High Frequency Trading A Practical Guide To Algorithmic Strategies And Systems

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High-Frequency
Trading

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High-Frequency
Trading
Second Edition
A Practical Guide to Algorithmic
Strategies and Trading Systems

Irene Aldridge

Cover image: © Crusitu Robert/iStockphoto
Cover design: John Wiley & Sons, Inc.
Copyright © 2013 by Irene Aldridge. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
The First Edition of High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems
was published by John Wiley and Sons, Inc. in 2010.
Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data:
Aldridge, Irene, 1975–
High-frequency trading: a practical guide to algorithmic strategies and trading systems/Irene
Aldridge.—2nd Edition.
pages cm.—(Wiley trading series)
Includes index.
ISBN 978-1-118-34350-0 (Cloth)—ISBN 978-1-118-42011-9 (ebk)—ISBN 978-1-118-43401-7 (ebk)—
ISBN 978-1-118-41682-2 (ebk) 1. Investment analysis. 2. Portfolio management. 3. Securities.
4. Electronic trading of securities. I. Title.
HG4529.A43 2013
332.64—dc23
2012048967
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1

To my family

Contents

Preface
Acknowledgments
Chapter 1 How Modern Markets Differ from Those Past
Media, Modern Markets, and HFT
HFT as Evolution of Trading Methodology
What Is High-Frequency Trading?
What Do High-Frequency Traders Do?
How Many High-Frequency Traders Are There?
Major Players in the HFT Space
Organization of This Book
Summary
End-of-Chapter Questions
Chapter 2 Technological Innovations, Systems, and HFT
A Brief History of Hardware
Messaging
Software
Summary
End-of-Chapter Questions
Chapter 3 Market Microstructure, Orders, and
Limit Order Books
Types of Markets
Limit Order Books
Aggressive versus Passive Execution
Complex Orders
Trading Hours
Modern Microstructure: Market Convergence and Divergence

xi
xiii
1
6
7
13
15
17
17
18
18
19
21
21
25
33
35
35
37
37
39
43
44
45
46

vii

Fragmentation in Equities
Fragmentation in Futures
Fragmentation in Options
Fragmentation in Forex
Fragmentation in Fixed Income
Fragmentation in Swaps
Summary
End-of-Chapter Questions
Chapter 4 High-Frequency Data
What Is High-Frequency Data?
How Is High-Frequency Data Recorded?
Properties of High-Frequency Data
High-Frequency Data Are Voluminous
High-Frequency Data Are Subject to the Bid-Ask Bounce
High-Frequency Data Are Not Normal or Lognormal
High-Frequency Data Are Irregularly Spaced in Time
Most High-Frequency Data Do Not Contain
Buy-and-Sell Identifiers
Summary
End-of-Chapter Questions
Contents

viii

Chapter 5 Trading Costs
Overview of Execution Costs
Transparent Execution Costs
Implicit Execution Costs
Background and Definitions
Estimation of Market Impact
Empirical Estimation of Permanent Market Impact
Summary
End-of-Chapter Questions
Chapter 6 Performance and Capacity of High-Frequency
Trading Strategies
Principles of Performance Measurement
Basic Performance Measures
Comparative Ratios
Performance Attribution
Capacity Evaluation
Alpha Decay
Summary
End-of-Chapter Questions
Chapter 7 The Business of High-Frequency Trading
Key Processes of HFT

46
50
51
51
51
51
52
52
53
53
54
56
57
59
62
62
70
73
74
75
75
76
78
82
85
88
96
96
97
97
98
106
110
112
116
116
116
117
117

Financial Markets Suitable for HFT
Economics of HFT
Market Participants
Summary
End-of-Chapter Questions

121
122
129
130
130

Chapter 8 Statistical Arbitrage Strategies

131

Practical Applications of Statistical Arbitrage
Summary
End-of-Chapter Questions
Chapter 9 Directional Trading Around Events
Developing Directional Event-Based Strategies
What Constitutes an Event?
Forecasting Methodologies
Tradable News
Application of Event Arbitrage
Summary
End-of-Chapter Questions
Chapter 10 Automated Market Making—Naïve
Inventory Models

Chapter 11 Automated Market Making II
What’s in the Data?
Modeling Information in Order Flow
Summary
End-of-Chapter Questions
Chapter 12 Additional HFT Strategies, Market Manipulation,
and Market Crashes
Latency Arbitrage
Spread Scalping
Rebate Capture
Quote Matching
Layering
Ignition

147
148
149
150
153
155
163
163
165
165
167
167
168
173
176
178
178
179
179
182
193
193
195
196
197
198
199
200
201

ix
Contents

Introduction
Market Making: Key Principles
Simulating a Market-Making Strategy
Naïve Market-Making Strategies
Market Making as a Service
Profitable Market Making
Summary
End-of-Chapter Questions

133
144
144

Pinging/Sniping/Sniffing/Phishing
Quote Stuffing
Spoofing
Pump-and-Dump
Machine Learning
Summary
End-of-Chapter Questions
Chapter 13 Regulation
Key Initiatives of Regulators Worldwide
Summary
End-of-Chapter Questions
Chapter 14 Risk Management of HFT
Measuring HFT Risk
Summary
End-of-Chapter Questions
Chapter 15 Minimizing Market Impact

Contents

Why Execution Algorithms?
Order-Routing Algorithms
Issues with Basic Models
Advanced Models
Practical Implementation of Optimal Execution Strategies
Summary
End-of-Chapter Questions
Chapter 16 Implementation of HFT Systems

201
201
202
202
207
208
208
209
209
222
223
225
225
244
244
245
245
247
258
262
269
269
270
271

Model Development Life Cycle
System Implementation
Testing Trading Systems
Summary
End-of-Chapter Questions

271
273
283
286
287

About the Author
About the Web Site
References
Index

288
290
291
303

P r e fa c e

f hiring activity is highest in profitable and rapidly expanding industries, then highfrequency trading (HFT) is by far the most successful activity in the financial sector
today. Take, for example, the Jobs classifieds in the Money and Investing section of
the Wall Street Journal on November 27, 2012. All five advertisements placed there
were for high-frequency trading and related roles. Morgan Stanley alone was hiring four candidates in its high-frequency trading operation. HFT candidates were
sought at all levels: associate vice presidents were required in HFT technology development, executive directors were needed in HFT strategy development, and vice
presidents were sought for in HFT operations. To warrant the investment into new
employees at all levels, prospective employees with HFT skills were clearly expected
to generate high returns for their employers for the foreseeable future.
Despite considerable hiring in the field, the high-frequency trading industry is still
in its infancy.While some claim that high-frequency traders comprise 60 to 70 percent
of all market participants, such numbers are seldom reached in reality. Scientific examinations find that HFTs still account for as little as 25 percent of all market activity
in such frequently traded instruments as the S&P 500 E-mini futures (see Kirilenko
et al., 2011). As Figure 1 shows, even in the very liquid S&P 500 ETF (NYSE: SPY),
high-frequency traders on average account for just 20 percent of daily trades.
As shown in Figure 1, the average levels of HFT participation in SPY remain remarkably stable: on most days in 2009 through 2012, 15 to 17 percent of all trades
in SPY can be attributed to HFTs. At the same time, evidence of resource allocation
to HFT suggests that the industry is growing at a rapid pace. A natural explanation
reconciling the two observations exists: HFT has low barriers to entry, yet it can be
extremely complex, requiring years of toiling with data to proficiently develop and
deploy trading models.
Indeed, as any successful HFT operator will tell you, development of consistently
profitable ultra-short-term trading strategies takes at least three years. While the
number may seem extreme, it is not really different from the time required to
develop proficiency or “block” in any other industry or specialization.

Average % of HFT-Initiated Trades in the S&P 500 ETF (NYSE: SPY)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%

09
20 11
09 03
20 12
10 14
20 01
10 26
20 03
10 10
20 04
10 21
20 06
10 04
20 07
10 20
20 09
10 09
20 10
10 21
20 12
11 08
20 01
11 19
20 03
11 01
20 04
11 14
20 06
11 17
20 07
11 29
20 10
11 05
20 11
12 23
20 02
12 06
20 03
12 16
20 04
12 27
20 06
12 11
20 07
12 23
20 08
12 31
10
15

FIGURE 1

Source: Aldridge (2012a)

PREFACE

xii

HFT is particularly complex as the discipline rests at the confluence of two already complicated areas of study: high-frequency finance and computer science.
Very few academic institutions offer programs that prepare students to be simultaneously competent in both areas. Most finance-trained people do not understand
computer programming, and most computer scientists do not have a grasp on the
required highly academic finance.
This book is written to fill that academic void: to supply true, accurate, and
up-to-date graduate-level information on the subject of high-frequency trading, as
well as to address the questions and opinions that many have about the subject. The
book has a companion web site, www.hftradingbook.com, where you can find practical examples, updates, and teaching materials. I hope you find the book informative
and helpful in your future endeavors.

Ac k n ow l e d g m e n t s

am extremely grateful to my husband for tireless encouragement and insightful
suggestions, to my son Henry for helping me keep a balanced perspective, to Gaia
Rikhye for terrific front-line edits, and to my wise editor Bill Falloon, über-patient
development editor Judy Howarth, diligent senior production editor Vincent
Nordhaus, and terrific publisher Pamela Van Giessen for making it all happen.
xiii

Chapter 1

How Modern
Markets Differ from
Those Past
S

tructural change is not new to trading in financial instruments. If fact, it is the
constancy of innovation that has helped drive the leadership of modern financial
institutions. High-frequency trading (HFT) has stepped into the limelight over the
past few years and delivered considerable operational improvements to the markets,
most of which have resulted in lower volatility, higher market stability, better market
transparency, and lower execution costs for traders and investors. This chapter of the
book provides the overview of dramatic changes that precipitated in the securities
markets over the past 50 years, and defines HFT and core strategies falling under the
HFT umbrella.
Over the past two decades, the demand for computer technology in consumer
markets has led to significant drops in hardware prices across the board, as discussed
in detail in Chapter 2 of this book. As a result, technology-enabled trading has become cost effective, and the ensuing investment into software has made trading platforms more accessible and more powerful. Additionally, the savings from lower errors
in message transmission and data input, higher reliability of order execution, and
continuity of business through computer code, deliver a business case for deepening
financial firms’ reliance on their technology systems. The escalating complexity of
regulations also requires more advanced reporting capabilities that are becoming prohibitively expensive without substantial platforms. The lower cost base squeezes margins further, and this puts pressure on the traditional full-service model. Figures 1.1
and 1.2 illustrate the financial services landscape circa 1970s and today.
In the 1970s and earlier, the market participants were organizations and individuals now considered “traditional” players. As Figure 1.1 shows, on the portfolio management or “buy” side, the markets engaged

■
■

■

Discretionary asset managers, including pension funds, mutual funds, and hedge funds.
retail flow, including individual “mom-and-pop” investors, and others with comparatively smaller capitalization.
Manual speculators, individuals involved in intraday proprietary trading for their
own account or for the account of their bank.
On the transaction facilitation, middle-men, or “sell” side, the markets supported

■

Manual market makers (representatives of broker-dealers), taking short-term inventory risk, providing quotations to the buy side, and generally facilitating the
buy-side trading for a fee.

The exchange
Discretionary asset
managers
Manual market
makers

Manual
arbitrageurs/prop
traders

HOw MODern MArkeTS DIFFer FrOM THOSe PAST

2
Retail flow

FIGURE 1.1 Financial Markets in the 1970s, before electronization

The
exchange

ATS, dark
pools

Manual
market makers

Discretionary
asset managers

Auto market
makers
Manual
arbitrageurs/
prop traders
Retail flow

FIGURE 1.2 Financial Markets Today

Quantitative
asset
managers

Automated
arbitrageurs/prop
traders

■■

A single not-for-profit exchange in each asset class was established to curtail wild
speculation by the exchange members and to lower transaction costs paid by the
investors.1

The highly manual and therefore labor-intensive financial landscape of the 1970s
was characterized by high transaction costs, leading to low turnover of securities; a
high degree of error associated with manual processing of orders, and relatively high
risk of trading, as traders predominantly relied on their experience and intuition as
opposed to science in making their bets on the markets.Yet, the 1970s were also high
margin businesses, with brokers receiving a large share of the spoils in the form of
large commissions and, ultimately, the proverbial “fat-cat” bonuses to the tune of tens
of millions of dollars.
Fast-forward to today’s markets, illustrated in Figure 1.2: new entrants successfully compete using lean technology and science to hash out precise investing models, reshaping the markets in the process:
■■

■■

Automated market makers, for example, broker-dealers and hedge funds, harness
the latest technology, studies of market microstructure, and HFT to deliver low
transaction costs, taking over market share from traditional broker-dealers.
Automated arbitrageurs, such as statistical arbitrage hedge funds and proprietary
traders, use quantitative algorithms, including high-frequency trading techniques,
to deliver short-term trading profits.
Multiple alternative trading venues, like new exchanges and dark pools, have
sprung up to address market demand for affordable quality financial matching
services.

These innovations have changed the key characteristics of the markets, and largely
for the better:
■■

■■

The markets now enjoy vastly democratic access: due to proliferation of low-cost
technology, anyone can trade in the markets and set quotes, a right formerly reserved to members of the exclusive connections-driven club of broker-dealers.
Plummeting transaction costs keep money in investors’ pockets; more on this
later.
Automated trading, order routing, and settlement deliver a new low degree of
error.

Most exchanges became not-for-profit only in the 1970s. From the time of their formation to the
1970s, however, the exchanges were very much for profit. In fact, the Buttonwood agreement of
1792 that laid foundation to the New York Stock Exchange, specified explicit profitability rules: no
broker was allowed to charge less than 0.25 percent of the transaction volume, a staggering commission by today’s standards.

3
How Modern Markets Differ from Those Past

■■

Quantitative money managers, such as mutual funds and hedge funds, are using
the precise science of economics, finance, and the latest mathematical tools to
chisel increasingly close forecasts of securities prices, improving profitability of
their investments.

The extreme competition among the new entrants and old incumbent market
participants, however, has also resulted in reduced margins for broker-dealers,
squeezing out technology-inefficient players.
The way trading is done has changed over time and these newer approaches affected the relative power of consumers and institutions. In the 1970s’ marketplace,
the trading process would often proceed as follows:

How Modern Markets Differ from Those Past

1. Brokers would deliver one-off trading ideas to their buy-side clients. The ideas
were often disseminated via countless phone calls, were based on brokers’ thenunique ability to observe markets in real time, and were generally required compensation in “soft-dollar” arrangements—if the customer decided to trade on
the idea, he was expected to do so through the broker who produced the idea,
and the customer would pay for the idea in the form of potentially higher broker
commissions.
2. If and when the customer decided to trade on the idea, the customer would
phone in the order to the broker or the broker’s assistant. Such verbal orders
frequently resulted in errors: the noise on the brokers’ trading floors often impeded correct understanding of customer instructions.
3. After receiving a customer’s order, the broker’s next steps would depend on the
size of the placed order: while large orders would be taken to the market right
away (potentially in smaller parcels), smaller orders would sit on the broker’s
desk, waiting for other similar orders to fill up a “round lot”—the minimum
order size executable on an exchange. Smaller customers were thus often at a
disadvantage, waiting for execution of their orders while the favorable market
price slipped away.
4. Once the order or several sequential orders comprised the order size acceptable
to the broker, the broker would route the order to the appropriate exchange.
5. Next, human representatives of the exchange, known as “specialists,” would
match the order and send the trade acknowledgments back to the broker. It is
well understood that the specialists often created preferential terms for some of
their connections, at the expense of orders of others. Such behavior rewarded
investment in connections and chummy networks, and resulted in exclusive Wall
Street cliques capable of significant price discrimination for in-group versus outof-group customers. Even though exchanges operated as not-for-profit organizations, influence peddling was common, and the markets were a long way away
from anything resembling an equal playing field for all participants.
6. The broker notified the client of execution and collected his commissions and
oversized bonuses.The brokers presided over the power of the markets and were
compensated as kings.
Figure 1.3 illustrates the traditional investing process prevalent circa 1970s.
Fast-forward 40-something years ahead, and the balance of power has shifted.
Customers have increased their expertise in quantitative analysis and are often better equipped for research than brokers. Brokers’ area of expertise has decreased in
scope from the all-encompassing sell-side research into securities behavior to a more
narrow, albeit still important area of algorithmic execution designed to help clients

1. Soft-dollar research
Customer,
e.g., mutual fund
Broker
Sales/Trader
2. Trading
6. Notify
clients of
execution

3. Wait for
other orders

$$$

5. Exchange
acknowledges
order execution

4. Place order(s)
on the exchange

The Exchange

FIGURE 1.3 Broker-centric Investing Process Prevalent before electronization

navigate the choppy intraday trading waters. with such buy-side investors, the market flow evolves according to the process in Figure 1.4:

Some customers go even further and prefer to do away with broker service altogether, building their own execution algorithms, keeping a higher share of the profits. Plummeting costs of technology have enabled fast distribution of tick data to all
interested parties, and now customers, not just brokers, can watch and time markets
and generate short-term forecasts of market behavior. Customers taking the largely

5
HOw MODern MArkeTS DIFFer FrOM THOSe PAST

1. Customers, not brokers, generate research based on forecasts of securities
movements and their existing allocations, all within the quantitative portfolio
management framework.
2. The customer places an order via electronic networks, greatly reducing errors
and misunderstandings. The order instantaneously arrives on the broker’s desktop.
3. The customer or the broker selects the broker’s optimal execution algorithm
designed to minimize the customer’s execution costs and risk, speed up execution whenever possible, and minimize observability of the customer’s trading
actions.
4. Selected algorithm electronically parcels out the customer’s order and routes
the order slices to relevant exchanges and other trading venues.
5. Trading venues match the customer’s order slices and acknowledge execution.
6. The broker sends the order acknowledgment back to the customer, and receives
his considerably lower commission. (In 1997, the lowest broker commission on
retail trades was offered by Merrill Lynch, and the commission was $70 per trade.
Today, Interactive Brokers charges about $0.70 per trade, a 100-fold reduction
in transaction costs available to clients.)

Customer,
e.g., mutual
fund

1. Generates
in-house
research

Broker
Sales/Trader

2. Trading orders
6. Notify
clients of
execution

3. Select
best
execution

5. Exchange
acknowledges
order execution

4. Place order(s)
on the exchange

The Exchanges: $
Trading Venues
(Exchanges,
Dark Pools, ATS): $

FIGURE 1.4 Modern Investing Process, Scenario 1: Brokers Provide Best execution for

Clients’ Orders

HOw MODern MArkeTS DIFFer FrOM THOSe PAST

broker-independent route are said to engage in “direct access” to the markets, and
their execution process consists of the following steps:
1. The broker grants the customer a privilege to access the exchange directly for
a negotiated per-trade or per-volume fee. To grant access, the broker may allow
the customer to use the broker’s own identification with a specific exchange.The
customer’s order routing systems then use the broker’s identification in order
messaging with the exchange.
2. Customer computer systems or human analysts generate a high- or low-frequency
portfolio allocation decision that involves one or more trading orders.
3. Customer uses his own order splitting and routing algorithms to optimally place
his orders directly with exchanges and other trading venues.
4. One or several exchanges and trading venues match the orders, acknowledg
execution directly to client.
5. The broker receives settlement information and charges the client for the privilege of using the broker’s direct access identification.
Figure 1.5 summarizes these steps.
■ Media, Modern Markets, and HFT
while the market-wide changes have disturbed the status quo on the broker-dealer
side and squeezed many a broker out of business, the changes to the society at large
have been mostly positive, depositing the saved dollars directly into investor pockets. Gone are the multimillion-dollar bonuses of many brokers taking phone orders

Customer,
e.g., mutual
fund

1. Generates
in-house
research

2. Grant
access to
exchanges

5. Pay broker
for access
$

4. Exchange
acknowledges
order execution

3. Place order(s)
on the exchange

Broker
Sales/Trader

The Exchanges:
$ Venues
Trading
(Exchanges,
Dark Pools, ATS): $

FIGURE 1.5 Modern Investing Process, Scenario 2: Clients Decide on Best execution, Access
Markets Directly

■ HFT as Evolution of Trading Methodology
Brokers who speak loudly against the HFT tend to rely on technical analysis in making their decisions of when to enter or exit a position. Technical analysis was one of

7
HOw MODern MArkeTS DIFFer FrOM THOSe PAST

and watching markets on their computer screens. The money has been redirected to
bank shareholders and end investors.
Clearly, not everyone is happy about such shifts in the industry, and the least happy
bunch happens to be brokers losing their income to automation. Stripped of the ability
to extract easy money out of investors’ pockets, brokers have been the most vocal opponents of high-frequency trading. Brokers like Arnuk and Saluzzi (2012), for example,
denounce automation, yet wax eloquent about those manual error-prone days when
investors were not allowed on exchanges and brokers were the fat cats of the world.
Some brokers, whose lifestyle has been significantly reduced by technology, attempt
to demonize HFT with an even more sinister goal in mind: they are seeking to lure in
investors to their outfits still charging exorbitant transaction costs under the guise of protecting the poor investor lambs from the HFT predators. Investors should take time to
compare costs of trading through a broker versus other available options. Chapters 5, 12,
and 15 of this book provide specific information to enable low-frequency investors to
estimate the risk of potentially adverse HFT, and take educated steps to managing said
risk, without relying on self-serving hype of selected brokers who refuse to catch up on
technical innovation, resorting to scare tactics at the expense of their clients instead.The
remainder of this chapter is devoted to explaining the evolutionary nature of HFT and
the definitions and overview of strategies that fall under the HFT umbrella.

How Modern Markets Differ from Those Past

the earliest techniques that became popular with many traders and is, in many ways,
a direct precursor to today’s sophisticated econometrics and other HFT techniques.
Technical analysts came in vogue in the early 1910s and sought to identify recurring
patterns in security prices. Many techniques used in technical analysis measure current
price levels relative to the rolling moving average of the price, or a combination of the
moving average and standard deviation of the price. For example, a technical analysis technique known as moving average convergence divergence (MACD) uses three
exponential moving averages to generate trading signals. Advanced technical analysts
would look at security prices in conjunction with current market events or general
market conditions to obtain a fuller idea of where the prices may be moving next.
Technical analysis prospered through the first half of the twentieth century, when
trading technology was in its telegraph and pneumatic-tube stages and the trading
complexity of major securities was considerably lower than it is today. The inability
to transmit information quickly limited the number of shares that changed hands,
curtailed the pace at which information was incorporated into prices, and allowed
charts to display latent supply and demand of securities. The previous day’s trades
appeared in the next morning’s newspaper and were often sufficient for technical
analysts to successfully infer future movement of the prices based on published information. In post-WWII decades, when trading technology began to develop considerably, technical analysis developed into a self-fulfilling prophecy.
If, for example, enough people believed that a “head-and-shoulders” pattern
would be followed by a steep sell-off in a particular instrument, all the believers
would place sell orders following a head-and-shoulders pattern, thus indeed realizing
the prediction. Subsequently, institutional investors have moved to high-frequency
econometric modeling using powerful computer technology, trading away technical
patterns. By now, technical analysis at low frequencies, such as daily or weekly intervals, is marginalized to work only for the smallest, least liquid securities, which are
traded at very low frequencies—once or twice per day or even per week.
Some technical analysis techniques, such as momentum or Bollinger bands, have
been successfully adopted and extended by modern-day quants in all investing frequencies. It has long been shown that human investors tend to pour money into strategies that worked in recent months. As a result, strategies working in the past month
are also likely to work the following month, forming a tradable momentum that can
be detected using simple technical moving-average-based indicators, as well as more
complex quantitative tools. Similarly, Bollinger bands detect deviation of prices the
prespecified number of standard deviations away from the mean. The concept of
statistical arbitrage extended Bollinger band principle to detect, for example, deviation of price differences from their long-running means. In this trading exercise,
commonly known as pairs trading, traders identify the overpriced and underpriced
financial instruments when the price of one instrument exceeds the price of another
by the prespecified number of standard deviations of price difference changes. More
generally, quants use Bollinger band ideas to pinpoint mean-reverting processes and
trade financial instruments with the expectation that the measured average quantity
will stay stable, or “stationary” in the language of statistics.
Another important investing and trading technique, known as fundamental analysis, originated in equities in the 1930s when traders noticed that future cash flows,

9
How Modern Markets Differ from Those Past

such as dividends, affected market price levels. The cash flows were then discounted
back to the present to obtain the fair present market value of the security. Graham
and Dodd (1934) were the earliest purveyors of the methodology and their approach
is still popular. Over the years, the term fundamental analysis expanded to include
pricing of securities with no obvious cash flows based on expected economic variables. For example, fundamental determination of exchange rates today implies
equilibrium valuation of the rates based on macroeconomic theories.
Fundamental analysis developed through much of the twentieth century. Today,
fundamental analysis refers to trading on the expectation that the prices will move
to the level predicted by supply-and-demand relationships, the fundamentals of economic theory. In equities, microeconomic models apply; equity prices are still most
often determined as present values of future cash flows. In foreign exchange, macroeconomic models are most prevalent; the models specify expected price levels
using information about inflation, trade balances of different countries, and other
macroeconomic variables. Derivatives are traded fundamentally through advanced
econometric models that incorporate statistical properties of price movements of
underlying instruments. Fundamental commodities trading analyzes and matches
available supply and demand.
Various facets of fundamental analysis are inputs into many high-frequency
trading models, alongside market microstructure. For example, event arbitrage
consists of trading the momentum response accompanying the price adjustment
of the security in response to new fundamental information. The date and time of
the occurrence of the news event is typically known in advance, and the content
of the news is usually revealed at the time of the news announcement. In highfrequency event arbitrage, fundamental analysis can be used to forecast the fundamental value of the economic variable to be announced, in order to further refine
the high-frequency process.
Like selected technical models, some fundamental models were adopted by
quants who extended the precision of their models, and often dramatically sped up
calculation of the relevant values. Fair values of equities following an earnings announcement were recomputed on the fly, enabling quants to reap the profits, at the
expense of fundamental traders practicing longhand analysis in Excel spreadsheets.
Speed, in fact, became the most obvious aspect of quant competition. Whoever
was able to run a quant model the fastest was the first to identify and trade on a
market inefficiency and was the one to capture the biggest gain. To increase trading
speed, traders began to rely on fast computers to make and execute trading decisions.
Technological progress enabled exchanges to adapt to the new technology-driven
culture and offer docking convenient for trading. Computerized trading became
known as systematic trading after the computer systems that processed run-time data
and made and executed buy-and-sell decisions.
High-frequency trading developed in the 1990s in response to advances in computer technology and the adoption of the new technology by the exchanges. From
the original rudimentary order processing to the current state-of-the-art all-inclusive
trading systems, HFT has evolved into a billion-dollar industry.
To ensure optimal execution of systematic trading, algorithms were designed to
mimic established execution strategies of traditional traders. To this day, the term

How Modern Markets Differ from Those Past

algorithmic trading usually refers to the automated “best execution” process—that
is, the optimization of buy-and-sell decisions once these buy-and-sell decisions
were made by another part of the systematic trading process or by a human portfolio manager. Algorithmic trading may determine how to process an order given
current market conditions: whether to execute the order aggressively (on a price
close to the market price) or passively (on a limit price far removed from the
current market price), in one trade or split into several smaller “packets.” As mentioned previously, algorithmic trading does not usually make portfolio allocation
decisions; the decisions about when to buy or sell which securities are assumed to
be exogenous.
The advances in computer technology over the past decades have enabled fully
automated HFT, fueling the profitability of trading desks and generating interest in
pushing the technology even further. Trading desks seized upon cost savings realized
from replacing expensive trader head count with less expensive trading algorithms
along with other advanced computer technology. Immediacy and accuracy of execution and lack of hesitation offered by machines as compared with human traders
has also played a significant role in banks’ decisions to switch away from traditional
trading to systematic operations. Lack of overnight positions has translated into immediate savings due to reduction in overnight position carry costs, a particular issue
in crisis-driven tight lending conditions or high-interest environments.
Banks also developed and adopted high-frequency functionality in response to demand from buy-side investors. Institutional investors, in turn, have been encouraged
to practice high-frequency trading by the influx of capital following shorter lock-ups
and daily disclosure to investors. Both institutional and retail investors found that investment products based on quantitative intraday trading have little correlation with
traditional buy-and-hold strategies, adding pure return, or alpha, to their portfolios.
Under the Dodd-Frank Act, banks were forced to close many of the proprietary
trading operations, but not HFT. In certain banks, the formerly prop-trading HFT is
alive and well in the market-making function, where it is now run with client rather
than bank capital and is often referred to as prehedging.
As computer technology develops further and drops in price, high-frequency systems are bound to take on an even more active role. Special care should be taken,
however, to distinguish HFT from electronic trading, algorithmic trading, and systematic trading. Figure 1.6 illustrates a schematic difference between high-frequency,
systematic, and traditional long-term investing styles.
Systematic trading refers to computer-driven trading decisions that may be held
a month or a day or a minute and therefore may or may not be high frequency. An
example of systematic trading is a computer program that runs daily, weekly, or
even monthly; accepts daily closing prices; outputs portfolio allocation matrices; and
places buy-and-sell orders. Such a system is not a high-frequency system.
Another term often mentioned in conjunction but not synonymous with HFT is
electronic trading. Electronic trading refers to the ability to transmit the orders electronically as opposed to telephone, mail, or in person. Since most orders in today’s
financial markets are transmitted via computer networks, the term electronic trading
is rapidly becoming obsolete.

