of the base currency for the period from the opening date to the value date. Quote CCY Interest % Interest rate of the quote currency for the period from the opening date to the value date. 6.1.3.2 Generated data • Cashflows The figure below illustrates the cashflows which are established in TRM for an FX spot transaction. The figure below illustrates the cashflows which are established in TRM for an FX forward transaction: The figure below illustrates the cashflows which are established in TRM for a non-deliverable forward transaction: The following section describes the cashflows when the feature FX Margin Result is used. FX Margin Result creates one cashflow of type Margin with following characteristics: Currency = quote currency Active From = Opening date of the transaction Value Date; Payment Date; From When; Until When; Active To = Value date of the transaction Fixing Rate; Fixing Quote = Spot Margin + Forward Margin Amount = transaction quote amount - quote amount we would have had without any margin 386 © Wall Street Systems IPH AB - Confidential 6 Forex 6.1 FX spot and FX forward 6.1.4 Processing This section describes the actions that can be done throughout the life of an FX transaction. 6.1.4.1 Early expiration You can force FX transactions to mature earlier than their value date. This process is referred to as early expiration. • Execution The following information is needed to process the early expiration: Information Description Early Expiration Date Date when the early expiration is executed. Value Date Date when the early expiration is settled. This cannot be later than the maturity date of the initial transaction. Amount to Expire Amount to be early-expired. This defaults to the amount left and is expressed in the same currency (base or quote) as the input amount of the initial transaction. You can enter any amount between 0 and the remaining amount of the initial transaction. Currency The currency in which the above amount is expressed, can be base or quote currency depending on the initial transaction. (Read-only.) Forward Points Forward points of the early expiration transaction. This defaults to the number of forward points between the early expiration date and the maturity date of the initial transaction. Deal Rate Deal rate for the early expiration transaction. By default, this is today’s date unless a Fixing/Action Date is specified at transaction level. Deal Rate = Original Deal Rate - Forward Points Original Deal Rate The deal rate of the initial transaction. (Read-only.) Quote Amount The corresponding amount of the transaction. Quote Currency Shows the currency of the deal. The currency can be quote or base depending on default Currency. The execution generates an early expiration transaction with the following attributes: If the original input amount was FX Base Amount: FX base amount = amount to expire If the original input amount was FX Quote Amount: FX quote amount = amount to expire Deal Rate = early expiration deal rate Opening date = date when the early expiration is done Value date = date when the early expiration is settled Kind = Early Expiration The remaining attributes are inherited from the initial transaction. • Cancellation You can undo the early expiration by canceling the early expiration transaction. • Redo You can redo the action on the generated transaction. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 387 6 Forex 6.1 FX spot and FX forward 6.1.4.2 Early expiration of NDFs You can force netted non-deliverable forwards to mature earlier than their value date. • Execution The following information is needed to process the early expiration of netted NDFs: Information Description Early Expiration Date Date when the early expiration is executed. By default, this is today's date unless a Fixing/Action Date is specified at transaction level. Value Date Date when the early expiration is settled. This cannot be later than the maturity date of the initial transaction. Base Currency Base currency of the transaction (information). Base Amount Left Amount left in base currency (information). Base Amount to Expire Defaults to the base amount left. (Modifiable if the initial deal was entered in base currency.) You can enter any amount between 0 and the amount left. Quote Currency Quote currency of the transaction (information). Quote Amount Left Amount left in quote currency (information). Quote Amount to Expire Defaults to the base amount left. (Modifiable if the initial deal was entered in base currency.) You can enter any amount between 0 and the amount left. Original Deal Rate The forward rate on the original NDF (information). FX Forward Rate The forward market rate at the date of Early Expiration. You can enter a different rate agreed with the counterparty. Netting Currency The currency in which the netting is calculated, either base or quote. (This is copied from the original deal and depends on the netting method specified on the instrument.) Forward Netting Amount Amount corresponding to the difference between the initial deal rate and the current forward rate (information). Discount Rate This is the rate to be used to discount the Forward Netting Amount to calculate the netting amount. (Modifiable) Netting Amount Amount to be settled, calculated as previously explained. The following fields are only visible if the initial NDF can be settled in a different currency to the netting currency. Information Description Settlement Currency Currency to use for settlement (information) Settlement FX Rate Cross rate between netting currency and settlement currency at settlement date (can be modified) Settlement Amount Final amount to be settled Early expiring a netted NDF results in the following: – All cashflows are closed at the original transaction’s maturity – A single netting cashflow is created at the early expiration date, where Amount = FX netting at maturity discounted to the early expiration date. The netting amount is calculated using the date basis and rate type defined for the interpolation method of the currency’s default curve. • 388 Redo © Wall Street Systems IPH AB - Confidential 6 Forex 6.1 FX spot and FX forward You can redo the action on the generated transaction. 6.1.4.3 Roll over You can defer the maturity of an FX transaction to a later date. This process is referred to as roll-over. See A.2.11 Allow Roll Over (FX) on page 717. • Execution If the Spot Rate for the roll-over equals the Original Deal Rate, the following information is needed to process the roll over: Information Description Roll Over Date Date when the roll over is done. The opening date of the roll over transaction. Value Date Value date of the roll over transaction. This corresponds to the maturity date of the initial transaction. Maturity Code Gap to add to the value date to calculate the maturity date. Maturity Date New maturity date of the FX deal. This must be later than the maturity date of the initial transaction. This defaults to the maturity code of the initial transaction. Amount Left Remaining amount of the initial transaction. (Read-only.) Amount Amount to roll over defaults to the amount left and is expressed in the same currency (base or quote) as the input amount of the initial transaction. You can enter any amount between 0 and the remaining amount of the initial transaction. Currency Shows the currency of the amount to roll over. The amount is expressed in either base or quote currency depending on the initial transaction. (Read-only.) The execution generates a roll over transaction with the following attributes: If the original input amount was FX Base Amount: FX Base amount = amount to roll over If the original input amount was FX Quote Amount: FX Quote amount = amount to roll over Deal Rate = roll over deal rate Opening Date = date when the roll over is done Maturity Date = new maturity date Kind = Roll Over The remaining attributes are inherited from the initial transaction. If the Spot Rate for the roll-over is different from the Original Deal Rate, the following additional information is needed to process the roll over and settle the subsequent difference: Information Description Settle Differential By default, this switch is off: the Spot Rate for the roll over is equal to the Original Deal Rate. Switch on if the Spot Rate for the roll-over is different from the Original Deal Rate. If this switch is on: the Spot Rate (see below) defaults to the spot rate of the market but can be modified. The roll over generates a netting cashflow to handle the settlement of the difference. Original Deal Rate The deal rate of the initial transaction. (Read-only.) Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 389 6 Forex 6.1 FX spot and FX forward Information Description Spot Rate Exchange spot rate of the roll over. This defaults to the Original Deal Rate. If Settle Differential is activated (see above), this field becomes available. The Spot Rate defaults to the spot rate of the market but can be modified. Note: Roll Over Date, Value Date, Maturity Code, Maturity Date, and Settle Differential are adjusted automatically. Base CCY Interest % Interest rate of the base currency for the period from the original settlement date to the new settlement date. Quote CCY Interest % Interest rate of the quote currency for the period from the original settlement date to the new settlement date. Forward Points Forward points of the roll over transaction. This defaults to the number of forward points from the roll over date to the maturity date. Note: Roll Over Date, Value Date, Maturity Code, and Maturity Date are adjusted automatically. Deal Rate Deal rate for the roll over. • If the Spot Rate for the roll-over is equal to the Original Deal Rate: • If the Spot Rate for the roll-over is different from the Original Deal Rate: Deal Rate = Original Deal Rate + Forward Points Deal Rate = Spot Rate + Forward Points Quote Amount The corresponding amount of the roll over transaction. (Read-only.) Quote Currency Shows the currency of the deal. The currency can be quote or base depending on default Currency.(Read-only.) Clear Packaging Clears all packages from the roll over transaction. The execution generates a roll over transaction as before with an additional cashflow as follows: A netting cashflow is created to handle the settlement of the difference Value Date = Roll over value date Currency = Roll over currency 2 Amount = Base Amount * Original Deal Rate - (-Base Amount * Spot Rate) • Cancellation You can undo the roll over by canceling the roll over transaction. • Redo You can redo the action on the generated transaction. 6.1.4.4 Roll over with margins You can specify margins in case you roll over FX transactions. A.2.12 Allow Roll Over (FX - Margin Result) on page 718 • Execution If the Spot Rate for the roll-over margin equals the Original Deal Rate, the following information is needed to process the roll over: 390 Information Description Roll Over Date Date when the roll over is done. The opening date of the roll over transaction. Value Date Date of the roll over transaction. Corresponds to the maturity date of the initial transaction. Maturity Code Gap to add to the value date to calculate the maturity date. © Wall Street Systems IPH AB - Confidential 6 Forex 6.1 FX spot and FX forward Information Description Maturity Date Maturity date of the roll over transaction. Amount Left Remaining amount of the initial transaction. (Read-only.) Amount The amount you want to roll over, which can be any amount between 0 and the remaining amount of the initial transaction. Defaults to the amount left and is expressed in the same currency (base or quote) as the input amount of the initial transaction. Currency Shows the currency of the transaction. The amount is expressed in either base or quote currency depending on the initial transaction. (Read-only.) The execution generates a roll over transaction with the following attributes: If the original input amount was FX Base Amount: FX Base amount = amount to roll over If the original input amount was FX Quote Amount: FX Quote amount = amount to roll over Deal Rate = roll over deal rate Opening Date = date when the roll over is done Maturity Date = new maturity date Kind = Roll Over Margin The remaining attributes are inherited from the initial transaction. If the Spot Rate for the roll-over margin is different from the Original Deal Rate, the following additional information is needed to process the roll over and settle the subsequent difference: Information Description Settle Differential Switch on if the Spot Rate for the roll-over is different from the Original Deal Rate. By default, this switch is off. Original Deal Rate The deal rate of the initial transaction. (Read-only.) Spot Rate The spot rate of the roll over transaction. If Settle Differential is activated, this field becomes available. Spot Rate defaults to the spot rate of the market but this value can be modified. Note: Roll Over Date, Value Date, Maturity Code, Maturity Date, and Settle Differential are adjusted automatically. Spot Margin Margin to apply to the near leg of the roll over transaction. If Settle Differential is enabled, Spot Margin defaults to the price. Note: Settle Differential is adjusted automatically. Final Spot Rate (Read-only.) Spot rate including margins. If Settle Differential is activated, then Spot Rate + (Sign * Spot Margin / 10000) Forward Points Forward points of the roll over transaction. This defaults to the number of forward points from the roll over date to the maturity date. Note: Roll Over Date, Value Date, Maturity Code, and Maturity Date are adjusted automatically. Forward Margin Margin applied on the far leg of the roll over transaction. Deal Rate Deal rate for the roll over. Deal Rate = Spot Rate + Forward Points Quote Amount The corresponding amount of the roll over transaction. (Read-only.) Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 391 6 Forex 6.1 FX spot and FX forward Information Description Quote Currency Shows the currency of the deal. The currency can be quote or base depending on default Currency.(Read-only.) The execution generates a roll over transaction as before with an additional cashflow as follows: A netting cashflow is created to handle the settlement of the difference Value Date = Roll over value date Currency = Roll over currency 2 Amount = Base Amount * Original Deal Rate - (-Base Amount * Spot Rate) • Redo You can redo the action on the generated transaction. 6.1.4.5 Netting Non-deliverable forwards (NDFs) are FX forward deals that can have a net settlement. Instead of exchanging principal amounts, the counterparties agree on the value date and the contractual spot rate. The difference between the actual spot rate and the contractual rate, multiplied by the nominal amount of the deal, is paid. See A.2.248 Non Deliverable Forward FX Instrument on page 837. • Setup The fixing parameters for the netting of non-deliverable forwards can be defined either at instrument level or at transaction level. Where the fixing parameters are defined depends on how narrow or open the instrument definition needs to be. The following information is required to set up netting for an NDF: Information Description Fixing Offset Number of days’ offset allowed, that is, the difference in days between the fixing date and the due date (default = 0). Fixing Subscenario Subscenario from which the FX spot rate is retrieved. Calendar Calendar to use when calculating the fixing date. Netting Method Home Currency: When this method is used the netting currency is set to either base or quote, if one of those is equal to the portfolio currency; otherwise, it defaults to the base currency. • Execution The following information is needed to process the netting: Information Description Netting Date Date when netting is executed. Netting Currency Currency used to compute netting amount, either base or quote depending on instrument setup (read-only). Note: You can change the netting currency in the FX Netting Currency field in the Transaction view. 392 Other Currency Shows the other currency involved (read-only). Original Deal Rate The forward rate on the original NDF (read-only). FX Rate The current FX rate. © Wall Street Systems IPH AB - Confidential 6 Forex 6.1 FX spot and FX forward Information Description Netting Amount Amount to be settled calculated in netting currency. The following fields are only visible if the initial NDF can be settled in a different currency to the netting currency. Information Description Settlement Currency Currency to use for settlement (read-only). Settlement FX Rate Cross rate between netting currency and settlement currency at settlement date (can be modified). Settlement Amount Final amount to be settled. The execution sets the amount of the netting cashflow to the calculated net settlement amount (P/L). • Cancellation You can undo the netting of cash settlements for an FX transaction. 6.1.4.6 Currency pair shift It is possible to split a position from one underlying currency pair into two new positions, each of which contains one of the currencies with a third currency (usually, the portfolio currency). This process is called an FX Pair Shift. • Setup The FX Pair Shift action is available on an FX transaction if the Allow FX Currency Pair Shift feature is included in the instrument definition: see A.2.7 Allow FX Currency Pair Shift on page 716. • Execution See the TRM User Guide for information about this action. 6.1.5 Position monitoring There are two basic methods for valuation of FX instruments: Theoretical or Quoted: • In the Theoretical method, each cashflow is discounted to the spot date using the cashflow currency interest rate, converted to the portfolio currency using the spot rate, then discounted from spot date to valuation date using the portfolio currency interest rate. See 6.1.5.2 Calculations - Theoretical valuation method on page 394. • In the Quoted method, the cashflow is valuated using the forward FX rate between the cashflow currency and the valuation currency, and discounted using the valuation currency interest rate. See 6.1.5.3 Calculations - Quoted valuation method on page 402. Theoretical corresponds to the zero-coupon method and quoted to the par method. 6.1.5.1 Setup By default, the figures are calculated using the Theoretical valuation method. This is the default behavior, but it can be overridden using Base Valuation Setup. See A.2.50 Base Valuation Setup on page 734. If you need more information about the methods used in these calculations, see Chapter 2 Market standards and calculations on page 33. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 393 6 Forex 6.1 FX spot and FX forward 6.1.5.2 Calculations - Theoretical valuation method In this section, numerical examples demonstrate how the figures are calculated for the example FX forward deal using the Theoretical valuation method. This example shows an FX forward Buy 1,000,000 USD/EUR 3M, with the following deal data. Setup data • Data Symbol Example Instrument Date Basis B Act/360 Point Factor p_fact 0.0001 (from currency) FX Forward Points p_fx From Market Valuation Method Theoretical Valuation Date Figure Date Risk Date Figure Date Risk Yield Type Continuous Portfolio data • Data Symbol Example FX Exposure Offset e_fx 0.01 Formula Transaction data • Data Symbol Example Opening Date dt_o 2004-06-24 Spot Date dt_s 2004-06-28 Value Date dt_v 2004-09-28 Nominal Amount A 1,000,000 FX Spot Rate S_0 1.187100 FX Forward Points p_fx -0.1560000 Currency USD Currency 2nd EUR Portfolio Currency EUR Base CCY Interest % r_0.b 1.100000% Quote CCY Interest % r_0.q 1.616348% Date basis B 360 = (F_0 - S_0) * 100 = (S_0 / F_0 / D.b - 1) / t_p Calculated transaction data • Data Symbol Example Formula Deal Rate F_0 1.185540 = 1.1871 + (-15.6) * 0.0001 = S_0 + p_fx * p_fact FX Quote Amount A.q -843,497.48 = -1,000,000 / 1.18554 = -A / F_0 Period t_p 0.2555556 = (2004/09/28 – 2004/06/28) / 360 = (dt_v – dt_s) / B 394 © Wall Street Systems IPH AB - Confidential 6 Forex 6.1 FX spot and FX forward • • • • Calculated transaction data - Base CCY Data Symbol Example Formula Discount Factor D.b 0.99719677 = 1/(1+0.011*0.2555556) =1 / (1 + r_0.b * t_p) Result Value (Local) V_bl.b 997,196.77 = 1,000,000 * 0.99719677 = A * D.b Result Value V_b.b 840,027.60 = 997,196.77 / 1.1871 = V_bl.b / S_0 Base CCY Yield % 1.104512% = POWER(D, -1 / t_p) -1 Implied Interest 1.100000% = (1.185540 / 1.187100 / 0.99588633 - 1) / 0.255556 = (F_0 / S_0 / D.q - 1) / t_p Calculated transaction data - Quote CCY Data Symbol Example Formula Discount Factor D.q 0.99588633 = 1 / (1 + 0.01616348 * 0.2555556) = 1 / (1 + r_0.q * t_p) Result Value (Local) V_bl.q -840,027.60 = -V_b.b Result Value V_b.q -840,027.60 = V_bl.q Quote CCY Yield % 1.626098% = POWER (D.q, -1 / t_p) -1 Implied Interest 1.616348% = (1.187100 / 1.185540 / 0.99719677 – 1) / 0.2555556 =(S_0 / F_0 / D.b - 1) / t_p Market data on Figure Date Data Symbol Example Figure date dt_f 2004-08-16 Days to Spot d_fs 2 Discount Rate r_d 3.048771% FX Conversion Rate S 1.200000 FX Forward F 1.325000 Base CCY Interest Rate r_f.b 1.067917% Quote CCY Interest Rate r_f.q 3.197691% Calculated market data on Figure Date Data Symbol Days to Maturity • Example Formula 43 = 2004/09/28 -2004/08/16 = dt_v - dt_f Time to Spot t_s 0.00555556 = 2 / 360 = d_fs / B Time to Maturity t_m 0.11944444 = (2004/09/28 -2004/08/16) / 360 = (dt_v - dt_f) / B Discount Factor Spot D_s 0.999830638 = EXP (-t_s * r_d) The market data specific to the base currency on the figure date Data Symbol Example Market Value Discount Factor D_V.b 0.998615345 Formula Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 395 6 Forex 6.1 FX spot and FX forward Data Symbol Example Formula Present Value Discount Factor D_P.b 0.998615345 = 0.999830638 * 0.998784501 = D_s * D_f.b Discount Factor Spot Forward D_f.b 0.99878450 = EXP(-(t_m - t_s) * r_f.b) The market data specific to the quote currency on the figure date • Data Symbol Example Formula Market Value Discount Factor D_V.q 0.996196063 Present Value Discount Factor D_P.q 0.996196062 = 0.999830638 * 0.996364809 = D_s * D_f.q Discount Factor Spot Forward D_f.q 0.996364809 = EXP (-r_f.q * (t_m - t_s)) 6.1.5.2.1 Valuation figures The valuation method used for this deal is the Theoretical method. Base currency figures • Data Symbol Example Formula Local Market Value Local_Market_Value 998,615.35 = 1,000,000 * 0.998615345 = A * D_V.b Market Value V 832,179.45 = 998,615.35 / 1.2000 = Local_Market_Value / S Quote currency figures • Data Symbol Example Formula Local Market Value V_l_q -840,288.87 = -843,497.48 * 0.996196063 = A.q * D_V.q Market Value V.q -840,288.87 = V_l_q 6.1.5.2.2 Result figures Base currency figures • Data Symbol Example Formula Total Profit (Local) Total_Profit_Local 1,418.58 = 998,615.35 – 997,196.77 = Local_Market_Value V_bl.b Total Profit Total_Profit.b -7,848.15 = 832,179.45 – 840,027.60 = V - V_b.b Quote currency figures • Data Symbol Example Formula Total Profit Total_Profit.q -261.26 = -840,288.87 – (-840,027.60) = V.q - V_b.q 396 © Wall Street Systems IPH AB - Confidential 6 Forex 6.1 FX spot and FX forward Profit Method = FX Forward • • Base currency figures Data Symbol Example Formula MtoM Profit (Local) MtoM_Profit_Local.b 1,587.73 = 1,000,000 * 0.998784501 – 997,196.77 = A * D_f.b - V_bl.b Accrued Interest (Local) Accrued_Interest_Local.b =0 Accrued Profit (Local) P_al =0 Other Profit (Local) Other_Profit_Local.b -169.16 = 1,418.58 1,587.73 – 0 - 0 = Total_Profit_Local.b MtoM_Profit_Local.b Accrued_Interest_Local.b – P_al FX Profit FX_Profit -9,021.23 = 1,000,000 * (1/1.2 – 1/1.1871) * 0.9961960626 = A * (1 / S - 1 / S_0) * D_V.q MtoM Profit MtoM_Profit.b 1,323.11 = 1,587.73 / 1.2 = MtoM_Profit_Local.b / S Other Profit Other_Profit_b -150.03 = -7,848.15 1,323.11 – (-9,021.23) = Total_Profit.b MtoM_Profit.b - FX_Profit Clean Market Value CMV_b 832,179.45 =V Quote currency figures Data Symbol Example Formula Accrued Interest (Local) Accrued_Interest.q =0 Accrued Profit (Local) P_al =0 MtoM Profit MtoM_Profit.q -403.60 = -843,497.48 * 0.996364809 – (-840,027.60) = A.q * D_f.q - V_b.q Other Profit Other_Profit_q 142.34 = -261.26 – (-403.60) – 0 = Total_Profit.q - MtoM_Profit.q - Accrued_Interest.q Clean Market Value CMV_q -840,288.87 = V.q Profit Method = FX IR Difference • Base currency figures Data Symbol Example Formula MtoM Profit (Local) MtoM_Profit_Local.b 2,288.57 = 1,000,000 * 0.998784501 – 997,196.77 - (-700.84) = A * D_f.b - V_bl.b Accrued_Interest_Local.b Accrued Interest (Local) Accrued_Interest_Local.b -700.84 = 997,196.77 * (-0.516348) * (2004/08/16 - 2004/06/28) / 360 = V_bl.b * (-dr) * (dt_f dt_s) / B Other Profit (Local) Other_Profit_Local.b -169.16 = 1,418.58 – 2,288.57 – (-700.84) =Total_Profit_Local.b MtoM_Profit_Local.b Accrued_Interest_Local.b Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 397 6 Forex 6.1 FX spot and FX forward Data Symbol Example Formula FX Profit FX_Profit -9,021.23 = 1,000,000 * (1/1.2 – 1/1.1871) * 0.996196063 = A * (1 / S - 1 / S_0) * D_V.q MtoM Profit MtoM_Profit.b 1,913.49 = (1,000,000 * 0.998784501 - 997,196.77) / 1.2 - (-590.38) = (A * D_f.b - V_bl.b) / S Accrued_Interest.b Accrued Interest Accrued_Interest.b -590.38 = -840,027.60 * 0.516348 * (2004/08/16 2004/06/08) / 360 = (V_bl.q) * dr * (dt_f dt_s) / B Other Profit Other_Profit.b -150.03 = -7,848.15 1,913.49 – (-590.38) – (-9,021.23) = Total_Profit.b MtoM_Profit.b Accrued_Interest.b FX_Profit Clean Market Value CMV_b 832,769.83 = 832,179.45 (-590.38) = V - Accrued_Interest.b Quote currency figures • Data Symbol Example Formula Accrued Interest (Local) Accrued_Interest_Local.b MtoM Profit MtoM_Profit.q -403.60 = -843,497.48 * 0.996364809 – (-840,027.60) = A.q * D_f.q - V_b.q Other Profit (Local) Other_Profit.q 142.34 = -261.26 – (-403.60) –0 = Total_Profit.q MtoM_Profit.q Accrued_Interest.q Clean Market Value CMV_q -840,288.87 = V.q =0 Profit Method = FX Interest Base currency figures • Data Symbol Example Formula MtoM Profit (Local) MtoM_Profit_Local.b 1,587.73 = 1,000,000 * 0.998784501 – 997,196.77 = A * D_f.b - V_bl.b Accrued Interest (Local) Accrued_Interest_Local.b Other Profit (Local) Other_Profit_Local.b -169.16 = 1,418.58 – 1,587.73 = Total_Profit_Local.b MtoM_Profit_Local.b FX Profit FX_Profit -9,055.68 = 1,000,000 * (1 / 1.2000 – 1 / 1.187100) = A * (1 / S - 1 / S_0) MtoM Profit MtoM_Profit.b 1,323.11 = 1,587.73 / 1.2000 = MtoM_Profit_Local.b / S Accrued Interest Accrued_Interest.b 0 = Accrued_Interest_Local.b / S Other Profit Other_Profit.b -115.58 = -7,848.15 – 1,323.11 – (-9,055.68) = Total_Profit.b MtoM_Profit.b - FX_Profit Clean Market Value CMV_b 832,179.45 = 832,179.45 - 0 = V - Accrued_Interest.b 398 =0 © Wall Street Systems IPH AB - Confidential 6 Forex 6.1 FX spot and FX forward • Quote currency figures Data Symbol Example Formula MtoM Profit (Local) MtoM_Profit_Local.q 186.78 = -843,497.48 * 0.996364809 – (-840,027.60) – (-590.38) = A.q * D_f.q - V_b.q Accrued_Interest.q Accrued Interest (Local) Accrued_Interest.q -590.38 = -840,027.60 *0.00516348) * (2004/08/16 2004/06/28) / 360 = V_bl.q * dr * (dt_f - dt_s) / B Other Profit (Local) Other_Profit.q 142.34 = -261.26 – 186.78 – (-590.38) = Total_Profit.q MtoM_Profit_Local.q Accrued_Interest.q Clean Market Value CMV_q -839,698.49 = -840,288.87 (-590.38) = V.q - Accrued_Interest.q Profit Method = FX IR DIfference No Discount • • Base currency figures Data Symbol Example Formula MtoM Profit (Local) MtoM_Profit_Local.b 2,288.57 = 1,000,000 * 0.998784501 997,196.77 - (-700.84) = A * D_f.b - V_bl.b Accrued_Interest_Local.b Accrued Interest (Local) Accrued_Interest_Local.b -700.84 = 997,196.77 * (-0.516348) * (2004/08/16 2004/06/28) / 360 = V_bl.b * (-dr) * (dt_f - dt_s) /B Other Profit (Local) Other_Profit_Local.b -169.16 = 1,418.58 2,288.57 - (-700.84) = Total_Profit_Local.b MtoM_Profit_Local.b Accrued_Interest_Local.b FX Profit FX_Profit -9,055.68 = 1,000,000 * (1/1.2 - 1/1.187100) = A * (1 / S - 1 / S_0) MtoM Profit MtoM_Profit.b 1,913.49 = (1,000,000 * 0.998784501 997,196.77) / 1.2 (-590.38) = (A * D_f.b - V_bl.b) / S Accrued_Interest.b Accrued Interest Accrued_Interest.b -590.38 = (-840,027.60) * 0.516348 * (2004/08/16 2004/06/28) / 360 = (V_bl.q) * dr * (dt_f - dt_s) / B Other Profit Other_Profit.b -115.58 = -7,848.15 1,913.49 - (-590.38) (-9,055.68) = Total_Profit.b - MtoM_Profit.b - Accrued_Interest.b - FX_Profit Clean Market Value CMV_b 832,769.83 = 832,179.45 - (-590.38) = V - Accrued_Interest.b Quote currency figures Data Symbol Example Formula MtoM Profit (Local) MtoM_Profit.q -403.60 = -843,497.48 * 0.996364809 (-840,027.60) = A.q * D_f.q - V_b.q Accrued Interest (Local) Accrued_Interest.q =0 Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 399 6 Forex 6.1 FX spot and FX forward Data Symbol Example Formula Other Profit (Local) Other_Profit.q 142.34 = -261.26 (-403.60) - 0 = Total_Profit.q - MtoM_Profit.q - Accrued_Interest.q Clean Market Value CMV_q -840,288.87 = V.q Profit Method = FX Implied Interest Base currency figures • Data Symbol Example Formula MtoM Profit (Local) MtoM_Profit_Local.b 94.71 = 1,000,000 * 0.998784501 – 997,196.77 – 1,493.03 = A * D_f.b - V_bl.b Accrued_Interest_Local.b Accrued Interest (Local) Accrued_Interest_Local.b 1,493.03 = 997,196.77 * 0.01100 * (2004/08/16 – 2004/06/28) / 360 = V_bl.b * r_0.b * (dt_f - dt_s) /B Other Profit (Local) Other_Profit_Local.b -169.16 = 1,418.58 – 94.71 -1,493.03 = Total_Profit_Local.b MtoM_Profit_Local.b Accrued_Interest_Local.b FX Profit FX_Profit -9,030.30 = 997,196.77 * (1 / 1.2000 – 1 / 1.187100) = V_bl.b * (1 / S – 1 / S_0) MtoM Profit MtoM_Profit.b 78.92 = 94.71 / 1.2000 = MtoM_Profit_Local.b / S Accrued Interest Accured_Interest.b 1,244.19 = 1,493.03 / 1.2000 = Accrued_Interest_Local.b / S Other Profit Other_Profit.b -140.96 = -7,848.15 – 78.92 - 1,244.19 – (-9,030.30) = Total_Profit.b - MtoM_Profit.b - Accrued_Interest.b - FX_Profit Clean Market Value CMV_b 830,935.27 = 832,179.45 -1,244.19 = V - Accrued_Interest.b Quote currency figures • Data Symbol Example Formula MtoM Profit (Local) MtoM_Profit.q 1,444.49 = -843,497.48 *0.996364809 – (-840,027.60) – (-1,848.09) = A.q * D_f.q - V_b.q Accrued_Interest.q Accrued Interest (Local) Accrued_Interest.q -1,848.08 = -840,027.60 * 0.01616348 * (2004/08/16 -2004/06/28) / B = V_bl.q * r_0.q * (dt_f - dt_s) /B Other Profit (Local) Other_Profit.q 142.34 = -261.26 – 1,444.49 – (-1,848.09) = Total_Profit.q - MtoM_Profit.q - Accrued_Interest.q Clean Market Value CMV_q -838,440.78 = -840,288.87 (-1,848.08) = V.q - Accrued_Interest.q 400 © Wall Street Systems IPH AB - Confidential 6 Forex 6.1 FX spot and FX forward Profit Method = FX Implied Yield • • Base currency figures Data Symbol Example Formula MtoM Profit (Local) MtoM_Profit_Local.b 95.69 = 1,000,000 * 0.998784501 – 997,196.77 - 1,492.05 = A * D_f.b - V_bl.b Accrued_Interest_Local.b Accrued Interest (Local) Accrued_Interest_Local.b 1,492.05 = 1,000,000*(POWER(1+0.0 1104512, -0.11944444) – POWER(1+0.01104512, -0.2555556)) =A* (POWER(1+Base_CCY_Yield, t_m) POWER(1+Base_CCY_Yield, -t_p)) Other Profit (Local) Other_Profit_Local.b -169.16 = 1,418.58 – 95.69 – 1,492.05 = Total_Profit_Local.b MtoM_Profit_Local.b Accrued_Interest_Local.b FX Profit FX_Profit -9,030.30 = 997,196.77 * (1 / 1.2000 – 1 / 1.187100) = V_bl.b * (1 / S – 1 / S_0) MtoM Profit MtoM_Profit.b 79.74 = 95.69 / 1.2000 = MtoM_Profit_Local.b / S Accrued Interest Accrued_Interest.b 1,243.37 = 1,492.05 / 1.2000 = Accrued_Interest_Local.b / S Other Profit Other_Profit.b -140.96 = -7,848.15 – 79.74 - 1,243.37 – (-9,030.30) = Total_Profit.b - MtoM_Profit.b - Accrued_Interest.b FX_Profit Clean Market Value CMV_b 830,936.08 = 832,179.45 - 1,243.37 = V - Accrued_Interest.b Quote currency figures Data Symbol Example Formula MtoM Profit (Local) MtoM_Profit.q 1,442.71 = -843,497.48 * 0.996364809 – (-840,027.60) = A.q * D_f.q - V_b.q Accrued_Interest.q Accrued Interest (Local) Accrued_Interest.q -1,846.30 = -843,497.48 * (POWER(1+0.01626098, 0.11944444) – POWER(1 + 0.01626098, - 0.2555556) = A.q * (POWER(1 + Quote_CCY_Yield, - t_m) POWER(1 + Quote_CCY_Yield, -t_p)) Other Profit (Local) Other_Profit.q 142.34 = -261.26 – 1,442.71 – (-1,846.30) =Total_Profit.q - MtoM_Profit.q - Accrued_Interest.q Clean Market Value CMV_q -838,442.56 = -840,288.87 (-1,846.30) = V.q - Accrued_Interest.q 6.1.5.2.3 Risk figures The risk method used for this FX forward deal is the Theoretical method. • Base currency figures Data Symbol Example Formula IR Exposure 1bp E_ip -9.94 = 1,000,000 * (-(0.11944444-0.00555556) * 0.01067917-t_s*D_f.b*D_s)/1.0*0.0001 = A * (-(t_m-t_s) * D_f.b * D_s - t_s *D_f.b* D_s) / S * 0.0001 FX Exposure E_fx 8,321.79 = 0.01 * 832,179.45 = e_fx * V Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 401 6 Forex 6.1 FX spot and FX forward Data Symbol Example Formula Effective Duration U_eff 0.1194444 = -9.94 / 832,179.45 / 0.0001 = -E_ip / V / 0.0001 Quote currency figures • Data Symbol Example Formula IR Exposure 1bp E_ipq 10.04 = -843,497.48 * (-(0.11944444-0.00555556) * 0.996364809*0.999830638-t_s*D_f.q*D_s) * 0.0001 = A.q * (-(t_m-t_s) * D_f.q * D_s - t_s * D_f.q * D_s) * 0.0001 FX Exposure E_fx Effective Duration U_eff =0 0.1194444 = 10.04 / (-840,288.87) / 0.0001 = -E_ipq / V.q / 0.0001 6.1.5.3 Calculations - Quoted valuation method In this section, numerical examples demonstrate how the different figures are calculated for the example FX forward deal using the Quoted valuation method. This example shows an FX forward Buy 1,000,000 USD/EUR 3M, with the following deal data. Transaction data Data Symbol Opening Date Example 2009-04-04 Spot Date dt_s 2009-04-07 Nominal Amount A_q 1,000,000 Deal Rate F_0 1.350000 FX Spot Rate S_0 1.400000 Base Spot FX Rate (Quote CCY) S_0_q 1.400000 Base Spot FX Rate (Base CCY) S_0_b 1.000000 Base FX Rate (Quote CCY) F_0_q 1.350000 Base FX Rate (Base CCY) F_0_b 1.000000 Base CCY Interest % r_0.b 2.000000% Maturity Date dt_m 2010-04-07 Date Basis (Base CCY) B_b 360 Date Basis (Quote CCY) B_q 360 Data Symbol Example Formula Base Amount A_b -740,740.74 =-A_q /F_0 IR Difference d_r 3.727042% =r_0.q*t_p_q / t_p_b -r_0.b Period t_p 1.0138889 =(dt_m-dt_s)/B_b Period (Quote CCY) t_p_q 1.0138889 =(dt_m-dt_s)/B_q Calculated transaction data 402 © Wall Street Systems IPH AB - Confidential 6 Forex 6.1 FX spot and FX forward Data Symbol Example Formula Base CCY Yield y_0.b 5.724808% =POWER(D_0_q, -1/t_p) - 1 Quote CCY Yield y_0.q 1.999724% =POWER(D_0_b,-1/t_p_q)-1 Discount Factor Base CCY: D_0_b 0.98012524 =1/(1+r_0_b * t_p_b) Quote CCY: D_0_q 0.94512077 =1/(1+r_0_q*t_p_q) Book/Reference Value Base CCY: V_b_b -700,089.46 =A_b * D_0_q Quote CCY: V_b_q 980,125.24 =A_q * D_0_b Data Symbol Example Formula Figure date dt_f 2009-06-15 Base CCY: D_V_b 0.971428368804 Market data on Figure Date Market Value Discount Factor Quote CCY: D_V_q Discount Factor Spot Base CCY: D_s_b 0.999862792158 Quote CCY: D_s_q FX Spot Rate FX Rate Time to maturity Base CCY: S_b 1.000000000 Quote CCY: S_q 1.2936 Base CCY: F_b 1.000000000 Quote CCY: F_q 1.2963 Base CCY: t_m_b 0.822222 =(dt_m- dt_f)/B_b Quote CCY: t_m_q 0.822222 =(dt_m - dt_f)/B_q 6.1.5.3.1 Valuation figures The valuation method used for this deal is the Quoted method. Data Market Value Result Value Symbol Example Formula Base CCY: V_b -719,576.57 =A_b * D_V_b / F_b Quote CCY: V_q 749,385.46 =A_q *D_V_q / F_q Base CCY: V_p_b -719,576.57 = A_b * D_V_b / F_0_b Quote CCY: V_p_q 719,576.57 = A_q * D_V_q / F_0_q 6.1.5.3.2 Result figures Data Symbol Example Formula Total Profit per CCY Base CCY: P_t_b 0.00 = V_b - V_p_b Quote CCY: P_t_q 29,808.89 = V_q - V_p_q Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 403 6 Forex 6.1 FX spot and FX forward Profit Method = FX Forward Data FX Profit MtoM Profit Other Profit Symbol Example Formula Base CCY: P_fx_b 0.00 =A_b * (1 / S_b-1 / S_0_b) * D_V_b Quote CCY: P_fx_q 57,072.17 = A_q * (1 / S_q-1 / S_0_q) * D_V_q Base CCY: P_mtom_b .00 =_b/D_s_b - V_p_b/D_s_b - P_fx_b Quote CCY: P_mtom_q -27,259.19 =V_q/D_s_q - V_p_q/D_s_q - P_fx_q Base CCY: 0.00 = P_t_b - P_fx_b - P_mtom_b Quote CCY: -4.09 = P_t_q - P_fx_q - P_mtom_q Profit Method = FX/IR Difference Data Symbol Example Formula Accrued Interest Base CCY: Ai_b .000000 =A_b*(1/S_0_b-1/F_0_b)*(t_p_b-t_m_b)/t_p_b Quote CCY: Ai_q -5,001.09 =A_q*(1/S_0_q-1/F_0_q) * (t_p_q t_m_q)/t_p_q Base CCY: .00 =P_fx_b Quote CCY: 57,072.17 =P_fx_q Base CCY: P_mtom_b_2 .00 =V_b/D_s_b - V_p_b / D_s_b - P_fx_b - Ai_b Quote CCY: P_mtom_q_2 -22,258.10 =V_q/D_s_q - V_p_q/D_s_q - P_fx_q - Ai_q Base CCY: .00 =P_t_b - P_fx_b - P_mtom_b_2 - Ai_b Quote CCY: -4.09 =P_t_q - P_fx_q - P_mtom_q_2 - Ai_q FX Profit MtoM Profit Other Profit Profit Method = FX/IR Difference No Discounting Data Symbol Example Formula Accrued Interest Base CCY: .00 =Ai_b Quote CCY: -5,001.09 =Ai_q Base CCY: P_fx_b_2 .00 =A_b*(1/S_b-1/S_0_b ) Quote CCY: P_fx_q_2 58,750.77 =A_q*(1/S_q-1/S_0_q) Base CCY: P_mtom_b_3 .00 = V_b/D_s_b - V_p_b / D_s_b - P_fx_b_2 Ai_b Quote CCY: P_mtom_q_3 -23,937.79 =V_q / D_s_q - V_p_q / D_s_q - P_fx_q_2 Ai_q Base CCY: missing .00 = P_t_b - P_fx_b_2 - P_mtom_b_3 - Ai_b Quote CCY: missing -4.09 =P_t_q - P_fx_q_2 - P_mtom_q_3 - Ai_q FX Profit MtoM Profit Other Profit 404 © Wall Street Systems IPH AB - Confidential 6 Forex 6.1 FX spot and FX forward Profit Method = FX Interest Data Accrued Interest FX Profit MtoM Profit Other Profit Symbol Example Formula Base CCY: Ai_b_3 -5,001.09 =A_b*(1 - F_0/S_0) * (t_p_b - t_m_b)/t_p_b Quote CCY: .00 =0 Base CCY: .00 =0 Quote CCY: 58,750.77 =P_fx_q_2 Base CCY: P_mtom_b_4 5,001.09 =V_b / D_s_b - V_p_b / D_s_b - P_fx_b_2 Ai_b_3 Quote CCY: P_mtom_q_4 -28,937.79 =V_q / D_s_q - V_p_q / D_s_q - P_fx_q_2 Base CCY: .00 =P_t_b - P_fx_b_2 - P_mtom_b_4 - Ai_b_3 Quote CCY: -4.09 =P_t_q - P_fx_q_2 - P_mtom_q_4 Profit Method = FX Implied Interest Data Accrued Interest FX Profit MtoM Profit Other Profit Symbol Example Formula Base CCY: Ai_b_2 -7,684.76 =A_b*r_0_q * (dt_f-dt_s)/B_q *D_0_q / S_b Quote CCY: Ai_q_2 2,904.41 =A_q*r_0_b * (dt_f-dt_s)/B_b *D_0_b / S_q Base CCY: P_fx_b_3 .00 =0 Quote CCY: P_fx_q_3 57,583.12 =V_b_q * (1/S_q-1/S_0_q) Base CCY: P_mtom_b_5 7,684.76 =V_b / D_s_b - V_p_b / D_s_b - P_fx_b_3 Ai_b_2 Quote CCY: P_mtom_q_5 -30,674.55 =V_q / D_s_q - V_p_q / D_s_q - P_fx_q_3 Ai_q_2 Base CCY: .00 =P_t_b - P_fx_b_3 - P_mtom_b_5- Ai_b_2 Quote CCY: -4.09 =P_t_q - P_fx_q_3 - P_mtom_q_5- Ai_q_2 Profit Method = FX Implied Yield Data Symbol Example Formula Accrued Interest Base CCY: Ai_b_4 -7,509.92 =A_b * (POWER(1+y_0.b,-t_m_b) -POWER(1+y_0.b,-t_p ))/S_b Quote CCY: Ai_q_4 2,880.82 =A_q * (POWER(1+y_0.q,-t_m_q) -POWER(1+y_0.q,-t_p ))/S_q Base CCY: .00 =0 Quote CCY: 57,583.12 =P_fx_q_3 Base CCY: P_mtom_b_6 7,509.92 =V_b / D_s_b - V_p_b / D_s_b - P_fx_b_3 Ai_b_4 FX Profit MtoM Profit Other Profit Quote CCY: P_mtom_q_6 -30,650.96 =V_q / D_s_q - V_p_q / D_s_q - P_fx_q_3 Ai_q_4 Base CCY: .00 =P_t_b - P_fx_b_3 - P_mtom_b_6- Ai_b_4 Quote CCY: -4.09 =P_t_q - P_fx_q_3 - P_mtom_q_6- Ai_q_4 6.1.5.3.3 Risk figures The risk method used for this FX forward deal is the Theoretical method: see 6.1.5.2.3 Risk figures on page 401. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 405 6 Forex 6.2 Average FX rate forward 6.2 Average FX rate forward An average rate forward gives the buyer the ability to create a hedge rate for a future exposure by locking in forward points and a spot rate today. At some point in the future, there is an averaging period of spot observations to determine an average rate which, when compared to the hedge rate, will set the payout. Unlike options, this hedge tool is a forward contract and has no premium cost associated with it. If the receivable currency is weaker during the averaging period compared to the hedge rate, the forward seller will make a payment to the forward buyer. Conversely, if the receivable currency appreciates during the averaging period, the forward buyer must make a payment to the forward seller. These structures are cash-settled. 6.2.1 Instrument setup Average FX rate forwards are based on an instrument type derived from the class FX. • Main characteristics Average FX rate forwards are set up in a similar way to non-deliverable FX forwards, except that you can configure the type of average rate forward in terms of observation dates and weights: Information Description Observation Method Choices are: Irregular and Business Days. • If you select Business Days, observation dates are defined for all business days (regarding the fixing currency at transaction level) between the spot date and the value date - the fixing offset (specified in the Netting page). • If you select Irregular, you can define the observation dates and weights at deal entry in the views Observation Date and Observation Schedule in Transaction Manager. Choices are: Irregular Weights and Equally Weighted (default). Weighting Method Note: Only editable when the observation method is Irregular. Average Rounding Method Average Rounding Rounding method and precision to be used for the average. See A.2.41 Average FX Rate Forward on page 728. 6.2.2 Deal capture 6.2.2.1 Input data In addition to the standard deal parameters, the following mandatory information is required to enter an average FX rate forward transaction. See 6.1.3.1 Input data on page 384. • Transaction view Note: This information defaults to the information defined at the instrument level. 