Electronic trading
High-frequency
trading

Latency requirement

High

Algorithmic trading

Low

Traditional and quant
investing

Stages of investing process
Portfolio selection

Generation
of trading signals

Execution

FIGURE 1.6 HFT versus Algorithmic (Systematic) Trading and Traditional Long-Term Investing

11
HOw MODern MArkeTS DIFFer FrOM THOSe PAST

Algorithmic trading is more complex than electronic trading and can refer to a variety of algorithms spanning order-execution processes as well as high-frequency
portfolio allocation decisions. The execution algorithms are designed to optimize
trading execution once the buy-and-sell decisions have been made elsewhere.
Algorithmic execution makes decisions about the best way to route the order to
the exchange, the best point in time to execute a submitted order if the order
is not required to be executed immediately, and the best sequence of sizes in
which the order should be optimally processed. Algorithms generating HFT signals make portfolio allocation decisions and decisions to enter or close a position
in a particular security. For example, algorithmic execution may determine that
a received order to buy 1 million shares of IBM is best handled using increments
of 100-share lots to prevent a sudden run-up in the price. The decision fed to the
execution algorithm, however, may or may not be high frequency. An algorithm
deployed to generate HFT signals, however, would generate the decision to buy
the 1 million shares of IBM. The high-frequency signals would then be passed on
to the execution algorithm that would determine the optimal timing and routing
of the order.
Successful implementation of HFT requires both types of algorithms: those generating HFT signals and those optimizing execution of trading decisions. This book
covers both groups of algorithms: those designed for generation of trading signals
(Chapters 8 through 11) and those for order execution designed to conceal information within (Chapter 15).Chapter 14 of the book also includes latest algorithms for
managing risk of HFT operations.
The intent of algorithmic execution is illustrated by the results of a survey conducted by Automated Trader in 2012. Figure 1.7 shows the full spectrum of responses from the survey. In addition to the previously mentioned factors related to
adoption of algorithmic trading, such as performance management and reporting,
both buy-side and sell-side managers also reported their use of the algorithms to be
driven by trading decision and portfolio management needs.

20%

40%

60%

80%

100%

Optimal execution
Systematic trading
Portfolio management
Pretrade analytics
Posttrade analytics
Risk and performance management
Hedging
News analytics
Broker performance management
Economic forecasting
Portfolio valuation and reporting
Other real-time models
Buy-side

Sell-side

FIGURE 1.7 reasons for Using Algorithms in Trading
Source: Automated Trader Survey, 2012

HOw MODern MArkeTS DIFFer FrOM THOSe PAST

True HFT systems make a full range of decisions, from identification of underpriced or overpriced securities through optimal portfolio allocation to best execution. The distinguishing characteristic of HFT is the short position holding times,
one day or shorter in duration, usually with no positions held overnight. Because of
their rapid execution nature, most HFT systems are fully systematic and are also examples of systematic and algorithmic trading. All systematic and algorithmic trading
platforms, however, are not high frequency.
Ability to execute an order algorithmically is a prerequisite for HFT in a given financial
instrument. As discussed in Chapter 3, some markets are not yet suitable for HFT, inasmuch as most trading in those markets is performed over the counter (OTC). According
to research conducted by Aite Group, equities are the most algorithmically executed asset
class, with over 50 percent of the total volume of equities expected to be handled by algorithms by 2010. As Figure 1.8 shows, equities are closely followed by futures. Advances
in algorithmic execution of foreign exchange, options, and fixed income, however, have
60%
50%
Equities

40%

Futures
30%

FX
Options

20%

Fixed income

10%
0%

2004

2005

2006

2007

2008

2009

2010

FIGURE 1.8 Adoption of Algorithmic execution by Asset Class
Source: Aite Group

■■ What Is High-Frequency Trading?
High-frequency trading is an umbrella term comprising several groups of strategies. Given the breadth of HFT, various market participants have somewhat divergent opinions
of what HFT actually stands for. This section discusses common definitions of HFT:
■■

A definition of HFT that includes all activity utilizing fast algorithmic execution. For
example, the Technology Subcommittee of the U.S. Commodity Futures Trading
Commission (CFTC), tasked with compiling a working definition of HFT, came
back with the following draft definition in June 2012:
High-frequency trading is a form of automated trading that employs:
■■

Algorithms for decision making, order initiation, generation, routing, or execution, for each individual transaction without human direction;

13
How Modern Markets Differ from Those Past

been less visible. As illustrated in Figure 1.8, the lag of fixed-income instruments can be
explained by the relative tardiness of electronic trading development for them, given that
many of them are traded OTC and are difficult to synchronize as a result.
While research dedicated to the performance of HFT is scarce relative to data on
long-term buy-and-hold strategies, anecdotal evidence suggests that most computerdriven strategies are high-frequency strategies. Systematic and algorithmic trading
naturally lends itself to trading applications demanding high speed and precision of
execution, as well as high-frequency analysis of volumes of tick data. Systematic trading, in turn, has been shown to outperform human-led trading along several key metrics. Aldridge (2009b), for example, shows that systematic funds consistently outperform traditional trading operations when performance is measured by Jensen’s alpha
(Jensen, 1968), a metric of returns designed to measure the unique skill of trading by
abstracting performance from broad market influences. Aldridge (2009b) also shows
that the systematic funds outperform nonsystematic funds in raw returns in times
of crisis. That finding can be attributed to the lack of emotion inherent in systematic
trading strategies as compared with emotion-driven human traders.
Furthermore, computers are superior to humans in such basic tasks as information gathering and lightning-fast analysis of a multitude of quotes and news.
Physiologically, the human eye cannot capture more than 50 data points per second,
as evidenced by an entirely different industry—cinematography. In modern movies,
the human eye is exposed to only 24 frames per second, which appear seamless to
most moviegoers. Even then, the majority of images displayed on sequential frames
involve continuously moving objects. In comparison, modern financial information
incorporates drastically bouncing quotes, the number of which can easily exceed
1,000 per second for just one financial instrument. Detecting inter-instrument information spillovers involves processing data for multiple assets and asset classes,
as discussed in Chapter 15. Where efficient processing of high volumes of information is key to profitable trading, technology-averse humans have little chance of
succeeding. HFT takes over.

■

■
■

low-latency technology that is designed to minimize response times, including proximity and co-location services;
high speed connections to markets for order entry; and
high message rates (orders, quotes or cancellations).

Such definition captures many high-frequency traders, yet also includes
95 percent of investors using algorithmic technology to execute their orders.
even a “mom-and-pop” retail investor entrusting his broker to execute his order
in the most efficient algorithmic manner becomes a high-frequency trader under
the definition proposed by the CFTC’s subcommittee on HFT. not surprisingly,
this definition generated strong dissent from many members of the subcommittee
itself.
■

The definition of HFT as a latency-sensitive subset of algorithmic trading. Gomber,
Arndt, Lutat, and Uhle (2011) proposed to define HFT as shown in Figure 1.9.
Under such definition, HFTs are algo traders “on steroids,” utilizing super-fast
technology to speed up algorithmic processes and drive models in supersonic
time. Interestingly, also under this definition, the HFTs do not engage in portfolio
construction or management, but generate trading signals, validating models, and
execute trades in any one security.
Latency sensitivity
High

Algorithmic trading

Medium

High-frequency trading

Quant portfolio management
Low

HOw MODern MArkeTS DIFFer FrOM THOSe PAST

Degree of automation
Portfolio
selection

Generation
of trading
signals

Model
validation

Trade
execution

FIGURE 1.9 HFT vs. Algorithmic Trading and Quant Portfolio Management
Source: Gomber, Arndt, Lutat and Uhle (2011)
■

The definition of HFT based on holding period of capital throughput. A survey of
hedge-fund managers, conducted by FInalternatives in 2009, generated the
following definition of HFT:
High-frequency trading comprises
■
■

Systematic,
Quant-based models

■■

With holding periods from a fraction of a second to one day (no positions
held overnight).

The survey was based on nearly 300 responses from hedge fund managers who
subscribe to FINalternatives (close to 10,000 questionnaires were sent out). It is
also worth noting that at the time, a prominent multibillion-dollar Greenwichbased hedge fund launched a high-frequency fund with an average position holding period of three days, a far departure from submicrosecond frequencies often
mentioned in connection with HFT. The fund was later retracted.
■■

The definition of HFT based on their observed market activity. Kirilenko, Kyle, Samadi,
and Tuzun (2011) identify high-frequency traders as market participants that generate high market volume, all the while holding low inventory. The researchers
use the definition to distinguish HFT from other market participants:
■■

Intermediaries, characterized by low inventory, but not high trading volume.

■■

Fundamental buyers, who are consistent net buyers intraday.

■■

Fundamental sellers, who are consistent net sellers within a given day.

■■

Small traders, generating low volume.

■■

Opportunistic traders, loosely defined as all other traders, not fitting the
definition of HFT or other categories above.

While a concrete definition of HFT has proven to be a challenge, most market
participants are comfortable with the range of strategies deployed by HFT, summarized in Figure 1.10.
■■ What Do High-Frequency Traders Do?
Despite the disagreements about the precise definition of HFT, most market participants agree that HFT strategies fall into the following four broad classes:
1.
2.
3.
4.

Arbitrage
Directional event-based trading
Automated market making
Liquidity detection

How Modern Markets Differ from Those Past

Such definition may rely on somewhat arbitrary cutoffs of low inventory and
high volume.
The definition of HFT based on behavior unattainable by human market participants. A
common definition used by brokers to segment their clients into HFT and nonHFT, this definition calls for attribution of trading activity of each specific account
into human feasible and human infeasible. For example, an account generating
200 orders per second would be deemed HFT, as would an account that consistently succeeds at locking in a penny gain day-in and day-out.
This book considers all of the definitions discussed here.

FIGURE 1.10 Major Categories of HFT Strategies

HOw MODern MArkeTS DIFFer FrOM THOSe PAST

Arbitrage strategies trade away price deviations from long-running equilibria or
relative asset mispricing, and can include multiple asset classes, as well as multiple
exchanges. Many HF arbitrage strategies detect price discrepancies in multiple securities, as discussed in Chapter 8. Several strategies arbitrage prices of the same asset
trading on different exchanges, are known as latency arbitrage strategies, and are discussed in Chapter 12. Most arbitrage strategies are based on assumptions of meanreversion of asset prices.
Statistical arbitrage models comprise a range of models, including cross-asset
models, where financial securities have strong statistical relationships. All the models included in the book are deep-rooted in economic theories, ruling out spurious
statistical relationships often developed using plain data mining and also known as
the Spaghetti Principle of Modeling (if one throws a plate of spaghetti filled with data
against the wall of statistics, something may stick; what sticks, however, may not have
any sound reason for sticking and is likely to fall apart in production). For example,
bonds and interest rate futures have been shown to possess considerable dependencies, and their values, as a result, tend to move in tandem. when prices of bonds or
interest rate futures deviate from their long-running price equilibrium for no obvious reason, statistical arbitrage trading may be feasible via buying the instrument
with a lower-than-expected price relative to the other instrument(s), and selling the
instrument with a higher-than-expected price relative to the other instrument(s).
Chapter 8 details many economic models, as well as the model estimation techniques and known results.
Directional strategies identify short-term trend or momentum. This class of
high-frequency strategies includes event-driven strategies, discussed in Chapter 9,
other strategies based on predictable short-term price movements, discussed in
Chapter 11, as well as the controversial ignition strategies, discussed in Chapter 12.
event arbitrage models show the methodology as well as performance of trading
on predictable and recurrent effects of news. Various types of news used in event
arbitrage are showcased in Chapter 9, which also includes references to the latest
relevant studies as well as specific practical examples.

■■ How Many High-Frequency Traders Are There?
The number of high-frequency traders largely depends on the definition of HFT used.
As mentioned earlier, under the CFTC draft definition proposed in June 2012, 19 out
of every 20, or 95 percent of all investors and traders would qualify as HFT. Kirilenko,
Kyle, Samadi, and Tuzun (2011), define HFTs as traders who produce large trading volume while holding little inventory, and find that HFTs account for about 30 percent of
volume in the Standard & Poor’s (S&P) 500 E-Mini markets.Aldridge (2012a) estimates
that HFTs comprise just 25 to 30 percent in EUR/USD foreign exchange futures and
that in the most liquid exchange-traded fund, the S&P 500 SPDR (NYSE:SPY), highfrequency traders on average represent fewer than 20 percent of market participants.
■■ Major Players in the HFT Space
Many HFT participants prefer to stay out of the limelight, all the while generating
considerable profits. The most well-known HFT outfits include Getco, Renaissance
Capital, and DE Shaw. Lesser-known but still very profitable players dedicated to
HFT include specialist firms like IV Capital, DKR Fusion, and WorldQuant.

17
How Modern Markets Differ from Those Past

Automated market-making strategies comprise perhaps the most traditional trading strategies, encompassing automated market making, a cost-effective and accurate
alternative to human broker-dealers, discussed in detail in Chapter 10.The category of
automated market making and liquidity provision includes both inventory-driven and
information-driven approaches. Inventory-driven methods tend to focus on joint minimization of the inventory risk and market risk, ensuring that the positions are within a
trader’s risk tolerance limits given market conditions, and hedged where appropriate.
Information-driven market-making models are built with the goal of minimizing the
risk of adverse selection, the risk of taking an opposite position to a better-informed
party. To minimize the number of such losing positions, high-frequency traders can
deploy a wide range of models that help forecast short-term directionality of markets, track the number of well-informed market players in the market waters, and
even help forecast impending lumps and shortages of liquidity, covered in Chapter 11.
These techniques allow traders to choose the quantities and levels of aggressiveness of
their orders based on expectations of surplus or dearth of liquidity.
Perhaps least palatable to the low-frequency investors are liquidity detection strategies, like pinging (also known as sniffing and sniping), quote stuffing, and spoofing,
addressed in Chapter 12. While this book focuses on explaining sound HFT strategies, the book attempts to draw a balanced perspective and include the methodology
behind controversial HFT as well. “Pinging” has been shown to exist on selected
venues (pinging was detected in dark pools). The nature of other strategies like “ignition strategies” have been mostly speculative, and no credible evidence of strategy
existence has been produced to date. Still, the hypothetical strategies like ignition
strategies have been included for completeness, accompanied by a brief analysis of
their feasibility, properties, and impact on the broader markets.

The line between HFT and other forms of trading, however, can be blurred. As mentioned earlier, HFT, and specifically automated market making, are becoming staples on
most trading desks in all the major banks. And the advantages of such developments are
easy to see: the new automated market-making “robots” are considerably more accurate,
inexpensive, and reliable than their human counterparts. Likewise, HFT can seamlessly
blend in with activities of statistical arbitrage. In Canada, for example, banks often list
most of their HFT in the statistical arbitrage category in the banks’ annual reports.
■■ Organization of This Book

How Modern Markets Differ from Those Past

This book is written with the explicit goal of providing the latest, yet applied and
ready-to-implement information to management and employees that are interested
in starting or enhancing their high-frequency trading operations, individuals
and institutions seeking to protect their and their clients’ trading activity against
high-frequency traders, as well as casual observers, seeking to better understand
modern financial markets.
Chapters 2 through 5 of the book explain the present-day frontiers in financial
markets. Chapter 2 describes technological evolution that has enabled algorithmic
and high-frequency trading. Chapters 3 through 5 lay the foundation of analysis via
description of modern microstructure, high-frequency data, and trading costs.
Chapters 6 and 7 delve into the economics of high-frequency trading. Chapter 6
describes methodologies for evaluating performance and capacity of HFT strategies,
and Chapter 7 outlines the business case of HFT.
Chapters 8 through 12 and 14 through 16 are devoted to actual implementation of
HFT. Chapters 8 through 12 dissect core models of today’s high-frequency strategies.
Chapter 14 focuses on risk measurement and management of high-frequency trading
as well as portfolio construction. Chapters 15 and 16 discuss the nuts-and-bolts in
implementation of HFT systems, as well as best practices in running and monitoring
HFT systems.
Chapters 13 and 15 focus on regulation of HFT and mitigation of HFT externalities. Chapter 13 presents a summary of current regulatory thought on HFT, discusses
models for detection of HFT market manipulation, as well as mathematics of foreseeing market-wide events like flash crashes. Chapter 15 of the book offers solutions
for low-frequency traders concerned about the impact of HFT on modern markets.
Chapter 15 discusses the latest order slicing techniques and their respective ability to
avoid information-prying HFTs, and may also prove useful to high-frequency traders
seeking to further expand capacity of their trading systems.
■■ Summary
■■
■■

High-frequency trading is an organic evolution of trading technology.
The technological evolution of financial markets created ability to replace
human-driven intermediation function with cost-effective technology, returning
broker compensation to end investors and bank shareholders.

■■

High-frequency trading strategies are well defined, and most of them are beneficial to the markets.

■■ End-of-Chapter Questions
1. Describe the major groups of today’s market participants. What role do they
play? How do they interact?
2. What are the core groups of strategies deployed by high-frequency traders?
3. How do high-frequency trading strategies relate to other trading strategies, such
as technical analysis, fundamental analysis, and quant strategies?
4. What are the major changes that have occurred in the financial markets over the
past 40 years?
5. What is algorithmic trading?
6. How do end investors benefit from high-frequency trading?

19
How Modern Markets Differ from Those Past

Chapter 2

Technological
Innovations,
Systems, and HFT
T

echnological innovation leaves the most persistent mark on the operations of
financial markets. While the introduction of new financial instruments, such as
EUR/USD in 1999, created large-scale one-time disruptions in market routines,
technological changes have a subtle and continuous impact on the markets. Over the
years, technology has improved the way news is disseminated, the quality of financial
analysis, and the speed of communication. The adoption of technology in financial
services, however, was greatly aided by the ever-plummeting costs of technological
improvements. This chapter examines the key developments that have occurred in
technology over the past several decades in the context of enabling modern financial
landscape.
■■ A Brief History of Hardware

Trading was institutionalized during the Roman Empire, when the first exchange in
currency in designated locations can be noted (benches or “bancas” were the direct
precursors of today’s banks). Gradual change guided the operations of trading firms
until the technological revolution of the twentieth century enabled the current state
of trading with rapid exchanges of information. As Figure 2.1 illustrates, over the
past 100 years or so the computational speed available to traders has increased exponentially, while the cost of computing has been falling steadily since the 1980s, after
reaching its peak.
The price decline in computer technology has been spectacular over the past
20 years. A computer system with 2 gigabytes of memory (RAM), 300 gigabytes of

hard drive space, and a 2-gigahertz processor cost several million dollars in 1995,
and was big enough to require its own room. In 2012, a computer with identical
specifications not only fits in a standard desktop case, it can also be found for as little
as $400 in any neighborhood Best Buy or other computer store.
The decline in the cost of computing can be largely traced to the efficiency of
scale in production of computer chips overseas. The demand for the increasingly
accessible and cheaper technology has, surprisingly, been driven not by the financial
services practitioners, but rather by more casual users of computer technology with
considerably thinner wallets. Over the past two decades, the latter demanders for
cost-efficient technology happened to be video game players, whose sheer scale and
desire for lifelike graphics has fueled the surge in mass production and plummeting
prices of fast technology. Financial firms have reaped the benefits of innovation and
cost efficiencies created by the activity of the video gaming industry.

Cost

FPGA
and GPU

TEcHnOlOGIcAl InnOvATIOnS, SySTEMS, AnD HFT

CPU × 4
CPU
Calculator
Crank handle
Slide rule

Computational
speed

Abacus
1900

2000

FIGURE 2.1 Evolution of Speed and costs of Technology over the Twentieth century

As shown in Figure 2.1, today’s advanced technologies comprise multicore central processing units (cPUs), field programmable gate arrays (FPGAs), graphics
processing units (GPUs), and the so-called massively parallel architecture chips. A
cPU is the brain of the computer and decides how to store information in memory.
Multicore cPUs use a shared memory for fast inter-cPU communication, while
each individual cPU schedules tasks and performs computations on a given process
branch or “thread.” Sample architecture of a multicore cPU is shown in Figure 2.2.
At the time this book was written, a multicore cPU could cost $100 and higher.
Unlike cPUs, where the majority of the space on the chip is occupied by memory and scheduler functions, the space on a sample GPU is largely devoted to the
computational operations, performed in the so-called arithmetic logic units (AlUs).
To further maximize efficiency of each chip, process threads are executed in parallel batches of identical size. These batches of threads are called warps. To minimize

CPU

Arithmetic
logic unit

CPU

Registers

CPU

Out-of-order scheduler

Local cache

Shared cache

DDR memory

FIGURE 2.2 Architecture of a Sample Multicore cPU
Source: Thomas, Howes and luk (2009)

RAM

...

CPU

RAM

CPU

ALU

RAM

Dynamic
Arbitration

Registers

CPU

ALU

CPU

Registers

CPU

ALU

CPU

Registers

CPU

Thread-aware scheduler

Dynamic arbitration

DDR bank

FIGURE 2.3 Architecture of a Sample GPU
Source: Thomas, Howes and luk (2009)

DDR bank

23
TEcHnOlOGIcAl InnOvATIOnS, SySTEMS, AnD HFT

latency, however, care should be taken to ensure that the threads of the process are
similar in terms of the number of loops and conditional exits. In other words, programming expertise is required to ensure that GPUs are deployed with maximum
efficiency. Figure 2.3 illustrates sample architecture of the GPU. A popular model of
a GPU is nvidia GTX series, which can retail for $100 to $700 per card.
FPGAs are an entirely different class of chips that do not have any fixed instruction
set architecture. Instead, an FPGA provides a blank slate of bitwise functional units
that can be programmed to create any desired circuit or processor. Some FPGAs

contain a number of dedicated functional units, such as multipliers and memory
blocks. Most of the area of an FPGA, however, is dedicated to the routing infrastructure the run-time connectivity of the FPGA’s functional units. Figure 2.4 shows the
architecture of a sample FPGA chip.

LUT

Logic Cluster

Input Select

Output Select

TEcHnOlOGIcAl InnOvATIOnS, SySTEMS, AnD HFT

RAM

Logic
Cluster

DSP

RAM

Logic
Cluster

DSP

RAM

Logic
Cluster

DSP

FIGURE 2.4 Architecture of a Sample FPGA chip
Source: Thomas, Howes and luk (2009)

The main distinction of FPGAs is that the programming code is written directly
onto the chip from the outset. FPGAs are programmed using special programming
languages, such as verilog or vHDl.The languages are similar to c programming language and are easy to learn. A special FPGA programming device translates verilog
or vHDl into Assembly language understood by the FPGA chips. In the absence of
FPGAs, trading programs need to be compiled and translated to the computer chips
like cPUs during program run time, requiring additional computer operations and
eating into the latency. The process of programming an FPGA is rather straightforward and inexpensive.While there exists a significant variation in costs of blank FPGA
chips and verilog or vHDl compilers and simulators, quality inexpensive options are
commonly available, once again produced to satisfy demand of video gamers. A blank
FPGA chip may cost anywhere from $4 to $5,000. The verilog software and simulators may be free (“open-source”) or $20,000. The software is then downloaded onto
the chip, using the process specific to the chip manufacturer. Programming of FPGA
chips is often taught in undergraduate electrical engineering programs, and tends
to be easy to learn. However, achieving a state-of-the-art FPGA system may require
arranging FPGAs in a format known as massively parallel processor array configuration,
demanding advanced understanding of hardware and software optimization.

Performance-wise, FPGAs tend to be superior to GPUs and cPUs, particularly
when used to simultaneously process a limited number of time series. Figure 2.5
shows a graphical comparison of efficiency of key hardware models. The horizontal axis of the figure shows the “input” size, or the number of independent variables simultaneously fed into the algorithm. The vertical axis shows the number of
computer “cycles” required to perform an operation involving the given number of
inputs. As Figure 2.5 illustrates, an FPGA posts best results when the number of inputs is less than 2,000. When the number of inputs exceeds this threshold, the speed
of an FPGA becomes comparable to that of a GPU.

Needleman-Wunsch

GPU
CPU(single thread)
CPU(4 thread)
FPGA

log10(O/ cles)

7
6
5

128
256
Input Size

512

1024

2048

FIGURE 2.5 comparative Performance of FPGA, GPU, Single cPU, and Quad cPU
Architectures
Source: Thomas, Howes and luk (2009)

The choice of a chip itself is not the single determinant of the speed of the computer program. The speed of each computer cycle is determined by the so-called
oscillator crystal within each machine and, most important, organization of the
program’s algorithm.
■ Messaging
Hardware is just one of many components of computer technology necessary for
achieving successful trading. Another crucial component is messaging, enabling
communication among hardware and software modules of various market participants. Just as speed is important in hardware, it is also important in messaging. In
fact, it is the speed of messaging that presents a hurdle or a bottleneck for trading
communication.

TEcHnOlOGIcAl InnOvATIOnS, SySTEMS, AnD HFT

Messaging protocols
Trading messaging is comprised of three levels of protocols, shown in Figure 2.6.The
most basic level of communication enables data streaming and is known as the User
Datagram Protocol (UDP). UDP is the “bare bones” data communication protocol,
lean in its implementation, and utilizing the fewest number of bytes and messages
to identify and deliver the stream of data. As a result, UDP is very fast, but does
not guarantee delivery of sent data. UDP is the same technology as the one used to
stream games and movies over the Internet, where loss of one packet here and there
does not significantly impact the viewer’s experience. In trading, UDP is sometimes
used to transmit quotes, the data that are refreshed continuously, and are, therefore,
not very sensitive to lost information. If a particular quote sent from an exchange
fails to reach a trader, the resulting impact may be deemed minimal: a new revised
quote is already on the way, retiring the lost quote upon hitting the trader’s account.
Complexity

FIX/ITCH/OUCH

TEcHnOlOGIcAl InnOvATIOnS, SySTEMS, AnD HFT

26
TCP/IP

UDP

FIGURE 2.6 Three levels of complexity of communication Protocols Used in Trading

The integrity of the quote process, however, can matter in trading model development. A trading algorithm developer may rely on the quote stream idiosyncrasies
to generate predictive signals about impending market movements. If the structure
of the historical quote stream used in model development differs significantly from
that of the quote stream encountered by the trader “in production” environment,
the calculated forecasts may cease working. care should be taken to ensure that the
data used in simulation and back-test of the algorithms is structurally compatible to
the data received in production environment. At a minimum, the algorithm designer
should ascertain that the frequency of quotes received in production matches that
in the historical data used in the back-test. More complicated data tests can also be
performed. For example, a rolling autocorrelation metric can be computed on the
two sets of data, and the distribution of the resulting metrics should be comparable
for successful algorithm design and implementation.

The next level of complexity in communication protocols is Transmission control
Protocol/Internet Protocol (TcP/IP). TcP/IP is another standard Internet communication protocol, presently used in most e-mail and Web-browsing communication. Unlike the UDP, where individual packets of information do not carry any
identifying monikers, all packets of a TcP/IP transmission are sequentially numbered, the total number of bytes within each packet is counted, and undelivered
or corrupt data is re-sent. As a result, TcP/IP provides a more secure framework
for information delivery, and is used to transmit orders, order acknowledgments,
execution acknowledgments, order cancellations, and similarly important information. As a trade-off, TcP/IP tends to be three times slower than UDP. Figure 2.7
summarizes common usage of UDP, TcP/IP and FIX in trading communication.

Trading venue

Quotes:
UDP + FIX

Trades:
TCP/IP + FIX

Trader

Both the UDP and TcP/IP, however, require an additional layer of communication to standardize messages of the trading process. Protocols like Financial Information eXchange (FIX), ITcH, OUcH, and FAST are used on top of UDP and
TcP to transmit data in a standardized machine-readable format. FIX protocol is
a free XMl-based text specification for quote, order, trade and related message
transmission. The FIX protocol comprises data field definitions, enumerations, and
various components, forming messages. Each message is then populated with the
user-generated data. Each field of the message, including the version of FIX used, the
time stamp, and other information, is separated from the following field by binary 1.
8=FIX.4.2 | 9=309 | 35=S | 34=5015 | 52=20070731-15:25:20 |
131=1185895365 | 301=0 | 55=USD/cAD | 167=FOR | 15=USD |
132=1.065450 | 133=1.065850 | 134=5000000.0 | 135=5000000.0 |
647=2000001.0 | 648=2000001.0 | 188=1.06545 | 190=1.06585 |
60=20070731-15:25:20 | 40=H | 64=20070801 | 10=178
FIGURE 2.8 Sample FIX Message

Figure 2.8 illustrates a sample FIX message, transmitting a quote for USD/cAD
exchange rate. The shown quote contains the following information:

TEcHnOlOGIcAl InnOvATIOnS, SySTEMS, AnD HFT

FIGURE 2.7 common Use of Protocols in Trading communication

■■

Version of FIX, “FIX.4.2” (field number 8)

■■

The time stamp of the message, “20070731-15:25:20” (field number 52)

■■

Security identifier, “USD/CAD” (field number 55)

■■

Security type, “FOR” for foreign exchange (field number 167)

■■

Base currency, “USD” for U.S.$ (field number 15)

■■

Best bid and best ask (fields 132 and 133, respectively)

■■

Sizes at the best bid and best ask (fields 134 and 135)
Transmission speed of communication messages depends on several factors:

■■

Size of message

■■

Connection bandwidth

■■

Technological Innovations, Systems, and HFT

TCP/IP and UDP “window” sizes, specifying how many bytes market participants
are willing to send and receive at per message “slice.” Once the system of one
market participant sends out a message, the message is sliced into the individual
parcels of a specified window length, a message header is attached to each parcel,
and the messages are sent out on their route. The UDP message header typically
identifies the destination, and consists of just 8 bytes. The TCP/IP message header
includes the sender and destination identifications, parcel sequence number, and
the total number of parcels comprising the message, among other variables. The
standard TCP/IP header is 20 bytes. The FIX header can be much more elaborate,
and is often in excess of 100 bytes.

While FIX is widely used, it is slow in comparison with Nasdaq’s protocols known
as ITCH and OUCH. The binary nature of ITCH and OUCH ensures that the messages arrive in the machine-readable format, using no processing time to convert
them from text to binary and back. In addition to the binary format, ITCH and
OUCH messages have a fixed message length, enabling faster transmission. OUCH
is the order entry protocol, while ITCH is the outbound quote and trade-data dissemination specification. Yet ITCH and OUCH support only a limited number of
messages. OUCH provides the platform for:
■■

Order entry.

■■

Replacement and cancellations.

■■

Receipt of execution acknowledgements.

ITCH is built for fast and lean quote and past trade data dissemination, and is able
to transmit:
■■

Order-level data.

■■

Trade messages.

■■

Net order imbalance data.

■

Administrative messages.

■

Event controls, such as start of day, end of day, and emergency market halt/resume.

For more complex messages, ITcH- and OUcH-enabled market participants are
often required to use FIX.

Core Message architecture
Tick information is transmitted among market participants using one or several
quote messaging specifications. FIX, ITcH, OUcH, and FAST are just a few message languages enabling transmission of critical trading information. Despite their
complicated acronyms, messaging is built around strikingly simple architecture, as
illustrated in Figure 2.9.

Session start

Heartbeat

Quote message

Order message

Order cancellation

Execution acknowledgment

Session end

FIGURE 2.9 core Message Architecture in Trading

As shown in Figure 2.9, every stream of quote and trade communication includes
the following key messages:
1. Session start is the message sent in the beginning of every communication
session, sometimes only once a day. The session start message notifies relevant
market participants that the entity is open for trading and desires to establish a
communication stream.
2. Heartbeat is a recurrent message that notifies the participant’s communication
parties that the participant is online, in a state of good technological health,
and open for business. Parties that fail to receive their communication partners’

TEcHnOlOGIcAl InnOvATIOnS, SySTEMS, AnD HFT

Order acknowledgment

3.
4.

5.
6.
7.
8.

Technological Innovations, Systems, and HFT

heartbeat messages for a preconfigured period of time often shut down the communication channel. The communication channel may then be reinstated using
the “session start” sequence.
Quote message is a message carrying quote information, such as best bid and ask
prices and sizes. Level II data, like the depth of the order book behind the best
bid and ask quotes, may also be transmitted using quote messages.
Order message is used to transmit actual order information. A typical order message includes a buy or sell identifier, an order type—a market, limit or other
specification, order size, and a desired execution price and validity period (day,
good-till-canceled) in the case of limit orders.
Order cancellation message includes the unique identifier of the previously placed
order that now needs to be canceled.
Order acknowledgment and order cancellation acknowledgment messages include confirmations of order placement or order cancellation, respectively.
Execution acknowledgment messages specify the details of execution: time of execution, obtained price, and execute quantity.
Session end message informs parties that a given trading entity has stopped trading and quoting for the day.

The resulting trade messaging flow comprises intuitive methodology to deliver
effective, reliable, and traceable communication. Most trading outfits log their daily
communication for easy reconciliation and fast identification of potential issues, such
as network connectivity problems, algorithm errors, and the like.

Speed and Security
Neither TCP/IP nor UDP incorporate encryption. In other words, most TCP/IP and
UDP messages are sent via Internet networks in plain text. FIX provides optional encryption at a considerable latency.While ITCH and OUCH send messages in a binary format,
most Nasdaq OMX messages are still sent unencrypted over the Internet networks.
What kind of risk do market participants face by sending unencrypted messages?
To answer this question, one needs to consider the current layout and flow of the Internet traffic. Today, most Internet traffic in the world flows through about 80 “core”
nodes. These nodes, such as major Internet service providers (ISPs) like Verizon,
have some security measures in place, limiting the incidence of spying activity at
these nodes. At the same time, nodes can be quite congested, slowing down messaging traffic without consideration to its urgency.
If the core nodes were to fail, 70 percent of Internet traffic would flow through
peer-to-peer networks, redundant backup structures in which the traffic would hop
from one local user to another, in a distributed fashion. While the peer-to-peer network configuration can allow the network participants to observe each other’s traffic
and read unencrypted messages in full, the peer-to-peer communication is sufficiently randomized to prevent any peer party to accumulate the entire message flow.
Still, peer-to-peer networks may be vulnerable to malicious intent, and the resulting
potential hijacking of the order flow could destroy markets and cause tremendous
losses for all market participants.

Client-server model

Trader 1

Trader 2

Internet

Peer-to-peer model

Trader 1
Internet

Trader 2

Internet

Reliable ISP
node
R

Trader 1

Internet

Co-location model

Internet

Dedicated
network

Trader 2

Dedicated
network

Execution venue

Moderately secure, but slow

Faster, but security can be
compromised by Trader 2

Fast and secure

FIGURE 2.10 Messaging Architecture in client-Server, Peer-to-Peer, and co-location Models

newark, nJ

New
York, NY

Washington,
DC

toronto,
Canada

Chicago,
IL

London,
U.K.

Frankfurt,
Germany

Sao paolo,
Brazil

tokyo,
Japan

0.314

3.400

9.470

15.175

65.763

74.383

109.414

141.640

9.784

15.291

65.533

74.153

109.100

141.756

13.270

14.175

69.083

78.164

111.960

140.640

10.795

75.233

83.853

118.884

136.910

80.740

89.360

123.485

127.595

8.620

183.253

215.825

183.253

215.825

new york, ny
Washington, Dc
Toronto, On
chicago, Il
london, U.K.
Frankfurt,
Germany
Sao Paolo, Brazil

4.057

249.950

FIGURE 2.11 latency Incurred by Electronic Signals Traveling over Optical Fiber networks

between Pairs of locations

31
TEcHnOlOGIcAl InnOvATIOnS, SySTEMS, AnD HFT

Figure 2.10 describes three common Internet communication models prevalent
in trading, including the so-called co-location model. In the co-location model,
traders’ servers are housed in the same secure facility as the exchange’s matching
servers. In the co-location scenario, trading servers have dedicated network access
to the exchange servers. The dedicated network access comprises a private secure
communication line from the trading servers directly to the exchange, minimizing
the risk of malicious intervention and ensuring a safe environment for all market
participants. co-location also provides such benefits as speed advantage: the servers
of a chicago trader co-located with nasdaq, for example, would allow the trader
to shave anywhere from 17 to 22 milliseconds in a round-trip order latency due
to the physical distance between new york and chicago, all in addition to the immeasurable savings resulting from the security of the co-located trading connection.
Figure 2.11 summarizes latency among selected co-location centers worldwide.

Within most co-location data centers, servers are positioned at various distances
from the exchange server itself, raising natural concerns about “fairness” of connections of all traders co-located in a given facility. A physical distance difference of as
little as 100 feet may result in one microsecond (one millionth of a second) time
delay on every message sent and received, giving traders co-located near the exchange servers a potential advantage. To address such issues, the Nasdaq co-location
center guarantees an equidistant length of fiber-optic cable from the servers to the
exchange to the servers of each trader co-located in the Nasdaq’s facility. The cable
lengths are identical down to the millimeter, and can be seen coiled near the servers
of traders physically close to servers of the exchange.
Although some market participants believe co-location to be unaffordably expensive, the real numbers point to the opposite. At a data center in Secaucus, New
Jersey, for example, a private company, Equinix, offers co-location-equivalent proximity services with the minimum monthly charges broken down as follows:
■■

■■
■■

Technological Innovations, Systems, and HFT

■■

A cabinet for the trader’s hardware equipped with biometric security scanners
and air-conditioning runs $1,500 per month.
A 20-amp 120-volt primary power source costs $350 per month.
An additional 20-amp 120-volt power source designed for redundancy costs an
additional $175 per month.
Finally, a connection to the ultra-fast communication network linking various data
centers around the world runs an additional $325 per month.

The grand total of the proximity setup adds up to just $2,350 per month, a negligible cost for any serious investor.

Network Throughput
The messaging architecture is a resource available to all market participants, yet it is not
free to all. Exchanges, for example, have to continuously enhance their infrastructure to
ensure that the bandwidth of their connections is broad enough to allow uninhibited message traffic among all interested traders. Perhaps the biggest challenge to exchanges and
other order-matching venues is the sheer volume of order cancellations. According to
Hautsch and Huang (2011), on Nasdaq, 95 percent of all limit orders are canceled within
one minute from the time the orders are placed. Hasbrouck and Saar (2011) report
similar activity grouped into brisk order placement and cancellation “runs.” While this
activity may seem malicious to an uninitiated observer, the explanation for such behavior
is quite simple: as described in detail in Chapters 10, automated market makers need to
quote close to the market price—“stay on top of the book”—in order to be successfully
and promptly matched, thus ensuring a steady revenue stream. Once the market moves
away from the quotes of the market maker, it is in the best interests of the market maker
to cancel the orders and to resubmit them at the new best bid and best offer prices. In addition, as explained in Chapter 12, on exchanges with time-price priority of limit order
books, market participants may place and then innocuously cancel excessive numbers
limit orders to secure their execution priority, in a practice known as “layering.”

In such dynamics, many trading venues are caught within a vicious circle: on the
one hand, they are competing to attract the market makers, but on the other, many
order-cancelling market makers are eroding network resources, resulting in missed
quotes and other delays for all market participants. Even the co-location does not
help fully navigate the bandwidth issue, as co-location space also faces capacity constraints: nasdaq has seen so much demand in its co-location hangar in Mahwah, new
Jersey, that it is reportedly running out of space to offer to the parties interested in
co-locating there. As discussed in chapters 3 and 12, a promising solution to the
network bandwidth issue, known as pro-rata execution, has been developed and implemented at selected exchanges.
■ Software

1.
2.
3.
4.
5.

Begin program.
check market conditions: Are market conditions suitable for market making?
If yes, start market making.
If no, wait one minute.
Repeat step 2.

The algorithm presented in Figure 2.13 is “nested,” or comprises two additional
algorithms marked in Figure 2.13 only as “check market conditions” and “Start
market making.” The nested tasks can be the critical “secret sauce” that distinguishes
good HFT systems from bad ones. Usually, the tasks are designed on the basis of
advanced research, where the task is selected among several competing ideas given

Process

Decision: if… then…

FIGURE 2.12 common Elements of an Algorithm

Start or End

33
TEcHnOlOGIcAl InnOvATIOnS, SySTEMS, AnD HFT

High-frequency trading systems are ultimately software applications deployed over
hardware and messaging described above. As with any software system, an HFT system begins with an idea, known as an algorithm in computer-science lingo, that is
subsequently coded in a chosen computer language into a full-blown software program. The term algorithm is properly defined as logic, or a sequence of high-level
actions, developed to explain to a computer how to implement a given task at hand.
The algorithm does not delve into the details of actual coding or programming the
system, but may still take into account the idiosyncrasies of the hardware and messaging structure on which the algorithm will be ultimately implemented. Algorithms
are often visualized in diagrams. The key elements of the algorithm diagrams are
summarized in Figure 2.12.
The algorithm elements shown in Figure 2.12 will be used throughout the book
to explain algorithm designs of common HFT strategies. Figure 2.13 illustrates the
step-by-step process of the following simple market-making algorithm:

positive results of rigorous testing. The two nested tasks shown in Figure 2.13 are
explained in detail in chapter 15.
Start

Are conditions fit for
market making?

Wait one minute

Yes
Run market making

End

FIGURE 2.13 Sample Market-Making Algorithm

TEcHnOlOGIcAl InnOvATIOnS, SySTEMS, AnD HFT

The term algorithm is often used synonymously with the terms high-frequency trading, systematic trading, electronic trading, and low-latency trading. The distinctions among
the terms, however, are significant enough to warrant some explanation. A system
usually refers to a highly methodical approach to a process. Systematic trading, therefore, is following some rigid frameworks, but does not have to be fully automated.
A trader can be considered systematic if he manually places trades when certain
indicators form a specific pattern. The term systematic was coined to distinguish traders practicing methodical allocations from traders using their intuition or discretion,
and hence known as discretionary traders. All high-frequency and algorithmic traders
are also systematic.
The term electronic describes the execution preferences of the trader: whether
he chooses to place orders electronically or, perhaps, over the telephone. All
high-frequency trading, algorithmic trading, and low-latency trading are necessarily
electronic, but systematic trading may involve nonelectronic components. The reverse, however, does not have to be the case; many electronic trading systems route
only orders that may or may not be placed algorithmically. As most markets and
traders are moving on to electronic platforms, however, the term electronic trading is
becoming implicit and obsolete.
Low-latency trading refers to trading that utilizes fast connectivity between traders and exchanges. As described in the previous section, latency measures the time
distance between the trader and the exchange. Most latency measurements are currently recorded in microseconds. High-frequency trading systems often also happen
to be low-latency, but the reverse does not have to hold: low-latency systems are
often deployed by low-frequency traders to obtain better prices on trades.
Once an algorithm is designed, it is broken down into components and coded in
a language understood by computers. The goal of coding is to accurately translate
the logic of the algorithm into computer “speak” and, in the process, to create as
little delay as possible during “run time,” when the computer will read and interpret

the code. The code written directly to FPGA chips is presently the fastest. Still,
many high-frequency traders deploy standard non-FPGA architecture and rely on
languages such as C++ and Java to code their systems. While C++ remains the fastest computer language easily understood by humans, many systems are coded in Java
with workarounds of its slowest components. Thus, for example, the famed Nasdaq
OMX system is reportedly coded in Java with Java garbage collection disabled and
replaced with C++-like direct memory access for increased speed. Chapter 16 describes best practices of coding implementation.
The code outlining the actual trading logic of an algorithm tends to be quite short.
In many successful cases, the trading logic comprises as few as 50 lines of code. In
addition to the actual decisions to buy and sell, however, every HFT system incorporates supporting quote data retrieval functionality that may number in 10,000+
lines of code, as well as the trade send-off and acknowledgment receipt applications
that can also take as much as 5,000 lines of code. Perhaps the most lengthy, yet mandatory, component of each HFT system is its risk management checks and balances,
which can total 50,000+ lines of code. Risk management of HFT is discussed in
detail in Chapter 14 of this book.
■■ Summary

■■ End-of-Chapter Questions
1. Would you encrypt your trading orders before transmitting them to the execution venue over the Internet? Explain.
2. Mr. Smith has read about the “arms race” of computer technology in the financial
services industry and decides to invest into the latest super computer to increase
the odds of fast order transmission. Is Mr. Smith’s investment justified? Where
does most message congestion occur in the cyber-universe today?
3. What is co-location?
4. On average, how much slower is the transmission of trade order messages in
comparison with quote messages?
5. What is a heartbeat?
6. The best offer on exchange A contains 300 units of instrument X, the best offer
on exchange B contains 500 units, and the best offer on exchange C contains just
100 units.Your customer wants you to buy 550 units on his behalf. How would
you break up the customer’s order and send them to exchanges under the minimal impact algorithm?

35
Technological Innovations, Systems, and HFT

Algorithmic execution is inseparable from today’s markets. It is a necessary function
that delivers considerable value to all investors, large and small. With plummeting
technology costs, most investors today can afford to build and use advanced algos,
including algos designed for high-frequency trading, previously available only to a
select few market participants. Services such as co-location provide added benefits
of security and speed.

Chapter 3

Market
Microstructure,
Orders, and Limit
Order Books
37

he study of market microstructure originated over four decades ago, and the
core principles remain true today: most market participants rely on limit orders
and market orders. These core order types remain most used despite an explosion
of various derivative order types. Despite the continuity of these key principles still,
much has changed. In the 1980s At one time, the peculiarities differentiating tick
data dynamics from daily and monthly data were observed, but there was no way to
incorporate the differences into a trading strategy. Today, that tick data can be captured easily and trades initiated quickly, it is possible to build trading strategies taking
into account market microstructures. This chapter delves into the modern microstructure of markets, describing orders, matching processes, and rebate structures,
among other issues defining today’s markets.
■■ Types of Markets

Financial markets are venues that allow investors and other market participants to
buy and sell securities with a peace of mind that all transactions will be properly
accounted and settled. In this respect, financial markets are not that different from
markets for other nonfinancial products, such as a neighborhood grocer. When a
customer enters a grocery store, he expects immediate execution of his transaction,
an exchange of his money for merchandise—food. The grocer’s cash register takes

Market Microstructure, Orders, and Limit Order Books

on the settlement function: the receipt itemizes the produce the customer bought
and the total amount of money the grocer collected, nowadays most often from the
customer’s account rather than in cash form.
Furthermore, the grocery customer expects that the food he acquires is in good
condition and that the transaction is permanent: that the grocer has full rights to sell
the customer the product. Most centralized financial markets incorporate similar
quality control for financial products: the products offered for purchase and sale on
the floors of each market tend to be standardized, and their quality can be ensured
via a thorough prelaunch due-diligence process as well as via the real-time data distribution to all market participants. For example, futures contracts traded on exchanges have a specific well-defined structure. Initial public offerings for stocks tend
to be well scrutinized. Yet, just like grocers do not evaluate suitability of particular
foods to each person, financial markets are unaware of a client’s risk profile or accreditation, leaving the risk of investing decisions to the traders themselves.
Since the beginning of trading history, most financial and nonfinancial markets have
been organized by product type. In nonfinancial settings, stores carrying lumber differ from stores selling clothes. Food markets used to be highly fragmented by type as
well: fishmongers, bakers, butchers, and ice-cream makers all used to have their own
shops, if not districts. Similarly, financial markets have been historically organized
by the type of the traded instrument, each trading only equities, futures, options,
or other securities. Recently, however, nonfinancial markets have been gearing toward megastores to increase their efficiency and take advantage of common distribution and procurement frameworks and skills. Similarly, many trading venues are now
venturing in the cross-asset space, with the traditional foreign exchange player iCap
launching a fixed-income trading offering, and equity exchange Best Alternative Trading Systems (BATS) considering entering the foreign exchange trading space.
The history of the financial exchanges is not always linear. The New York Stock
Exchange (NYSE), for example, was first formed as a for-profit entity at the end of
the eighteenth century, when two dozen stockbrokers signed an agreement to stop
undercutting each other’s commissions and instead retain at least 0.25 percent of
each trade. In subsequent years, as the U.S. economy grew, more public listings became available, and the interest in investing grew from the U.S. public, stockbroking
became increasingly lucrative and seats on the NYSE rose in value.
During major recessions, however, lavish lifestyles of stockbrokers drew the scrutiny of money-losing investors and regulators. In 1934, in the midst of the Great
Depression, the NYSE was required to register and accept oversight from the then
newly formed U.S. Securities and Exchange Commission (SEC). In 1971, during the
post–Vietnam War recession, the NYSE was converted into a not-for-profit entity
in a bid to cap excessive compensation of brokers and transfer some of their intake
to the investors. The nonprofit mandate failed to live up to its expectation, with
exchange-registered brokers creating a secondary market for their seats on the exchange that by the 1990s had reached multiple-million-dollar price tags.
The past two decades have witnessed increasing competition in the exchange
space, and these competitive market forces appear to have succeeded in helping
investors retain a larger share their earnings away from brokers. New exchanges,

■■ Limit Order Books
The cumulative trade size of all limit orders available to meet incoming market orders at any given time on a specific trading venue is known as liquidity. The larger
the number of limit order traders available on the exchange, and the larger the size
of each trader’s limit orders, the more liquid the given trading venue. Liquidity is
also necessarily finite in today’s markets: the number of limit orders is measurable,
and each limit order has a finite size. Liquidity was first defined by Demsetz (1968).
To account for limit orders, the majority of contemporary exchanges are organized as so-called centralized limit order books (CLOBs), also referred to as a double-sided auction.The CLOBs were pioneered in the United States in the early 1970s
and adopted in Europe in the 1980s. In a CLOB model, all incoming limit orders
are recorded in a “book”: a table with columns corresponding to sequential price
increments, and rows recording sizes of limit orders posted at each price increment.
Figure 3.1 illustrates the idea. The limit order book information can be distributed
to all other market participants as Level II data, discussed in detail in Chapter 4.
In theory, limit order books are often assumed to be symmetric about the market
price, with the distribution of limit buy orders mirroring that of limit sell orders.
Furthermore, in many risk management applications, order books are also assumed

39
Market Microstructure, Orders, and Limit Order Books

such as Nasdaq, deployed technology in lieu of bonus-collecting human traders,
transferring some of the resulting savings into the pockets of investors and producing other benefits in the process. Technology has lowered error rates, increased
execution times, and, perhaps most importantly, increased transparency of process
to investors. Other early exchanges, such as the Chicago Mercantile Exchange, followed trajectories similar to that of NYSE, and today face competition from relatively new exchange entrants, such as the Intercontinental Commodity Exchange (ICE).
Today’s equity markets comprise over a dozen various exchange venues, run
by now-industry stalwarts such as the NYSE and Nasdaq, and relatively recent arrivals, such as BATS, DirectEdge, and others. Since all equity exchanges are subject to U.S. SEC oversight and trade standardized products, exchanges presently
compete to differentiate their offerings mainly on liquidity and costs. In a bid to
attract liquidity (more on this later in this chapter), most exchanges have done
away with membership fees and now offer free registration. In addition, equity
exchanges are differentiating themselves on price structures, not only rewarding
large traders but also segmenting traders based on whether they place market
orders or limit orders.
In addition to the regular exchanges, a new breed of matching venues has emerged,
known as dark pools. Unlike an exchange, where the entire limit order book is available for observation, dark pools do not disclose their limit order books, instead
keeping them “in the dark.” Trading in a dark limit order book has appealed to large
investors who are concerned about the information they may reveal by placing their
orders in a traditional exchange, a lit market. Liquidnet is an example of an equities
dark pool.

Price: …

Sell 400

Sell 300

Sell 400

Sell 300
Sell 600

Buy 300 Buy 300
200

Sell 300

Buy 600
200

200

Sell 300 Sell 300

200

Sell 400

200

Sell 300

200

Sell 700

200

Buy 300

200

Buy 300

200

Buy 300 Buy 300

200

200
200

20.03 20.04 20.05 20.06 20.07 20.08 20.09 20.10 20.11 20.12 20.13 …
Best bid

Best ask/offer

FIGURE 3.1 sample snapshot of a Limit Order Book. All limit buy orders are on the left-hand
side of the book; all limit sell orders are on the right-hand side of the book.

MArkeT MIcrOsTrucTure, OrDers, AnD LIMIT OrDer BOOks

to follow normal bell-curve distributions. neither of the assumptions tends to hold:
order books are seldom normal and are often asymmetric.
As Figure 3.2 shows, when a new limit order arrives, it is placed into a limit order
queue corresponding to its price. since all prices in today’s markets are subject to a
minimum increment, or tick, price-based bins are clearly delineated. The limit buy
orders at the highest price form the best bid, with the price of these orders reflected
in the best bid price, and the aggregate size reported as the best bid size. similarly,
the limit sell orders posted at the lowest price form the best ask, with respective
price and size information. Best ask is sometimes referred to as best oﬀer. At any given
moment of time, there exists a finite aggregate size of all limit orders posted at each
price.
When a market buy order arrives, it is matched with the limit sell orders, beginning with those placed at the best ask price. If the size of the incoming market buy order is greater than the size of the best ask queue, the market order “sweeps” through
other offer queues in the direction of increasing price, “eating up” liquidity available
at those price ticks. sweeping leaves a significant gap in limit orders on the ask side,
instantaneously increasing the bid-ask spread, and potentially inducing slippage in
subsequent market buy orders. The order-matching process is similar for market sell
orders that end up matched with the available limit buy orders aggregated on the bid
size of the book. Limit buy orders with the prices equal or higher than the prevailing
best bid are executed like market buy orders. similarly, low-priced limit sell order
are usually treated as market sell orders.
If the size of the incoming buy order is smaller than the size of the best ask, and
the aggregate best ask queue is composed of several limit sell orders placed at the
best ask price, the decision of which of the limit sell orders is matched against the
market buy order may differ from one exchange to another. While most exchanges
at present practice price-time priority, also known as the first-in-first-out (FIFO)

Best bid

Best ask = best offer

Bid-ask spread

price

A large market sell order
sweeps the bids in the book,
realizes lower aggregate price,
changes the best bid

Price
New best bid
Best ask = best offer

A new limit buy order
arrives at a price lower
than the best bid

Bid-ask spread

Price

A new limit buy order arrives
at a price higher than the best
bid but lower than the best ask

41
FIGURE 3.2 sample Dynamics in a Limit Order Book

execution schedule for limit orders, several other exchanges now match a fixed
proportion of each limit order at a given price in a process known as pro-rata
matching.
In time-price priority, or FIFO, execution, the limit order that arrived first is also
the first of that price bin to be matched with the incoming market order. Figure 3.3
illustrates the FIFO matching process. FIFO, known as the continuous auction, has
been shown to enhance transparency of trading via the following measures (see
Pagano and roell, 1996; Jain, 2005; and Harris, 2003):
■

■

reducing information asymmetry—all traders have access to the limit order
book information.
enhancing liquidity—a cLOB structure incentivizes traders to add limit orders,
thereby increasing market liquidity.
cLOB’s organization supports efficient price determination by providing a fast
and objective order-matching mechanism.
uniform rules for all market participants ensure operational fairness and equal
access.

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Price

A market sell order arrives

Price
The “oldest” limit buy order placed at the best bid earliest is executed first;
if the market sell is not filled completely with the oldest limit order, the
market sell is next matched with the second oldest limit buy order placed
at the best bid. The process continues until the market sell order is
matched in full or the best bid queue is exhausted.

FIGURE 3.3 Price-Time Priority execution

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While most execution venues are based on FIFO, some exchanges, like
chicago Mercantile exchange (cMe), chicago Board Options exchange (cBOe),
Philadelphia stock exchange (PHLX), and Intercontinental commodity exchange
(Ice) have switched to pro-rata execution schedules. cMe’s pro-rata schedule
matches an incoming market buy order with a fixed proportion of each limit order
posted at the best ask. similarly, an incoming sell order is matched with equal fractions of all of the limit orders posted at the best bid. The larger the limit order at the
best bid and the best ask, therefore, the larger the fill of that order. Figure 3.4 shows
the pro-rata process.

A market sell order arrives

Price
An incoming market sell order is matched with a constant proportion of
every limit buy order placed at the best bid price, independently of the
arrival times of the orders.

FIGURE 3.4 Pro-rata execution

The main advantage of the pro-rata matching from the exchange point of view is
the built-in incentives for traders to place large limit orders, and, therefore, to bring
liquidity to the exchange. The pro-rata matching encourages traders to post large
limit orders without special compensation like rebates discussed below, thereby increasing exchange profitability. In addition, pro-rata matching eliminates incentives
to place and then cancel limit orders with the intent to secure time priority of execution, reducing message traffic to and from the exchange.
In a nutshell, the pro-rata incentive works as follows: a trader desiring to execute
a limit order knows that only a fraction of his order will be filled under the pro-rata
schedule.The exact size of the filled portion of the order will depend on the cumulative
size of limit orders placed at the same price by other limit order traders. The higher
the aggregate size of limit orders in a specific price bin, the lower the percentage of all
orders that will be filled in response to an incoming market order of the opposite sign.
To increase his chances of filling the entire order, therefore, the trader is likely to place
a limit order with a larger size than his intended order, with the explicit hope that the
fraction of the order that will get filled is of the exact size as his intended order.
■ Aggressive versus Passive Execution

More aggressive buy orders

More aggressive sell orders
More passive sell orders

More passive buy orders

Bid-ask spread
FIGURE 3.5 Aggressive and Passive Orders: An Illustration

A limit order far away from the market price (a low-priced limit buy order, or a
high-priced limit sell order) is considered passive. The closer the limit order is to the
market price, the more aggressive is the order. A market order is the most aggressive
order, “crossing the spread” to be matched with the best-priced limit order on the
opposite side of the limit order book. Limit orders crossing the spread are treated
like market orders in the execution queue, and are also considered aggressive.
While market orders enjoy immediate and nearly guaranteed fills, market orders
cross and pay the spread, incur transaction fees of the exchange and broker-dealers,
and face price uncertainty. In today’s markets, price uncertainty can be the costliest
component associated with the market order execution. From the time the market

43
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Orders can be described as passive or aggressive. Aggressive orders do not mean
malicious orders, and passive orders do not indicate orders that are destined to be
taken advantage of. Instead, the aggressiveness or passivity of orders refers to the
proximity of the order price to the prevailing market price. Figure 3.5 illustrates
the concept.

order is placed to the time the execution is recorded, the market price may “slip,”
resulting in worse execution than the prevailing price at the time the market order
was placed. The slippage may be due to several factors:
■■

■■

Market Microstructure, Orders, and Limit Order Books

Several market orders may arrive at the exchange and be executed between the
time a given market order is placed and the time it is executed. Each of the arriving market orders may deplete the matching liquidity in the order book, adversely
moving the market price. Such a situation is particularly common at times of news
releases, when many traders and their algorithms simultaneously process information and place orders in the same direction.
A market order that is large relative to the available depth of the order book may
sweep through the book, executing fractional pieces of the order against limit
orders at different price levels.
Additional market conditions, such as market disruptions, may also result in significant slippage.