406 Information Description Observation Method Choices are: Irregular and Business Days. • If you select Business Days, observation dates are defined for all business days (regarding the fixing currency at transaction level) between the spot date and the value date - the fixing offset (specified in the Netting page). • If you select Irregular, you can define the observation dates and weights at deal entry in the views Observation Date and Observation Schedule in Transaction Manager. © Wall Street Systems IPH AB - Confidential 6 Forex 6.2 Average FX rate forward Information Description Weighting Method Choices are: Equally Weighted (default) and Irregular Weights. If you select Irregular Weights, you will need to enter the weights manually at the transaction level in the Observation Date view. Note: Only editable when the observation method is Irregular. Average Rounding Method Average Rounding Rounding method and precision to be used for the average. The Fixing Calendar field can be edited at the transaction level to enable the user to specify the calendar to be used to generate the observation dates. The Fixing Subscenario field can be edited to specify the subscenario to be used for FX rates observations. When the observation method is set to Business Days, the observation dates are defined by the business days (according to the fixing calendar specified at the transaction level) between spot date and value date – fixing offset (specified at the instrument level in the Netting page) If you selected to use the Irregular method, you need to provide the relevant information in order to generate the observation dates. • Observation Schedule view Information Description Start Date Defaults to the spot date of the transaction. End Date Defaults to the transaction value value - the fixing offset. Method Combined with the specified frequency defines how often the cashflows will be generated. (Used with Frequency.) • Days, Business Days, Weeks, Months or Years: One flow every specified frequency days or business days or weeks or months or years. For example, if you select year and you specify a frequency of 1, you will have one flow every year; a frequency of 2, one flow every two years, and so on. • Times/Year: The specified frequency determines how many times per year. For example, if you specify a frequency of 1, the cashflows will be generated once per year; if you specify 2, the cashflows will be generated twice per year. • Last of Month: One flow the last day of every specified frequency month. • Months (sticky): The same as Last of Month, if the end date falls at month end, otherwise like Months. • ISDA Dates (Q): 15 March, 15 June, 15 Sept. and 15 Dec. • IMM Dates (M): One flow every 3rd Wednesday of every specified frequency month • Manual: Select if you want to be able to enter the dates directly in the Observation Date view. When this method is selected, the dates will no longer be generated from the transaction, and the following fields are cleared and are no longer editable. Frequency Number of time units (to be used with Method). Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 407 6 Forex 6.2 Average FX rate forward Information Description Convention Convention used to adjust the observation dates: • Backward - previous business day • Following - next business day • Modified Backward - previous business day except if not in the same month (next in this case) • Modified Following - next business day except if not in the same month • None - no adjustment. (previous in this case) Holiday Calendar Additional calendar to supplement the calendar specified in the Fixing Calendar column (at the transaction level). Roll from Start Yes or No: When set to Yes, dates are calculated from Start Date rather than from the End Date. Long Stub Yes or No: To change the first coupon period to a long first coupon. By default, it is a short first coupon when the period is broken. For example, selecting Yes in the Roll from Start field causes a long last coupon. Fixed Roll Date • Specific date to be used in the schedule each year, without reference to the year: for example, 15 March annually. Observation Date Information Description Observation Date If you selected to enter the observation dates manually (Manual method in the Observation Schedule view), enter the dates, otherwise the dates generated from the inputs in the observation schedule are displayed. Weight Enter the weight if you selected the Irregular Weights method. 6.2.2.2 Generated data The generated cashflows are the same as for non-deliverable forwards, i.e. two pseudo FX settlement flows and one netting flow. 6.2.3 Processing This section describes the actions that can be done throughout the life of an average FX rate forward transaction. These actions are similar to those that can be done on non-deliverable forwards except for the differences explained further on. 6.2.3.1 Early expiration This action remains unchanged to FX non-deliverable forwards, except that the defaulted FX Forward Rate is replaced by the average of the already observed FX Rate and Forward FX rate based on the early expiration date: • Execution Right-click the transaction and select Early Expiration. As well as the usual information for an early expiration on a standard FX non-deliverable forward, the following information is required: 408 Information Description Avg FX Observed Rate Average value of already observed Fx rates. © Wall Street Systems IPH AB - Confidential 6 Forex 6.3 Open Window FX Forward (FX Time Option) Information Description Avg FX Forecasted Rate Average value of the forecast value of FX Rate (observations in the future according to the early expiration date). Avg FX Forward Rate Average value of the observed and forecast FX rates. See 6.1.4.2 Early expiration of NDFs on page 388. 6.2.3.2 Netting The netting action is similar to the netting action of a non-deliverable forward FX instrument, except that the FX Rate is replaced by the Average FX Rate. • Execution Right-click the netting cashflow and select Execute Netting. As well as the usual information for a netting action on a standard FX non-deliverable forward, the following information is needed: Information Description Avg FX Rate Defaults to the average value of past observation dates. Netting Amount Computed and rounded according to the values defined at the instrument and transaction levels. As usual, the execution of this action sets the amount of the netting cashflow, and stores the netting price in the Nominal Rate field at the cashflow level. See 6.1.4.5 Netting on page 392. 6.2.4 Position monitoring 6.2.4.1 Setup You need to use the specific valuation feature Average FX Rate Valuation to support specific Quoted valuation needed for this instrument. See A.2.42 Average FX Rate Valuation on page 728. 6.2.4.2 Calculations With this valuation feature Average FX Rate Valuation, the average rate forward is taken instead of forward FX rate when computing market value. Indeed, the cashflow is converted using the forward rate between cashflow currency and valuation currency before being discounted with valuation currency interest rate. The average rate is computed with the already observed FX rates and forecasted FX rates for the future dates regarding the valuation. This average FX rate is visible in Figure FX Rate. The Theoretical valuation is the same as for FX non-deliverable forward instruments. See 6.1.5 Position monitoring on page 393. 6.3 Open Window FX Forward (FX Time Option) An open window FX forward differs from a regular FX Forward in that the owner of the contract can choose the date (from within a defined time window) when the forward cashflows are exchanged. This means that the transaction is specified in terms of a maturity window rather than a single maturity date. The owner of the contract must also be specified. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 409 6 Forex 6.3 Open Window FX Forward (FX Time Option) 6.3.1 Instrument setup Open Window FX Forward instruments are based on an instrument type derived from the class FX-TIME-OPTION. Main characteristics • The main characteristics of an Open Window FX Forward instrument are defined using the primary feature FX Time Option. – Date information It is possible to define the periods for which the start and end of the exercise window are derived. – Information Description Value Date Period Period from which start of exercise window is derived. Maturity Date Period Period from which end of exercise window is derived. Time option owner It is possible to define the owner (counterparty or portfolio owner). Information Description Base Currency Base and quote currencies for the instrument. Quote Currency Leave these fields blank if you want to specify the currencies when you enter the deal. Transaction Sign Owner Sign to be applied to the transaction: Any (default), Buy/Lend, or Sell/Borrow: • Select Any or leave this field blank if you want to specify the direction of the transaction when you enter the deal. • Select either Buy/Lend or Sell/Borrow if you want this to be the direction of the transactions, that is, the direction cannot be modified at deal entry. Owner of the contract. Select Counterparty or Portfolio Owner. Leave this field blank if you want to specify the owner when you enter the deal. Note: This is used with Optimal maturity method when you are using the valuation approach FX Time Option Valuation. See A.2.198 FX Time Option on page 810. 6.3.2 Deal capture In addition to the standard deal parameters, the following information is required to enter an open window FX forward transaction: Information Description Value Date Start of the exercise period Maturity Date End of the exercise period. Time option owner The person who chooses the exercise day of the transaction (Portfolio Owner or Counterparty). If the owner is not defined at instrument level, it can be specified at the transaction level. Note: This is used with Optimal maturity method when you are using the valuation approach FX Time Option Valuation Method. 410 © Wall Street Systems IPH AB - Confidential 6 Forex 6.3 Open Window FX Forward (FX Time Option) 6.3.3 Processing This section describes the actions that can be done throughout the life of an FX transaction. 6.3.3.1 Exercise Within the window period, it is possible to exercise the transaction. That is, to determine the payment dates of the cashflows. • Execution The following information is needed to process the early expiration: Information Description Early Expiration Date Date when the exercise is done. Value Date Date when the early expiration is settled. This cannot be later than the maturity date of the initial transaction. Amount Left Remaining amount of the initial transaction. (Read-only.) Amount to Expire Amount to be exercised. This defaults to the amount left and is expressed in the same currency (base or quote) as the input amount of the initial transaction. You can enter any amount between 0 and the remaining amount of the initial transaction. Currency The currency in which the above amount is expressed, can be base or quote currency depending on the initial transaction. (Read-only.) Deal Rate Agreed forward rate for the exercised transaction. Quote Amount The corresponding amount of the transaction. Quote Currency Shows the currency of the deal. The currency can be quote or base depending on default Currency. By default, this is today’s date unless a Fixing/Action Date is specified at transaction level. 6.3.4 Position monitoring 6.3.4.1 Setup Time option valuation is chosen with the feature FX-TIME-OPTION-METHOD. Information Description Maturity Method Choose from Earliest, Latest, Optimal Valuation Modes Choose from Benchmark, Default, Theoretical. 6.3.4.2 Calculations This section describes the valuation and provides numerical examples to illustrate the calculations of Open Window FX Forward (FX Time Option) deals. 6.3.4.2.1 Valuation FX Time Option instruments use a special valuation feature FX Time Option Valuation (A.2.199 FX Time Option Valuation on page 811). This valuation method simply creates a virtual payment date for the forward cashflows, and then uses the standard fixed method for key figures. That is, the calculation of an Open Window FX Forward (FX Time Option) deal is similar to that of a regular FX Forward (6.1 FX spot and FX forward on page 383), except that we need to assume a payment date (from within a defined time window). To do this, the user chooses a maturity method from the available methods: • Earliest: Calculate open transactions with maturity at the start of the window. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 411 6 Forex 6.3 Open Window FX Forward (FX Time Option) Latest: Calculate open transactions with maturity at the end of the window. • For Earliest or Latest method, the payment date is directly copied from the window. Optimal: Calculate open transactions with maturity at either start (earliest) or end (latest) of the window, so that the value for the owner is maximized. Refer to the following section for a detailed description of the calculation. • Optimal method calculation For the Optimal method, the following logic is used to determine whether the start or end date of the window should be chosen as the virtual payment date to obtain the best value for the time option owner. (To set up the owner refer to 6.3.1 Instrument setup on page 410.) Let Ab and Aq be the (absolute) amounts of the bought and sold currencies, respectively, and Sb and Sq the corresponding spot exchange rates against the portfolio currency. Let D1b , D2b , D1q , D2q be the discount factors for the two currencies (superscript q or b) for the start and the end of the window (subscript 1 or 2). Then, if we own the right to choose the exercise date (Owner set to Portfolio Owner), the closer date is chosen if Equation 6-1 S b Ab D1b − S q Aq D1q > S b Ab D 2b − S q Aq D 2q Otherwise, the end date of the window is chosen. If the counterparty owns the right to choose (Owner set to Counterparty), then the decision logic is reversed. If Quoted valuation method is used, the closer date is chosen if Equation 6-2 Quoted valuation method Fb1 Ab D1p − Fq1 As D1p > Fb2 Ab D 2p − Fq2 As D 2p where now all discount factors are in portfolio currency, and Fi j are forward FX rates between the cashflow and portfolio currencies. If the currency pair’s figure spot date is within the window period, the start date used in the valuation is the spot date corresponding to the figure date. Result calculations are similar to those of an FX forward maturing on the virtual payment date. However, accrued interest is always calculated for the maturity period, regardless of the virtual payment date. 6.3.4.3 Numerical examples The numerical examples in this section demonstrate how the different figures are calculated for the example Open Window FX forward deal using the Theoretical valuation method. This example shows an FX forward Buy 1,000,000 USD/EUR 3M, with the following deal data: Setup • Data Valuation Method 412 Symbol Example Theoretical © Wall Street Systems IPH AB - Confidential 6 Forex 6.3 Open Window FX Forward (FX Time Option) • • Transaction data Data Symbol Example Opening Date dt_o 2007-11-09 Spot Date dt_s 2007-11-13 Nominal Amount A 1,000,000 Deal Rate F_0 2.050000 FX Spot Rate S_0 2.010000 Base FX Spot Rate S_B.b 1.430000 (base) Base FX Spot Rate S_B.q 1.405594 (quote) Base FX Rate F_B.* 1.434600 Base CCY Interest % r_0.b 5.000000% Value Date dt_v 2008-06-16 Maturity Date dt_m 2008-12-15 Date Basis (Base CCY) B 360 Date Basis (Quote CCY) B.q 365 Symbol Example Formula 1,000,000.00 =A Calculated transaction data Data Amount (Base CCY) • Amount (Quote CCY) A.q -487,804.88 = -A / F_0 FX Forward Points p_fx 400 =10000*(F_0-S_0) IR Difference dr -1.862483% = (S_0 / F_0 / D.b - 1) / t_p-r_0.b Quote CCY Interest % r_0.q End Period t_p 1.1055556 =(dt_m-dt_s)/B Other important calculated transaction data Data Symbol Example Formula Discount Factor D.b 0.94761779 =1/(1+r_0.b*t_p) 1,000,000.00 =A Base Value (Base CCY) • Base Value (Quote CCY) BaseValue.q -497,512.44 =-A / S_0 Result Value (Base CCY) ResultValue.b 662,669.79 =ResultValueLocal.b /S_B.b Result Value (Quote CCY) ResultValue.q -662,669.59 =ResultValueLocal.q * S_B.q Local Result Value (Base CCY) ResultValueLocal.b 947,617.79 = A * D.b Local Result Value (Quote CCY) ResultValueLocal.q -471,451.64 =-ResultValueLocal.b / S_0 Data Symbol Example Figure Date dt_f 12/12/2007 Market Data on Figure Date Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 413 6 Forex 6.3 Open Window FX Forward (FX Time Option) Data Symbol Example FX Spot Rate (Base CCY) F_S.b 1.4844 FX Spot Rate (Quote CCY) F_S.q 1.390697 Calculated Market Data on Figure Date • Data Symbol Example Formula FX Convert (Base CCY) S 0.673673 = 1 / F_S.b FX Convert (Quote CCY) S.q 1.390697 =F_S.q MV Discount Factor Start (Base CCY) D_V.s.b 0.961217301872 MV Discount Factor Start (Quote CCY) D_V.s.q 0.970243996748 MV Discount Factor End (Base CCY) D_V.e.b 0.925429031747 MV Discount Factor End (Quote CCY) D_V.e.q 0.942867984024 Discount Factor Spot (Base CCY) D_s 0.99975004706 Discount Factor Spot (Quote CCY) D_s.q 0.99975004706 6.3.4.3.1 Window start Key Figures on Figure Date Data Symbol Example Formula Local Market Value (Base CCY) LocalMarketV alue.s.b 961,217.30 =A*D_V.s.b Local Market Value (Quote CCY) LocalMarketV alue.s.q -473,289.75 =A.q*D_V.s.q Market Value (Base CCY) V.s.b 647,546.01 =LocalMarketValue.s.b * S Market Value (Quote CCY) V.s.q -639,631.06 =LocalMarketValue.s.q * S.q Result Figures - Method FX Forward Data Symbol Example Formula Local Total Profit (Base CCY) TotalProfitLo cal.s.b 13,599.51 =LocalMarketValue.s.b ResultValueLocal.b Local Total Profit (Quote CCY) TotalProfitLo cal.s.q -1,838.12 = LocalMarketValue.s.q ResultValueLocal.q Total Profit (Base CCY) TotalProfit.s. b -15,123.77 = V.s.b - ResultValue.b Total Profit (Quote CCY) TotalProfit.s. q 4,466.95 =V.s.q - ResultValue.q Local MtoM Profit (Base CCY) MtoMProfitLo cal.s.b 13,839.83 = A * D_V.s.b/D_s ResultValueLocal.b 414 © Wall Street Systems IPH AB - Confidential 6 Forex 6.3 Open Window FX Forward (FX Time Option) Data Symbol Example Formula Local MtoM Profit (Quote CCY) MtoMProfitLo cal.s.q -2,663.78 = A.q * D_V.s.q/D_s.q ResultValueLocal.q AccruedInterestLocal.s.q Local Accrued Interest (Quote CCY) AccruedInter estLocal.s.q 707.33 = ResultValueLocal.q * dr * (dt_f dt_s) / B Local Other Profit (Base CCY) Other_Profit _Local.b -240.32 =TotalProfitLocal.s.b-MtoMProfitLoca l.s.b 118.33 =TotalProfitLocal.s.q MtoMProfitLocal.s.q AccruedInterestLocal.s.q Local Other Profit (Quote CCY) FX Profit (Base CCY) FXProfit.s.b -25,627.83 = A * (1/F_S.b-1/S_B.b) FX Profit (Quote CCY) FXProfit.s.q 7,411.44 = BaseValue.q * (F_S.q-S_B.q) MtoM Profit (Base CCY) MtoMProfit.s. b 9,323.52 = MtoMProfitLocal.s.b / F_S.b MtoM Profit (Quote CCY) MtoMProfit.s. q -3,704.51 =MtoMProfitLocal.s.q * F_S.q Accrued Interest (Quote CCY) AccruedInter est.s.q 983.69 =AccruedInterestLocal.s.q * S.q Other Profit (Base CCY) Other_Profit _h 1,180.55 = TotalProfit.s.b - MtoMProfit.s.b FXProfit.s.b -223.67 = TotalProfit.s.q - FXProfit.s.q -MtoMProfit.s.q -AccruedInterest.s.q Other Profit (Quote CCY) 6.3.4.3.2 Window end Key Figures on Figure Date Data Symbol Example Formula Local Market Value (Base CCY) LocalMarket Value.e.b 925,429.03 =A*D_V.e.b Local Market Value (Quote CCY) LocalMarket Value.e.q -459,935.60 =A.q*D_V.e.q Market Value (Base CCY) V.e.b 623,436.43 =LocalMarketValue.e.b * S Market Value (Quote CCY) V.e.q -639,631.06 =LocalMarketValue.e.q * S.q Data Symbol Example Formula Local Total Profit (Base CCY) TotalProfitLo cal.e.b -22,188.76 =LocalMarketValue.e.b ResultValueLocal.b Local Total Profit (Quote CCY) TotalProfitLo cal.e.q 11,516.04 = LocalMarketValue.e.q ResultValueLocal.q Total Profit (Base CCY) TotalProfit.e. b -39,233.36 = V.e.b - ResultValue.b Total Profit (Quote CCY) TotalProfit.e. q 23,038.53 =V.e.q - ResultValue.q Result Figures - Method FX Forward Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 415 6 Forex 6.4 FX swap Data Symbol Example Formula Local MtoM Profit (Base CCY) MtoMProfitLo cal.e.b -21,957.39 = A * D_V.e.b/D_s ResultValueLocal.b Local MtoM Profit (Quote CCY) MtoMProfitLo cal.e.q 10,693.71 = A.q * D_V.e.q /D_s.qResultValueLocal.q AccruedInterestLocal.e.q Local Accrued Interest (Quote CCY) AccruedInter estLocal.e.q 707.33 = ResultValueLocal.q * dr * (dt_f dt_s) / B Local Other Profit (Base CCY) -231.37 =TotalProfitLocal.e.b MtoMProfitLocal.e.b Local Other Profit (Quote CCY) 114.99 =TotalProfitLocal.e.q MtoMProfitLocal.e.q AccruedInterestLocal.e.q FX Profit (Base CCY) FXProfit.e.b -25,627.83 = A * (1/F_S.b-1/S_B.b) FX Profit (Quote CCY) FXProfit.e.q 7,411.44 =BaseValue.q * (F_S.q-S_B.q) MtoM Profit (Base CCY) MtoMProfit.e .b -14,792.10 =MtoMProfitLocal.e.b / F_S.b MtoM Profit (Quote CCY) MtoMProfit.e .q 14,871.71 =MtoMProfitLocal.e.q * F_S.q Accrued Interest (Quote CCY) AccruedInter est.e.q 983.69 = AccruedInterestLocal.e.q * F_S.q Other Profit (Base CCY) OtherProfit.e .b 1,186.57 =TotalProfit.e.b - FXProfit.e.b MtoMProfit.e.b Other Profit (Quote CCY) OtherProfit.e .q -228.31 =TotalProfit.e.q - MtoMProfit.e.q AccruedInterest.e.q - FXProfit.e.q 6.4 FX swap A currency swap transaction in the inter-bank market is the simultaneous purchase and sale of a given amount of foreign exchange for two different value dates. Both purchase and sale are with the same counterparty. A common type of swap is spot against forward. The dealer buys a currency as a spot market transaction and simultaneously sells the same amount back to the same counterparty as a forward transaction. Since this is executed as a single transaction with the same counterparty, TRM has a separate trade entry for FX swap transactions. In TRM, FX swaps belong to the instrument class FX-SWAP. 6.4.1 Instrument setup FX swaps are based on an instrument type derived from the class FX-SWAP. They are set up in a similar way to FX spot/forward instruments. • FX Swap main characteristics For an FX swap, you may want to set up maturity date and value date information. The maturity of the contract is calculated using the periods specified for both the maturity date and the value date. For example, to define a 3M/6M forward FX swap, you need to specify 3M for both periods. 