By contrast, the price of a limit order is fixed when the order is placed. A limit order
is added to the limit order book, where it “sits” until the prevailing market price reaches
it and a market order is executed against it. Limit orders also generally avoid “crossing
the spread,” a cost of paying the market spread incurred by market orders. Highly aggressive limit orders executed as market orders cross the spread, but obtain as good or
better execution price than their specified limit price. Limit orders are also subject to
positive or negative transaction costs, which vary from one trading venue to another.
For all their price advantages, limit orders are subject to an important risk—the
risk of nonexecution. A limit order is executed only when it is matched with a market order of the opposite direction. A market price may quickly move away from a
limit order, leaving it unexecuted. An unexecuted limit order may present a particular problem when placed to close a position, and misses the opportunity to eliminate
market risk of the trade. And yet, unexecuted limit orders placed to open a position
also incur a cost, that of the opportunity to engage in the trading strategy.
■■ Complex Orders
In response to competition from new entrants in the matching business, trading venues have diversified their order offerings. For example, in response to competition
from dark pools, selected exchanges expanded the number of available orders, creating so-called iceberg orders. Iceberg orders allow limit-order traders to display only a
portion of their order in the limit order book, and keep the rest of their liquidity in
the dark. In FIFO limit order books, iceberg orders are executed on a time priority
basis: when matched against a smaller order, the nonexecuted part of the iceberg is
being placed back at the end of their limit-order book queue. Unlike the orders in a
dark pool, the size information of an iceberg is revealed after the iceberg is matched
in part or in full: the matched size is disseminated to other traders as a trade tick. As
a rule, iceberg orders cost more than do limit and market orders.

Other specialized orders have sprung up as well, to generate additional revenues
from higher transaction costs and to serve the following potential needs of customers:
■■

■■

Speed of execution. Orders in this category try to enable the fastest execution possible and include, in addition to the vanilla market order, a market-on-close order
that often guarantees to catch the closing price, a midpoint match order that bests
the best bid limit order by attempting to negotiate crossing only half of the prevailing spread, and the sweep-to-fill order simultaneously clears the order book
of the size requested in the order. The sweep-to-fill order may be executed faster
than the market order, since a large market order is often executed by sweeping
the limit order book gradually over time.
Price improvement. Such orders include a block order in options that improves the
price by obtaining large-volume discounts on transaction costs.
Privacy. Privacy-providing orders deliver dark liquidity, and include iceberg orders
and hidden orders, among others. The hidden order, as its name suggests, is not
displayed in the limit order books. The iceberg order displays a limited portion
of the order in the limit order book, as discussed in the beginning of this section.
Time to market. Orders in the time-to-market group include fill-or-kill orders for
market orders desiring the most immediate liquidity. A fill-or-kill order is canceled if the matching liquidity is not immediately available. Conversely, a goodtill-canceled limit order falling in the same order category is kept in the limit
order book until it is canceled or another maximum period of time set by the
trading venue (e.g., a quarter).
Advanced trading. These orders include additional quantitative triggers, such as implied volatility in options.
Algorithmic trading. Orders in this category offer execution via order-slicing algorithms, such as percentage of volume (POV), described in detail in Chapter 17.

■■ Trading Hours
Traditionally, many trading venues operated from 9:30 a.m. to 4:00 p.m. Eastern
time. In today’s globalized markets, more effort is placed on expanding accessibility
of trading. As a result, many exchanges today offer premarket trading and afterhours
trading, cumulatively known as extended-hours trading. Extended hours in equities,
for example, allow market access from 4:00 a.m. to 8:00 p.m. Eastern time. The
extended-hours volume is considerably thinner than that observed during the normal trading hours. Still, selected brokers use the after-hours trading to fill their
customers’ market-on-close orders.

45
Market Microstructure, Orders, and Limit Order Books

■■

Limit risk. Most trading venues and broker-dealers now offer a range of orders for
containing market risk. The order examples include hard and trailing stop orders,
where the position is liquidated when a price move exceeds the predetermined
threshold in the adverse direction (see Chapter 14 for more information on stops).

■■ Modern Microstructure: Market Convergence

and Divergence

The electronization of markets has left an indelible footprint on all modern markets,
streamlining some aspects of trading and fragmenting others. Among the trends in
market convergence are the following developments:
■■

■■

Most markets today can be accessed via Financial Information eXchange (FIX)
messaging protocol. The FIX protocol is an XML-like specification that allows
market participants to send and receive quotes, orders, and order cancellation
and execution acknowledgments, among other messages necessary for fast and efficient trading. The FIX protocol is administered by an independent not-for-profit
body, further facilitating proliferation of the protocol.
Most markets worldwide are now designed as limit order books (LOBs). The
Singaporean Stock Exchange was one of the last entities to use a different market
structure, but converted to LOB in the past decade.

Among the key trends in market divergence is the progressing fragmentation of
markets among the asset classes:
■■

Market Microstructure, Orders, and Limit Order Books

46
■■

■■

■■
■■

Equities are subject to the National Best Bid and Offer (NBBO) rule, whereas all
equities are to be executed at the aggregated and disseminated NBBO or better
price. If the exchange is unable to execute an incoming market order at the NBBO,
the exchange is obligated to route the order to an exchange with NBBO quotes.
Futures exchanges do not have centralized pricing, but are subject to unique margining and daily mark-to-market requirements.
Foreign exchange markets do not have centralized quotes or exchanges at all. All
trades are continued to be negotiated over the counter (OTC), even though many
OTC platforms are now fully electronic. Yet selected large market participants
may be granted access to an interdealer network, an exchange-like entity.
Option markets are numerous, with little activity on average.
Following the Dodd-Frank regulation, new asset classes such as fixed income and
swaps will be coming online or expanding in electronic forms. Each of the asset
classes has distinct peculiarities, resulting in further fragmentation of the overall
securities frontier.

Fragmentation exists within each asset class as well.The following sections discuss
peculiarities within selected asset classes.
■■ Fragmentation in Equities
U.S. equities can be traded in dark pools and on lit exchanges. Dark pools are
exchange-like entities where the order book is “dark”—not displayed to any participant of that pool. According to Pragma Securities (2011), about 22 percent of

1. The exchange can compete to attract the top-of-the-book liquidity—limit orders priced at NBBO or better.
2. The exchange can compete to attract market orders, while simultaneously serving as a proprietary market maker posting NBBO limit orders.
The two business models of exchanges readily translate into the new fee structures of exchanges. In addition to clearing fees, exchanges now offer divergent
pricing for suppliers of liquidity and takers of liquidity. Depending on whether
the exchange follows the business model 1 or 2, the exchange may pay liquidity
providers for posting limit orders, or pay takers of liquidity for bringing in market orders. Such payments, amounting to negative transaction costs, are known
as rebates.

47
Market Microstructure, Orders, and Limit Order Books

the U.S. aggregate equity volume is presently traded in the dark pools. The singular
advantage of dark pools lies in their ability to match large orders without revealing
information associated with the order size, as the orders are not observable. The
frequently cited disadvantages of dark pools include the lack of transparency and
related issues. Unlike “lit” exchanges, dark pools do not offer differentiated pricing
for limit and market orders—the dark pool limit order book is not disclosed to
market participants.
The remaining 78 percent of the U.S. equity volume is executed on “lit” exchanges—venues where the order book is fully transparent and can be disseminated in full to interested market participants. But even within the lit markets
category, the landscape is quite fragmented as the exchanges compete to set
optimal fees.
In the lit exchanges, the U.S. equities are required to be executed at the NBBO
or better quotes, compiled from the best bid and ask quotes available on all the
member exchanges and disseminated by the Securities Information Processor
(SIP). The aggregated best quotes are then disseminated back to exchanges as
NBBO references. The NBBO execution rule was put forth by the Securities and
Exchange Commission (SEC) in 2005 under the Regulation NMS, with the explicit
purpose of leveling the playing field: under the NBBO rule, every best limit order,
whether placed by a large institution or an individual investor, has to be displayed
to all market participants. (Prior to the NBBO rule, individual investors were at
the mercy of broker-dealers, who often failed to route investors’ limit orders to
exchanges, even when said limit orders were at the top of the market—better than
the best quote available at the time.) Under the NBBO rule, exchanges that cannot
execute at the NBBO due to the dearth of liquidity are required to route incoming market orders to other exchanges where the NBBO is available. As a result,
traders placing market orders on lit exchanges are guaranteed that their orders are
executed at the best possible prices available nationwide. Dark pools are exempt
from the NBBO requirement.
Under the NBBO rule, exchanges can match trades only when they can execute
at the NBBO, that is, when the NBBO-priced limit orders are recorded within
their limit order books. Such NBBO limit orders can be achieved using two distinct
approaches:

The two different business models have driven the exchanges into two distinct
camps, “normal” and “inverted” exchanges, based on their fee structure. The normal exchanges offer the following fees: normal exchanges charge traders for placing market orders, taking away liquidity, and offer rebates for placing limit orders,
bringing in liquidity. The nYse, for example, charges $0.21 for a 100-share market
order, and pays anywhere from $0.13 to $0.20 for a 100-share limit order. The exact
value of the nYse rebate is determined by the aggregate monthly volume of the
trader—the higher the volume, the higher the rebate. The nYse fee structure displayed online on May 14, 2012, is shown in Figure 3.6.
In contrast, the so-called “inverted” exchanges pay traders small rebates to remove liquidity (place market orders), and charge fees to place limit orders. Boston
exchange (nasdaq OMX BX) is an example of an inverted exchange. There, traders
with market orders for fewer than 3.5 million shares per day are paid $0.0005 per
share, while traders placing market orders for 3.5 million or more shares per day are
paid $0.0014 per share. Traders adding displayed limit orders under 25,000 per day
are charged $0.0015 to $0.0018 per share. Yet, large limit order traders—traders
placing limit orders for 25,000 shares per day or more—are paid rebates at the rate
of $0.0014 per share. The snapshot of distribution of trading costs on the BX as of
October 10, 2012, is shown in Figure 3.7.
As a result of the regulatory framework and pricing divergence among equity
exchanges in the united states, various exchanges show different rates of availability
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48
NYSE Arca Rates per 100 Shares
TAPE A
(NYSE-LISTED)
Tier

Fee for
Routing to Routing
Removing
NYSE2
to Other
Venues

Tier Requirement(s)

Rebate
for
Adding1

Tier 1

NYSE Arca Daily
Adding as of % of
US CADV in excess
of 0.70%

$ (0.30)

$ 0.30

$0.21/$0.23

$ 0.30

Tier 2

NYSE Arca Daily
Adding as of % of
US CADV in excess
of 0.30%

$ (0.29)

$ 0.30

$0.21/$0.23

$ 0.30

Tier 3

NYSE Arca Daily
Adding as of % of
US CADV in excess
of 0.20%

$ (0.25)

$ 0.30

$0.21/$0.23

$ 0.30

Step-Up NYSE Arca Daily
Tier 1
Adding as % of US
CADV in excess of
0.15% over the

$ (0.295)

$ 0.30

$0.21/$0.23

$ 0.30

FIGURE 3.6 Fee structure of Orders Placed and routed to and from nYse
Source: nYse web site

FIGURE 3.7 Fees on nasdaq OMX BX, an Inverted exchange
Source: nasdaq web site

20
NYSE

Share of trades [%]

NASDAQ
ARCA

10
BATS

EDGA

BOSTON

BYX
EDGX
PHLX
NSX

40
60
Availability [%]

FIGURE 3.8 Availability of nBBO versus share Volume
Source: Pragma securities (2011)

100

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of nBBO on their order books as well as different market shares. As the intuition
would suggest, the exchanges able to provide the highest occurrence of nBBO
quotes are the ones able to secure the highest market share. Figure 3.8 displays the
relationship between the nBBO availability rates and the market share rates. As
shown in Figure 3.8, nasdaq and nYse on average have the highest availability of
nBBO and obtain the highest share of trades.

Percentage of trades executed at each venue, given that a certain set of venues had the inside price.
ALL
ALL BUT BX
ALL BUT BX, BYX
ALL BUT BX, BYX, EDGA

ARCA

BATS BOSTON BYX

EDGA

EDGX NASDAQ

NSX

NYSE

PHLX

FIGURE 3.9 Percentage of Trades executed at each Trading Venue When nBBO Is Present at
certain Venues
Source: Pragma securities (2011)

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Figure 3.9 illustrates what happens when the nBBO is available on all or only
some exchanges. When the best bid and the best ask at nBBO are available on all
exchanges, over 30 percent of trade volume is executed at the BX, where the inverted fee structure attracts market order traders seeking nBBO liquidity. When
every exchange except for BX has the nBBO limit orders, a similarly high number
trades is routed to the BATs Y-exchange (BYX). BYX, like BX, offers inverted fee
structure, but with much smaller fees and rebates for removing liquidity. When the
nBBO is not available solely on BX and BYX, the 30+ percent market share moves
to Direct edge’s eDGA, an exchange with normal but low fee structure. When the
nBBO is available everywhere except for BX, BYX, and eDGA, the trading volume
moves on largely to the nYse, although nasdaq and BATs also benefit from the flow.
The economic incentives associated with inverted price structures clearly work: the
asymmetric order flow enjoyed by BX creates the first-taker advantage for nasdaq,
the parent company of BX.
High market share of trades does not alone contribute to the profitability of the
exchange, as other fees can provide significant contributions to the bottom line of
the exchanges. For example, both normal and inverted exchanges charge traders’
fees for routing orders to other trading venues when the nBBO is not available on
the current exchange. Thus, even an exchange with lowest proportion of nBBO
can remain profitable by attracting enough orders and charging fees for routing said
orders elsewhere.
■ Fragmentation in Futures
Futures exchanges operated in a manner similar to equity exchanhes, but without
rebate pricing implemented or foreseeable at the time this book was written. In a
bid to attract liquidity, and unlike the rebate structure prevalent in equities, futures

exchanges have been deploying pro-rata matching, discussed earlier. Other differences among futures exchanges are predominantly based on their operational and
risk management decisions, such as when to draw the circuit breakers and so on,
described in detail in Chapter 13.
■■ Fragmentation in Options
Various options exchanges have sprung up over the past decade. A majority of the
exchanges, however, operate on similar principles and are driven by the same group
of market makers.
Due to the sheer number of options with different expiration dates and strike price
combinations, most options are barely traded. The same 10 or so broker-dealers
tend to provide liquidity on most equity options markets, with large spreads being
common.
The relative lack of activity in options trading enables market surveillance for
insider information. A large trade in the long-dated option or an option with a
strike price far away from the current market price of the underlying usually
represents a bet on someone’s special knowledge, not yet revealed to the rest of
the markets.
■■ Fragmentation in Forex

■■ Fragmentation in Fixed Income
While most fixed income traditionally traded OTC, some signs point to a potential
near-term exchange-ization of the fixed-income market. Thus, iCAP has planned
to launch a fixed-income matching engine using the Nasdaq OMX technology. The
iCAP offering would further target institutional investors by providing a one-second
validity of all top-of-the-book quotes.
■■ Fragmentation in Swaps
Swaps have also traditionally traded OTC, with privately negotiated contracts. Under the Dodd-Frank Act, swaps are required to be standardized and traded electronically on exchanges. A new class of trading venues, collectively known as swaps
execution facilities (SEFs), was jointly shaped by the industry and regulators at the time
this book was written.

Market Microstructure, Orders, and Limit Order Books

In Forex, interdealer brokers begin competing with broker-dealers for direct access to end traders. The traditionally interdealer brokers Currenex and iCAP, for
example, now accept selected institutional customers. In breaking with other exchanges, iCAP offers a 250-microsecond validity on all of its top-of-the-book foreign
exchange (forex) quotes.

■■ Summary
Modern markets are complex businesses ever concerned with streamlining their
operations with the goal of delivering the most immediate, cost-effective service
to their customers. The competition of trading venues has led to the innovation
and evolution in methods, pricing, and service models of exchanges and alternative
trading systems. While technology remains the key driver in development of faster
and leaner offerings, the solutions are becoming more customer-centric, producing
trading products customized to clients’ unique execution needs.
■■ End-of-Chapter Questions

Market Microstructure, Orders, and Limit Order Books

1. What is the difference between the normal and inverted exchanges?
2. What type of orders would you use to buy a large quantity? Why?
3. You are given the task of developing an algorithm optimizing liquidation (selling) of a large equity position.Your aim is to develop an algorithm that maximizes execution costs while minimizing speed of liquidation process. How would
you develop such an algorithm giving normal and inverted price structures of
modern equity exchanges?
4. You are receiving Level I and Level II data on a certain futures contract from
a well-known exchange. At 13:45:00:01:060 GMT, the aggregate liquidity reported at the best bid of 12.7962 comprises 325 contracts. The next tick of data
is a trade print with a timestamp of 13:45:00:01:075 GMT, recording a trade of
900 contracts at 12.7962. The following tick is a 13:45:00:01:095 GMT quote
citing the best bid of 12.7962 with the size of 325 contracts. What has happened
in the market from 13:45:00:01:060 GMT to 13:45:00:01:095 GMT?
5. The current right-hand side of the limit order book for a particular stock on a
given exchange shows the following information: Best Ask: 100 shares at 35.67,
200 shares at 35.68, 100 shares at 35.69.What is the average price per share you
are likely to receive on your market buy order of 250 shares if the National Best
Bid is advertised as 35.67? What if the National Best Bid is 35.65 instead?
6. Is an iceberg order passive or aggressive?
7. The last recorded trade price in a given options market is 2.83. The prevailing best bid is 2.65 and the prevailing best ask is 2.90. Is a limit order to buy
10 contracts at 2.85 passive or aggressive? Why?
8. A quantitative researcher (“quant”) develops his investing models using daily
closing prices. What order types should an execution trader use to execute the
quant’s buy-and-sell decisions?

Chapter 4

High-Frequency
1
Data
T

rade and quote information is often distributed in Level I or Level II formats.
Level I quotes include the best bid price, best ask price, best bid size, best ask
size, and last trade price and size, where available. Level II quotes include all changes
to the order book, including new limit order arrivals and cancellations at prices away
from the market price. This chapter describes the details of data quotations and sampling methodologies and contrasts the data with their low-frequency counterparts.
■■ What Is High-Frequency Data?

High-frequency data, also known as tick data, are records of live market activity.
Every time a customer, a dealer, or another entity posts a so-called limit order to buy
b
s units of a specific security with ticker X at price q, a bid quote qtb is logged at time
tb to buy Stbb units of X. Market orders are incorporated into tick data in a different
way, as discussed in this chapter.
When the newly arrived bid quote qtbb has the highest price relative to all other preb
viously arrived bid quotes in force, qtb becomes known as “the best bid” available at time
tb. Similarly, when a trading entity posts a limit order to sell s units of X at price q, an
a
a
ask quote qtaa is logged at time ta to sell Sta units of X. If the latest qta is lower than all
other available ask quotes for security X, qtaa becomes known as “the best ask” at time ta.
What happens to quotes from the moment they arrive largely depends on the
venue where the orders are posted. Best bids and asks posted directly on an exchange
will be broadcast to all exchange participants and other parties tracking quote data.
In situations when the new best bid exceeds the best ask already in force on the exchange,qtbb ≥ qtaa , most exchanges will immediately “match” such quotes, executing a
1

A version of this chapter appears in F. Fabozzi, ed., Encyclopedia of Financial Models (3 volume set)
(Hoboken, NJ: John Wiley & Sons, 2012).

High-Frequency Data

trade at the preexisting best ask,qtaa at time tb. Conversely, should the newly arrived
best ask fall below the current best bid, qta ≤ qtb , the trade is executed at the preexa
b
b
isting best bid, qtb at time ta.
Most dark pools match bids and asks by “crossing the spread,” but may not broadcast the newly arrived quotes (hence the mysterious moniker, the “dark pools”).
Similarly, quotes destined for the interdealer networks may or may not be disseminated to other market participants, depending on the venue.
Market orders contribute to high-frequency data in the form of “last trade” information. Unlike a limit order that is an order to buy a specified quantity of a security
at a certain price, a market order is an order to buy a specified quantity of a security
at the best price available at the moment the order is “posted” on the trading venue.
As such, market orders are executed immediately at the best available bid or best
ask prices, with each market buy order executed at the best ask and each market sell
matched with the best bid, and the transaction is recorded in the quote data as the
“last trade price” and the “last trade size.”
A large market order may need to be matched with one or several best quotes, generating several “last trade” data points. For example, if the newly arrived market buy order
is smaller in size than that of the best ask, the best ask quote may still remain in force on
most trading venues, but the best ask size will be reduced to reflect that the portion of
the best ask quote has been matched with the market order.When the size of the incoming market buy order is bigger than the size of the corresponding best ask, the market
order consumes the best ask in its entirety, and then proceeds to be matched sequentially with the next available best ask until the size of the market order is fulfilled. The
remaining lowest-priced ask quote becomes the best ask available on the trading venue.
Most limit and market orders are placed in so-called “lot sizes”: increments of certain
number of units, known as a lot. In foreign exchange, a standard trading lot today is
US$5 million, a considerable reduction from a minimum of $25 million entertained by
high-profile brokers just a few years ago. On equity exchanges, a lot can be as low as one
share, but dark pools may still enforce a 100 share minimum requirement for orders. An
order for the amount other than an integer increment of a lot size, is called “an odd lot.”
Small limit and market “odd lot” orders posted through a broker-dealer may be
aggregated, or “packaged,” by the broker-dealer into larger-size orders in order to
obtain volume discounts at the orders’ execution venue. In the process, the brokers
may “sit” on quotes without transmitting them to an executing venue, delaying execution of customers’ orders.
■■ How Is High-Frequency Data Recorded?
The highest-frequency data are a collection of sequential “ticks,” arrivals of the latest
quote, trade, price, order size, and volume information. Tick data usually has the
following properties:
■■

A timestamp

■■

A financial security identification code

■■

■■
■■

An indicator of what information it carries:
■■

Bid price

■■

Ask price

■■

Available bid size

■■

Available ask size

■■

Last trade price

■■

Last trade size

Security-specific data, such as implied volatility for options
The market value information, such as the actual numerical value of the price,
available volume, or size

55
High-Frequency Data

A timestamp records the date and time at which the quote originated. It may be the
time at which the exchange or the broker-dealer released the quote, or the time when
the trading system has received the quote. At the time this article is written, the standard
“round-trip” travel time of an order quote from the ordering customer to the exchange
and back to the customer with the acknowledgment of order receipt is 15 milliseconds
or less in New York. Brokers have been known to be fired by their customers if they are
unable to process orders at this now standard speed. Sophisticated quotation systems,
therefore, include milliseconds and even microseconds as part of their timestamps.
Another part of the quote is an identifier of the financial security. In equities, the
identification code can be a ticker, or, for tickers simultaneously traded on multiple
exchanges, a ticker followed by the exchange symbol. For futures, the identification
code can consist of the underlying security, futures expiration date, and exchange code.
The last trade price shows the price at which the last trade in the security cleared.
Last trade price can differ from the bid and ask. The differences can arise when a
customer posts a favorable limit order that is immediately matched by the broker
without broadcasting the customer’s quote. Last trade size shows the actual size of
the last executed trade.
The best bid is the highest price available for sale of the security in the market.The
best ask is the lowest price entered to buy the security at any particular time. In addition to the best bid and best ask, quotation systems may disseminate “market depth”
information: the bid and ask quotes entered posted on the trading venue at prices
worse than the best bid and ask, as well as aggregate order sizes corresponding to
each bid and ask recorded on the trading venue’s “books.” Market depth information
is sometimes referred to as the Level II data and may be disseminated as the premium
subscription service only. In contrast, the best bid, best ask, last trade price, and size
information (“Level I data”) is often available for a small nominal fee.
Panels A and B of Figure 4.1 illustrate a 30-second log of Level I high-frequency
data recorded by New York Stock Exchange (NYSE) Arca for Standard & Poor’s
Depositary Receipts (SPDR) S&P 500 exchange-traded fund (ETF; ticker SPY) from
14:00:16:400 to 14:02:00:000 GMT on November 9, 2009. Panel A shows quote

A. HF Data for S&P 500 ETF Recorded from 14:00:16:400 to
14:02:00:000 GMT: Best Bid, Best Ask, and Last Trade Data
108.05

Quote

108.04
108.03
108.02
108.01
14:01:58:700

14:01:54:050

14:01:49:400

14:01:44:750

14:01:40:100

14:01:35:450

14:01:30:800

14:01:26:150

14:01:21:500

14:01:16:850

14:01:12:200

14:01:07:550

14:01:02:900

14:00:58:250

14:00:53:600

14:00:48:950

14:00:44:300

14:00:39:650

14:00:35:000

14:00:30:350

14:00:25:700

14:00:21:050

14:00:16:400

108.00

Time
Bid

Ask

Last Trade Price

B. HF Data for S&P 500 ETF Recorded from 14:00:16:400 to
14:02:00:000 GMT: Bid Size, Ask Size, and Last Trade Size
161
141
121
101
Quote

HIgH-FrEquENcy DATA

81
61
41
21
1
Time
Bid Size

Ask Size

Last Trade Size

FIGURE 4.1 Level I High-Frequency Data recorded by NySE Arca for SPy from 14:00:16:400
to 14:02:00:000 gMT on November 9, 2009. Data source: Bloomberg

data: best bid, best ask and last trade information, while panel B displays corresponding position sizes (best bid size, best ask size, and last trade size).
■ Properties of High-Frequency Data
High-frequency securities data have been studied for many years.yet they are still something of a novelty to many academics and practitioners. unlike daily or monthly data sets
commonly used in much of financial research and related applications, high-frequency

data have distinct properties, which simultaneously can be advantageous and intimidating
to researchers. Table 4.1 summarizes the properties of high-frequency data. Each property and its advantages and disadvantages are discussed in detail later in the article.
Table 4.1 Summary of Properties of High-Frequency Data
Pros

Cons

Voluminous

Large numbers of
observations carry lots of
information.

High-frequency data are
difficult to handle manually.

Subject to bid-ask Unlike traditional data
bounce
based on just closing
prices, tick data carry
additional supply-anddemand information in the
form of bid and ask prices
and offering sizes.

Bid and ask quotes can
carry valuable information
about impending
market moves, which
can be harnessed to the
researcher’s advantage.

Bid and ask quotes are
separated by a spread.
Continuous movement
from bid to ask and back
introduces a jump process,
difficult to deal with through
many conventional models.

Not normally
or lognormally
distributed

Many tradable models are
still to be discovered.

Traditional asset pricing
models assuming
lognormality of prices do
not apply.

Durations between data
arrival carry information.

Most traditional models
require regularly spaced
data; need to convert highfrequency data to some
regular intervals, or “bars”
of data. Converted data are
often sparse (populated
with zero returns), once
again making traditional
econometric inferences
difficult.

Each day of highfrequency data
contains the number of
observations equivalent to
30 years of daily data.

Returns computed from
tick are not normal or
lognormal.

Irregularly spaced Arrivals of tick data are
in time
asynchronous.

Do not include
buy or sell
trade direction
information

Level I and Level II data do
not include information
on whether the trade was
a result of a market buy or
a market sell order

Data are leaner without
trade direction information;
trade information is more
difficult for bystanders to
extract.

The information on whether
a trade is buyer initiated or
seller initiated is a desired
input in many models.

■■ High-Frequency Data Are Voluminous
The nearly two-minute sample of tick data for SPY shown in Figure 4.1 contained
over 2,000 observations of Level I data: best bid quotes and sizes, best ask quotes and
sizes, and last trade prices and sizes. Table 4.2 summarizes the breakdown of the data
points provided by NYSE Arca for SPY from 14:00:16:400 to 14:02:00:000 GMT on
November 9, 2009, and SPY, Japanese yen futures, and a euro call option throughout
the day on November 9, 2009. Other Level I data omitted from Table 4.2 include
cumulative daily trade volume for SPY and Japanese yen futures, and “greeks” for
the euro call option. The number of quotes observed on November 9, 2009, for SPY
alone would comprise over 160 years of daily open, high, low, close, and volume data
points, assuming an average of 252 trading days per year.