416 © Wall Street Systems IPH AB - Confidential 6 Forex 6.4 FX swap For maturity and value date information: Information Description Gap Set Gap set used for supplying the value date periods; these in turn are used to define exact dates. Value Date Period Value date period used to calculate the value date for the instrument at deal entry. If this is specified at the instrument level, it is used as default in the transaction and cannot be modified. Maturity Date Period Maturity period used to calculate the maturity date for an instrument at deal entry, for example, 6M or 1Y. If you specify the maturity date period in the instrument setup, this is used as the default in the transaction and cannot be modified. Spot Days Number of business days between opening and value dates. Defaults to currency spot days when left blank. Note: It is recommended not to specify the spot days in the instrument setup as these are taken by default from the spot days of the two currencies at deal entry. Calendar Calendar and Holiday Calendar used to calculate the value date. Holiday Calendar If you enter both a Calendar and a Holiday Calendar, the value date calculation takes both calendars into account. Note: When you define the Calendar or Holiday Calendar in one date setup, the Calendar fields in all date setup pages applied to the instrument default to the same values. Spot Time Cut-off time for operations. Spot Time Zone For global operations, a cut-off time has to be defined: deals before that time have the number of spot days calculated from that day; deals after that time have the spot days calculated from the following day. Define a time (Spot Time) within a selected time zone (Spot Time Zone). The market convention is 5 p.m. New York time. A.2.193 FX Swap on page 807. • Currency information You can specify the currencies of the FX swap either in the instrument setup or at deal entry. See A.2.192 FX Setup on page 806. • Forward points calculation You can specify whether forward points are taken from the market or calculated. If you do not define a method for obtaining or calculating forward points, the FX spot rate is taken from the market and the forward points need to be input manually. See A.2.175 FX Forward on page 797. • FX cross rate calculation For an FX swap where neither currency is the portfolio base currency, you need to define how the FX rates (Base Spot FX and Base FX Rate) are calculated. See A.2.171 FX Cross Method on page 796. For an FX swap, it is also possible to set up: • Cashflow and transaction charge rules • Manual charges • Branch codes • Competitive Rates (FX Swap) Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 417 6 Forex 6.4 FX swap • FX Swap Margin. See Appendix A Features on page 713. 6.4.2 Market information 6.4.2.1 Currencies Some additional parameters need to be defined for the currencies which are relevant to your FX transactions: see the TRM User Guide. 6.4.2.2 Quotations and market information Quotations for currencies can be viewed and modified in Rate Monitor. It is possible to define market information feeds for each currency (for example, from Reuters): see the TRM User Guide. 6.4.3 Deal capture 6.4.3.1 Input data In addition to the standard deal parameters, the following information is needed to enter an FX swap transaction: • FX swap (input forward points) In addition to the standard deal parameters, the following information is required to enter an FX swap transaction where the forward points are input manually: Information Description Base Currency (Currency) Base currency of the transaction. Quote Currency (Currency 2nd) Quote currency of the transaction. Value Date Date of the near leg (spot transaction). Maturity Date Date of the far leg (forward transaction) and maturity of the contract. FX Base Spot Amount Amount of the near leg (spot transaction) in the base currency. FX Quote Spot Amount Amount of the near leg (spot transaction) in the quote currency. Nominal/Spot Rate Exchange rate of the near leg (spot transaction). FX Forward Points Forward points for the transaction. Deal Rate Exchange rate of the far leg = Nominal / Spot Rate + FX Forward Points (+ Margins if applicable) • Uneven FX swap In addition to the standard deal parameters, the following information is required to enter an uneven FX swap transaction, where the input amount of the near leg is different from the input amount of the far leg: 418 Information Description Base Currency (Currency) Base currency of the transaction. © Wall Street Systems IPH AB - Confidential 6 Forex 6.4 FX swap Information Description Quote Currency (Currency 2nd) Quote currency of the transaction. Value Date Date of the near leg (spot transaction). Maturity Date Date of the far leg (forward transaction) and maturity of the contract. FX Base Spot Amount Amount of the near leg (spot transaction) in the base currency. FX Quote Spot Amount Amount of the near leg (spot transaction) in the quote currency. FX Base Amount Amount of the far leg (forward transaction) in the base currency. FX Quote Amount Amount of the far leg (forward transaction) in the quote currency. Nominal/Spot Rate Exchange Rate of the near leg (spot transaction) FX Forward Points Forward points for the transaction. Deal Rate Exchange rate of the far leg = Nominal / Spot Rate + FX Forward Points (+ Margins if applicable) • FX swap (with interest rate) In addition to the standard deal parameters, the following information is required to enter an FX swap transaction with interest rate where the forward points are input manually: Information Description Base Currency (Currency) Base currency of the transaction. Quote Currency (Currency 2nd) Quote currency of the transaction. Value Date Date of the near leg (spot transaction). Maturity Date Date of the far leg (forward transaction) and maturity of the contract. FX Base Spot Amount Amount of the near leg (spot transaction) in the base currency. FX Quote Spot Amount Amount of the near leg (spot transaction) in the quote currency. Nominal/Spot Rate Exchange Rate of the near leg (spot transaction) FX Finance Rate Implied borrowing rate for an FX swap transaction. FX Forward Points Forward points for the transaction. Deal Rate Exchange rate of the far leg = Nominal / Spot Rate + FX Forward Points (+ Margins if applicable) 6.4.3.2 Generated data • Cashflows Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 419 6 Forex 6.4 FX swap The figure below illustrates the cashflows which are established in TRM for an FX swap transaction. The figure below illustrates the cashflows which are established in TRM for a forward FX swap transaction. 6.4.4 Processing This section describes the actions that can be done throughout the life of an FX swap. 6.4.4.1 Early expiration You can force the forward leg of an FX swap to mature earlier using the action Early Expiration. • Execution The following information is needed to process the early expiration: Information Description Early Expiration Date Date when the early expiration is executed. By default, this is today’s date unless a Fixing/Action Date is specified at transaction level. Opening Date must be after the near leg of the initial FX swap. Value Date Date when the early expiration is settled. This cannot be later than the maturity date of the initial transaction. Amount Amount to be early-expired. This defaults to the amount left and is expressed in the same currency (base or quote) as the input amount of the initial transaction. You can enter any amount between 0 and the remaining amount of the initial transaction. Deal Rate Deal rate for the early expiration transaction. Deal Rate = Original Spot Rate - Forward Points Forward Points Forward points of the early expiration transaction. This defaults to the number of forward points between the early expiration date and the maturity date of the initial transaction. The execution generates an early expiration transaction with the following attributes: 420 © Wall Street Systems IPH AB - Confidential 6 Forex 6.4 FX swap If the original input amount was Base Amount: FX Base amount = amount to expire If the original input amount was Quote Amount: FX Quote amount = amount to expire Deal Rate = early expiration deal rate Opening date = date when the early expiration is done Value date = date when the early expiration is settled Kind = Early Expiration The remaining attributes are inherited from the initial transaction. • Cancellation You can undo the early expiration by canceling the early expiration transaction. 6.4.4.2 Roll over You can defer the maturity of the forward leg of an FX swap to a later date. This process is referred to as roll-over. See A.2.11 Allow Roll Over (FX) on page 717. • Execution If the Spot Rate for the roll-over equals the Original Deal Rate, the following information is needed to process the roll over: Information Description Roll Over Date Date when the roll over is done. Maturity Date New maturity date of the FX deal. This must be later than the maturity date of the initial transaction. Amount Amount to roll over defaults to the amount left and is expressed in the same currency (base or quote) as the input amount of the initial transaction. You can enter any amount between 0 and the remaining amount of the initial transaction. Forward Points Forward points of the roll over transaction. This defaults to the number of forward points from the roll over date to the maturity date. Deal Rate Deal rate for the roll over. Deal Rate = Original Spot Rate + Forward Points The execution generates a roll over transaction with the following attributes: If the original input amount was FX Base Amount: FX Base amount = amount to roll over If the original input amount was FX Quote Amount: FX Quote amount = amount to roll over Deal Rate = roll over deal rate Opening Date = date when the roll over is done Maturity Date = new maturity date Kind = Roll Over The remaining attributes are inherited from the initial transaction. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 421 6 Forex 6.5 Cost-of-funding FX swap If the Spot Rate for the roll-over is different from the Original Deal Rate, the following additional information is needed to process the roll over and settle the subsequent difference: Information Description Settle Differential Switch on if the Spot Rate for the roll-over is different from the Original Deal Rate. By default, this switch is off. Spot Rate If Settle Differential is activated, this field becomes available. Spot Rate defaults to the spot rate of the market but this value can be modified. The Forward Points and Deal rate are adjusted automatically. Base CCY Interest % Interest rate of the base currency for the period from the original settlement date to the new settlement date. Quote CCY Interest % Interest rate of the quote currency for the period from the original settlement date to the new settlement date. Deal Rate Deal rate for the roll over. Deal Rate = Spot Rate + Forward Points The execution generates a roll over transaction as before with an additional cashflow as follows: A netting cashflow is created to handle the settlement of the difference Value Date = Roll over value date Currency = Roll over currency 2 Amount = Base Amount * Original Deal Rate - (-Base Amount * Spot Rate) • Cancellation You can undo the roll over by canceling the roll over transaction. 6.4.4.3 Currency pair shift It is possible to split a position from one underlying currency pair into two new positions, each of which contains one of the currencies with a third currency (usually, the portfolio currency). This process is called an FX Pair Shift. • Setup The FX Pair Shift action is available on an FX swap transaction if the Allow FX Currency Pair Shift feature is included in the instrument definition: see A.2.7 Allow FX Currency Pair Shift on page 716. • Execution See the TRM User Guide for information about this action. 6.4.5 Position monitoring Figures for FX swaps are calculated in the same way as the figures for FX forwards: see 6.1.5 Position monitoring on page 393. 6.5 Cost-of-funding FX swap Cost-of-funding FX swaps are a special case of FX swap, where the nominal amount for the far leg is based on the nominal amount of the near leg and an interest rate component. This instrument enables you to set up defaulting for the interest rate/spread value. Then, at deal entry, the base amount of the far leg will be defaulted to the base amount of the near leg with the interest computed between the value date and the maturity date of the FX swap. 422 © Wall Street Systems IPH AB - Confidential 6 Forex 6.5 Cost-of-funding FX swap This interest is computed based on the interest rate and the spread value according to date basis of the base currency. FX quote amounts are defaulted as usual from base amounts by using FX rate/forward points. 6.5.1 Instrument setup The set up is the same as for a standard FX swap except that you need to attach the trading feature FX Swap Cost-of-Funding. • cost-of-funding characteristics Information Description Active from/to Set active from and to dates if you want the defaulting to be used only for a given period. Currency Currency you want to specify. C-o-F Curve The default curve from which the interest rate will be defaulted. Note: Only IR quotes (i.e. curve with fixing/interest calculation usage) defined with the Bootstrap Yield Curve feature are available. C-o-F Spread Curve The default spread curve from which the spread will be defaulted. Scenario The default scenario from which the values will be retrieved. Method Defaulting method: Ask, Bid, Bid/Ask (Spread Against), Bid/Ask (Spread in Favor), or Mid. • If you select Bid/Ask (Spread Against): if you are buying the base currency of the quoted currency pair, the Ask price is used; if you are selling the base currency of the quoted currency pair, the Bid price is used. • If you select Bid/Ask (Spread in Favor): if you are buying the base currency of the quoted currency pair, the Bid price is used; if you are selling the base currency of the quoted currency pair, the Ask price is used. See A.2.194 FX Swap Cost-of-Funding on page 807. 6.5.2 Deal capture 6.5.2.1 Input data In addition to the standard FX swap deal parameters, the following information is needed to enter a cost-of-funding FX swap: Hint: You will need to display the following columns in the Transaction view: C-o-F Curve, C-o-F Rate, C-o-F Spread %, C-o-F Spread Curve, C-o-F Subscenario, and C-o-F Tenor. Label Value C-o-F curve ID of the curve to be used to default the cost-of-funding rate. Editable Mandatory Y N Defaults to the curve specified at instrument level for the base currency, otherwise, it is empty. C-o-F Subscenario Subscenario to be used to compute the cost-of-funding rate. By default, it is empty. Y N C-o-F Tenor Fixing period to be used to retrieve the cost-of-funding rate. By default, it is empty. Y N Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 423 6 Forex 6.5 Cost-of-funding FX swap Label Value Editable C-o-F Rate Defaults to the rate defined at the curve level for the specific tenor, otherwise, defaults to the interpolated rate between the transaction value date and the maturity date according to the date basis and rate type set up at the curve level. Mandatory Y Y Note: For a forward-forward FX swap, the forward FX rate computed between the value and maturity dates. C-o-F Spread Curve Defaults to the spread curve defined at instrument level, otherwise, it is left empty. Y N C-o-F Spread % If the C-o-F Spread Curve is populated then the displayed value for the tenor is equal to the maturity date, otherwise, it is left empty. Y N FX Finance Rate(*) Computed from C-o-F Rate and C-o-F Spread: N Y N Y FX Finance Rate = C-o-F Rate + C-o-F Spread Quote Currency Yield Yield computed from quote amounts of the FX swap as follows: QuoteCurrencyYield = (FXQuoteAmount-FXQuoteSpotAmount)* B / MaturityDate - ValueDate * 1 / FXQuoteSpotAmount where • B is the date basis defined at the currency level for the quote currency (Currency Editor - Journal page). 6.5.3 Processing The actions you can perform on a cost-of-funding swap are the same as for a standard FX swap, see 6.4.4 Processing on page 420. 6.5.4 Position monitoring Figures for cost-of-funding swaps are calculated in the same way as for FX swaps: see 6.4.5 Position monitoring on page 422. 424 © Wall Street Systems IPH AB - Confidential Chapter 7 Index 7.1 Index types TRM supports the following index types: • Simple index A simple index does not contain information on composition; it is a simple instrument to which a price can be input. It can be used as an underlying for derivatives, and the price is used for valuation and payoff calculations. It is also used in performance measurement for return comparison. • Composite index A composite index is an index defined in the product as a basket of several equities, discount papers, or bonds, for example, CAC-40. If you do not want to manage the composition in TRM, the composite index is treated as a simple index. • Derived index A derived index is an index derived from several simple indexes. They can be composites, but are treated as simple: their internal composition is not considered. A derived index can be re-balanced. It can be used in performance measurement whenever internal performance (allocation) is not needed • Performance index A performance index is a special type of composite index, used to compute the payback of a specific issue. TRM implements the following two index performance formulae to compute the index value. – Performance averaging index This is calculated as follows: N 1--Index i N∑ i=1 ------------------------------ –1 1 --P P ∑ Indexj j=1 where: 1 Index i = ----------------------NbComp NbComp ∑ w k Comp i, k k=1 P = number of observation dates for the denominator N = number of observation dates for the numerator NbComp = number of components of the index Wk = weight of kst component of the index Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 425 7 Index 7.2 Instrument setup Compi,k = value of the kst component at time i – Performance Totaling Index This is calculated as follows: N Index j – Index j – 1 -⎞ ⎞ ∑ Max ⎛⎝ Floor ;Min ⎛⎝ Cap ;--------------------------------------------⎠⎠ Index j – 1 j=1 where: 1 Index i = ----------------------NbComp NbComp ∑ W k Comp i, k k=1 N = number of observation dates for the numerator Floor = predefined constant floor value Cap = predefined constant cap value NbComp = number of components of the index Wk = weight of kst component of the index Compi,k = value of the kst component at time i 7.2 Instrument setup Index instruments must be set up in the following order: 7.2.1 Simple Index Index instruments are based on an instrument type derived from the class INDEX. • Main characteristics (Quoted page): This information enables you to either enter the quotation manually in Rate Monitor, or to retrieve it automatically in real-time. Information Description Price Type information Index. Quote Handling Index. Currency Currency of the index. Note: Real-time market information is set up for the instrument in the Market Info page. See A.2.203 Index on page 813. It is also possible to set up: • 426 Branch codes. See Appendix A Features on page 713. © Wall Street Systems IPH AB - Confidential 7 Index 7.2 Instrument setup 7.2.2 Composite Index Composite Index instruments are based on an instrument type derived from the class INDEX. • Main characteristics Features INDEX-COMPOSITE (primary) and QUOTED must be used. See A.2.205 Index Composite on page 814. This feature allows you to define the information in the instrument setup tabs as described in the following sections. 7.2.2.1 Structure Defines the principal characteristics of the index. Information Description Currency Reference currency for the index, used as the basis of index calculations. Composition Type Defines the component types used in this index: DEBT-SECURITY (bond, quoted Discount Paper), EQUITY, and COMPOSITE (other composite index). Weight Cap The max % of the market value a single component can attain. Calculation Method Defines how Composite Indexes are calculated. The following methods can be used to take the outflows (coupons, dividends and bond accrued interest) into account: • Clean Price: Used mainly for bonds. Only takes into account price return, not accrued interest or cashflows. Unlike the other methods, this method discards the accrued interest from the calculations of bond indices. • Hold Cash On Security: Cashflows are held under security until the index is revised, but not reinvested. In which case, the field amount contains the amount of the cashflow, and is populated when the cashflow is detached from the security (in security currency). The amounts between two rebalancings are added to the security amount (price * units) and eventually, accrued interest before being converted to index currency. • Hold Cash On Index: Cashflows are held under index until the index is revised, but not reinvested. In which case, the field amount contains the amount of the cashflow converted to the index currency, and is populated when cashflow is detached from the security. The amounts between two rebalancings are added to the market value of the index. • Reinvest Cash On Security: The amount of the cashflow is reinvested on the security from which it is detached. TRM calculates a factor to simulate reinvestment of the cash in the security itself (stored in the Rebalance page). • Reinvest Cash On Index: The amount of the cashflow is reinvested in the index. TRM calculates a factor which is applied to the whole index (stored in the Rebase page). Rounding Precision Rounding precision to be applied in calculations. Rounding Method Rounding method to be applied in calculations. Input Method Defines how weightings are input (see 7.2.2.3 Composition on page 429). Available methods are: • Units/Nominal: the absolute units for the component • Market Value: the market value of the component in index currency • Weight %: the % of the total market value of the component • Outstanding: number of times the outstanding units/nominal (typically 1). Available for Bond and Equity • Free Float: same as above but with the units available for trading. Available only for Equity. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 427 7 Index 7.2 Instrument setup 7.2.2.2 Base Periodically models the revisions of the index including the initial definition Information Description From Date of the revision To Read-only. Date up to which this revision is valid. Index Value • For the initial base the default is 100. This can be changed if you want to start the index with another value. For example, to manage the CAC-40 today, you would use the CAC-40’s current value. • For revision bases this is defaulted to the last known frozen base (from the previous day). It can be changed (if incorrect in the database for example) but should normally not be changed: it will be used as the base for index calculations for every date until the next revision. Market Value The total market value of the index in the index currency. It is automatically set with Calculate (see Actions). It can also be forced, and then Calculate will adjust composition to match it. Last Market Value Read-only. Attributes • Error: calculation of the base is impossible (incorrect base/component attributes and/or inputs/market value) • Keep Market Value: affects Calculate button behavior (see below); always on • Modified: composition has been modified for this base and calculation must be when input method is Weight %. done before saving Actions • Copy composition from template Initializes an index from one or more template indexes, available only for the initial base. The template must be selected for this action to be visible. A factor can be used to scale template composition. The action can be executed several times to combine several templates. • Duplicate previous composition Duplicates composition which can be manually revised: when using outstanding and free float methods this does automatic revision without requiring manual intervention (it re-fetches new market information at revision time). Only on revision bases (when you have more than one base). • Update composition attributes Automatically sets or resets the Keep Input flag for all the components of the base, so component flags need not be set or reset manually (see 7.2.2.3 Composition on page 429). • Calculate... This button is used to recalculate the specified base when Components are added, removed, or modified. The calculation makes sure that the setup of the base is consistent: that the sum of all the components amount matches the market value of the base and, if input method is weight %, that the inputs sum to 100%. The calculation is affected by the Keep Market Value switch of the base and the Keep Inputs flags of the components. When Keep Market Value is switched on, the system adjusts component inputs that are not marked with Keep Input. Otherwise the market value can be re-calculated. When the input method is Weight %, the Keep Market Value flag is forced to True. Note: If the flags are set in a way that makes resolution of the equation impossible, Calculate... flags the base with the attribute Error, and the instrument cannot be saved. It is possible to 428 © Wall Street Systems IPH AB - Confidential 7 Index 7.2 Instrument setup temporarily save an index with an inconsistent base by unswitching the attributes manually, but the user must fix the problem before using the index. 7.2.2.3 Composition Defines the composition of the index for a given base Information Description Base Date Reference of the base (corresponds to Base "From"). Component Id of the component; available components are filtered according to index type. Currency Read-only. Currency of the component, retrieved from component characteristics. Calendar Calendar of the component, retrieved from component characteristics. FX Rate Cross-rate between Component currency and index currency, defaulted from fixing scenario. Can be changed by the user. It is the base rate used in calculation relative to this base for this component. Component Value Price of the component. This is defaulted from the fixing scenario and can be changed by the user. It is the base price used in calculations relative to this base for this component. Input It is the base weight for this component. The significance of this weight depends on the input method defined in the index structure (see 7.2.2.1 Structure on page 427). Units/Nominal Read-only. This is the absolute weight in units (for equities) or in nominal (for bonds) which is calculated for the component depending on the input method. Accrued Interest For bond index, amount of accrued interest for the component at base date. Amount Read-only. Shows the amount of the component for the base in index currency. The sum of the amount of all components for a base gives the base market value of the index. Attributes Keep Input forces the Calculate action to keep the input for this component. 7.2.2.4 Rebase Stores the impact of cashflows, depending on the method of calculation. This is used when cashflows are impacted at index level. Information Description Date Date of the market value shift Old Value Market value of the index before the external event was taken into account New Value Market value of the index including the impact of the external event. Cash Amount to be added to index MV from the specified date onwards. Source Read-only. Shows what event triggers the rebasing. Manual means that the user can enter it manually, and in which case, it is modifiable in the editor. Other choices are: Amortization, Cash Dividend, Coupon, Split. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 429 7 Index 7.2 Instrument setup 7.2.2.5 Rebalance Stores the impact of cashflows, depending on the method of calculation. This is used when cashflows are impacted at component level. It is also used to compensate for the effect of equity splits. Information Description Date Date of the CA to be balanced. Component Id of the component; available components are filtered according to index type. Old Units/Nominal Number of units before rebalancing New Units/Nominal Number of units after rebalancing Cash Amount to be added to component MV from the specified date onwards. Source Read-only. Shows what event triggers the rebasing. Manual means that the user can enter it manually, and in which case, it is modifiable in the editor. 7.2.3 Derived Index Features INDEX-DERIVED (primary) and QUOTED must be used. 7.2.3.1 Structure Defines the currency, index type, and maximum weight for any component for the corresponding index composition. Information Description Currency Reference currency for the index, used as the basis of index calculations. Composition Type Index is the only available type. Weight Cap The max % of the market value a single component can attain. Input Method Defines how weightings are input (see 7.2.3.3 Composition on page 431). Available methods are: • Units/Nominal: the absolute units for the component • Weight %: the % of the total market value of the component. Rounding Precision Rounding precision to be applied in calculations. Rounding Method Rounding method to be applied in calculations. Calculation Method Not used for a derived index. 7.2.3.2 Base Periodically models the revisions of the index including the initial definition 430 Information Description From Date of the revision To Read-only. Date up to which this revision is valid. Index Value • For the initial base the default is 100. This can be changed if you want to start the index with another value. • For revision bases this is defaulted to the last known frozen base (from the previous day). It can be changed (if incorrect in the database for example) but should normally not be changed: it will be used as the base for index calculations for every date until the next revision. © Wall Street Systems IPH AB - Confidential 7 Index 7.2 Instrument setup Information Description Market Value The total market value of the index in the index currency. It is automatically set with the Calculate... button (see Actions). It can also be forced, and then calculate will adjust composition to match it. Last Market Value Read-only. Attributes • Error: calculation of the base is impossible (incorrect base/component attributes and/or inputs/market value) • Keep Market Value: affects Calculate button behavior (see below); always on when method is %. • Modified: composition has been modified for this base and calculation must be done before saving Actions • Copy composition from template Initializes an index from one or more template indexes, available only for the initial base. The template must be selected for the action to be visible. A factor can be used to scale template composition. The action can be executed several times to combine several templates. • Duplicate previous composition Duplicates composition which can be then manually revised. Only on revision bases (when there is more than one base). • Update composition attributes Automatically sets or resets the Keep Input flag for all the components of the base: this is a shortcut (see 7.2.3.3 Composition on page 431). • Calculate... This button recalculates the specified base when Components are added, removed, or modified. The calculation makes sure that the setup of the base is consistent: that the sum of all the components amount matches the market value of the base and, if input method is Weight %, that the inputs sum to 100%. The calculation is affected by the Keep Market Value switch of the base and the Keep Inputs flags of the components. When Keep Market Value is switched on, the system adjusts component inputs that are not marked with Keep Input. Otherwise the market value can be re-calculated. When the input method is Weight %, the Keep Market Value flag is forced to True. Note: If the flags are set in a way that makes resolution of the equation impossible, Calculate... flags the base with the attribute Error, and the instrument cannot be saved. It is possible to temporarily save an index with an inconsistent base by unswitching the attributes manually, but the user must fix the problem before using the index. 7.2.3.3 Composition Defines the composition of the index for a given base. Information Description Base Date Reference of the base (corresponds to Base "From"). Component Id of the component; available components are indexes. Currency Read-only. Currency of the component, retrieved from component characteristics. Calendar Read-only. Calendar of the component, retrieved from component characteristics. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 431 7 Index 7.2 Instrument setup Information Description FX Rate Cross-rate between Component currency and index currency, defaulted from fixing scenario. Can be changed by the user. It is the base rate used in calculation relative to this base for this component. Component Value Price of the component. This is defaulted from the fixing scenario and can be changed by the user. It is the base price used in calculations relative to this base for this component. Input It is the base weight for this component. The significance of this weight depends on the input method defined in the index structure (see above). Units/Nominal Read-only. This is the absolute weight in units which is calculated for the component depending on the input method. Amount Read-only. Shows the amount of the component for the base in index currency. The sum of the amount of all components for a base gives the base market value of the index. Attributes Keep Input forces the Calculate action to keep the input for this component. 7.2.3.4 Schedule Defines rebalance schedules, which will be used to generate rebalance dates. Information Description Start Date Date from when rebalancing starts. End Date Date when rebalancing stops (if you do not know if it will stop, just use a distant future date). Method Specifies how the rebalancing dates are calculated. Frequency A function of the Method selected. For example, if method is Months, entering 3 here gives a frequency of 3 months. Convention Business convention to be followed. Roll from Start Yes or No. Date Type Select Re-balance. 7.2.3.5 Rebalance Date Shows rebalance dates. Information Description Date Date when rebalancing is executed. Actions • Generate Generates a set of rebalance dates according to the schedules. If Method is "Days" or "Business Days" and Frequency is 1, only the first rebalance date is generated; next rebalance dates are generated by clicking Rebalance (see below). • Rebalance Performs index rebalancing. The input method for the index must be Weight %. The system creates rows in the Rebalance page for the components of the index to adjust their units so that the percentages match the definition of the base. It is possible to trigger this action automatically via an activity (see 7.4 Processing on page 440). 432 © Wall Street Systems IPH AB - Confidential 7 Index 7.2 Instrument setup 7.2.3.6 Rebalance Stores the impact of re-balancing. Information Description Date Date of rebalancing. Component Id of the component. Old Units/Nominal Number of units before rebalancing. New Units/Nominal Number of units after rebalancing. Cash Amount to be added to component MV from the specified date onwards. Source Read-only. Shows what event triggers the rebasing. Manual means that the user can enter it manually, and in which case, it is modifiable in the editor. 7.2.4 Performance averaging index • Main characteristics Features INDEX-AVERAGING (primary) and QUOTED must be used. See A.2.204 Index Averaging on page 813. This feature allows you to define the following information in the instrument setup tabs: 7.2.4.1 Structure Defines the currency, index type, and maximum weight for any component for the corresponding index composition. Information Description Currency Reference currency for the index, used as the basis of index calculations. Composition Type Defines the component types used in this index: equities, bonds or indexes. Weight Cap The max % of the market value a single component can attain. Calculation Method Clean Price is the only method supported. Rounding Precision Rounding precision to be applied in calculations. Rounding Method Rounding method to be applied in calculations. Input Method Defines how weightings are input (see 7.2.4.3 Composition on page 435). Available methods are: • Units/Nominal: the absolute units for the component • Market value: the market value of the component in index currency • Weight %: the % of the total market value of the component • Outstanding: the number of times the outstanding units/nominal (typically 1). Available for Bond and Equity. • Free Float: same as above, but with the units available for trading. Available only for Equity. 7.2.4.2 Base Periodically models the revisions of the index including the initial definition Information Description From Date of the revision Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 433 7 Index 7.2 Instrument setup Information Description To Read-only. Date up to which this revision is valid. Index Value • For the initial base the default is 100. • For revision bases this is defaulted to the last known frozen base (from the previous day). It can be changed (if incorrect in the database for example) but should normally not be changed: it will be used as the base for index calculations for every date until the next revision. Market Value The total market value of the index in the index currency. It is automatically set with Calculate (see Actions). It can also be forced and then Calculate will adjust composition to match it. Last Market Value Read-only. Attributes • Error: calculation of the base is impossible (incorrect base/component attributes and/or inputs/market value) • Keep Market Value: affects Calculate button behavior (see below); always on when method is %. • Modified: composition has been modified for this base and calculation must be done before saving Actions • Copy composition from template Initializes an index from one or more template indexes, available only for the initial base. The template must be selected for the action to be visible. A factor can be used to scale template composition. This action can be repeated to combine several templates. • Duplicate previous composition Duplicates composition which can then be manually revised: when using outstanding and free-float methods, this does automatic revision without manual intervention (it re-fetches new market information at revision time). Only on revision bases. • Update composition attributes Automatically sets or resets the Keep Input flag for all the components of the base: this is a short cut (see 7.2.4.3 Composition on page 435). 434 © Wall Street Systems IPH AB - Confidential 7 Index 7.2 Instrument setup • Calculate... This button recalculates the specified base when Components are added, removed, or modified. The calculation makes sure that the setup of the base is consistent: that the sum of all the components amount matches the market value of the base, and if the input method is Weight %, that the inputs sum to 100%. The calculation is affected by the Keep Market Value switch of the base, and the Keep Inputs flags of the components. When Keep Market Value is switched on, the system adjusts component inputs that are not marked with Keep Input. Otherwise the market value can be re-calculated. When input method is Weight %, the Keep Market Value flag is forced to True; when the input method is Outstanding or Free Float, it is forced to False. Note: If the flags are set in a way that makes resolution of the equation impossible, Calculate... flags the base with attribute Error, and the instrument cannot be saved. It is possible to temporarily save an index with an inconsistent base by unswitching the attributes manually, but the user must fix this problem before using the index. 7.2.4.3 Composition Defines the composition of the index for a given base. Information Description Base Date Reference of the base (corresponds to Base "From"). Component Id of the component; available components are filtered according to index type. Currency Read-only. Currency of the component, retrieved from component characteristics. Calendar Read-only. Calendar of the component, retrieved from component characteristics. FX Rate Cross-rate between Component currency and index currency, defaulted from fixing scenario. Can be changed by the user. It is the base rate used in calculation relative to this base for this component. Component Value Price of the component. This is defaulted from the fixing scenario and can be changed by the user. It is the base price used in calculations relative to this base for this component. Input It is the base weight for this component. The significance of this weight depends on the input method defined in the index structure (see above). Units/Nominal Read-only. This is the absolute weight in units (for equities) or in nominal (for bonds) which is calculated for the component depending on the input method. Amount Read-only. Shows the amount of the component for the base in index currency. The sum of the amount of all components for a base gives the base market value of the index. Attributes Keep Input forces the Calculate action to keep the input for this component. 7.2.4.4 Rebalance Balances the impact of any equity splits. Information Description Date Date of the CA to be balanced. Component Id of the component; available components are filtered according to index type. Old Units/Nominal Number of units before split. New Units/Nominal Number of units after split. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 435 7 Index 7.2 Instrument setup Information Description Cash Amount to be added to component MV from the specified date onwards. Source Read-only. Shows what event triggers the rebasing. Manual means that the user can enter it manually, and in which case, it is modifiable in the editor. 7.2.4.5 Schedule Defines schedules, used to generate numerator and denominator dates. Information Description Start Date Date from when generation starts. End Date Date when generation stops (if you do not know when generation will stop, just use a distant future date). Method Defines how the generation dates are calculated. Frequency A function of the Method selected. For example, if method is Months, entering 3 here gives a frequency of 3 months. Convention Business convention to be used. Roll from Start Yes or No. Date Type Use Avg. Numerator and Avg. Denominator. 7.2.4.6 Denominator Date and Numerator Date These pages show the dates when performance calculations are performed Information Description Date Input Date of the calculation. Observation Date Date when the price is retrieved for the components following the given calendar. Calendar For each Date Input there must be as many records as distinct calendars in the components. Observation date might be different for each calendar. Actions • Generate Generates a set of Numerator and Denominator dates according to the schedules and individual calendars of the components. 7.2.5 Performance totaling index • Main characteristics Features INDEX-TOTALING (primary) and QUOTED must be used. See A.2.215 Index Totaling on page 821. This feature allows you to define the information in the instrument setup tabs described in the following sections. 436 © Wall Street Systems IPH AB - Confidential 7 Index 7.2 Instrument setup 7.2.5.1 Structure Defines the currency, index type, and maximum weight for any component for the corresponding index composition. Information Description Currency Reference currency for the index, used as the basis of index calculations. Composition Type Defines the component types used in this index: equities, bonds or indexes. Weight Cap The max % of the market value a single component can attain. Calculation Method Clean Price is the only supported method. Rounding Precision Rounding precision to be applied in calculations. Rounding Method Rounding method to be applied in calculations. Input Method Defines how weightings are input (see 7.2.5.3 Composition on page 438). Available methods are: • Units/Nominal: the absolute units for the component • Market value: the market value of the component in index currency • Weight %: the % of the total market value of the component • Outstanding: the number of times the outstanding units/nominal (typically 1). Available for Bond and Equity. • Free Float: same as above but with the units available for trading. Available only for Equity. 7.2.5.2 Base Periodically models the revisions of the index including the initial definition Information Description From Date of the revision To Read-only. Date up to which this revision is valid. Index Value • For the initial base the default is 100. • For revision bases this is defaulted to the last known frozen base (from the previous day). It can be changed (if incorrect in the database for example) but should normally not be changed: it will be used as the base for index calculations for every date until the next revision. Market Value The total market value of the index in the index currency. It is automatically set with Calculate (see Actions). It can also be forced and then calculate will adjust composition to match it. Last Market Value Read-only. Attributes • Error: calculation of the base is impossible (incorrect base/component attributes and/or inputs/market value) • Keep Market Value: affects Calculate button behavior (see below); always on • Modified: composition has been modified for this base and calculation must be when method is %. done before saving Actions • Copy composition from template Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 437 7 Index 7.2 Instrument setup Initializes an index from one or more template indexes, available only for the initial base. The template must be selected for the action to be visible. A factor can be used to scale template composition. This action can be repeated to combine several templates. • Duplicate previous composition Duplicates composition which can be then manually revised: when using outstanding and free float methods this does automatic revision without requiring manual intervention (it re-fetches new market information at revision time). Only on revision bases. • Update composition attributes Automatically sets or resets the Keep Input flag for all the components of the base: this is a short cut (see 7.2.5.3 Composition on page 438). • Calculate... This button recalculates the specified base when Components are added, removed, or modified. The calculation makes sure that the setup of the base is consistent: that the sum of all the components amount matches the market value of the base and, if input method is Weight %, that the inputs sum to 100%. The calculation is affected by the Keep Market Value switch of the base and the Keep Inputs flags of the components. When Keep Market Value is switched on, the system adjusts component inputs that are not flagged with Keep Input. Otherwise the Market Value can be re-calculated. When input method is Weight %, the Keep Market Value flag is forced to True; when method is Outstanding or Free Float it is forced to False. Note: If the flags are set in a way that makes resolution of the equation impossible, Calculate... marks the base with attribute Error, and the instrument cannot be saved. It is possible to temporarily save an index with an inconsistent base by unswitching the attributes manually, but the user must fix this problem before using the index. 7.2.5.3 Composition Defines the composition of the index for a given base 438 Information Description Base Date Reference of the base (corresponds to Base "From"). Component Id of the component; available components are filtered according to index type. Currency Read-only. Currency of the component, retrieved from component characteristics. Calendar Read-only. Calendar of the component, retrieved from component characteristics. FX Rate Cross-rate between Component currency and index currency, defaulted from fixing scenario. Can be changed by the user. It is the base rate used in calculation relative to this base for this component. Component Value Price of the component. This is defaulted from the fixing scenario and can be changed by the user. It is the base price used in calculations relative to this base for this component. Input It is the base weight for this component. The significance of this weight depends on the input method defined in the index structure (see above). Units/Nominal Read-only. This is the absolute weight in units (for equities) or in nominal (for bonds) which is calculated for the component depending on the input method. Amount Read-only. Shows the amount of the component for the base in index currency. The sum of the amount of all components for a base gives the base market value of the index. © Wall Street Systems IPH AB - Confidential 7 Index 7.2 Instrument setup Information Description Attributes Keep Input forces the Calculate action to keep the input for this component. 7.2.5.4 Rebalance Balances the impact of any equity splits Information Description Date Date of the CA to be balanced. Component Id of the component; available components are filtered according to index type. Old Units/Nominal Number of units before rebalancing New Units/Nominal Number of units after rebalancing Cash Amount to be added to component MV from the specified date onwards. Source Read-only. Shows what event triggers the rebasing. Manual means that the user can enter it manually, and in which case, it is modifiable in the editor. 7.2.5.5 Totaling Defines cap and floor to use in totaling formula (see – Performance Totaling Index on page 426). Information Description Floor The floor to use in the totaling formulae. Cap The cap to use in the totaling formulae. 7.2.5.6 Schedule Defines schedules, used to generate totaling dates. Information Description Start Date Date from when generation starts. End Date Date when generation stops (if you do not know if it will stop, just use a date very far in the future). Method Defines how the generation dates are calculated. Frequency A function of the Method selected. For example, if method is Months, entering 3 here gives a frequency of 3 months. Convention Business convention to be used. Roll from Start Yes or No. Date Type Use average numerator and denominator for date types. 7.2.5.7 Totaling Date This page shows the dates when performance calculation is done. Information Description Date Input Date of the calculation. Observation Date The date when the price will be retrieved for the components following the given calendar. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 439 7 Index 7.3 Market information Information Description Calendar For each Date Input there must be as many records as there are distinct calendars in the components. The Observation Dates for each calendar can be different. Actions • Generate Generates a set of totaling dates according to the schedules and individual calendars of the components. 7.3 Market information Rate Monitor is used to visualize and maintain index prices. See the TRM User Guide for more information. 7.4 Processing This section describes the processing that you can perform, either manually in the relevant application, or automatically, as an activity, in Activity Monitor. 7.4.1 Revision Revision is a manual process which consists of updating an index to reflect the market more accurately. This operation is done in the Instrument Editor by creating a new base and a new composition. Note: It is also possible to import revisions using one of the TRM connectivity tools. 7.4.2 Freezing Index Values Rate Monitor enables you to view both calculated and quoted (Q) values, but only the quoted values are used by the rest of the system. Values of composite, derived and performance indexes are calculated automatically in real time according to market data changes (FX rates or component values). It is nevertheless important to be able to freeze these results at any time. In Rate Monitor, use the command Command - Freeze to freeze these values; the current content of the calculated cells are copied to the Quoted (Q) cells. When you have frozen these values, use the Save button to store them in the database like any other standard price. Both index values and detailed composition information are stored. Note: You can import Quoted (Q) values directly from an external data feed, either as a replacement or in parallel, by using another scenario and/or subscenario. You can also use the Index Freeze activity in Activity Manager to perform the freeze. Note: See the TRM User Guide for general information on running activities, and also specific information on the activity parameters. 440 © Wall Street Systems IPH AB - Confidential 7 Index 7.4 Processing 7.4.3 Updating Factors and Cash Use the activity Index Adjustment in Activity Manager to automatically update factors and cash. This activity reads the characteristics of the underlyings, and depending on the Index Type and the Calculation Method, inserts the relevant information into the Rebase and Rebalance pages. Note: See the TRM User Guide for general information on running activities, and also specific information on the activity parameters. 7.4.4 Rebalancing A common use for a derived index is to rebalance the index periodically, so that each component weight is readjusted to the original percentage weighting. After the setup of rebalancing dates is done, (see setup above), you can execute rebalancing for an index directly in the editor, by clicking Rebalance. You can also use the Index Rebalance activity in Activity Manager to perform this task. Note: See the TRM User Guide for general information on running activities, and also specific information on the activity parameters. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 441 7 Index 7.4 Processing 442 © Wall Street Systems IPH AB - Confidential Chapter 8 Cash 8.1 Bank account Bank account balances and any interest accrued on a bank account are displayed in the system as transactions. Bank accounts can be used either: to track your own bank balance by checking your current position adjusted by the existing balance, and to calculate the estimated accrued interest on the bank account; or, if you represent an In-house Bank (that is, you hold accounts for your subsidiaries), you can calculate end-of-day balances and provide your subsidiaries with the appropriate information, as well as calculating any accrued interest on the accounts. You need to set up one instrument to calculate bank balances, and another which is specifically used to calculate accrued interest. Both instruments are assigned to accounts in the Accounts page of Client Editor: see the TRM User Guide for more information. It is recommended that a separate Balance portfolio is defined for the balance and interest-calculation transactions. One reason is that you can restrict update access to the balance information to people in the back office, while the trading portfolios can only be updated by people in the front office and middle office. If you operate as an In-house Bank, you may also find it useful to have a Balance portfolio for each of the bank accounts of your subsidiaries. Note: Information about how to assign balance instruments to accounts and how to create Balance portfolios is described in the TRM User Guide. Bank account balances and interest-calculation instruments belong to the instrument class BANK-ACCOUNT. 8.1.1 Instrument setup Both bank account balance and bank account interest instruments share the same primary feature. 8.1.1.1 Bank account balance Bank account balance instruments are assigned to the accounts for which you want to calculate the balance. The balance can either be derived from payable cashflows in the system, or from paid cashflows. It is also possible to define in how much detail you want the balance to be calculated, for example, if you need one balance transaction per counterparty. Balance instruments do not require any specific set up. They are simply recognized by the following features in the Bank-Account instrument class: • The primary feature Bank Account Balance (see A.2.45 Bank Account Balance on page 729) • The valuation feature Bank Account Method (see A.2.47 Bank Account Valuation on page 732). 8.1.1.2 Bank account interest-calculation Interest-calculation instruments are assigned to the accounts for which you want to calculate the accrual of interest. • Main characteristics Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 443 8 Cash 8.1 Bank account The bank account interest instrument uses the same primary feature as the bank account balance instrument (see 8.1.1.1 Bank account balance on page 443). • Trading information – Interest accrual parameters For bank balances, you can specify the interest rates used, and the method and frequency that interest is accrued. Information Description Date Basis Date basis used to calculate accrued interest for this instrument. Interest Rate Curve Underlying yield curve (set up in IR Quote and Yield Curve Editor) used for interest calculation. Note: If you specify a yield curve (and/or Period, Positive Spread, or Negative Spread), you do not need to specify any Ladder values (see Ladder Rule and Ladder). – Period Period of the underlying yield curve to be used for interest calculation (for example, O/N). Scenario Rate scenario to be used for calculating interest for this instrument. Interest realization parameters You can specify how the accrued interest is realized on the balance. Information Description Frequency Frequency of interest realization (if Method = Periodically). Frequency Unit Method Unit of time to use for interest realization: Business Days, Days, Months, Weeks, or Years. Method of realizing interest: • At Withdrawal - not applicable. • Periodically - interest is realized at regular intervals (see Frequency field). • Settlement Method At Expiration - not applicable. Interest payment method: Capitalize to compound interest or Settle to receive or pay interest. See A.2.46 Bank Account Interest on page 730. 8.1.2 Deal capture Bank account balances and interest transactions are system-generated transactions, performed by scheduled activities (see the TRM User Guide for more information). Once the activity has run, the transactions are generated in the Bank Account Balances application. 8.1.2.1 Generated data • Transaction Transaction Type = Balance Counterparty = Bank that holds the balance, unless the balances are calculated by counterparty • Cashflows – 444 One cashflow per balance (only if the balance has changed) © Wall Street Systems IPH AB - Confidential 8 Cash 8.1 Bank account – If the interest is unrealized: daily accrued interest – If the interest is realized: realized interest cashflows or the capitalizing balance cashflow. 8.1.3 Processing This section describes the processing that you can perform, either manually in the relevant application, or automatically, as an activity, in Activity Manager. See the TRM User Guide for information about these activities and how to set up activities in general. 8.1.3.1 Calculating bank account balance and interest Bank account balance and accrued interest-calculation transactions are generated by the activity Bank Account Balances which you can schedule to run as often as required (see the TRM User Guide for more information). 8.1.3.2 Realize AI Bank account accrued interest can be realized automatically or manually (for automatic realization, see the TRM User Guide). You can realize interest manually, by right-clicking on the transaction in the Transaction view of the Bank Account Balances application and selecting the Realize AI action. • Execution The following information is needed to process the realization: Information Description Date Date of the action i.e. the realization date. Opening Date The opening date of the transaction. Payment Date By default, the Payment Date is the realization date. However, you can change the default. Amount Amount of the realized interest cashflow. By default, this is the total amount of accrued interest, but it can be changed to a lesser amount if you do not want to realize the total amount. Interest Sign Positive: To receive interest. Negative: To pay interest. Settlement Method Capitalize or Settle. The accrued interest is either settled or capitalized. Note: By default, the settlement method will be the one defined in the Interest Realization page of Instrument Editor. Interest Bank ID of a bank if you want to settle the interest realization in a specific bank, which differs from the default bank. Interest Account ID of a bank account if you want to settle the interest realization in a specific account, which differs from the default bank account. Update Realization Date Switch on to allow the next interest realization date to be automatically updated. Note: It is not possible to realize accrued interest for future dates using the Realize AI action. • Cancellation Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 445 8 Cash 8.2 Call account You can cancel interest manually by right-clicking on the transaction in the Transaction view of the Bank Account Balances application and selecting the Undo Realize AI action. The following information is needed to process the cancellation: Information Description Date Date of the action i.e. the undo realization date. By default the date is today's date. 8.2 Call account Call Account is similar to a normal bank account. The client can withdraw and deposit funds (lend or borrow) from the account whenever it is necessary. The funds earn interest on the account at a rate that is fixed daily. The interest is accrued and paid or capitalized at regular intervals. The client can withdraw all or part of the interest from the account when interest is payable (without first having to capitalize the interest). The main difference between Call Money and Call Account is the presumed length of the transaction. Call Money is assumed to mature on a daily basis, while Call Account is automatically rolled over every day. In TRM, call account instruments belong to the instrument class CALL-ACCOUNT. 8.2.1 Instrument setup Call accounts are based on an instrument type derived from the instrument class CALL-ACCOUNT. • Main characteristics The following basic information may be captured when defining a call account instrument. Information Description Currency Currency of the call account. Balance information Minimum and maximum balance allowed on the call account. Notice period information Required notice period for calling the money. – Interest accrual parameters For call accounts, you can specify the interest rates used, and the method and frequency that interest is accrued on the call account. – Interest realization parameters You can also specify how the accrued interest is realized on the call account. See A.2.82 Call Account on page 747. For a call account instrument, it is also possible to set up: • Spot date calculation • Cashflow and transaction charge rules • Manual charges • Branch codes. See Appendix A Features on page 713. 446 © Wall Street Systems IPH AB - Confidential 8 Cash 8.2 Call account 8.2.2 Deal capture Call account transactions are entered in the Call Account trading mode of Transaction Manager’s Call Manager layout. Note: See the TRM User Guide for more information about this Transaction Manager layout. 8.2.