57
High-Frequency Data

Property of HF Data Description

Table 4.2 Summary Statistics for Level I Quotes for Selected Securities on November 9, 2009
Quote Type

Best bid quote
Best bid size
Best ask quote
Best ask size
Last trade price
Last trade size
Total

High-Frequency Data

SPY, 14:00:16:400 to
14:02:00:000 GMT

SPY, All Day

USD/JPY Dec. 2009
Futures, All Day

EUR/USD Call Expiring Dec. 2009
with Strike Price of 1.5100, All Day

4 (3%)

5,467 (3%)

6,320 (5%)

1,521 (3%)

36 (29%)

38,948 (19%)

39,070 (32%)

5,722 (11%)

4 (3%)

4,998 (2%)

6,344 (5%)

1,515 (3%)

35 (28%)

38,721 (19%)

38,855 (32%)

5,615 (11%)

6 (5%)

9,803 (5%)

3,353 (3%)

14 (0%)

20 (16%)

27,750 (14%)

10,178 (8%)

25 (0%)

125

203,792

123,216

49,982

The quality of data does not always match its quantity. Centralized exchanges
generally provide accurate data on bids, asks, and size. U.S. equity exchanges are required by law to archive and maintain reliable records of every tick of data, as well as
to submit best quotes within one minute of their occurrence to the U.S. centralized
ticker tape known as the Securities Information Processor (SIP). The information on the
limit order book beyond the best bid and best offer is known as Level II data and can
be obtained via special subscription.
In decentralized markets, such as foreign exchange and the interbank money market, no market-wide quotes are available at any given time. In such markets, participants are aware of the current price levels, but each institution quotes its own prices
adjusted for its order book. In decentralized markets, each dealer provides his own
tick data to his clients. As a result, a specific quote on a given financial instrument at
any given time may vary from dealer to dealer. Reuters, Telerate, and Knight Ridder,
among others, collect quotes from different dealers and disseminate them back, improving the efficiency of the decentralized markets.
There are generally thought to be three anomalies in interdealer quote discrepancies. First, each dealer’s quotes reflect that dealer’s own inventory. For example, a
dealer that has just sold a customer $100 million of USD/CAD would be eager to diversify the risk of his position and avoid selling any more of USD/CAD. Most dealers,
however, are obligated to transact with their clients on tradable quotes.To incite his clients to place sell orders on USD/CAD, the dealer temporarily raises the bid quote on
USD/CAD. At the same time, to encourage his clients to withhold placing buy orders,
the dealer raises the ask quote on USD/CAD. Thus, dealers tend to raise both bid and
ask prices whenever they are short in a particular financial instrument and lower both
bid and ask prices whenever they are disproportionately long in a financial instrument.
Second, in an anonymous marketplace, such as a dark pool, dealers as well as other market makers may “fish” for market information by sending indicative quotes that
are much off the previously quoted price to assess the available demand or supply.
Third, Dacorogna et al. (2001) note that some dealers’ quotes may lag real market prices. The lag is thought to vary from milliseconds to a minute. Some dealers
quote moving averages of quotes of other dealers. The dealers who provide delayed
quotes usually do so to advertise their market presence in the data feed. This was
particularly true when most order prices were negotiated over the telephone, allowing a considerable delay between quotes and orders. Fast-paced electronic markets
discourage lagged quotes, improving the quality of markets.

■ High-Frequency Data Are Subject

to the Bid-Ask Bounce

Average Hourly Spread, EUR/USD

Spread on the
weekend of Oct
18–19, 2008

pips

15
10
5
0
15-Oct-2008

17-Oct-2008

22-Oct-2008
Dates

24-Oct-2008

FIGURE 4.2 Average Hourly Bid-Ask Spread on Eur/uSD Spot for the Last Two Weeks of
October 2008 on a Median Transaction Size of uS$5 Million

59
HIgH-FrEquENcy DATA

In addition to trade price and volume data long available in low-frequency formats,
high-frequency data comprise bid and ask quotes and their associated order sizes. Bid
and ask data arrive asynchronously and introduce noise in the quote process.
The difference between the bid quote and the ask quote at any given time is known
as the bid-ask spread. The bid-ask spread is the cost of instantaneously buying and
selling the security. The higher the bid-ask spread, the higher the gain the security
must produce in order to cover the spread along with other transaction costs. Most
low-frequency price changes are large enough to make the bid-ask spread negligible
in comparison. In tick data, however, incremental price changes can be comparable
or smaller than the bid-ask spread.
Bid-ask spreads usually vary throughout the day. Figure 4.2 illustrates the average bid-ask spread cycles observed in the institutional Eur/uSD market for the
last two weeks of October 2008. As Figure 4.2 shows, the average spread increases
significantly during Tokyo trading hours, when the market is quiet. The spread then
reaches its lowest levels during the overlap of the London and New york trading sessions, when the market has many active buyers and sellers. The spike in the spread
over the weekend of October 18–19, 2008, reflects the market concern over the
subpoenas issued on October 17, 2009, to senior Lehman executives in a case relating to potential securities fraud at Lehman Brothers.
Bid-ask spreads typically increase during periods of market uncertainty or instability.
Figure 4.3, for example, compares average bid-ask spreads on Eur/uSD in the stable
market conditions of July–August 2008 and the crisis conditions of September–October
2008. As the figure shows, the intraday spread pattern is persistent in both crisis and
normal market conditions, but the spreads are significantly higher during crisis months
than during normal conditions at all hours of the day. As Figure 4.3 also shows, the spread
increase is not uniform at all hours of the day.The average hourly Eur/uSD spreads increased by 0.0048 percent (0.48 basis points or pips) between the hours of 12 gMT and

3.50
3.00
2.50
2.00

Crisis Conditions,
Sept-Oct 2008

1.50

Normal Market Conditions,
July-August 2008

1.00
0.50

22-0

20-22

18-20

16-18

14-16

12-14

10-12

8-10

6-8

4-6

2-4

0.00
0-2

Average Hourly Bid-Ask Spread of EUR/USD, pips

Effect of the Credit Crisis on Bid-Ask Spreads of EUR/USD

Hour of the Day (GMT)

FIGURE 4.3 comparison of Average Bid-Ask Spreads for Different Hours of the Day during
Normal Market conditions and crisis conditions

HIgH-FrEquENcy DATA

16 gMT, when the London and New york trading sessions overlap. From 0 to 2 gMT,
during the Tokyo trading hours, the spread increased by 0.0156 percent, over three times
the average increase during the Newyork/London hours.
As a result of increasing bid-ask spreads during periods of uncertainty and crises, the
profitability of high-frequency strategies decreases during those times. For example,
high-frequency Eur/uSD strategies running over Asian hours incurred significantly
higher costs during September and October 2008 as compared with normal market
conditions. A strategy that executed 100 trades during Asian hours alone resulted in
1.56 percent evaporating from daily profits due to the increased spreads, while the
same strategy running during London and New york hours resulted in a smaller but
still significant daily profit decrease of 0.48 percent. The situation can be even more
severe for high-frequency strategies built for less liquid instruments. For example,
bid-ask spreads for NZD/uSD (not shown) on average increased three times during
September–October in comparison with market conditions of July–August 2008.
While tick data carry information about market dynamics, it is also distorted by the
same processes that make the data so valuable in the first place. Dacorogna et al. (2001)
report that sequential trade price bounces between the bid and ask quotes during market
execution of orders introduce significant distortions into estimation of high-frequency
parameters. corsi, Zumbach, Muller, and Dacorogna (2001), for example, show that
the bid-ask bounce introduces a considerable bias into volatility estimates. The authors
calculate that the bid-ask bounce on average results in –40 percent first-order autocorrelation of tick data. corsi et al. (2001) as well as Voev and Lunde (2007) propose to
remedy the bias by filtering the data from the bid-ask noise prior to estimation.

In addition to real-time adjustments to bid-ask data, researchers deploy forecasting techniques to estimate the impending bid-ask spread and adjust for it in models
ahead of time. Future realizations of the bid-ask spread can be estimated using the
model suggested by Roll (1984), where the price of an asset at time t, pt, is assumed
to equal an unobservable fundamental value, mt, offset by a value equal to half of the
bid-ask spread, s. The price offset is positive when the next market order is a buy, and
negative when the trade is a sell, as shown in equation (3):
s
pt = mt + It
2

(3)

1, market buy at ask
 −1, market sell at bid
If either a buy or a sell order can arrive next with equal probability, then E[It] = 0,
and E[∆pt] = 0, absent changes in the fundamental asset value, mt. The covariance of
subsequent price changes, however, is different from 0:


where It = 

s2
cov [ ∆ pt , ∆ pt +1 ] = E [ ∆ pt ∆ pt +1 ] = − 4

(4)

As a result, the future expected spread can be estimated as follows:
E [ s ] = 2 − cov [ ∆ pt , ∆ pt +1 ] whenever cov [ ∆ pt , ∆ pt+1 ] < 0

(

)

1 a
t , if ta ≥ tb
qt + qtb where tm =  a

(5)
a
b
2
 tb , otherwise
The latter condition for tm reflects the continuous updating of the mid-quote estim
mate: q̂t is updated whenever the latest best bid, qtbb , or best ask quote, qtaa , arrives,
at tb or ta respectively.
Another way to sample tick quotes into a cohesive data series is by weighing the
latest best bid and best ask quotes by their accompanying order sizes:
qtbb staa + qtaa stb
s
b
qt =

(6)
staa + stbb
q̂tmm =

where qtbb and Stbb is the best bid quote and the best bid available size recorded at time
a
tb (when qtb became the best bid), and qtaa and Sta is the best bid quote and the best bid
b
available size recorded at time ta.

High-Frequency Data

Numerous extensions of Roll’s model have been developed to account for contemporary market conditions along with numerous other variables. Hasbrouck
(2007) provides a good summary of the models.
To use standard econometric techniques in the presence of the bid-ask bounce, many
practitioners convert the tick data to “midquote” format: the simple average of the latest
bid and ask quotes.The midquote is used to approximate the price level at which the market is theoretically willing to trade if buyers and sellers agreed to meet each other halfway
on the price spectrum. Mathematically, the midquote can be expressed as follows:

■■ High-Frequency Data Are Not Normal or Lognormal

High-Frequency Data

Many classical models assume lognormality of prices, allowing price diffusion models to work seamlessly, and resulting in several pricing models, such as Black-Scholes,
to be considered fair approximations of market evolutions of related financial instruments. A necessary condition for lognormality of prices is the normal distribution
of sequential price changes. As this section shows, however, sequential changes in
most of the tick data, like midquotes and size-weighted quotes and trades, do not
follow normal distribution, yet distribution of sequential trade ticks is close to that
of normal. Trade tick data are, therefore, the best choice for modelers assuming
lognormal prices.
Figure 4.4 compares the histograms of simple returns computed from midquote
(panel A), size-weighted midquote (panel B) and trade-price (panel C) processes for
SPDR S&P 500 ETF data recorded as they arrive throughout November 9, 2009.The
data neglect the time difference between the adjacent quotes, treating each sequential quote as an independent observation. Figure 4.5 contrasts the quantile distribution plots of the same data sets with the quantiles of a standard normal distribution.
As Figures 4.4 and 4.5 show, the basic midquote distribution is constrained
by the minimum “step size”: the minimum changes in the midquote can occur at
half-tick increments (at present, the minimum tick size is $0.01 in equities). The
size-weighted midquote forms the most continuous distribution among the three
distributions discussed. Figure 4.5 confirms this notion further and also illustrates
the fat tails present in all three types of data distributions.
As clearly shown in Figure 4.5, of the three methodologies, tick-by-tick trade
returns most closely fit the normal distribution, when heavy tails past four standard
deviations are ignored. Midquote values and size-weighted midquotes alike begin to
deviate from normality at just two standard deviations, while trade returns follow
the normal up to four standard deviations.
■■ High-Frequency Data Are

Irregularly Spaced in Time

Most modern computational techniques have been developed to work with regularly
spaced data, presented in monthly, weekly, daily, hourly, or other consistent intervals. The traditional reliance of researchers on fixed time intervals is due to:
■■

■■
■■

Relative availability of daily data (newspapers have published daily quotes since
the 1920s).
Relative ease of processing regularly spaced data.
An outdated view that “whatever drove security prices and returns, it probably did not
vary significantly over short time intervals.” (Goodhart and O’Hara 1997, pp. 80–81)

By contrast, high-frequency observations are separated by varying time intervals. One way to overcome the irregularities in the data are to sample it at certain

-2

-1

0
1

4
x 10-4

x 105

-4

-2

B. SW Midquote Simple Quotes

0.01 0.02 0.03 0.04

C. Trade Data Simple Quotes

0
-0.04 -0.03 -0.02 -0.01

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

0
-6

x 104

8
x 10-4

Panel A: Midquote simple returns
Panel B: Size-weighted midquote simple returns
Panel c: Last trade price simple returns

FIGURE 4.4 Histograms of Simple returns computed from Midquote (Panel A), Size-Weighted Midquote (Panel B)
and Trade Price (Panel c) Processes for SPy Data recorded as They Arrive throughout November 9, 2009

0
-4

0.2

-3

A. Midquote Simple Quotes

x 105

0.4

0.6

0.8

1.2

1.4

1.6

1.8

A. Midquote Simple Quotes

x 10-4

Quantiles of Input Sample

3
2
1
0
-1
-2
-3
-4
-5

-4

-2

-3

-1

Standard Normal Quantiles
8

B. SW Midquote Simple Quotes

x 10-4

Quantiles of Input Sample

6
4
2
0
-2
-4
-6
-5

-4

-3

-2
-1
0
1
2
Standard Normal Quantiles

C. Trade Data Simple Quotes

0.04

Quantiles of Input Sample

0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-5

-4

-3

-2
-1
0
1
2
Standard Normal Quantiles

FIGURE 4.5 quantile Plots of Simple returns of Midquote (Panel A), Size-Weighted Midquote
(Panel B) and Trade-Price (Panel c) Processes for SPy Data recorded as They Arrive throughout
November 9, 2009
Panel A: Midquote returns
Panel B: Size-weighted midquote returns
Panel c: Trade price returns

predetermined periods of time—for example, every hour or minute. For example,
if the data are to be converted from tick data to minute “bars,” then under the traditional approach, the bid or ask price for any given minute would be determined as
the last quote that arrived during that particular minute. If no quotes arrived during
a certain minute, then the previous minute’s closing prices would be taken as the
current minute’s closing prices, and so on. Figure 4.7, panel A illustrates this idea.
This approach implicitly assumes that in the absence of new quotes, the prices stay
constant, which does not have to be the case.
Dacorogna et al. (2001) propose a potentially more precise way to sample quotes:
linear time-weighted interpolation between adjacent quotes. At the core of the interpolation technique is an assumption that at any given time, unobserved quotes lie
on a straight line that connects two neighboring observed quotes. Figure 4.6, panel
B illustrates linear interpolation sampling.
As shown in Figure 4.6, panels A and B, the two quote-sampling methods produce
quite different results.
Mathematically, the two sampling methods can be expressed as follows:
quote sampling using closing prices:
qˆt = qt,last

(7)

quote sampling using linear interpolation:
t − tlast
tnext − tlast

(8)

where qt is the resulting sampled quote, t is the desired sampling time (start of a new
minute, for example), tlast is the timestamp of the last observed quote prior to the
sampling time t, qt,last is the value of the last quote prior to the sampling time t, tnext is
the timestamp of the first observed quote after the sampling time t, and qt,next is the
value of the first quote after the sampling time t.
Figures 4.7 and 4.8 compare histograms of the midquote data sampled as closing prices and interpolated, at frequencies of 200 ms and 15 s. Figure 4.9 compares quantile plots of closing prices and interpolated distributions. As Figures
4.7 and 4.8 show, oft-sampled distributions are sparse, that is, contain more zero
returns than distributions sampled at lower frequencies. At the same time, returns
computed from interpolated quotes are more continuous than closing prices, as
Figure 4.9 illustrates.
A. Last-tick sampling

B. Interpolated sampling
*

*
*

*
Second 1

Second 2

Second 3 Time

FIGURE 4.6 Data-Sampling Methodologies

*
Second 1

*
Second 2

Second 3 Time

65
HIgH-FrEquENcy DATA

qˆt = qt,last + (qt,next − qt,last )

2.5

Midquote Closing Prices 200 ms

x 105

1.5

0.5

0
-8

-6

-4

-2

8
x 10-4

Midquote Closing Prices 15 s
1600
1400

HIgH-FrEquENcy DATA

66
1200
1000
800
600
400
200
0
-1

-0.5

0.5

1.5
x 10-3

FIGURE 4.7 Midquote “closing quotes” Sampled at 200-ms (top) and 15-s Intervals

Instead of manipulating the interquote intervals into the convenient regularly
spaced formats, several researchers have studied whether the time distance between
subsequent quote arrivals itself carries information. For example, most researchers agree that intertrade intervals indeed carry information on securities for which
short sales are disallowed; the lower the intertrade duration, the more likely the
yet-to-be-observed good news and the higher the impending price change.

2.5

Midquote Interpolated Quotes 200 ms

x 105

1.5

0.5

0
-8

-6

-4

-2

10-4

Midquote Interpolated Quotes15 s

1400

1200

67
HIgH-FrEquENcy DATA

1000

800

600

400

200

0
-1

-0.8

-0.6

-0.4

-0.2

0.2

0.4

0.6

0.8

x 10-3

FIGURE 4.8 Midquote “Time-Interpolated quotes” Sampled at 200-ms (top) and 15-s Intervals

Duration models are used to estimate the factors affecting the time between any
two sequential ticks. Such models are known as quote processes and trade processes,
respectively. Duration models are also used to measure the time elapsed between
price changes of a prespecified size, as well as the time interval between predetermined trade volume increments. The models working with fixed price are known
as price processes; the models estimating variation in duration of fixed volume increments are known as volume processes.

Midquote Closing Prices 200 ms

x 10-4

Quantiles of Input Sample

4
2
0
-2
-4
-6
-8
-5

-3

-2

-1
0
1
2
Standard Normal Quantiles

Midquote Interpolated Quotes 200 ms

x 10-4

6
4
Quantiles of Input Sample

HIgH-FrEquENcy DATA

-4

2
0
-2
-4
-6
-8
-5

-4

-3

-2

-1

Standard Normal Quantiles

FIGURE 4.9 quantile Plots: closing Prices versus Interpolated Midquotes Sampled at 200 ms

Durations are often modeled using Poisson processes that assume that sequential
events, like quote arrivals, occur independently of one another.The number of arrivals between any two time points t and (t + t) is assumed to have a Poisson distribution. In a Poisson process, λ arrivals occur per unit time. In other words, the arrivals
occur at an average rate of (1/λ). The average arrival rate may be assumed to hold

constant, or it may vary with time. If the average arrival rate is constant, the probability of observing exactly k arrivals between times t and (t + t) is
1 −λτ
e
(λτ )k , k = 0, 1, 2,...
(9)
k!
Diamond and Verrecchia (1987) and Easley and O’Hara (1992) were the first
to suggest that the duration between subsequent ticks carries information. Their
models posit that in the presence of short-sale constraints, intertrade duration can
indicate the presence of good news; in markets of securities where short selling is
disallowed, the shorter the intertrade duration, the higher the likelihood of unobserved good news. The reverse also holds: in markets with limited short selling and
normal liquidity levels, the longer the duration between subsequent trade arrivals, the higher the probability of yet-unobserved bad news. A complete absence of
trades, however, indicates a lack of news.
Easley and O’Hara (1992) further point out that trades that are separated by a
time interval have a much different information content than trades occurring in
close proximity. One of the implications of Easley and O’Hara (1992) is that the entire price sequence conveys information and should be used in its entirety whenever
possible, strengthening the argument for high-frequency trading.
Table 4.3 shows summary statistics for a duration measure computed on all trades
recorded for SPY on May 13, 2009. As Table 4.3 illustrates, the average intertrade
duration was the longest outside of regular market hours, and the shortest during
the hour preceding the market close (3:00 to 4:00 p.m. ET).
The variation in duration between subsequent trades may be due to several other
causes. While the lack of trading may be due to a lack of new information, trading inactivity may also be due to low levels of liquidity, trading halts on exchanges,
P[(N (t + τ ) − N (t )) = k ] =

Intertrade Duration (milliseconds)
Hour (ET)

No. of Trades

Average

Median

Std. Dev.

Skewness

Kurtosis

4:00–5:00 a.m.

170

19,074.58

5,998

47,985.39

8.430986

91.11571

5:00–6:00 a.m.

306

11,556.95

4,781.5

18,567.83

3.687372

21.92054

6:00–7:00 a.m.

288

12,606.81

4,251

20,524.15

3.208992

16.64422

7:00–8:00 a.m.

514

2,995

11,706.72

4.288352

29.86546

3.775796

23.56566

8:00–9:00 a.m.

7,096.512

767

4,690.699

1,997

9:00–10:00 a.m.

1,089

2,113.328

1,934

10:00–11:00 a.m.

1,421

2,531.204

1,373

11:00–12:00 p.m.

1,145

3,148.547

1,526

4,323.262

3.240606

17.24866

749

4,798.666

1,882

7,272.774

2.961139

13.63373

12:00–1:00 p.m.

7,110.478
24,702.9
3,409.889

3.5185

24.6587

3.959082

28.53834

1:00–2:00 p.m.

982

3,668.247

1,739.5

5,032.795

2.879833

13.82796

2:00–3:00 p.m.

1,056

3,408.969

1,556

4,867.061

3.691909

23.90667

3:00–4:00 p.m.

1,721

2,094.206

1,004

2,684.231

2.9568

15.03321

4:00–5:00 p.m.

423

7.264483

69.82157

5:00–6:00 p.m.

6:00–7:00 p.m.

8,473.593
73,579.23
1,077,663

1,500

24,718.41

30,763

113,747.8

2.281743

7.870699

19,241

1,849,464

0.707025

1.5

High-Frequency Data

Table 4.3 Hourly Distributions of Intertrade Duration Observed on May 13, 2009, for SPY

High-Frequency Data

and strategic motivations of traders. Foucault, Kadan, and Kandel (2005) consider
that patiently providing liquidity using limit orders may itself be a profitable trading
strategy, as liquidity providers should be compensated for their waiting. The compensation usually comes in the form of a bid-ask spread and is a function of the waiting time until the order limit is “hit” by liquidity takers; lower intertrade durations
induce lower spreads. However, Dufour and Engle (2000) and Hasbrouck and Saar
(2002) find that spreads are actually higher when traders observe short durations,
contrasting the time-based limit order compensation hypothesis.
In addition to durations between subsequent trades and quotes, researchers have been
modeling durations between fixed changes in security prices and volumes. The time interval between subsequent price changes of a specified magnitude is known as price duration. Price duration has been shown to decrease with increases in volatility. Similarly, the
time interval between subsequent volume changes of a prespecified size is known as the
volume duration. Volume duration has been shown to decrease with increases in liquidity.
Using a variant of the volume-duration methodology, Easley, Lopez de Prado,
and O’Hara (2011) propose volume-based sampling of high-frequency data. In the
volume-based approach, the researchers define a clock unit as a “bucket” of certain
trade volume, say 50 futures contracts. The volume clock then “ticks” whenever the
bucket is filled. Thus, the 50-contract volume clock advances whenever 50 singlecontract trades arrive in sequence. The 50-contract volume clock advances twice
when a 100-contract trade is executed.
The information content of quote, trade, price, and volume durations introduces
biases into the estimation process, however. If the available information determines
the time between subsequent trades, time itself ceases to be an independent variable, introducing substantial endogeneity bias into estimation. As a result, traditional
estimates of variance of transaction prices are too high in comparison with the true
variance of the price series.
■■ Most High-Frequency Data Do Not

Contain Buy-and-Sell Identifiers

Neither Level I nor Level II tick data contain identifiers specifying whether a given
recorded trade was a result of a market buy order or a market sell order, yet some
applications call for buy-and-sell trade identifiers as inputs into the models. To overcome this challenge, four methodologies have been proposed to estimate whether a
trade was a buy or a sell from Level I data:
■■

Tick rule

■■

Quote rule

■■

Lee-Ready rule

■■

Bulk volume classification

The tick rule is one of the three most popular methodologies used to determine
whether a given trade was initiated by a buyer or a seller, in the absence of such

information in the data set. The other two popular methods are the quote rule and
the Lee-ready rule, after Lee and ready (1991). The newest method is the bulk volume classification (BVc), due to Easley, Lopez de Prado, and O’Hara (2012).
According to the tick rule, the classification of a trade is performed by comparing the price of the trade to the price of the preceding trade; no bid or offer quote
information is taken into account. Each trade is then classified into one of the four
categories:
■

Uptick, if the trade price is higher than the price of the previous trade.

■

Downtick, if the trade price is lower than the price of the previous trade.

■

Zero-uptick, if the price has not moved, but the last recorded move was an uptick.

■

Zero-downtick, if the price has not moved, but the last recorded move was a
downtick.

A. Uptick: The trade is classified as a buy
(initiated by a market buy order)

B. Zero-uptick: The trade is classified as a buy

Price

Trade

Price
Time
Time
C. Downtick: The trade is classified as a sell

Price

Trade

D. Zero-downtick: The trade is classified as a sell

Price
Trade

Time

FIGURE 4.10 An Illustration of the Tick rule, used to classify Trades into Buys and Sells

71
HIgH-FrEquENcy DATA

If the trade’s price differs from that of the previous trade, the last trade is classified as an uptick or a downtick, depending on whether the price has moved up or
moved down. If the price has not moved, the trade is classified as a zero-uptick or a
zero-downtick, depending on the direction of the last nonzero price change. According
to Ellis, Michaely, and O’Hara (2000), in 1997–1998, the tick rule correctly classified
77.66 percent of all Nasdaq trades. Figure 4.10 illustrates the tick rule.
The low proportion of correctly classified trades may be due to specifically to
regulatory issues in equities. For example, Asquith, Oman, and Safaya (2008) report
that the observed misclassifications are due at least in part to regulations requiring that short sales of stocks be executed on the uptick or zero-uptick (known as
the uptick rule), the rule the Securities and Exchange commission (SEc) repealed
in 2007. Because nearly 30 percent of equity trades are short sales, Asquith et al.
(2008) suggest that regulation-constrained short sales alone may be responsible for
the observed errors in trade classification. In the absence of short-sale constraints, all
of the preceding trade classifications are likely to be much more precise. On futures
data, free from the uptick rule, Easley et al. (2012) indeed find that the tick rule
delivers much higher accuracy in classifying trades into buyer initiated and seller

Price

Prevailing midquote
Best Offer

Trade
Best Bid
Best Bid

Trade is closer to the
prevailing bid, is classified
as buyer-initiated

Time

FIGURE 4.11 Example of the quote rule classification

HIgH-FrEquENcy DATA

initiated. According to Easley et al. (2012) calculations, the tick rule correctly classifies 86.43 percent of all trades of E-mini futures on the S&P 500.
The quote rule is another way to classify quotes also documented by Lee and
ready (1991) and Ellis et al. (2000). under this rule, a trade is a buy (sell) if the
trade price is above (below) the average of the bid and the ask quotes prevailing at
the time. If the trade price happens to be exactly at the midpoint of the prevailing
bid and ask, the trade is not classified. While the quote rule is used often and has
been shown to correctly classify 76.4 percent of all trades on Nasdaq (see Ellis et
al., 2000), the definition of prevailing quote may be subject to interpretation and can
potentially deliver a worse result than the tick rule. For example, Lee and ready
(1991) point out that quotes and trades are often reported out of sequence, making
determination of the prevailing quote difficult. Specifically, they show that with the
introduction of electronic books, quotes are often recorded ahead of the trades that
triggered them. They propose to mitigate this situation by using the quotes at least
five seconds ahead to classify trades. In 1991, five seconds was Nasdaq’s median delay
in reporting trades. However, the validity of the rule may have deteriorated over the
past two decades as markets gained considerable speed since Lee and ready’s study
was published. Figure 4.11 shows an example of the quote rule classification.
The so-called Lee-ready rule classifies trades first using the quote rule. The
trades occurring at the midpoint between the prevailing bid and ask quotes are not
classified under the quote rule, and are subsequently classified using the tick rule.
Once again, Lee and ready (1991) emphasize matching trades with quotes that occurred at least five seconds prior in order to avoid erroneous sequencing of quotes.
Dufour and Engle (2000) follow the five-second rule, while Ellis et al. (2000) object
to it, showing that the trade reporting delay may differ depending on the end user’s
system. Ignoring the five-second delay, Ellis et al. (2000) show that the Lee-ready
rule correctly classifies just 81.05 percent of all trades as either buy or sell-initiated,
a small improvement over the tick classification.

To further increase the accuracy of trade classification, Easley et al. (2012) propose
a methodology that produces a probabilistic estimate of a particular volume generated by a market buy or a market sell order. The rule, named bulk volume classification,
works as follows: for every unit of time or volume (a “volume bar,” say every 100 shares
traded), BVC assigns the probability of the observed volume being a buy as follows:
p −p 
Pr(Vτ = B) = Z  τ τ −1 
 σ∆P 

(10)

where:
Vτ is the total volume observed during time or volume interval τ .
Pτ − Pτ −1 is the price difference observed between the two subsequent time or
volume bars,τ −1 and τ .

σ P is the standard deviation of sequential time or volume-clock based price
changes.
Z is the pdf of a standard normal distribution.
The buyer-initiated trade volume can then be estimated as
(11)

According to the BVC, the probability of a specific volume’s being generated by a
market sell order then becomes:
p p 
Pr(Vτ = S ) = 1 − Pr(Vτ = B) = 1 − Z  τ − τ −1 
 σP 

(12)

And the respective size of the seller-initiated volume is then

 p p 
VτS = Vτ 1 − Z  τ − τ −1  
(13)
 σ P  

Easley et al. (2012) apply the BVC methodology to E-mini futures and show that
the BVC rule correctly classifies 86.6 percent of all trades when time bars are used,
and 90.7 percent of all trades when the volume clock is used instead of the timebased clock.
■■ Summary
Tick data differ dramatically from low-frequency data. Utilization of tick data creates
a host of opportunities not available at lower frequencies. A multitude of possible
sampling and interpolation techniques creates diverse angles for data exploration.

73
High-Frequency Data

 p − pτ −1 
B
Vτ = Vτ Z  τ

 σ P 

Various methods of organizing and interpreting the discreet ticks of data deliver different statistical properties of the resulting time series.
■■ End-of-Chapter Questions
1. What are the key properties of high-frequency data?
2. What types of data messages are most frequent?
3. What data sampling technique produces high-frequency time series most closely
fitting the normal distribution?
4. What are the key differences between the tick trade classification rule and quote
rule, Lee-Ready rule, and bulk volume classification rule?
5. Consider a trade executed at time t at 17.01, the best bid quote prevailing at
time t.The previous trade, executed at time t – 1, was executed at 17.00. Should
the trade at time t be classified as buyer initiated or seller initiated under the
quote rule? How should the trade completed at time t be classified under the
tick rule?

High-Frequency Data

Chapter 5

Trading Costs
T

rading costs can make or break the profitability of a high-frequency trading
strategy. Transaction costs that may be negligible for long-term strategies are
amplified dramatically in a high-frequency setting.
This chapter focuses on the transparent and implicit costs that impact high-frequency
trading.
■■ Overview of Execution Costs

According to classical finance, markets are seamless, that is, they possess the following
characteristics:
■■
■■

Markets are uniform in their structure.
Markets are consolidated; a price of a specific financial instrument is instantaneously updated wherever the instrument is traded.

■■

Prices immediately reflect all fundamental information.

■■

No transaction costs exist.

■■

Orders of all sizes can be executed instantaneously—markets are infinitely liquid,
with each price queue in the limit order book containing infinite number of limit
orders.

■■

Traders have unlimited borrowing power.

■■

No short-sale constraints exist.

■■

Market price is invariant to order size.

In real life, securities markets have frictions: prices incorporate information over
time, markets differ in their structure and depth, markets can be highly fragmented,
and issues like transaction costs further distort markets away from their textbookperfect models. Costs known prior to trading activity are referred to as transparent or

explicit, and costs that have to be estimated are known as latent or implicit. Likewise,
the transparent costs are known with certainty prior to trading, and implicit costs
are not known before trading takes place, yet implicit costs can be estimated from
the costs’ historical distribution inferred from the data of past trades.
■■ Transparent Execution Costs
Transparent execution costs are generally known ahead of trading; they comprise
broker commissions, exchange fees, and taxes. This section considers each of the
transparent costs in detail.

Broker Commissions
Brokers charge commissions for
■■
■■

Facilitating “best execution” of client orders: executing client orders according to
client specifications.
Serving as the opposite side, or counterparty, to clients’ orders in over-the-counter
(OTC) arrangements.

■■

Providing custody of assets.

Trading Costs

■■

Providing connectivity to exchanges, dark pools, and other trading venues.

■■

Clearing trades from their execution to settlement and reporting trading activity.

■■

Delivering leverage and margin to clients.

■■

Other custom services.

Some broker-dealers may charge their customers additional fees for access
to streaming market data and other premium information, such as proprietary
research. Paid-for broker research is becoming increasingly obsolete as customers
compete by retaining secrecy of their investment strategies. And while best execution presently accounts for a significant percentage of revenues for many brokers, clients with understanding of high-frequency data often choose to move away
from brokers’ best execution models, preferring to build their proprietary execution engines in-house instead. The latest best execution models are discussed in
Chapters 15 of this book.
Broker fees can be fixed per order or month, or variable per trade size, trade
value, or monthly volume. Broker commissions may also depend on the total
business the broker receives from a given firm, various trade “bundling” options,
and the extent of “soft-dollar,” or implicit, transactions that the broker provides
in addition to direct execution services. Broker commissions are negotiated well
in advance of execution. The differences in cost estimates from one executing
broker to another can be significant and are worth understanding to ensure favorable pricing.
Figure 5.1 shows the broker costs for metals trading offered by Interactive Brokers.

FIGURE 5.1 Broker Commissions on Metal Trading Offered by Interactive Brokers
Source: Interactive Brokers web site

exchange Fees

taxes
According to Benjamin Franklin, “in this world nothing can be said to be certain, except death and taxes.” Taxes are charged from the net profits of the trading operation
by the appropriate jurisdiction in which the operation is domiciled. High-frequency
trading generates short-term profits that are usually subject to the full tax rate, unlike investments of one year or more, which fall under the reduced-tax capital gains

77
TrAdINg COsTs

Exchanges match orders from different broker-dealers or electronic communication networks (ECNs) and charge fees for their services. The core product of every
exchange is the liquidity, or presence of open buy-and-sell interest, that traders are
looking to transact on the exchange.
Liquidity is created by open limit orders; limit buy orders placed at prices below
the current ask provide liquidity, as do limit sell orders placed at prices above the
current bid. Market orders, on the other hand, are matched immediately with the
best limit orders available on the exchange, consuming liquidity. Limit orders can
also consume liquidity; a limit buy placed at or above the market ask price will be
matched immediately with the best available limit sell, thus removing the sell order
from the exchange. similarly, a limit sell placed at or below the market bid price will
be immediately matched with the best available bid, as a market sell would.
To attract liquidity, exchanges may charge fees or pay rebates for orders consuming
liquidity or for orders supplying liquidity. As discussed in Chapter 3, exchanges that
charge for liquidity-removing orders and pay for liquidity-supplying orders are known
as normal exchanges. Exchanges that pay for orders that remove liquidity and charge
for orders that supply liquidity are called inverted. At the time this book was written,
most U.s. equity exchanges deployed rebates in either normal or inverted models.
selected exchange ECNs in other countries now also offer rebate-based programs.
Exchange fees and fees of other trading venues can also vary by order type. Complicated orders, such as hidden-size orders like iceberg orders, or algo-enabled orders,
like volume-weighted average price (VWAP) orders, carry associated cost premium.
Like broker commissions, exchange fees are negotiated in advance of execution.

umbrella in most jurisdictions. A local certified or chartered accountant should be
able to provide a wealth of knowledge pertaining to proper taxation rates. Appropriate tax rates can be determined in advance of trading activity.
Proposals to tax individual trading transactions surface and fade over time, with
most jurisdictions deciding against transaction taxes in the long run. Aldridge
(2012b) estimates that a 0.05 percent tax imposed on every transaction of IBM
stock, for example, is likely to wipe out as much as one third of trading volumes,
ultimately resulting in severe contractions of economic growth.
■■ Implicit Execution Costs
At the tick level of data, transparent costs are being increasingly dominated by implicit costs of the opportunity cost of investment, the bid-ask spread, latency or
slippage, and related market impact. Additional implicit costs tracked by researchers
and traders include the costs of price appreciation and market timing.

Bid-Ask Spreads

Trading Costs

Bid-ask spreads are not known in advance. Instead, they are stochastic or random
variables that are best characterized by the shape of the distribution of their historical values.
The bid-ask spread is the difference between the best ask and the best bid at any
given point in time, and represents the cost of instantaneous liquidation of a trading
position. The spread can also be seen as the premium paid by traders desiring immediate execution via market orders. On the flip side of the argument, the spread
is the compensation paid to the patient traders providing liquidity through limit
orders. The limit order traders take considerable risk of entering a losing position in
the markets, the risk that increases with market volatility. As a result, limit traders’
compensation also has to rise in times of higher uncertainty, a fact reflected in variability of the bid-ask spread in relation to volatility. Bid-ask spreads are discussed in
detail in Chapter 4.

Slippage or Latency Costs
Latency cost, commonly known as slippage, is the adverse change in the market
price of the traded security that occurs from the time an investment decision is
made until the time the trade is executed. Slippage often accompanies market
orders and refers to the difference between the best quote observed by the trader
immediately prior to placing the order and the realized market price. The following example illustrates the concept of the latency cost or slippage. The trading
strategy identifies a stock (e.g., IBM) to be a buy at $56.50, but by the time the
market buy order is executed, the market price moves up to $58.00. In this case,
the $1.50 differential between the desired price and the price obtained on execution is the cost of latency.

In the media, slippage is often portrayed as the evidence of the great divide between the haves and have-nots of the technological arms race. In reality, slippage is
not solely dependent on the speed of trading activity. Instead, slippage is also a direct
function of the a) liquidity available in the market and b) the number of market orders
that have arrived to consume that liquidity. When many market participants simultaneously place market orders, the orders erode the finite liquidity and move the market price at high speeds in the process, as Figure 5.2 illustrates. As a result, slippage
is typically larger during periods of high trading activity, for example, at market open
t = 12:13:01:005614:Algorithm A observes best bid and best offer and places a market sell order.

Best bid

Best ask = best offer

Bid-ask spread

Price

t = 12:13:01:005616: Alarge market sell order placed earlier by algorithm B arrives at the trading
venue’s matching engine.

A large market sell order
sweeps the bids in the book,
realizes lower aggregate price,
changes best bid

t = 12:13:01:005618: A market sell order placed earlier by algorithm C arrives at the trading venue’s
matching engine.

TrAdINg COsTs

Another market sell order changes best bid

t = 12:13:01:005625: The market sell order placed by algorithm A finally arrives at the trading
venue’s matching engine, is executed at a much lower best bid than the one observed 11
microseconds earlier.

Market sell order sent by algorithm A

FIGURE 5.2 slippage Illustration

and market close times, as well as times immediately following major macroeconomic announcements. The activity of other market participants can be forecasted in
a probabilistic framework in the context of market impact, discussed next.
Still, latency due to technology alone can have a substantial impact on traders’
performance. Stoikov and Rolf (2012), for example, find that ultra-fast trading infrastructure delivers significant profitability under certain forecasting assumptions.
Specifically, Stoikov and Rolf (2012) define cost of latency as the expected value
of dollar-denominated savings resulting from executing with slow and fast (lowlatency) infrastructures:
COL =

Trading Costs

[St+l − St]

(1)

where St+l is the price obtained at time t with latency l and St is the price obtained on
the same financial instrument at the same time t when latency l approaches zero. The
authors observe that the cost of 10 milliseconds of communication delay is about
twice that of an algorithm configured to run on only 1 millisecond of latency. In
turn, 100 milliseconds of latency result in threefold latency cost as compared to that
of an algo using 1 millisecond execution latency. An algorithm using infrastructure
with a delay of 1 minute incurs an associated cost of four times greater than the algorithm with just 1 millisecond latency.
The shortcomings of technology resulting in latency costs may or may not reside
in the trader’s domain. Specifically, latency can occur in any of the following nodes
of order routing:
1. Trader’s systems. Slow systems and network architecture cause delays in processing
and interpreting quotes.
2. Networks. Congestion and interruptions in network communications may disrupt
timely execution and can delay transmission of orders. In addition, geographic
differences between the location of the trader’s servers and the location of the
execution venue can cause latency by virtue of physical communication delays.
Distances increase the time each quote or trade has to travel to their destinations, increasing trading latency. Latencies between major financial centers of
the world are reported in Chapter 2. Co-location and private network connections with trading venue servers may help alleviate these issues.
3. Broker-dealers. Delays in broker-dealer routing engines prompted innovations of
direct market access.
4. Execution venues. Execution venues may experience overloads of simultaneous
orders resulting in an order-processing backlog and subsequent delay in execution. Such situations most often occur in high-volatility environments.
While latency costs are random and cannot be known with precision in advance of a
trade, distribution of latency costs inferred from past trades can produce the expected
cost value to be used within the trading strategy development process. Fast infrastructure, backup communication systems, and continuous human supervision of trading
activity can detect network problems and route orders to their destinations along alternative backup channels, ensuring a continuous transmission of trading information.

Price Appreciation and Timing Risk Costs
Both price appreciation and timing risk costs describe market risk incurred during
execution of a large position broken down into a series of child orders (see Chapter 15
for a discussion of child orders).
The price appreciation cost refers to the forecasted loss of investment value during the execution of a large position. The timing cost refers to random, unforecasted
price movement ahead of execution of a child order.
The following EUR/USD trade illustrates the concept of a price appreciation
cost. A trading strategy determines that EUR/USD is undervalued at 1.3560, and
a buy order of $100 million EUR/USD is placed that must be executed over the
next three minutes. The forecast turns out to be correct, and EUR/USD appreciates
to 1.3660 over the following two minutes. The price appreciation cost is therefore
50 bps per minute. The price appreciation cost is due to the fundamental appreciation of price, not the trading activity in EUR/USD.
The cost of timing risk describes by how much, on average, the price of the traded
security can randomly appreciate or depreciate within 1 second, 10 seconds, 1 minute, and so on from the time an investment decision is made until the market order
is executed. The timing risk cost applies to active market timing activity, usually
executed using market orders. The timing risk cost does not apply to limit orders,
where the execution price is fixed.

The opportunity cost is the cost associated with inability to complete an order. Most
often, opportunity cost accompanies limit order–based strategies, when the market
price does not cross the specified limit price. However, market orders can also fail to
execute, for example, when the market does not have the liquidity sufficient to fulfill
the order. On a U.S. equity exchange, a market order may fail to execute when the
exchange does not have the limit orders posted at the National Best Bid and Offer
(NBBO), as discussed in Chapter 3. The opportunity cost is measured as the profit
expected to be generated had the order been executed.

Market Impact Costs
Market impact cost measures the adverse change in the market price following an
order. Market impact is rapidly becoming the dominant transaction cost. In equities,
according to the ITG Global Trading Cost Review (2010), market impact consumed
0.387 percent of the total dollar amount traded. Per report, the total amount of
trading costs averaged 0.476 percent of turnover, with only 0.089 percent of the
dollar volume spent on commissions. These figures were comparable in the U.S., EU,
U.K., and Japanese equity markets; higher transaction costs were reported in emerging markets. In futures, both market impact and transaction costs appear lower, yet
market impact costs still dominate: according to Aldridge (2012c), market impact observed in Eurobund futures (FGBL) on Eurex is 0.020 percent of the dollar volume.

81
Trading Costs

Opportunity Costs

Institutional transaction costs in the futures and forex markets tend to be in the $5 to
$10 per every $1 million volume traded, or 0.0005 to 0.0010 percent of executed
dollar volume. This section considers the cause and estimation of market impact.
■■ Background and Definitions

Trading Costs

All trades and orders convey information. The mere fact that a trader is placing his
own money or reputation on the line to bet on a particular direction of the market
informs other market participants of the trader’s belief.
The information contained in a trade observation is much more potent than that
in an opinion of a news analyst. Analysts are typically compensated via a salary, often
irrespective of whether their prognoses come true. At the same time, traders are
usually compensated via a percentage of profits they derive from their trading, with
each trade having direct implications on the trader’s welfare. As a result, trades are
viewed as potent signals about beliefs of impending market moves. The larger the
order, the more credible the trading signal.
Both aggressive and passive orders (market orders and limit orders) are credible
signals—market orders are commitments to buy or sell a security immediately at the
best market price, and limit orders are commitments to buy or sell at a predefined
price when the opposite market trade is available. As such, both market orders and
limit orders emit market impact. Unlike market orders, however, limit orders can be
canceled. As a result, limit orders make less credible signals than market orders, and
the intensity and even the direction of market and limit orders may differ.
The idea of an order as a credible signal was first published in 1971. The thought
of signaling in the markets was so revolutionary at the time that the author of the
research dared to publish the theory only under an assumed name, Bagehot, after a
famous English nineteenth-century journalist covering topics in economics.
The mere existence of market impact runs against core principles of classical
finance. In the idealized financial world, under the concept of market efficiency,
considered to be the optimal steady state in most classical asset pricing models, the
following conditions are assumed to hold:
■■

Everyone simultaneously receives the same information.

■■

Everyone interprets information in identical way.

■■

Only the fundamental information, such as earnings announcements or interest
rates, affects security prices. Past price trends and other nonfundamental information has no relevance to security prices.
All the relevant information is impounded into prices immediately upon
information arrival, resulting in a sharp step function of security prices moving
from one fundamental level to the next. Trades themselves carry no information,
as all the information is already contained in prices. Figure 5.3 illustrates the
perfect markets’ response to an arrival of positive fundamental news, as well as to
periods without any news arrivals.

Price

A market buy order carrying fundamental info
arrives here.

Time

Price

Time
A market buy order without fundamental information arrives
here.

FIGURE 5.3 Classical Finance View on How Perfect Markets Incorporate Fundamental

Information

■

Market buy orders are on average followed by a rise in prices of the traded securities, while market sell orders on average result in lower prices.

83
TrAdINg COsTs

In reality, traders interpret news differently, a result of divergent investment
horizons, education, effort and experiences. On the subject of the impending
price movement, opinions of long-term investors are likely to differ from those
of short-term investors (see Hasbrouck, 1991, for example), a fact that has allowed both short-term and long-term investors to coexist without eating each
other’s proverbial lunch. similarly, investors deploying technical market analysis
disagree with quants and fundamental analysts. Traders poring over the information 15 hours a day are also likely to have an opinion different from a casual
investor briefly analyzing his mutual fund statements only quarterly. Finally, a
seasoned professional may have a point of view divergent from that of a newbie.
All of these factors contribute to the markets’ deviation from idealized conditions, and make trades and even orders able to carry information to other
market participants.
In addition, most information is impounded into prices gradually, as first noted
by Kyle (1985), and not instantaneously, as the study of classical finance would
prefer. Every trade is a result of a buy order meeting a sell order. Often, a trade
is a product of one market order meeting an opposing limit order, although two
price-meeting limit orders of opposite direction may also be matched to form a
trade. A trade is a product of opposing forces: supply and demand, and, in theory,
each trade does not move the markets much. In the short-term reality, however,
the opposite holds:

■

TrAdINg COsTs

Limit buy-and-sell orders also generate a market impact in anticipation of a future
trade (see Harris, 1997; Parlour and seppi, 2007; Boulatov and george, 2008; and
rosu, 2010). As a result, limit orders have also been shown to be followed by a
persistent price change (see Eisler, Bouchaud, and Kockelkoren, 2009; and Hautsch
and Huang, 2011). While a completed trade is an irreversible and most credible
signal, limit orders are cancelable indications of trading interest, and, as a result,
are smaller in magnitude than that for market orders. Hautsch and Huang (2011)
and Aldridge (2012c) estimate the market impact of a limit order to be about
25 percent of that of a similar market order. The direction of the price change following a limit order may be reversed relative to that of a comparable market order,
depending on how far is the limit order price away from the market price.

Figure 5.4 illustrates gradual adjustment of prices in response to positive news
and no news observed in actual trading conditions. When positive news arrives, the
market price tends to overshoot its fundamental level, with the overshoot component gradually settling or decaying to its fundamental level.
Information leakage accompanying orders and trades is hardly new: for years,
broker-dealers and other market participants with access to tick-level data competed
on being able to “read the ticker tape” and infer short-term price forecasts from that.
By continuously watching the ticker tape, manual market makers would learn the
information content of trades and adjust their quotes according to their short-term
predictions—in the process resembling a manual variant of today’s high-frequency
trading. As markets become increasingly computerized, however, the ticker tape is
moving increasingly fast, and it is now literally impossible for a human eye to parse
ticker-tape information in real time.

Price

Temporary
Market impact

Time
A market buy order carrying fundamental info
arrives here.

Price

Temporary
Market impact

Time
A market buy order without fundamental information arrives
here.

FIGURE 5.4 Price reaction to Trades Observed in real Life

This phenomenon of real-life price changes following news and orders is known
as market impact (MI). MI can be attributed to several factors including:
■

■

In the trading world with heterogeneous traders possessing different beliefs and
information, MI is the negotiation or tâtonnement process via which traders’ information and beliefs are impounded into the security prices.
Both market and limit orders represent traders’ commitments of money and reputation, and therefore form credible signals to other market participants who may
choose to trade in the same direction.
Every market buy (sell) order temporarily depletes liquidity supply on the ask
(bid) side of the order book, driving the next market buy (sell) order to be
matched against a higher (lower) best available limit order price.

■ Estimation of Market Impact

Event: Incoming market order,
either a buy or a sell
Previous
trade(s)

t-2

Trade
resulting
from order
execution

Last trade
prior to the
order
t-1

Pretrade impact

Posttrade impact

FIGURE 5.5 Estimation of Market Impact for an Order Arriving at an Exchange at Time t*

85
TrAdINg COsTs

The metric of MI answers the question, “How much would the trader move the price
if he were to make the trade?” Figure 5.5 illustrates the MI determination for a single
order. The impact of the order incoming to the exchange at time t*, for example,
can be measured as the price change observed after time t* relative to the last trade
price recorded before t*, as illustrated in Figure 5.5. The selected postorder reference trade time t can be measured in clock time, trade time, tick time, or volume
time. In clock time, time t is selected as x time units, say 10 seconds, post order
arrival time t*. In trade time, the MI is measured y number of trades following the
order observed at t*. In tick time, the impact is computed z ticks, quote revisions or
trades, past the order. Finally, in volume time, the impact is measured when the aggregate trade volume following the order of interest reaches at least V trading units
(e.g., shares or contracts). Tick-time and trade-time MI is computationally easier to
estimate than clock-time or volume-time impact.
While the exact impact following a future trade can never be known in advance of the
trade, the expected MI can be estimated using historical data and trade-specific characteristics. The logic for estimating expectation of MI is similar to the logic used to forecast
price levels: while the exact future price can never be pinpointed with full precision,

TrAdINg COsTs

an expectation of the future price can be formed based on some auxiliary metrics. The
expected MI can be measured in an event-study framework using recent historical data.
MI can turn a profitable strategy into a losing one. A strategy that relies on repeating trades, for example, may be distorted by MI, with sequential trades obtaining
much worse prices than expected.
As noted earlier, MI is a function of order size: the larger the trade, the more
credible the information conveyed by the trade, the higher the impact the trade
generates. The exact evolution or functional form of MI is important: a trader can
increase the size of his investment while remaining profitable when the MI grows
slowly with trade size (see Farmer, gerig, Lillo, and Waelbroeck, 2009). glosten
(1987) and Easley and O’Hara (1987) were the first to note that MI can be broken down into two distinct functional parts: permanent and temporary MI. Permanent MI impounds fundamental information into prices in a manner consistent with
the classical financial theory and the efficient market hypothesis (see Fama, 1970).
Temporary MI is the noise component that first overshoots the fundamental price
level and then decays with time until the fundamental price level is reached.
The precise shapes of permanent and temporary MI functions have been subjects
of competing theories. Breen, Hodrick and Korajczyk (2002) and Kissell and glantz
(2002), for example, suggested that MI is a linear function of the order size (MIt ∝
Vt*).Lillo, Farmer, and Mangegna (2003), however, detected a power law specification ( MIt ∝ (Vt* )β ). The latest research on the topic (see Huberman and stanzl,
2004; and gatheral, 2009), however, reconciles the linear and power-law specifications by finding an order-size-based linear relationship for the permanent MI and
time-based power-law decay for temporary impact, as shown in Figure 5.6.
For market orders, the MI appears strongly concave in the order size, and the
signs of market orders are autocorrelated in time: market buy orders tend to follow other market buy orders, and vice versa. A model unifying the preceding facts
expresses the MI function as follows (Eisler, Bouchaud, and Kockelkoren, 2009):
p
t = ∑ [G(t,t* ) t* (v * )θ +n * ] + p∞
t
t
t*< t
Permanent market impact
Permanent market impact

Order size
Order size
Temporary market impact:
a power decay in time alone
Temporary market impact:
a power decay in time alone
Time
Market buy order
Time

FIGURE 5.6 Functional Form of Market
Marketbuy
Impact:
orderPermanent and Temporary Components

(2)

where:
vt is the volume of the trade at time t*
*

t is the sign of the trade at time t*
*

nt is the independent noise term that models any price change not induced by news
*

G(t, t*) is the propagator function, which describes, on average, how prices
respond to a single trade over time; G(t, t*) decays with time
The MI of an individual order recorded at time t* is then

MIt * = G(t,t * )t (vt )θ + nt
*

(3)

The MI propagator function G(t, t*) has to decay with time, and in a specific way, to
satisfy the high autocorrelation of direction of subsequent trades. If G did not decay,
price returns would be proportional to the signs of the trades and returns would
be highly autocorrelated in time. According to Eisler, Bouchaud and Kockelkoren
(2009), G decays as follows:
G(t,t * ) ~ |t − t * |− β

(4)

C( l ) = (tt + l ) ~ ( l )−γ

(5)

G(t, t*) further has the following boundary properties:

∂pt
(6)
∂ξt
where ξt = ∈tvtθ~N(0,σ) is normally distributed with mean zero and standard
deviation σ.
In addition to trade size and time, however, MI has been empirically shown to
depend on other variables. In equities, MI has been shown to depend on:

(

)

G t → t* =

■■
■■

■■

Intertrade durations (see Dufour and Engle, 2000)
Stock-specific characteristics, such as industry and earnings of the issuing company (see Breen, Hodrick, and Korajchyk, 2002; Lillo, Farmer, and Mantegna,
2003; and Almgren, Thum, Hauptmann, and Li, 2005)
Volatility and spread (Ferraris, 2008)
In futures, MI has been found to vary with:

■■

Liquidity (see Burgardt, Hanweck, and Lei, 2006)

■■

Intertrade durations and volatility (see Aldridge, 2012c)

87
Trading Costs

where = 1 − γ , and γ <1 is the decay parameter in the correlation of subsequent trade
2
signs:

The size and the direction of MI of a limit order has been found to depend
on the size of the order as well as on the order’s proximity to the best quote on
the opposing side of the market. For buy limit orders placed on Nasdaq within
the spread (see Hautsch and Huang, 2011, for details), orders than went on
to be matched with the best ask experienced a positive MI, just as market buy
orders would. Buy limit orders placed within the spread that became the best
bid quotes on average experienced a negative MI of the size comparable to that
of the orders matched with the best ask. The MI of a limit buy order that was
posted inside the spread and became the best bid, however, varied with the size
of the order:
■

■

small-sized buy limit orders, with a size matching the depth at the bid, placed
inside the spread that became best bids were on average followed by negative MI.
Midsized (seven times larger than depth at the bid) were followed by a small
positive MI, about 20 percent of the absolute MI experienced by small orders.
Large orders (15 times larger than depth at the bid) were followed by a medium
positive MI, about 50 percent of the absolute MI experienced by small orders.
Figure 5.7 summarizes the findings.

■ Empirical Estimation of Permanent Market Impact

Data preparation
MI can be estimated using both Level I and Level II tick data, as well as data containing trade stamps only. Level II data allow one to precisely pinpoint arrivals of limit
and market orders: an increase in the aggregate size at a specific price level on the
bid size indicates an arrival of a limit buy order. A decrease in the top-of-the-book
liquidity on the bid side indicates an arrival of a market sell order.
5

4.5

5.5

4
3.5
3
2.5
2

1.82

1.5

Buy LO→Ask
Buy LO→Bid
Permanent Impact

1
0.5
0

10
15
Event time

Quote Change (Basis Point)

TrAdINg COsTs

5.37

4.84

4.5
4

Small buy LO→Bid
Mid buy LO→Bid
Big buy LO→Bid
Permanent Impact

3.5
3
2.5
2
1.5

1.82
0

5 10 15 20 25 30 35 40 45 50
Event time

FIGURE 5.7 Market Impact of Limit Orders Observed on Nasdaq
Source: Hautsch and Huang (2011)

When using Level I or trade data, however, one comes across the challenge of
separating buyer- and seller-initiated orders and trades. Over the years, researchers
have developed several methodologies to separate buys and sells: tick, quote, Leeready, and bulk volume classification, discussed in detail in Chapter 4.