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a call account transaction: • Transaction view Information Description Movement/Initial Balance Initial movement (inflow or outflow) on the call account. Interest Rate At contract level, this is the last roll over rate. Roll Over Date Date of the next roll over. Capitalize Account Transaction number of an alternative call account on which to realize the capitalized interest. This amount can be zero if the initial movement is intended to open the account only, and does not involve a deposit or withdrawal of funds. Interest rate and balance information defined at instrument level default to the date in the Roll Over Date field. If the Roll Over Date field is empty, then today’s date is used. If no interest rate is available for today, then the rate applied yesterday is used. Similarly, if no balance is available, then the closing balance from the previous day is shown. 8.2.2.2 Generated data Movements on call accounts can be viewed in the Movement view of Call Manager. • Movement view Information Description Movement ID Log number for each movement carried out on a transaction. This number is used to identify individual movements when multiple identical movements are performed on the same transaction on the same day. Interest Rate At movement level, this is the interest rate of the movement. If the transaction has not yet been rolled over, the previous interest rate is displayed. Once the transaction has been rolled over, the rate is updated from the underlying yield curve. If no underlying curve has been defined and a rate change has been agreed with the counterparty, this rate needs to be updated manually. 8.2.3 Processing This section describes the actions that can be done throughout the life of a call account transaction. 8.2.3.1 Update account A call account instrument needs to be updated each day. • Execution – Automatic updating of a call account is done using the Call Money Account Update activity. This activity should be scheduled to run on a daily basis to ensure that the call account instrument is updated each day. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 447 8 Cash 8.2 Call account The following information is needed to process the activity: Parameter Description Minimum Transaction State Minimum transaction state the call account transaction needs to have to be included in the process Portfolio Portfolio containing the call account transaction. Owner Client (portfolio owner) of the portfolio. Counterparty Counterparty of the call account transaction. Counterparty Main Group Counterparty main group of the call account transaction. Counterparty Group Counterparty group of the call account transaction. Instrument ID of the call account instrument. Instrument Group Instrument group to which the call account instrument belongs. Currency Currency of the call account transaction. Interest Rate Curve Yield curve attached to the call money or call account instrument. Note: See the TRM User Guide for information about these activities and how to set up activities in general. 8.2.3.2 New movement It is possible to make a deposit or withdrawal (movement) on a call account. • Execution To include new movements on call account transactions, execute the New Movement processing action on the transaction for which you want to include additional lending or borrowing. In the new row that is added in the Movement view, the following data is required. Information Description Interest Rate Interest rate for the new movement. Amount Amount of the movement. 8.2.3.3 Change interest It is possible to change the interest rate but not create a new movement on a call account using the Change Interest processing action. • 448 Execution Information Description Date Date from when the new interest rate applies. Rate New interest rate. © Wall Street Systems IPH AB - Confidential 8 Cash 8.2 Call account 8.2.3.4 Expire A call account with no outstanding balance can be closed by selecting the Expire right-click action on the call account transaction. • Execution Information Description Closing Date Date when the call account expires. Note that call accounts can have a zero balance and still remain active in the system for future transactions if required; they are not automatically closed when the balance is zero. 8.2.3.5 Update balance You can update the balance using the Update Balance right-click action. • Execution Information Description From Start and end dates of the period for which you want to update the balance. To 8.2.3.6 Update AI You can update accrued interest on call account transactions using the Update AI action. • Execution Information Description Date Date on which you want to recalculate the accrued interest. Rate New interest rate you want to use to recalculate the accrued interest. 8.2.3.7 Realize interest You can realize accrued interest on call account transactions using the Realize AI action. • Execution Information Description Date Date of the action. Opening Date Opening date of the realized interest cashflow. Payment Date By default, the Payment Date is the realize date + payment offset. However, you can change the given default date. Amount Amount of the realized interest cashflow. By default, this is the total amount of accrued interest, but it can be changed to a lesser amount if you do not want to realize the total. Settlement Method Capitalize or Settle. The accrued interest is then either settled or capitalized with the nominal amount of the transaction, depending on the Settlement Method. Note that it is not possible to realize AI for future dates using this action. • Cancellation You can cancel the action using Undo Realize AI. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 449 8 Cash 8.3 Call money 8.2.3.8 Dormant/Pledged You can mark call accounts as being dormant (no transactions allowed) or pledged (restricted movements). • Execution Use the Dormant/Pledged processing action. You are then prompted for new minimum/maximum values: for a dormant account, the minimum and maximum values are both zero. 8.3 Call money Call Money is an overnight deposit used in the wholesale banking market. Although such transactions are normally expired the following day, they can also be rolled over and the interest rate changed. It is possible to increase/decrease the principal of the original deal. In addition, the interest can be paid, capitalized, or simply accrued. The main difference between Call Money and Call Account is the presumed length of the transaction. Call Money is assumed to mature on a daily basis, while Call Account is automatically rolled over every day. In TRM, call money instruments belong to the instrument class CALL-MONEY. 8.3.1 Instrument setup Call Money instruments are based on an instrument type derived from the class CALL-MONEY. • Main characteristics The following basic information may be captured when defining a call money instrument. Information Description Currency Currency of the call money. Balance information Minimum and maximum balance allowed on the call money. Notice period information Required notice period for calling the money. – Interest accrual parameters For call money, you can specify the interest rates used, and the method and frequency that interest is accrued on the call money. – Interest realization parameters You can also specify how the accrued interest is realized on the call money. – Roll over parameters You can define the frequency of the roll over and the convention used. See A.2.84 Call Money on page 750. • Valuation approach See A.2.85 Call Money Valuation on page 750. For a call money instrument, it is also possible to set up: • Spot date calculation • Cashflow and transaction charge rules 450 © Wall Street Systems IPH AB - Confidential 8 Cash 8.3 Call money • Manual charges • Branch codes. See Appendix A Features on page 713. 8.3.2 Deal capture Call money transactions are entered in the Call Money trading mode of Transaction Manager’s Call Manager layout. Note: See the TRM User Guide for more information about this Transaction Manager layout. 8.3.2.1 Input data • Transaction view In addition to the standard deal parameters, the following information is required to enter a call money transaction: Information Description Movement/Initial Balance Change in amount (inflow or outflow) that occurs. Interest Rate Interest rate of the movement. If the transaction has not yet been rolled over, the previous interest rate is displayed. Once the transaction has been rolled over, the rate is updated from the underlying yield curve. If no underlying curve has been defined and a rate change has been agreed with the counterparty, this rate needs to be updated manually. Roll Over Date Date of the next roll over. Capitalize Account Transaction number of an alternative call money instrument on which to realize the capitalized interest. Interest rate and balance information defined at instrument level default to the date in the Roll Over Date field. If the Roll Over Date field is empty, then today’s date is used. If no interest rate is available for today, then the rate applied yesterday is used. Similarly, if no balance is available, then the closing balance from the previous day is shown. 8.3.2.2 Generated data Movements of call money can be viewed in the Movement view of Call Manager. • Movement view Information Description Movement ID Log number for each movement carried out on a transaction. Settlement instructions are also displayed in this view. 8.3.3 Processing This section describes the actions that can be done throughout the life of a call money transaction. 8.3.3.1 Roll over Call money is assumed to mature on a daily basis, unless it is prolonged through roll over. Roll over of call money can be done either manually or automatically using an activity. Normally, the roll over of call instruments should be done as soon as the relevant fixing rates are available. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 451 8 Cash 8.3 Call money • Setup The frequency and conventions for the roll over are determined in the instrument definition. • Execution – Manual roll over of call money instruments is done using the Roll Over action in the Transaction view of Call Manager. If you want to change the amount or interest rate for a call money transaction during roll over, you can enter the changes directly in the following fields: Interest %, Movement, or Closing Amount). If you enter changes in any of these fields, the selected transaction is automatically rolled over. You can enter changes in the fields even after you have selected the Roll Over command. – Automatic roll over is done using the Call Money Roll Over activity. This activity ensures that any unrolled transactions are prolonged automatically at the end of the business day instead of the system creating expiry instruments. The Call Money Account Update activity is then used to update the balances after the roll over. Note: See the TRM User Guide for information on the activity parameters for these activities and how to set up activities in general. • Undo Roll Over You can also undo this action by selecting Undo Roll Over. 8.3.3.2 New movement When rolling over call money transactions, it is possible to include additional lending or borrowing (movements). It is also possible to include new movements after the roll over has been carried out. • Execution To include new movements in call money transactions, execute the New Movement action on the transaction for which you want to include additional lending or borrowing. This command is only available for transactions that have been rolled over and applied. In the new row that is added in the Movement view, the following data is required. Information Description Interest Rate Interest rate for the new movement. Amount Amount of the movement. 8.3.3.3 Expire Call money transactions are expired when there is no longer any lending or borrowing (balance is zero). Note: TRM will not allow you to expire the transaction before the current roll over date. 452 © Wall Street Systems IPH AB - Confidential 8 Cash 8.3 Call money • Execution – Call money transactions are manually expired using the Expire action in Call Money Manager. Information Description Opening Date Date on which the call money transaction is expired. Value Date Value date for the call money transaction. This date defaults from the Roll Over Date. (Interest) Payment Date By default, it is the expiry date. However, you can change this date to a later date at which you want interest to be paid. When the transaction is expired, the interest is realized and a payable cashflow is created for the realized interest. 8.3.3.4 Update balance To update the balance, use the Update Balance right-click action. • Execution Information Description From Start and end dates of the period for which you want to update the balance. To 8.3.3.5 Update AI You can update accrued interest on call money transactions using the Update AI action. • Execution Information Description Date Date on which you want to recalculate the accrued interest. Rate New interest rate you want to use to recalculate the accrued interest. 8.3.3.6 Realize interest • Execution You can realize accrued interest on call money transactions using the Realize AI action. Information Description Date Date of the action. Opening Date Opening date of the realized interest cashflow. Payment Date By default, the Payment Date is the realize date + payment offset. However, you can change the given default date. Amount Amount of the realized interest cashflow. By default, this is the total amount of accrued interest, but it can be changed to a lesser amount if you do not want to realize the total. Settlement Method Capitalize or Settle. The accrued interest is then either settled or capitalized with the nominal amount of the transaction, depending on the Settlement Method. Note that it is not possible to realize AI for future dates using this action: you cannot enter a date that is equal to or later than the transaction’s roll over date. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 453 8 Cash 8.4 Cash • Cancellation You can cancel the action using Undo Realize AI. 8.3.4 Position monitoring 8.3.4.1 Setup Call money transactions are valued by discounting the future cashflows from the maturity date of the roll-over. 8.4 Cash Movements in cash, be it payments or receipts, or transfers, that are not generated directly from a transaction need to be defined as individual instruments. They can then be entered in Transaction Manager as deals in the same way as any other type of instrument. Payment cash instruments are based on an instrument type derived from the class CASH. Note: It is also possible to define cash forecast instruments: see 8.5 Forecast on page 459. 8.4.1 Payment Payment cash instruments represent stand-alone movements of cash, and can be either a negative flow (payment) or a positive flow (receipt). 8.4.1.1 Instrument setup The following basic information may be captured when defining the instrument. This information is relevant to any kind of payment (or receipt). • Main characteristics Information Description Transaction Sign Sign of the payment. If the sign is not defined at instrument level, it needs to be specified separately for each payment transaction. Currency Currency of the payment. Leave this field blank if you want to specify the currency when you enter the payment in Transaction Manager. Rounding parameters Method and precision used to round cashflow amounts. Cashflow Type details Type and subtype assigned to a cashflow. For a generic payment instrument: select Payment. Attribute parameters Attributes of the cashflow: Nominal Amount, Not Bookable, Not Payable, or Pseudo. Client and bank account details The client (portfolio-owner) making the payment, and the client’s bank account information. Counterparty and bank account details The counterparty of the payment, and the counterparty’s bank account information. See A.2.91 Cash Payment on page 754. 454 © Wall Street Systems IPH AB - Confidential 8 Cash 8.4 Cash For a payment instrument it is also possible to set up: • Spot date and value date calculations • Cashflow and transaction charge rules • Manual charges • Branch codes. See Appendix A Features on page 713. 8.4.1.2 Deal capture 8.4.1.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a payment instrument: Information Description Currency Currency of the payment. Nominal Amount Amount of the payment. Value Date Date when the payment is made. This defaults to the spot date of the transaction if the value date has not been specified in the instrument definition. Value Date Code If the Value Date Setup feature is applied at instrument level, you can enter the value date period you want to use to calculate the value date for the transaction, for example, 3M (3 months). Note: If you specify a value date period in the instrument setup, this is used by default and cannot be modified. 8.4.1.2.2 Generated data • Cashflows – One cashflow per payment transaction. 8.4.1.3 Processing Apart from the standard processing actions which are common to all transactions (such as Duplicate and Package), there are no other actions in Transaction Manager that are specific to payment instruments. Settlement of cashflows and reconciliation of payments and receipts with the bank account are managed in Settlement Processing and Settlement Reconciliation: see the TRM User Guide for more information. 8.4.2 Transfer Transfers are also set up as cash instruments. Transfers differ from a payment transaction in that they have two cashflows rather than one: one to debit the account making the payment, and the other to credit the account receiving the payment. Transfer instruments are based on an instrument type derived from the class CASH. 8.4.2.1 Instrument setup The following basic information may be captured when defining the instrument. This information is relevant to any kind of cash transfer. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 455 8 Cash 8.4 Cash Main characteristics • Information Description Transaction Sign Sign of the transfer. If the sign is not defined at instrument level, it needs to be specified separately for each transfer transaction. Currency Currency of the transfer. Leave this field blank if you want to specify the currency when you enter the transfer in Transaction Manager. Rounding parameters Method and precision used to round cashflow amounts. Cashflow Type details Type and subtype assigned to a cashflow. For a generic transfer instrument: select Payment. Attribute parameters Attributes of the cashflow: Nominal Amount, Not Bookable, Not Payable, or Pseudo. Client and bank account details The client (portfolio-owner) making the transfer, and the client’s bank account information. Counterparty and bank account details The counterparty of the transfer, and the counterparty’s bank account information. See A.2.326 Transfer (cash) on page 874. For a transfer instrument it is also possible to set up: • Spot date and value date calculations • Cashflow and transaction charge rules • Manual charges • Branch codes. See Appendix A Features on page 713. 8.4.2.2 Deal capture 8.4.2.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a transfer instrument: Information Description Currency Currency of the transfer. Nominal Amount Amount of the transfer. Value Date Date when the transfer is made. This defaults to the spot date of the transaction. Value Date Code If the Value Date Setup feature is applied at instrument level, you can enter the value date period you want to use to calculate the value date for the transaction, for example, 3M (3 months). Note: If you specify a value date period in the instrument setup, this is used as the default in the transaction and cannot be modified: see A.2.339 Value Date Setup on page 879. 8.4.2.2.2 Generated data • 456 Cashflows © Wall Street Systems IPH AB - Confidential 8 Cash 8.4 Cash – A transfer generates two cashflows: one negative cashflow for the source account and one positive cashflow for the target account. – If Counterparty = Owner, then the cash instructions are reversed. 8.4.2.3 Processing Apart from the standard processing actions which are common to all transactions (such as Duplicate and Package), there are no other actions in Transaction Manager that are specific to transfer instruments. Settlement of cashflows and reconciliation of transfers with the bank account are managed in Settlement Processing and Settlement Reconciliation: see the TRM User Guide for more information. 