Basic estimation Model
data points separated into buys and sells are ready for estimation of permanent MI.
Under the assumption of linear functional form, the permanent MI can be estimated
using a linear regression with the following specification:

∆Pt,τ = ατ + βτ Vt + βτ −1Vt +1 +…+ β1Vt +τ −1 + ε t,τ

(7)

where t is the time of the trade, τ is the number of posttrade ticks or time units in
the event window at which the trade impact is measured, Vt is the size of the trade
observed at time t, and ∆Pt,τ is the normalized price change from time t to time τ
and can be expressed as shown in equation (8):

∆Pt,τ = ln( Pτ ) − ln( Pt )

(8)

 estimated five trade ticks following each
 and β
Figures 5.8 and 5.9 show α
5
trade on tick data of every trading day in 2009 and 2010 for Eurobund futures
(FgBL), per Aldridge (2012c). As Figure 5.8 and 5.9 show, buyer-initiated trades
5

x 10-5

Buys, Daily Intercept, Post-Trade

1.5

0.5

T-Statistic

Coefficient

Intercept, 5-ticks Post-Trade

0
January 2009

0
December 2010
Date

 5 of Model (7) Estimated on Buyer-Initiated Trades in Eurobund
FIGURE 5.8 daily Intercept α

Futures, 2009–2010

TrAdINg COsTs

2.5

Buys, Daily Size Coefficient, Post-Trade

x 10-7

-1
January 2009

T-Statistic

Coefficient

Size Coefficient, 5-ticks Post-Trade

-5
December 2010
Date

 of Model (7) Estimated on Buyer-Initiated Trades in
FIGURE 5.9 daily size Coefficient β
5
Eurobund Futures, 2009–2010

TrAdINg COsTs

90
display the following properties. The 5-tick market impact of buy trades exhibits
 often reach 10,
very strong positive dependency on trade size: the t-statistics of β
5
as shown on the right axis of Figure 5.9, indicating that the dependency on trade size
is 99.999 percent statistically significant. While the MI’s dependency on trade size is
 , is small: as the left
highly persistent, the actual value of the coefficient estimate, β
5
−7

axis shows, β 5 is on the order of 10 , in other words, for every 100 contracts of
Eurobund futures traded, the futures price directly attributable to the trading size on
average rose by only 0.001 percent five ticks after each trade. The observed results
are largely invariant from one day to the next, with clear exceptions at the end of
each quarter when the statistical significance of the estimates appears to dip to zero,
possibly due to regular rollovers of futures.
 , the average increase in FgBL price obFigure 5.8 plots daily estimates of α
served following buyer-initiated trades that cannot be attributed to trade sizes. As the
α value (left) axis in Figure 5.8 shows, the average size-independent component of
price increase following buy trades is on the order of 10−5, or about 100 times larger
than the price change attributable to trade size. As such, the size-independent market impact dominates size-dependent impact for trades under 100 Eurobund futures
contracts, resulting in the following Eurobund-futures specific feature: FgBL trades
of 1 or 100 contracts incur comparable market impact! Trades larger than 100 FgBL
contracts, however, generate substantial size-dependent impact. The observed size is highly statistically persistent, with accompanying t-ratios
independent impact α
ranging from about 5 to 20, as the right axis of Figure 5.8 notes. seller-initiated
5

trades incur a similar scale of market impact, yet in the opposite direction, as Figures
5.10 and 5.11 show.
0.5

Sells, Daily Intercept, Post-Trade

x 10-5

Intercept, 5-ticks Post-Trade
0

-0.5

-5

-1

-10

-1.5

-15

-2

-20

-2.5
January 2009

-25
December 2010
Date

 5 of Model (7) Estimated on seller-Initiated Trades in Eurobund
FIGURE 5.10 daily Intercept α

x 10-7

Sells, Daily Size Coefficient, Post-Trade

Sell Coefficient, 5-ticks Post-Trade

-2

-10

-4

-20

-6
January 2009

-30
December 2010

 of Model (7) Estimated on seller-Initiated Trades in
FIGURE 5.11 daily size Coefficient β
5

Eurobund Futures, 2009–2010

91
TrAdINg COsTs

Futures, 2009–2010

The statistical meaningfulness, or the explanatory power, of model in the equation (7) applied to buyer-initiated trades is quite low, however, as measured by the
adjusted r-squared of the model and ranging from 1 to 2 percent, as Figure 5.12
illustrates. To put the 1 to 2 percent adjusted r-squared in perspective, though, one
needs to consider the adjusted r-squared on predictive power of generalized autoregressive conditional heteroskedasticity (gArCH), a popular volatility estimation
model used in many commercial applications. The r-squared of predictive power
of gArCH usually hits only about 5 percent. In other words, while the r-squared
of the model of equation (7) is quite low in principle, it is comparable to r-squared
estimates of other popular models.
 in
The strong significance of the intercept α
the model of equation (7) invites questions about what kind of additional variables,
 . Commercial models for
if any, can help the unexplained variation captured by α
estimation of market impact often deploy additional explanatory variables, such as the
observed spread, short-term volatility, and intertrade durations.To analyze the potential impact of these variables, one can extend the model of equation (7) as follows:

Additional Explanatory Variables

∆Pt,τ = ατ + βV ,τ Vt + βσ ,τ σ t + β S,τ S t + βT ,τ T t + ε t,τ

(9)

where:

TrAdINg COsTs

■

As before, ∆Pt,τ represents the τ-tick change in price,
∆Pt,τ = ln( Pτ ) − ln( Pt −τ )

0.03

(10)

Buys, Adj. R-squared, Size Regression, Post-Trade

0.025

0.02

0.015

0.01

0.005

0
January 2009

December 2010
Date

FIGURE 5.12 Explanatory Power of the Linear Market Impact Estimator of Equation (7)

■■
■■

Vt denotes the size of the trade recorded at t
σ t is the estimate of short-term volatility, and can be measured in several ways,
as standard deviation, or as a log change of high and low prices during a predefined
pretrade period beginning τ* ticks before the trade tick t, as first suggested by
Garman and Klass (1980):

(

) (

)

σ t = ln PHigh,[t −τ *,t −1] − ln PLow,[t −τ *,t −1]
■■

S t is the average spread observed during the τ* ticks preceding each trade. In data
containing quotes, the average spread is the mean difference between the best offer and the best bid:
st =

■■

1 t −1
∑ Ask j − Bid j
τ − 1 j=t −τ

(12)

When quote data is unavailable, the average effective spread can still be estimated
by assuming that sequential price changes occur at intervals equal to the effective
spread. Such an assumption generally holds true whenever a buy follows a sell and
vice versa, as the market buy is executed at the best ask, and the market sell hits
the best bid. The resulting expression for the average effective spread is shown in
equation (19), an approximation noted by Aldridge (2012c):
(13)

Finally, T t is the average clock time between every two subsequent trades:
Tt =

1 t −1
∑ t j − t j−1
τ − 1 j=t −τ

(14)

Aldridge (2012c) estimates equation (9) in FGBL data. In FGBL, the additional
explanatory variables influence the resulting market impact, but do not eliminate
the statistical significance of the intercept, or change the value of the trade size
coefficient, βV,τ. The impact of intertrade durations, T t, is consistent with that
described by Dufour and Engle (2000): MI is lower when average intertrade durations are shorter. According to Dufour and Engle (2000), the observation is likely
due to the following: shorter intertrade durations allow more gradual impounding
of information into prices, resulting in lower price changes in response to each
trade.
Causality The estimates of MI coefficients obtained from models of equations (7)
and (9) can be questioned from the following perspective: since MI is measured several ticks after each trade, is it possible that other trade ticks determine the impact
and its relationship with trading volume? For example, could the size of a trade truly
impact the size and directions of the following trades, which in turn would exaggerate market impact and make it appear dependent on the original trade size, instead
of the follow-up trade sizes?

93
Trading Costs

1 t −1
st =
∑ |ln(Pj ) − ln(Pj−1)|where Pj ≠ Pj−1
τ − 1 j=t −τ
■■

(11)

To answer these questions, one can deploy the so-called vector autoregressive
(VAR) model (different from value-at-risk,VaR, model), first proposed by Hasbrouck
(1991), and later extended by Dufour and Engle (2000).The VAR model answers the
following key cause-and-effect question: does MI influence direction of subsequent
trades, or does direction and size of trades influence MI to a greater degree? In addition, the VAR model allows us to test for auxiliary effects, such as any persistent
irregularities during different times of day.
The Dufour and Engle (2000) specification of the VAR model that ascertains causality within five ticks from the time of each trade can be written as follows:
5

j =1
5

t =8
18

j =0
5

j =1

t =8

j =1

∆Pt = ∑a j ∆Pt − j + ∑γ t Dt,i + ∑b jQ i− j + ε i

(15)

Q i = ∑c j ∆Pt − j + ∑δ t Dt,i + ∑d jQ i− j + ϑi

(16)

where
Ri is the instantaneous market impact following a trade tick i, calculated as a onetick log return, that is, as a difference of logarithms of the price of tick i, and the
price of the previous trade tick i-1.

Trading Costs

∆Pt = ln( Pt ) − ln( Pt −1 )

(17)

Qi is the direction of the trade i, with Qi =1 when a trade is a result of a buy
market order, and Qi =−1 for seller-initiated trades
Dt,i is a “dummy” variable indicating the hour of the day:

1, if trade i occursin hour t
Dt,i = 

0,otherwise
bj and dj, in turn, are functions of trade size:

(18)

b j = α j + β jln(Vj )

(19)

d j = θ j + ρ jln(Vj )

(20)

Equation (15) measures dependency of posttrade one-tick MI Ri on the following
data: lagged one-tick market impact of five preceding trades, time of day when each
trade occurred, contemporaneous and lagged direction of five preceding trades, Q,
and the product of contemporaneous and lagged trade direction and trade size QV.
Equation (16) considers how well the same explanatory variables predict the direction of the next trade. In other words, equation (16) considers whether the past
five one-tick returns, time of day, directions and sizes of the previous five trades can
predict the direction of the impending trade.
Tables 5.2 and 5.3 show results of estimation of equations (15) and (16), respectively, on Eurobund futures data for May 6, 2009, a regular trading day exactly one

Table 5.2

Results of OLS Estimation of VAR model, Equation (15), on Eurobund futures
(FGBL) Trade Tick Data for May 6, 2009 Ri

Independent Variable: Ri−j

Independent Variable: Q i−j

Independent Variable: Vi Q i−j

α0

4.1 E-05 (67.4)

β0

1.9 E-07 (25.9)

0.347 (71.1)

α1

–1.3 E-05 (–18.6)

β1

8.5 E-09 (1.0)

0.151 (29.0)

α2

–2.8 E-06 (–3.9)

β2

2.7 E-08 (3.5)

0.080 (15.2)

α3

2.7 E-06 (3.8)

β3

2.5 E-08 (3.2)

0.061 (11.8)

α4

7.7 E-06 (11.0)

β4

8.4 E-09 (1.0)

–0.306 (-62.5)

α5

–2.4 E-05 (–37.6)

β5

–1.1 E-07 (–14.8)

Adj. R2 = 46.25%
Dependent variable is the one-tick return, Ri. T-statistics are reported in parentheses, bold-font values represent statistical
significance of 99.999 percent and higher. Source: Aldridge (2012d).

Table 5.3 Results of OLS Estimation of VAR Model, Equation (16), on FGBL Trade Tick Data
for May 6, 2009 Qi
Independent Variable: Ri−j

Independent Variable: Q i−j

Independent Variable: Vi Q i−j

–841.5 (–18.1)

θ1

0.462 (75.8)

ρ1

2.0 E-04 (2.8)

–94.1 (–1.8)

θ2

0.163 (24.6)

ρ2

1.6 E-04 (2.1)

184.5 (3.6)

θ3

0.068 (10.1)

ρ3

1.4 E-04 (1.9)

55.7 (1.1)

θ4

0.032 (4.7)

ρ4

1.3 E-04 (1.8)

–10.2 (–0.2)

θ5

0.010 (1.7)

ρ5

2.4 E-04 (3.3)

Adj. R2 = 39.29%
Dependent variable is trade direction, Q i. T-statistics are reported in parentheses and bold-font values represent statistical
significance of 99.999 percent and higher. Source: Aldridge (2012d).

95
Trading Costs

year prior to the “flash crash.” As shown in Table 5.2, instantaneous MI is indeed
determined by MI accompanying previous trades, contemporaneous and lagged
trade sign, and concurrent trade size. Trade sizes of previous trades have shown to
produce little impact on future MI. The hourly dummy variable measuring the effects of the time of day was statistically significant only for the 10 to 11 GMT time
period. The trades executed between 10 and 11 GMT had a lower market impact
than trades executed at other hours of the day. This could, potentially be due to price
trending in response to macroeconomic news. Interestingly, the explanatory power
of the regression, measured by Adj. R2, was 46.25 percent—a substantial figure.
As Table 5.3 shows, neither the trade size nor the market impact generated by past
trades (except the most recent trade) play a significant role in determining direction
of upcoming trades. Instead, the direction of the subsequent trades is almost entirely
determined by the direction of immediately preceding trades, buy or sell, independent of the size of those trades or the market impact each of the preceding trades
generates. Specifically, according to the estimates presented in Table 5.3, on May 6,
2009, an FGBL trade immediately following a buy had a 46.2 percent likelihood of
also being a buy; while a trade following two consecutive buys had a 62.5 percent
probability of being a buy. A trade following three consecutive buys was 69.3% likely
to be buyer initiated, and after four sequential buy trades, the probability of observing a buy rose to 72.5 percent, a large number. The hourly dummy in the trade

sign equation happened to be only significant from 16 to 17 GMT (11:00 a.m. to
noon ET). The hourly dummy from 16 to 17 GMT was positive, indicating a preponderance of buy FGBL trades during that hour on May 6, 2009. As with the estimates of the return equation (15), equation (16) showed a high adjusted R2 of nearly
40 percent, indicating a high explanatory power of the given variables.
A question that begs further investigation is whether market conditions change
dramatically one year later during the flash crash of May 6, 2010. Tables 5.4 and
5.5 present the answers: May 6, 2010 (flash crash), values exhibit little difference
from a regular market day May 6, 2009, one year prior.
As shown in Aldridge (2012c), estimates of equation (15) recorded on May 6,
2009, are very similar to those estimated on the data of the flash crash, implying that
the MI model performs well in most market conditions. As Aldridge (2012c) also
shows, the model of equation (15) makes robust out-of-sample predictions of future
market impact, delivering 99.9 percent accurate predictions of MI based on parameters estimated as much as 30 minutes ahead of a given trade.
■■ Summary

Trading Costs

Transaction costs present a considerable hurdle for high-frequency trading systems.
Among all costs, however, market impact accounts for the most significant proportion of costs. Understanding and measuring the current cost structure is imperative
to designing profitable systems.
■■ End-of-Chapter Questions
1.
2.
3.
4.
5.
6.
7.
8.

What costs are present in the financial markets?
What are latent costs? How do they differ from transparent costs?
Which type of cost is most dominant in today’s markets?
What kind of tax structure do high-frequency traders face?
What is market impact? Why does it exist?
Can market impact following a market buy order be zero? Explain.
Can expected market impact of a buy order be negative? Explain.
What is a permanent market impact? How different is it from temporary market
impact?
9. What market impact accompanies limit orders?

Chapter 6

Performance and
Capacity of HighFrequency Trading
Strategies
97

ver the past few years, several studies attempted to measure high-frequency
trading (HFT) performance and capacity. The results vary from author to author. Many different metrics have been developed over time to illuminate a strategy’s
performance. This chapter summarizes the most popular approaches for performance measurement and discusses strategy capacity and the length of time required
to evaluate a strategy. The chapter also discusses estimation of capacity and illustrates
capacity of HFT with specific examples.
■■ Principles of Performance Measurement
One can manage only something measurable. Performance measurement is therefore a critical function of investment management and of HFT.While many metrics
developed for standard investment management apply well in a high-frequency
setting, several other metrics have been developed specifically to evaluate HFT
activity.
At the heart of a successful investment management of HFT lie three P’s:
■■ Precision
■■

Productivity

■■

Performance

Performance and Capacity of High-Frequency Trading Strategies

The first P, precision of mathematical metrics, refers to the exactitude required to
quickly and reliably separate winning strategies from the losing ones. Statistical tools
also help ascertain whether a strategy apparent profitability is a short-term fluke or
a statistically solid predictor of performance.
Standardized metrics, when applied uniformly across all investment strategies,
deliver the second P, productivity of the investment process. Statistical tools are
highly scalable and can be rapidly deployed to optimize a diverse array of investing
ideas.
The third P, performance, is particularly relevant to high-frequency systems. In
an environment where data points from multiple sources arrive with nanosecond
frequency, proper measuring systems are necessary. Monitoring systems equipped
with the latest portfolio tracking and risk-management capabilities are critical for
effective and sustainable investing.
The three P’s share one key requirement: data.The simplest, least processed, data,
such as tick data, is most informative and has consequently proven to be very valuable. Trade-by-trade data can reveal the short-term risks of the trading strategy, and
to allow risk-mitigating approaches for strategy improvement. Additionally, most
granular data allows to quickly and accurately identify strategy dependencies on specific market events or financial instruments, feeding back into strategy development
and forming stronger, longer-lasting trading systems. Finally, tick data allow investment managers to monitor and evaluate performance of trading strategies in real
time without losing the opportunity to limit losses and enhance profitability along
the way.
■■ Basic Performance Measures

Return
Trading strategies may come in all shapes and sizes, but they share one characteristic
that makes comparison across different strategies feasible—return. Return can be
expressed as a dollar difference in prices but is most often considered as a percentage change in value. The resulting dimensionless measure is independent of the price
level of the financial instrument under consideration and allows easy cross-strategy
and cross-asset comparison of performance:
Pt1
−1
Pt 0
Simple return of equation (1) is illustrated in Figure 6.1.
An equivalent log return metric is shown in equation (2):
Rt1 =

rt1 = ln ( Pt1 ) − ln ( Pt 0 )

(1)

(2)

It can be shown that at high frequencies, simple returns of equation (1) are nearly
identical to log returns defined by equation (2). The choice of the return metric is
often dependent on the application and mathematics of the estimation models.

P, Price

Pt 1 – Pt 0

Pt 0
t0

Time

FIGURE 6.1 illustration of a Simple return

Volatility

1 N
σˆ t2 = ∑ i=1( Rt −i − Rt )
N
where Rt is a simple average of N observations preceding time t.
2

■

(3)

Weighted average deviation, emphasizing later observations, is also used often:

∑ w i ( Rt −i − Rt )
= i=1 N
∑ i=1w i
N

σˆ t

Price

Time

FIGURE 6.2 example of a Low-Volatility Market Condition

(4)

99
PerFOrMAnCe And CAPACiTy OF HigH-FrequenCy TrAding STrATegieS

Volatility of returns measures how much the return moves up and down around its
average value. The movement of returns, often known as dispersion, is often taken
as a measure of risk. Figures 6.2 and 6.3 illustrate low-volatility and high-volatility
conditions, drawn comparatively to each other.
At least a dozen measures of volatility exist, each metric assessed over a specific
period of time: round-trip trade, minute, day, month, and so on. The most common
measures of volatility include:
Simple standard deviation of returns is by far the most popular measure of volatility.

Price

Time

FIGURE 6.3 example of a High-Volatility Condition

∑ w iRt −i , and w is the “data importance” weight corresponding
where R = i=1N
∑ i=1w i
N

to each individual returns Ri. All wi are often chosen to add up to 1 and to increase
toward the most current observation:

∑ i=1w i = 1

(5)

w i > w i+1 > w i+2 >  > w i+N

(6)

■

PerFOrMAnCe And CAPACiTy OF HigH-FrequenCy TrAding STrATegieS

100

Average of open, high, low, and close prices is another metric of volatility

σˆ t =

■

Pt −N + max ( Pτ ∈t −N ,t −1 ) + min ( Pτ ∈t −N ,t −1 ) + Pt −1

(7)
4
High minus low recorded during a specific period of time is useful in analyses
where many lagged variables are present. The high minus low metric avoids endogeneity problem inherent with standard deviation and lagged returns: since standard deviation is computed from lagged returns, the analysis comparing lagged
returns and standard deviation is faulty by design.

σˆ t = max ( Pτ ∈t −N ,t −1 ) − min ( Pτ ∈t −N ,t −1 )
■

(8)

Average square returns recorded over a certain period of time is yet another
metric of volatility. This one has been shown to work particularly well with applications like generalized autoregressive conditional heteroskedasticity (gArCH)
(see Bollerslev, 2005):
1 N
2
σˆ t2 = ∑ i=1( Rt −i )
N

(9)

Drawdown
drawdown is a measure of historical loss. it is recorded as a maximum loss relative to
the highest previous value, the latter often referred to as the water mark. investment
managers typically receive performance fees only after they exceed the highest water
mark on record.

Price

|Drawdown 2| > |Drawdown 1|

|Drawdown 1|

Time

FIGURE 6.4 Maximum drawdown Computation, Scenario 1

Maximum drawdown identifies the biggest drop of price or value in history of
the investment, and helps illustrate potential downside risk. Figures 6.4 and 6.5 illustrate computation of maximum drawdown.
Formally, maximum drawdown is a measure of tail risk popular among practitioners that documents the maximum severity of losses observed in historical data. As
such, maximum drawdown records the lowest peak-to-trough return from the last
global maximum to the minimum that occurred prior to the next global maximum
that supersedes the last global maximum.The global maximum measured on the past
data at any point in time is known as high water mark. A drawdown is then the lowest
return in between two successive high water marks. The lowest drawdown is known
as the maximum drawdown:
max Drawdown = maxτ Pt ∈τ − minτ Pt ∈τ ∀t1 < t2
1

(10)

Win ratio
Win ratio explains what portion of the trades, trading days or trading months ended
profitably:
#Trading Periods Gain >0
(11)
WinRatio =
Total #Trading Periods
Win ratios help compare accuracy of predictive signals of strategies: better
forecasts result in higher win ratios. Win ratios also help in monitoring run-time
Price

|Drawdown 3|

|Drawdown 1|

FIGURE 6.5 Maximum drawdown Computation, Scenario 2

101
PerFOrMAnCe And CAPACiTy OF HigH-FrequenCy TrAding STrATegieS

in risk management, the concept of maximum drawdown is closely related to value-at-risk, a measure of worst quantity of losses, described in detail in Chapter 14.

Win Ratio = # +ve Gain Days/# Trading Days

Dec

Oct

Nov

Sep

Aug

Jul

Jun

Apr

May

Mar

Jan

Feb

100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%

FIGURE 6.6 A decline in Win ratio Shown May indicate that the Strategy is reaching Capacity

performance. As a simplest metric, win ratio can be used to assess whether present
performance record is consistent with prior performance. A decline in the win ratio
may indicate that the strategy is reaching capacity, as Figure 6.6 illustrates.
Similar, but more advanced, tests for evaluating consistency of run-time performance are described in Chapter 14.

average Gain/loss
PerFOrMAnCe And CAPACiTy OF HigH-FrequenCy TrAding STrATegieS

102

Average gain and average loss are two metrics, statistically closely related to maximum
drawdown. The average loss is also a close cousin of the concept of expected loss, discussed in Chapter 14. The average gain measures the average profitability of the strategy when a positive result is recorded. Similarly, the average loss computes the average
total for all trades, days or months when the strategy delivered negative performance.
Considered in conjunction with the win ratio, average gain and loss metrics may
deliver additional insights. For example, a strategy with high win ratio may tolerate
lower average gain relative to the observed average loss, while low win ratio requires
a high average gain as compared with the average loss. The outcomes of various win
ratio and average gain/loss combinations are shown in Figure 6.7.
Formally, for the strategy to deliver positive performance, the following inequality must hold:
E [ R ] ≥ (WinRatio ) ∗ E [Gain ] + (1 − WinRatio ) ∗ E [ Loss ]
High
WinRatio
High Gain/Loss

Low Gain/Loss

Low
WinRatio
High
drawdowns

High
volatility

FIGURE 6.7 Outcomes of Win ratio and Average gain/Loss Combinations

(12)

The inequality of equation (12) can be used as first step litmus test for evaluating
performance of candidate investing strategies and manager credibility.

Correlation
Correlation measures co-movement of strategy returns with those of another strategy or financial instrument:

ρ1,2 = ∑ t ( R1,t − E [ R1 ]) ( R2,t − E [ R2 ])

(13)

ρ1,2
ρ1,2

R 1 >0 =

∑ t ( R1,t − E [R1 ]) ( R2,t − E [R2 ]) R >0

(14)

R 1 <0 =

∑ t ( R1,t − E [R1 ]) ( R2,t − E [R2 ]) R <0

(15)

In both equations (14) and (15) financial instrument 1 is taken as a reference. Equation (14) computes the correlation for the “up” states of returns of financial instrument
1, while equation (15) does the same for the “down” states. A strategy delivering returns negatively correlated to those of the existing portfolio helps buffer core portfolio’s losses in the “down” states, and is much more valuable than the strategy delivering
positively correlated returns and thereby amplifying losses of wider portfolio.

Alpha and Beta
Alpha and beta are two now-mainstay measures of investment performance that are
equally well suited for evaluation of high-frequency strategies. At its most basic level,
alpha measures the return achieved by the strategy abstracted of any influences by
the reference portfolio or the broader markets, measured by, say, the S&P 500 index. Thus, alpha reflects the performance of the strategy that is independent of the
prevailing market conditions. A positive alpha is desirable. Strategies with a negative

103
Performance and Capacity of High-Frequency Trading Strategies

When two strategies with low correlation are combined in a portfolio, traditional
portfolio management theory suggests that the resulting portfolio is diversified (i.e.,
allows one strategy to pull up returns when performance of another strategy temporarily declines).
Simple correlation, however, may no longer be sufficient in delivering robust
measurements of co-movement of financial instruments. The main problem with
simple correlation is the following observation: prices of financial instruments display increasingly divergent correlations in rising and in falling markets. Specifically,
when broad market indices rise (a market entity such as Standard & Poor’s [S&P]
500, for example) correlations vary from any two financial instruments to any other
two financial instruments. When the broad market indices fall, however, returns of
most financial instruments become highly correlated. Such divergent correlation in
different states of the markets is known as the asymmetric or tail correlation that can be
computed by dividing the data sample into points when price returns of one of the
instruments measured are positive and negative:

alpha are generally avoided, unless the negative-alpha strategy signals can be profitably used to trade “in reverse”—buy when the strategy advises to sell and vice versa.
Beta, however, is a multiplier that measures exactly how the strategy responds
to the current market trends. A positive beta indicates that the strategy is likely to
deliver positive performance when the reference portfolio rises in value. A negative
beta shows that, on average, the strategy is likely to perform better when the reference portfolio declines. depending on the investor’s cumulative portfolio, either
positive or negative beta may be preferable.
Alpha and beta are estimated using a linear regression (OLS):
Ri,t =α i + β i Rp,t + ε i,t

PerFOrMAnCe And CAPACiTy OF HigH-FrequenCy TrAding STrATegieS

104

(16)

where Ri,t is the return on a high-frequency strategy i observed over a unit of time t,
Rp,t is the return on the reference portfolio observed over the same period of time, αi
and βi are the parameters to be estimated, and ei,t is the “statistical estimation error”
specific to each observation when equation (16) is applied to data. By the assumptions of the model of equation (16), the errors ei,t average to zero.
Figure 6.8 graphically illustrates alpha and beta, as computed from a scatterplot of
returns: the returns of the reference portfolio are plotted along the horizontal axis,
and the contemporaneous returns on the HF strategy are plotted along the vertical
axis.When a straight line is fitted through the data, the slope of the line is beta. Alpha
is the intercept, or the point where the line intersects the vertical axis.

Skewness and Kurtosis
Skewness and kurtosis are additional parameters used to describe the distribution
of returns of the strategy. Skewness describes the tendency of the strategy to deliver
positive or negative returns. Positive skewness of a return distribution implies that
the strategy is more likely to post positive returns than negative returns. Figure 6.9
illustrates possible skewness scenarios.
Kurtosis measures the likelihood of extreme occurrences, that is, of severely
positive and severely negative returns relative to normal returns. When kurtosis is

* *
*

*
*

FIGURE 6.8 graphical representation of Alpha and Beta

Zero-skewness: S = 0
Frequency

E [R ] = mean

Positive skewness: S > 0
Frequency

E [R ]

Negative skewness: S < 0
Frequency

E [R ]

FIGURE 6.9 Skewness Values and Their Meaning in distribution of returns

Normal kurtosis: K = 3
Frequency

E [R] = mean

High kurtosis (“fat tails”): K > 3
Frequency

E [R]

Low kurtosis (“narrow distribution”): K < 3
Frequency

E [R]

FIGURE 6.10 Kurtosis Values and Their Meaning in distribution of returns

105
PerFOrMAnCe And CAPACiTy OF HigH-FrequenCy TrAding STrATegieS

high, extreme returns are likely. When kurtosis is low, extreme returns are unlikely.
Figure 6.10 illustrates the idea of kurtosis.
The average return, volatility, and maximum drawdown over a prespecified window of time measured at a predefined frequency are the mainstays of performance
comparison and reporting for different trading strategies. in addition to the average return, volatility, and maximum drawdown, practitioners sometimes quote
skewness and kurtosis of returns when describing the shape of their return distributions. As usual, skewness illustrates the position of the distribution relative to the

return average; positive skewness indicates prevalence of positive returns, while
negative skewness indicates that a large proportion of returns is negative. Kurtosis
indicates whether the tails of the distribution are normal; high kurtosis signifies “fat
tails,” a higher-than-normal probability of extreme positive or negative events.
■■ Comparative Ratios
While average return, standard deviation, and maximum drawdown present a picture of the performance of a particular trading strategy, the measures do not lend
to an easy point comparison among two or more strategies. Several comparative
performance metrics have been developed in an attempt to summarize mean, variance, and tail risk in a single number that can be used to compare different trading
strategies. Table 6.1 summarizes the most popular point measures.
Table 6.1 Performance Measure Summary
Sharpe ratio
(Sharpe, 1966)

SR =

Adequate if returns are normally
distributed.