8.4.3 Complex payment A complex payment instrument allows you to define a payment instrument with multiple cashflows in the same currency. The direction (transaction sign) and cashflow type of each individual cashflow within the one payment instrument can be configured separately. Note that if you need to define a complex payment instrument consisting of different currencies, you should use an FX deal instead. Complex payment instruments are based on an instrument type derived from the class CASH. 8.4.3.1 Instrument setup The following basic information may be captured when defining the instrument. This information is relevant to any kind of complex payment. • Main characteristics Information Description Transaction Sign Sign of the initial payment transaction. If the sign is not defined at instrument level, it needs to be specified separately for each payment transaction at deal entry. The parameters of the initial payment are defined in the Movement Leg page. • Cashflow Leg characteristics Information Description ID Number representing the order in which the payment is made. The ID of the initial transaction = 0. The ID is displayed in the Origin column in Transaction Manager’s Cashflow view. Payment Sign Select from: Any, Negative, or Positive. The payment sign for the cashflow leg is relative to the transaction sign of the initial payment transaction. Currency Currency of the payment. Leave this field blank if you want to specify the currency when you enter the payment in Transaction Manager. Rounding parameters Method and precision used to round cashflow amounts. Cashflow Type details Type and subtype assigned to a cashflow. For a generic transfer instrument: select Payment. Attribute parameters Attributes of the cashflow: Nominal Amount, Not Bookable, Not Payable, or Pseudo. Client and bank account details The client (portfolio-owner) making the transfer, and the client’s bank account information. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 457 8 Cash 8.4 Cash Information Description Counterparty and bank account details The counterparty of the transfer, and the counterparty’s bank account information. See A.2.102 Complex Payment (cash) on page 757. For a complex payment instrument it is also possible to set up: • Spot date and value date calculations • Cashflow and transaction charge rules • Manual charges • Branch codes. See Appendix A Features on page 713. 8.4.3.2 Deal capture 8.4.3.2.1 Input data In addition to the standard deal parameters, the following information is required to enter a complex payment instrument: Information Description Currency Currency of the payment. Nominal Amount Amount of the payment. Value Date Date when the payment is made. This defaults to the spot date of the transaction. Value Date Code If the Value Date Setup feature is applied at instrument level, you can enter the value date period you want to use to calculate the value date for the transaction, for example, 3M (3 months). Note: If you specify a value date period in the instrument setup, this is used as the default in the transaction and cannot be modified: see A.2.339 Value Date Setup on page 879. 8.4.3.2.2 Generated data • Cashflows – A complex payment generates multiple cashflows – All cashflows are in the same currency – The sign and type of each cashflow can be different. 8.4.3.3 Processing Apart from the standard processing actions which are common to all transactions (such as Duplicate and Package), there are no other actions in Transaction Manager that are specific to complex payment instruments. Settlement of cashflows and reconciliation of payments and receipts with the bank account are managed in Settlement Processing and Settlement Reconciliation: see the TRM User Guide for more information. 458 © Wall Street Systems IPH AB - Confidential 8 Cash 8.5 Forecast 8.5 Forecast A cash forecast instrument can be defined to record cashflow forecasts in the system. Using a dual-currency forecast instrument, it is possible to view cash exposures in two different currencies. Forecast instruments are based on an instrument type derived from the class FORECAST. 8.5.1 Instrument setup The following basic information may be captured when defining a forecast instrument. • Main characteristics Information Description Currency Currency of the cashflow forecast. Rounding parameters Method and precision used to round cashflow amounts. Price Type Price type for the quotation used to determine which FX rate is used in risk calculations. See A.2.153 Forecast on page 784. For a forecast instrument it is also possible to set up: • Spot date and value date calculations • Cashflow and transaction charge rules • Manual charges • Branch codes. See Appendix A Features on page 713. 8.5.1.1 Dual-currency forecast Using a dual-currency forecast instrument, it is possible to view forecast exposures in two different currencies. Dual-currency cashflow forecast instruments are set up in the same way as single currency forecasts, except that they are set up with a different primary feature. See A.2.126 Dual Currency Forecast on page 772. 8.5.2 Deal capture Forecast exposures are imported into TRM using the Forecast Exposures from CMM activity which you can schedule to run as often as required (for example, nightly). These forecasts can then be retrieved in the Forecast Exposure Board for further monitoring or processing. Note: See the TRM User Guide for more information about importing cashflow forecasts into TRM and managing cashflow forecasts in general. 8.5.3 Processing This section describes the actions that can be done throughout the life of a forecast exposure. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 459 8 Cash 8.6 Cost-of-carry 8.5.3.1 Adjust In some rare cases, it may be necessary to adjust the amount of a forecast. This can be done using the Adjust right-click action on the selected forecast. • Execution Information Description Active From Date from when the adjustment applies. Adjustment Amount Amount of the adjustment. Active Until Method Date until when the adjustment applies: Active Until • Until Next Import – the adjustment applies until the next time the activity to import the forecasts from CMM is run, at which time the adjustment is deactivated (but not deleted). • Until Specific Date – the adjustment applies until the date defined in the Active Until field, at which time the adjustment is deactivated (but not deleted). • Always – the adjustment applies indefinitely. Date until when the adjustment applies when Active Until Method = Until Specific Date. An Adjustment flow is added to the forecast exposure. 8.5.3.2 Calculate figures The Calculate Figures right-click action calculates the figures for forecast exposures and displays the results in Forecast Exposure Board’s Figures view. 8.5.3.3 Drill Down The Drill Down action on a retrieved forecast exposure allows you to drill down further into the forecast exposure’s underlying details, for example, to see the underlying component cashflow forecasts of a global forecast amount at a specific date. The underlying components are displayed in Forecast Exposure Board’s Exposure Drilldown view. 8.6 Cost-of-carry Cost-of-carry is used to capture the internal funding cost of outstanding cash. The cost-of-carry balance can be used to monitor how much cash is outstanding for a position and to calculate the accrued interest on the balance. Cost-of-carry can be calculated automatically for any portfolios with a position. Cost-of-carry balances and any accrued interest are displayed in the system as transactions: there is one cost-of-carry transaction per currency dealt in the portfolio. In order to calculate the cost-of-carry of a position, a cost-of-carry instrument needs to be defined and assigned to the portfolio. Only one cost-of-carry instrument needs to be set up to calculate both the balances and the accrued interest. Note: Information about how to assign cost-of-carry instruments to portfolios is described in the TRM User Guide. Cost-of-carry instruments are based on an instrument type derived from the class COST-OF-CARRY. 460 © Wall Street Systems IPH AB - Confidential 8 Cash 8.6 Cost-of-carry 8.6.1 Instrument setup Cost-of-carry instruments are assigned to the portfolios for which you want to calculate the cost associated with funding a position. The balance can either be derived from payable cashflows in the system, or from paid cashflows. Cost-of-carry balance instruments are assigned to portfolios in the Cost of Carry page of Portfolio Editor: see the TRM User Guide for more information. • Main characteristics Cost-of-carry instruments (that do not have accrued interest calculated on the balance) do not require any specific setup. They are simply recognized by the following features in the Cost of Carry instrument class: • – The primary feature COST-OF-CARRY-BALANCE (see A.2.106 Cost of Carry Balance on page 760) – The valuation feature COST-OF-CARRY-METHOD (see A.2.108 Cost of Carry Valuation on page 761). Interest information Cost-of-carry instruments that have accrued interest calculated on the balance use the feature COST-OF-CARRY-INTEREST and require the following setup: – Interest accrual parameters There are some additional parameters that must be defined to calculate the accrual of interest on the cost-of-carry balance. You can specify the interest rates used, and the method and frequency that interest is accrued. Note that if the feature COST-OF-CARRY-INTEREST is not defined in the instrument setup, interest will not be calculated on the cost-of-carry balance. Information Description Date Basis Date basis used to calculate accrued interest for this instrument. Interest Rate Curve Underlying yield curve used for interest calculation. Note: If you specify a yield curve, you do not need to specify any Ladder values (see Ladder Rule and Ladder). – Period Period of the underlying yield curve to be used for interest calculation (for example, O/N). Scenario Rate scenario to be used for calculating interest for this instrument. Interest realization parameters You can specify how the accrued interest is realized on the balance. Information Description Frequency Frequency of interest realization (if Method = Periodically). Frequency Unit Method Unit of time to use for interest realization: Business Days, Days, Months, Weeks, or Years. Method of realizing interest: • At Withdrawal - not applicable. • Periodically - interest is realized at regular intervals (see Frequency field). • Settlement Method At Expiration - not applicable. Interest payment method: Only Capitalize is used for cost-of-carry. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 461 8 Cash 8.6 Cost-of-carry See A.2.107 Cost of Carry Interest on page 760. 8.6.2 Deal capture Cost-of-carry transactions are system-generated transactions, performed by scheduled activities (see the TRM User Guide for more information). When an activity has run, you can view the transactions in the Cost of Carry application. 8.6.2.1 Generated data • Transaction – One transaction per currency: Transaction Type = Balance Counterparty = Portfolio-owner • Cashflows – One cashflow per balance (only if the balance has changed) – Daily accrued interest (if the Cost of Carry Interest feature is assigned to the instrument). – If the interest is realized: realized interest cashflows. – If zero-balancing is used: another balance cashflow with the opposite sign. A zero balance cashflow is also generated the next day. 8.6.3 Processing This section describes the processing that you can perform, either manually in the relevant application, or automatically, as an activity, in Activity Manager. 8.6.3.1 Calculating cost-of-carry balance and interest Cost-of-carry balance and accrued interest-calculation transactions are generated by the activity Cost of Carry which you can schedule to run as often as required (see the TRM User Guide for more information). 8.6.3.2 Realizing cost-of-carry interest Cost-of-carry accrued interest can be realized automatically or manually (for automatic realization, see the TRM User Guide). You can realize interest manually, by right-clicking on the transaction in the Transaction view of the Cost of Carry application and selecting the Realize AI action. • 462 Execution © Wall Street Systems IPH AB - Confidential 8 Cash 8.6 Cost-of-carry The following information is needed to process the realization: Information Description Date Date of the action i.e. the realization date. Opening Date The opening date of the transaction. Payment Date By default, the Payment Date is the realization date. However, you can change the default. Amount Amount of the realized cost-of-carry interest cashflow. By default, this is the total amount of accrued interest, but it can be changed to a lesser amount if you do not want to realize the total amount. Zero Balancing Yes or No (default). Update Realization Date • Yes - the accrued cost-of-carry interest and the cost-of-carry balance are closed out, so that the next day, the starting cost-of-carry balance is zero when the cost-of-carry activity is run. • No - the accrued cost-of-carry interest is realized today, and the next day, the starting cost-of-carry balance is today's balance. Switch on to allow the next interest realization date to be automatically updated. Note: It is not possible to realize accrued interest for future dates using the Realize AI action. • Cancellation You can cancel interest manually by right-clicking on the transaction in the Transaction view of the Cost of Carry application and selecting the Undo Realize AI action. The following information is needed to process the cancellation:. Information Description Date Date of the action i.e. the undo realization date. By default the date is today's date. 8.6.3.3 Setting the cost-of-carry balance to zero It is possible to close out the outstanding cost-of-carry balance without realizing any interest using the activity Cost of Carry Zero Balancing. See the TRM User Guide for more information. Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 463 8 Cash 8.6 Cost-of-carry 464 © Wall Street Systems IPH AB - Confidential Chapter 9 Futures 9.1 Forward rate agreement A Forward Rate Agreement (FRA) is an obligation between two parties to enter into a deposit or discount contract in the future at a predefined interest rate. An FRA is an off-balance sheet instrument where the underlying contract is not entered at expiry, but the difference between the pre-agreed rate and the actual rate at expiry is settled between the two parties. The date on which the comparison is made is known as the fixing date. Payment of the interest differential is made up-front, at the start of the future period. The amount is therefore calculated on a discounted basis since it is settled in advance. FRA contracts are traded in reversed sign (the market convention). This means that the purchase of an FRA creates a negative position and a negative interest rate risk, whereas the sale of an FRA produces a positive position and a positive interest rate risk. The most common maturities for FRAs are between 1 and 12 months and the US dollar is the major currency used. FRAs are labeled by period (for example, 3M/6M means a contract that starts in three months and ends in six). 9.1.1 FRA deposit and FRA discount The following basic information may be captured when defining the instrument. This information is relevant to any kind of FRA contract (discount paper or deposit). For more information relating to the setup and structure of specific types of FRA, see 9.1.2 Australian FRA on page 476. 9.1.1.1 Instrument setup Forward rate agreements are based on an instrument type derived from the class FRA. • Main characteristics The following basic information may be captured when defining the instrument. This information is relevant to any kind of FRA contract (discount paper or deposit). Information Description Currency Currency of the FRA (that is, if it is a listed forward rate agreement). Leave this field blank if you want to specify the currency at deal entry (if you are defining an OTC forward rate agreement). Date Basis Date basis of the instrument. If the date basis is not defined at instrument level, it needs to be specified separately for each transaction. Rounding parameters Method and precision used to round cashflow amounts. Yield Type Yield type of the forward rate agreement. Principal Subtype Type of principal or interest cashflows, if you want to override the default settings. Interest Subtype Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 465 9 Futures 9.1 Forward rate agreement • Netting parameters Information Description Fixing Offset Minimum number of days’ offset allowed, that is, the difference in days between the fixing date and the due date (default = 0). Leave this field blank if you want to specify the fixing offset when you enter the deal. Fixing Subscenario Prices scenario from which the floating rate is retrieved (for example, EUR/USD Spot 9:00 London, or EUR/USD Spot 9:00 Tokyo). Leave this field blank if you want to specify it when you enter the deal. Calendar Calendar to use when calculating the fixing date. Switches Activate the switches that apply to the instrument. • Settlement Currency Settlement Currency - switch on if the P/L cashflow is paid in a different currency. Currency in which the P/L cashflow is paid (if the switch Settlement Currency is switched on). Leave this field blank if you want to specify the settlement currency when you enter the deal. Payment Offset Number of business days after which effective payment of the P/L is made Fixing Rate ID of the yield curve used to calculate the closing price of the forward contract. The forward contract is fixed with the price and TRM calculates the profit/loss using this closing price and the deal rate. Leave this field blank if you want to specify it when you enter the deal. Fixing Period Length of time for which fixing is to be executed (for example, 3M, 6M, 1Y, and so on). Leave this field blank if you want to specify the fixing period when you enter the deal. See A.2.157 Forward Rate Agreement (Deposit) on page 786 and A.2.158 Forward Rate Agreement (Discount) on page 787. • Date information For listed FRA contracts, you must specify the fixing, settlement, and maturity information. See A.2.156 FRA Dates on page 785. For OTC FRA contracts, you need to set up the FRA period information. The maturity date and value date of the contract is calculated using these values. Information Description Calendar parameters Calendars used to calculate the dates. Gap Set Gap set used for supplying the available value/maturity periods for an OTC FRA contract; these in turn are used to define exact dates. Gap Specific gap (within the gap set) defined for the FRA period. This value is used to calculate the value date and maturity date for an OTC FRA contract at deal entry. If you specify the gap period in the instrument setup, this is used as the default in the transaction and cannot be modified. If you leave this field blank, you need to select the gap period in the Maturity Code field at deal entry. The system will then calculate the FRA periods automatically. See A.2.163 FRA Periods on page 790. • 466 Quotation information © Wall Street Systems IPH AB - Confidential 9 Futures 9.1 Forward rate agreement For listed FRA discount contracts, specify the quote information as Yield. See A.2.274 Quoted on page 849. It is also possible to set up: • Branch codes • Cashflow and transaction charge rules • Manual charges • Spot date calculation. See Appendix A Features on page 713. 9.1.1.2 Deal capture 9.1.1.2.1 Input data In addition to the standard deal parameters, the following information is required to enter an FRA contract: Information Description Currency Currency of the transaction. If you specified the currency in the instrument setup (for example, for a US T-Bill), this is used as the default currency in the transaction and cannot be modified. Maturity Code Maturity code used to calculate the FRA periods. From this code, the date for the maturity of the underlying contract and the official date when money is transferred (expiry of the FRA) are calculated. If you defined the specific FRA periods in the instrument setup, these are used as the default in the transaction and cannot be modified. Maturity Date Date when the transaction matures. If you enter a maturity code, the date is calculated automatically; otherwise you can enter the date manually. If the maturity definition parameters are defined at instrument level, these are used by default and cannot be modified. Value Date Date when the transaction starts. This defaults to the spot date of the transaction. Nominal Amount Amount of the forward rate agreement. This is equal to the principal (the amount on which the interest is calculated). FRAs are traded in reversed sign. This means that the nominal amount is negative for the purchase of an FRA, whereas the sale of an FRA is denoted by a positive nominal amount. Deal Rate Rate of return of the underlying forward contract. Fixing Rate Yield curve used when fixing the cashflow. Fixing Period Interest period from which the quotation is retrieved when fixing the interest rate of the transaction, for example, 1M, 3M, or 1Y. Fixing (Max) Offset (Maximum) number of business days before the interest date. Fixing Offset The fixing of the interest occurs on this date. Fixing Subscenario Rate scenario from which the interest rate is retrieved (for example, EUR/USD Spot 9:00 London or EUR/USD Spot 9:00 Tokyo). Fixing Calendar Calendar used for fixing. 9.1.1.2.2 Generated data • Transaction Book Value (discount style): Transaction & Risk Management Module (TRM) Instruments: Processing and Calculations 467 9 Futures 9.1 Forward rate agreement BV = rounder (A*D) where: D = discount factor A = nominal amount rounder depends on instrument rounding parameters •