E[ r ] − r f

σ [r]

, where
r1 +  + rT
E[ r ] =
T

σ [r] =

Performance and Capacity of High-Frequency Trading Strategies

106

( r1 − E[ r ])2 +  + ( rT − E[ r ])2
T −1

The Sharpe ratio of high-frequency trading
strategies: SR = E[ r ]
σ [r]
Treynor ratio
(Treynor, 1965)

Treynori =

E[ ri ] − r f

βi

βi is the regression coefficient of trading
returns on returns of the investor’s reference
portfolio, such as the market portfolio.
Jensen’s alpha
(Jensen, 1968)

α i = E[ ri ] − r f − β i ( rM − r f )
bi is the regression coefficient of trading
returns on returns of the investor’s
reference portfolio, such as the market
portfolio.

Adequate if returns are normally
distributed and the investor wishes to split
his holdings between one trading strategy
and the market portfolio.

Measures trading return in excess of the
return predicted by CAPM. Adequate
if returns are normally distributed and
the investor wishes to split his holdings
between one trading strategy and the
market portfolio, but can be manipulated
by leveraging the trading strategy.

Measures based on lower partial moments (LPMs):
LPM of order n for security i:
1T
LPM ni (τ ) = ∑ max[τ − rit ,0]n
T t =1
where t is the minimal acceptable return;
n is the moment: n = 0 is the shortfall probability, n = 1 is the expected shortfall, n = 2 for t = E[r] is the
semivariance.
According to Eling and Schuhmacher (2007), more risk-averse investors should use higher-order n.
LPMs consider only negative deviations of returns from a minimal acceptable return. As such, LPMs are deemed
to be a better measure of risk than standard deviation, which considers both positive and negative deviations
(Sortino and van der Meer, 1991). Minimal acceptable return can be zero, risk-free rate, or average return.

table 6.1 (Continued)
Omega
(Shadwick and
Keating, 2002;
Kaplan and
Knowles, 2004)
Sortino ratio
(Sortino and
van der Meer,
(1991)
Kappa 3
(Kaplan and
Knowles, 2004)
Upside
Potential ratio
(Sortino, van
der Meer, and
Plantinga, 1999)

Ωi =

E[ ri ] − τ
+1
LPM1i (τ )

E[ ri ] − τ

Sortinoi =

Κ3i =

UPRi =

E[ ri ] − τ is the average return in excess of
the benchmark rate.

( LPM2i (τ ))1/2
E[ ri ] − τ

( LPM3i (τ ))1/3
HPM1i (τ )

( LPM2i (τ ))

1/2

where HPM = higher partial moment
1T
HPM ni (τ ) = ∑ max[ rit − τ ,0]n
T t =1

According to Eling and Schuhmacher
(2007), this ratio gains from the
consistent application of the minimal
acceptable return t in the numerator as
well as in the denominator.

Measures based on drawdown: frequently used by CTAs, according to Eling and Schuhmacher (2007, p.5),
“because these measures illustrate what the advisors are supposed to do best—continually accumulating
gains while consistently limiting losses (see Lhabitant, 2004).” MDi1 denotes the lowest maximum
drawdown, MDi2 the second lowest maximum drawdown, and so on.
Calmari =

Sterling ratio
(Kestner, 1996)

Sterlingi =

Burke ratio
(Burke, 1994)

Burke i =

MDi1 is the maximum drawdown.

E[ ri ] − r f
− MDi1
E[ ri ] − r f
1 N
− ∑ MDij
N k =1
E[ ri ] − r f

(

)

1/2

2

 k∑=1 MDij 
N

1 N
∑ MDij
N k =1
is the average maximum
drawdown.
−

(

)

1/2

2
N
 k∑=1 MDij 

is a type of variance
below the Nth largest drawdown; accounts
for very large losses.

Value-at-risk–based measures.
Value-at-risk (VaRi) describes the possible loss of an investment, which is not exceeded with a given
probability of 1−α in a certain period. For normally distributed returns, VaRi = −(E[ ri ] + zα σ i ) , where
zα is the a-quantile of the standard normal distribution.
Excess return
on value at risk
(Dowd, 2000)
Conditional
Sharpe ratio
(Agarwal and
Naik, 2004)

Excess R on VaR =

E[ r ] − r f

Conditional Sharpe =

Not suitable for non-normal returns.

VaRi
E[ r ] − r f
CVaRi

The advantage of CVaR is that it satisfies
certain plausible axioms (Artzner et al.,
1999).

CVaRi = E[ − rit |rit ≤ − VaRi ]
(Continued)

107
Performance and Capacity of High-Frequency Trading Strategies

Calmar ratio
(Young, 1991)

table 6.1 (Continued)
Modified
Sharpe ratio
(Gregoriou and
Gueyie (2003)

Modified Sharpe =

Suitable for non-normal returns.

E[ r ] − r f
MVaRi

Cornish-Fisher expansion is calculated as
follows:
MVaRi = −(E[ ri ] + σ i ( zα + ( zα 2 − 1)Si / 6
+ ( zα 3 − 3zα )EK i /24 − (2zα 3 − 5zα )Si2 /36))
where Si denotes skewness and EKi the
excess kurtosis for security i (Favre and
Galeano, 2002).

Performance and Capacity of High-Frequency Trading Strategies

108

The first generation of point performance measures were developed in the 1960s
and include the Sharpe ratio, Jensen’s alpha, and the Treynor ratio. The Sharpe ratio
is probably the most widely used measure in comparative performance evaluation; it
incorporates three desirable metrics—average return, standard deviation, and the cost
of capital borrowed for strategy leverage.
The Sharpe ratio was designed in 1966 by William Sharpe, later a winner of the
Nobel Memorial Prize in Economics; it is a remarkably enduring concept used
in the study and practice of finance. A textbook definition of the Sharpe ratio is
R − RF
SR =
, where R is the annualized average return from trading, σR is the
σR
annualized standard deviation of trading returns, and RF is the risk-free rate (e.g.,
Fed Funds) that is included to capture the opportunity cost as well as the position
carrying costs associated with the trading activity. It should be noted that in most
instruments HFT with no positions carried overnight, the position carrying costs are
zero. Therefore, the high-frequency Sharpe ratio is computed as follows:
SR =

R
σR

What makes the Sharpe ratio an appealing measure of performance, in comparison with, say, raw absolute return? Surprisingly, the Sharpe ratio is an effective
metric for selecting mean-variance efficient securities.
Consider Figure 6.11, for example which illustrates the classic mean-variance
frontier. In the figure, the Sharpe ratio is the slope of the line emanating from the
risk-free rate and passing through a point corresponding to a given portfolio (M for
market portfolio), trading strategy, or individual security.The bold line tangent to the
mean-variance set of all portfolio combinations is the efficient frontier itself. It has
the highest slope and, correspondingly, the highest Sharpe ratio of all the portfolios in the
set. For any other portfolio, trading strategy, or individual financial instrument A, the
higher the Sharpe ratio, the closer the security is to the efficient frontier.
Sharpe himself came up with the metric when developing a portfolio optimization mechanism for a mutual fund for which he was consulting. Sharpe’s mandate was to develop a portfolio selection framework for the fund with the following

Slope = Sharpe ratio
Sharpe M
Portfolio M
Portfolio A
Sharpe A

FIGURE 6.11 Sharpe ratio as a Mean-Variance Slope. The market portfolio has the highest slope

and, correspondingly, the highest Sharpe ratio.

109
PerFOrMAnCe And CAPACiTy OF HigH-FrequenCy TrAding STrATegieS

constraint: no more than 5 percent of the fund’s portfolio could be allocated to a
particular financial security. Sharpe then created the following portfolio solution: he
first ranked the security universe on what now is known as Sharpe ratio, then picked
the 20 securities with the best performance according to the Sharpe ratio measure,
and invested 5 percent of the fund into each of the 20 securities. equally weighted
portfolio allocation in securities with the highest Sharpe ratios is just one example of
a successful Sharpe ratio application.
Jensen’s alpha is a measure of performance that abstracts from broad market influences, capital asset pricing model (CAPM)-style. Jensen’s alpha implicitly takes into
consideration the variability of returns in co-movement with chosen market indices.
The third ratio, the Treynor ratio, measures the average return in excess of the
chosen benchmark per unit of risk proxied by beta from the CAPM estimation.
While these three metrics remain popular, they do not take into account the
tail risk of extreme adverse returns. Brooks and Kat (2002), Mahdavi (2004),
and Sharma (2004), for example, present cases against using Sharpe ratios on
non–normally distributed returns. The researchers’ primary concerns surrounding
the use of the Sharpe ratio are linked to the use of derivative instruments that result
in an asymmetric return distribution and fat tails. ignoring deviations from normality may underestimate risk and overestimate performance. new performance
measures have been subsequently developed to capture the tail risk inherent in the
returns of most trading strategies.
A natural extension of the Sharpe ratio is to change the measure of risk from standard deviation to a drawdown-based methodology in an effort to capture the tail risk
of the strategies. The Calmar ratio, Sterling ratio, and Burke ratio do precisely that.
The Calmar ratio, developed by young (1991), uses the maximum drawdown as the
measure of volatility.The Sterling ratio, first described by Kestner (1996), uses the average drawdown as a proxy for volatility. Finally, the Burke ratio, developed by Burke
(1994), uses the standard deviation of maximum drawdowns as a volatility metric.
in addition to ignoring the tail risk, the Sharpe ratio is also frequently criticized
for including positive returns in the volatility measure. The argument goes that only

Performance and Capacity of High-Frequency Trading Strategies

110

the negative returns are meaningful when estimating and comparing performance of
trading strategies. In response, a “Greek” class of ratios extended the Sharpe ratio by
replacing volatility with the average metrics of adverse returns only. These adverse
return metrics are known as lower partial moments (LPMs) and are computed as
regular moments of a distribution (i.e., mean, standard deviation, and skewness),
except that the data used in computation comprises returns below a specified benchmark only. Thus, a metric known as Omega, developed by Shadwick and Keating
(2002) and Kaplan and Knowles (2004), replaces the standard deviation of returns
in the Sharpe ratio calculation with the first LPM, the average of the returns that
fell below the selected benchmark. The Sortino ratio, developed by Sortino and van
der Meer (1991), uses the standard deviation of the returns that fell short of the
benchmark, the second LPM, as a measure of return volatility in the Sharpe ratio
calculation. The Kappa 3 measure, developed by Kaplan and Knowles (2004), replaces the standard deviation in the Sharpe ratio with the third LPM of the returns,
the skewness of the returns below the benchmark. Finally, the Upside Potential ratio, produced by Sortino, van der Meer, and Platinga (1999), measures the average
return above the benchmark (the first higher partial moment) per unit of standard
deviation of returns below the benchmark.
Value-at-risk (VaR) measures, discussed in detail in Chapter 14, also gained considerable popularity as metrics able to summarize the tail risk in a convenient point
format within a statistical framework. The VaR measure essentially identifies the
90 percent, 95 percent, or 99 percent Z-score cutoff in distribution of returns (the
metric is also often used on real dollar distributions of daily profit and loss). A VaR
companion measure, the conditional VaR (CVaR), also known as expected loss (EL),
measures the average value of return within the cutoff tail. Of course, the original
VaR assumes normal distributions of returns, whereas the returns are known to be
fat-tailed. To address this issue, a modified VaR (MVaR) measure was proposed by
Gregoriou and Gueyie (2003) and takes into account deviations from normality.
Gregoriou and Gueyie (2003) also suggest using MVaR in place of standard deviation
in Sharpe ratio calculations.
How do these performance metrics stack up against each other? It turns out that
all metrics deliver comparable rankings of trading strategies. Eling and Schuhmacher
(2007) compare hedge fund ranking performance of the 13 measures listed and conclude that the Sharpe ratio is an adequate measure for hedge fund performance.
■■ Performance Attribution
Performance attribution analysis, often referred to as “benchmarking,” goes back to
the arbitrage pricing theory of Ross (1977) and has been applied to trading strategy performance by Sharpe (1992) and Fung and Hsieh (1997), among others. In a
nutshell, performance attribution notes that t-period return on strategy i that invests
into individual securities with returns rjt in period t, with j = 1, …, J, has an underlying factor structure:
(17)
Rit = ∑ x jt rjt
j

where xjt is the relative weight of the jth financial security in the portfolio at time t,
∑ x jt = 1 . The jth financial security, in turn, has a period-t return that can be
j

explained by K systematic factors:
rjt = ∑ λ jk Fkt + ε jt

(18)

where Fkt is one of K underlying systematic factors in period t, k = 1, …, K, l is
the factor loading, and ejt is the security j idiosyncratic return in period t. Following Sharpe (1992), factors can be assumed to be broad asset classes, as well as individual stocks or other securities. Combining equations (17) and (18), we can express
returns as follows:
Rit = ∑ x jt λ jk Fkt + ∑ x jtε jt
j,k

(19)

reducing the large number of financial securities potentially underlying strategy i’s
returns to a small group of global factors. Performance attribution to various factors
then involves regressing the strategy’s returns on a basket of factors:
Rit = α i + ∑ bik Fkt + uit

(20)

■■

■■
■■

Three equity classes: MSCI U.S. equities, MSCI non–U.S. equities, and IFC
emerging market equities
Two bond classes: JPMorgan U.S. government bonds and JPMorgan non–U.S.
government bonds
One-month Eurodollar deposit representing cash
The price of gold proxying commodities and the Federal Reserve’s trade-weighted
dollar index measuring currencies in aggregate.

Performance attribution is a useful measure of strategy returns for the following
reasons:
■■

■■

The technique may accurately capture investment styles of black-box strategies in
addition to the details reported by the designer of the strategy.
Performance attribution is a measure of true added value of the strategy and lends
itself to easy comparison with other strategies.

111
Performance and Capacity of High-Frequency Trading Strategies

where bk measures the performance of the strategy that can be attributed to factor
k, ai measures the strategy’s persistent ability to generate abnormal returns, and uit
measures the strategy’s idiosyncratic return in period t.
In the performance attribution model, the idiosyncratic value added of the strategy is the strategy’s return in excess of the performance of the basket of weighted
strategy factors.
Fung and Hsieh (1997) find that the following eight global groups of asset classes
serve well as performance attribution benchmarks:

■■

Near-term persistence of trending factors allows forecasting of strategy performance based on performance attribution (see, for example, Jegadeesh and
Titman, 2001).

The bottom line in the performance attribution analysis is this: if the high-frequency strategy under consideration exhibits high dependency on a benchmark, it
may be cheaper to invest into the benchmark instead of the HF strategy, particularly
when development and transaction costs as well as the associated risks are taken into
account. That is, when the performance attribution beta is high, and alpha is low, it
might be more effective to invest into the benchmark, particularly when any one of
the following conditions holds:
■■

■■
■■

Investing into benchmark can be passive or simply costs less in terms of aggregate
transaction costs.
The benchmark has lower drawdown risk.
The benchmark is more liquid than the instrument traded in the HFT strategy,
and the benchmark therefore faces a lower liquidation risk.

■■ Capacity Evaluation

Performance and Capacity of High-Frequency Trading Strategies

112

Over the past few years, HFT strategies have been erroneously called low-capacity
strategies. One study, for example, based its low-capacity conclusions for HFT on
a major gaffe—an assumption that all high-frequency traders solely use market
orders to complete their trades. In such an analysis, market impact dominates
and multiplies in fast trading, leaving high-frequency traders unable to profitably enter or liquidate their positions. The maximum capacity of a high-frequency
market-order trading strategy then amounts to the liquidity available at the best
bid or best offer at a specific time when each market sell or buy order, respectively, is placed.
In reality, as later chapters of this book describe, most HFT strategies place and
execute limit orders, with very few market orders placed in the mix. Market orders
in HFT are generally used at times when markets take an unexpected wrong turn
and the trader’s inventory has to be liquidated—fast.
Limit orders generate much smaller market impact than do market orders, as
Chapter 5 of this book explains. Still, even strategies relying solely on limit orders
do not enjoy infinite capacity since two variables in addition to market impact also
adversely affect performance of HFT strategies. These variables are probability of
execution and transparent execution costs.1
Transparent execution costs, also described in Chapter 5 of this book, affect the
profitability of round-trip trades, yet are predictable as they tend to be known ahead
of each trade. Execution costs on selected venues may be positive or negative, depending on the venue’s business model.
Strategy capacity has been shown to be a function of trading costs and asset liquidity by Getmansky,
Lo, and Makarov (2004).
1

The probability of execution is simple for market orders: it is always close to 1.
The probability of execution of limit orders, however, is not known with certainty at
the time the order is placed. For a limit order to be executed, it needs to
1. Become the best available price—best bid or best ask—the process also known
as “reaching the top of the book.”
2. Be matched with or crossed by a market order or an aggressive limit order.
As a result, the probability of execution for limit orders is variable and depends
on the following factors:
■■
■■
■■
■■
■■
■■

The distance of the limit order price from the market price.
Market volatility.
The number of other limit orders available at the same price or closer to market.
The size of the limit order.
The rate of arrival of same-side limit orders.
The rate of arrival of opposing market orders and aggressive limit orders.

max S s.t.∑ t S Q t (1 + MI t −1 ) Pt Prt ( Execution ) − Ct  ≥ 0 and ∑ t Q t = 0 (21)
where
S is the size of each order in the strategy, assuming the strategy can be executed
using trades of equal size S.
Q t is the direction of the order placed at time t: Q t =1 when the order is a buy, and
Q t = −1 when the order is a sell.

113
Performance and Capacity of High-Frequency Trading Strategies

A limit order placed far away from the market price faces a tangible risk of nonexecution: the market price may never reach limit orders placed far away from the
market.The probability of the market price crossing the limit order, in turn, depends
on the market volatility—the higher the volatility, the more likely is the market price
to hit the level specified by the limit order. The congestion of limit orders also matters, as each limit placed at a given price will be stored in a queue and executed
according to a scheme specific to the execution venue; as discussed in Chapter 3,
the most common matching schemes are the first-in-first-out (FIFO) and pro-rata
algorithms. Under the FIFO arrangements, the larger limit orders face a larger risk
of nonexecution: large limit orders may be only partially executed before the market
moves away, leaving some of the limit order in the queue. With a pro-rata algorithm,
the opposite holds: all orders are executed on a fixed proportion of their sizes; small
orders may take a long time to execute in full.
The higher the number of other limit orders arriving at the same price as the
trader’s close to market price, the steeper the competition for market orders, and
the less likely the limit order to be matched. However, the higher the arrival rate of
opposing market orders, the higher the probability of execution.
Algebraically, the maximum size of a limit order (capacity) S deployed by a
high-frequency strategy can be expressed as follows:

M It−1 is the market impact generated by the previous order placed by the HFT
strategy, and impacting the market conditions at time t; only the market impact
that has not fully decayed by time t needs to be considered.
Pt is the price of the order or, in case of a market order, the price obtained upon
execution.
Prt ( Execution ) is the probability that the order placed at time t will be executed;
this probability can be assumed to be 1 for market orders.

Finally, Ct is the cost of execution of the order placed at time t; this cost includes
broker fees and other costs discussed in Chaper 5 of this book that affect the
bottom-line profitability of high-frequency strategies.

PerFOrMAnCe And CAPACiTy OF HigH-FrequenCy TrAding STrATegieS

114

As shown in Chapter 5, market impact (Mi) can be probabilistically estimated. in
addition to the magnitude of Mi following an average order, the probability of execution can be estimated as well by noting the statistics of when a market price crosses
limit orders placed at various points away from the market. Assuming that the trade
signals of an HFT system deliver credibly positive results, the capacity of the system is
then determined by a trade-off between market impact and probability of execution.
To further increase the capacity of an HFT strategy, market and limit orders may
be potentially sequenced. Figure 6.12 shows a decision tree for evaluating the optimal capacity of an HF trading system.

Does the strategy
use market orders?

Does the strategy
use limit orders?

Yes

What is the
max liquidity at profitable
prices?

What size
can execute
now?

Can market
and limit orders be
sequenced to increase
capacity?

How does the
current cost
structure affect
capacity?

FIGURE 6.12 Basic Framework for evaluating Capacity of HFT Strategies

ding et al. (2008) conjecture that when the amount of capital deployed is lower than
the strategy capacity, the strategy performance may be positively related to its capitalization. However, once capitalization exceeds strategy capacity, performance becomes negatively related to the amount of capital involved. Chapter 15 discusses the latest research
on optimizing order execution and potentially increasing strategy capacity further.

Length of the Evaluation Period
Most portfolio managers face the following question in evaluating candidate trading
strategies for inclusion in their portfolios: how long does one need to monitor a strategy in order to gain confidence that the strategy produces the Sharpe ratio advertised?
Some portfolio managers have adopted an arbitrarily long evaluation period: six
months to two years. Some investors require a track record of at least six years. Yet
others are content with just one month of daily performance data. It turns out that,
statistically, any of the previously mentioned time frames is correct if it is properly
matched with the Sharpe ratio it is intended to verify. The higher the Sharpe ratio,
the shorter the strategy evaluation period needed to ascertain the validity of the
Sharpe ratio.
If returns of the trading strategy can be assumed to be normal, Jobson and Korkie
(1981) showed that the error in Sharpe ratio estimation is normally distributed with
mean zero and standard deviation
s = [(1/T)(1 + 0.5SR2)]1/2.
For a 90 percent confidence level, the claimed Sharpe ratio should be at least
1.645 times greater than the standard deviation of the Sharpe ratio errors, s. As a result, the minimum number of evaluation periods used for Sharpe ratio verification is
Tmin = (1.6452/SR2)(1 + 0.5SR2).

115

Table 6.2 Minimum Trading Strategy Performance Evaluation Times Required for
Verification of Reported Sharpe Ratios
Claimed Annualized
Sharpe Ratio

No. of Months Required (Monthly
Performance Data)

No. of Months Required (Daily
Performance Data)

0.5

130.95

129.65

1.0

33.75

32.45

1.5

15.75

14.45

2.0

9.45

8.15

2.5

6.53

5.23

3.0

4.95

3.65

4.0

3.38

2.07

Performance and Capacity of High-Frequency Trading Strategies

The Sharpe ratio SR used in the calculation of Tmin, however, should correspond to
the frequency of estimation periods. If the annual Sharpe ratio claimed for a trading
strategy is 2, and it is computed based on the basis of monthly data, then the corresponding monthly Sharpe ratio SR is 2/(12)0.5 = 0.5774. However, if the claimed
Sharpe ratio is computed based on daily data, then the corresponding Sharpe ratio
SR is 2/(250)0.5 = 0.1054. The minimum number of monthly observations required
to verify the claimed Sharpe ratio with 90 percent statistical confidence is then just
over nine months for monthly performance data and just over eight months for daily

performance data. For a claimed Sharpe ratio of 6, less than one month of daily performance data is required to verify the claim. Table 6.2 summarizes the minimum
performance evaluation times required for verification of performance data for key
values of Sharpe ratios.
■■ Alpha Decay
In addition to the performance metrics outlined earlier, HFT strategies can be evaluated on the basis of alpha decay, the erosion of alpha with time. The erosion of alpha
may be due to the lack of execution in strategies relying on limit orders, or due to
the poor latency infrastructure used for transmission of market orders. In either
case, alpha decay can be measured and forecasted.
The alpha decay observed due to latency can be estimated as a distribution of
market impact costs observed in a particular financial instrument a finite period of
time after each trading decision was made.
Alpha decay of a strategy using limit orders measures the opportunity cost associated with failure to execute on trading signals of the strategy. Alpha decay is strategy
specific and should be assessed based on the signals generated by the given strategy.
■■ Summary
Performance and Capacity of High-Frequency Trading Strategies

116

Statistical tools for strategy evaluation allow managers to assess the feasibility and
appropriateness of high-frequency strategies to their portfolios. As traders’ and investment managers’ understanding of HFT deepens, new metrics are deployed to
capture the variability among HFT strategies. As a quick test of strategy feasibility,
the Sharpe ratio remains the favorite.
■■ End-of-Chapter Questions
1. What is the Sharpe ratio? What are its drawbacks? How can it be enhanced?
2. What is the Sortino ratio?
3. Suppose a performance attribution analysis on a given high-frequency trading
strategy finds strong dependence of trading gains on changes in the S&P 500.
What are the implications for the trading strategy? Discuss.
4. Why does market impact enter calculation of strategy capacity? Why does probability of execution?
5. What is alpha decay and why does it exist?

Chapter 7

The Business of
High-Frequency
Trading
C

ontrary to popular belief, the business of high-frequency trading (HFT) is not
entirely the business of trading, nor is it a business of pure research. Instead,
most of HFT is the business of technology. As such, the economics of building an
HFT operation differ considerably from those of a traditional trading floor. This
chapter explains the economic nuts and bolts of a successful HFT organization.
■■ Key Processes of HFT
The central value proposition of HFT is enabled by tick-by-tick data processing and
high capital turnover. The technology behind identifying small changes in the quote
stream is what differentiates this business and enables a trader to send rapid-fire signals to open and close positions.
Processing every tick of data on multiple financial instruments is possible only via
automated trading. Evaluating data separated by microseconds, interpreting reams of
market information, and making trading decisions in a consistent continuous manner
is too complex a task for a human brain. Affordable fully automated HFT systems,
however, can make fast, efficient, and emotionless decisions.
Figure 7.1 illustrates a sample deceivingly simple process used to develop HFT
systems. Just like any software development activity, the HFT process begins with
a concept of the final product: a trading idea that becomes a quantitative model.
The concept, or a prototype, may be a 20-line piece of code written in a modeling language, such as MatLab, and shown to produce hypothetical profitability on
a selection of data.

117

FIGURE 7.1 Algorithm design and reevaluation Process

THE BusInEss oF HIgH-FrEquEnCy TrAdIng

118

The next step is a back-test: a process whereby the concept is tested on a large
volume of tick data. Two years is generally considered a sufficient amount of tick
data to ascertain validity of the concept. Back-test best practices are discussed in
Chapter 16 of this book. The model is tested on “out-of-sample” or “clean” swath of
data, a series of quotes and trades unused in the initial proof of concept activity. If the
model performs satisfactorily out-of-sample, the model is moved into paper trading.
Models that fail the back-test are generally discarded.
Following a successful back-test, the models are moved into the preproduction or
paper-trading phase. Paper trading emulates real-time trading activity without placing actual orders, but keeps track of the orders in a program-generated log. Except
for the order-placement functionality, the paper-trading phase is typically a fully
programmed HFT system. As such, the paper-trading stage is a perfect “sandbox”
for testing all other aspects of the HFT system: data receipt and processing, runtime generation of trading signals, position accounting, archiving of data, and risk
management. To ascertain the correctness of the paper HFT system, the back-test
algorithm is typically run at the end of each trading day on data collected in paper
trading—any deviations observed between the back-test and paper trading are noted
and investigated.
When paper trading and the back-test are properly programmed, both should deliver identical results. A month of clean paper trading fully reconciled with back-test
results is usually considered to be sufficient to move the system into a low-amount
live trading or “production.”
The transition to production is often loaded with its own set of challenges, described in detail in Chapter 16. Trade execution and real-time portfolio accounting can be complex coding exercises, and have to be executed perfectly to avoid
unexpected malfunctions and losses. Extended production runs with little capital
at stake help iron out various code issues and ensure a smooth and effective trading
functionality.

This section demonstrates that in the development of a successful HFT system,
human time is functionally split as follows:
■■

■■

119
The Business of High-Frequency Trading

■■

Quant HFT model development/proof of concept including back-tests: 15 percent
Quant HFT models, the core examples of which are described in Chapters 8
through 11 of this book, are the road maps for trading.The output of quant models
is a set of persistent indicators built to identify trading opportunities.
Risk management principles, model validation and policy development: 10 percent
Competent risk management, discussed in Chapter 14, prevents seemingly
harmless glitches in the code, market data, market conditions, or the like from
throwing off trading dynamics and causing large losses. The objective of risk management is to assess the extent of potential damages and to create infrastructure
to mitigate damaging conditions during run-time, and to build a system of warnings, failure breaks, and processes with the goal to eliminate or limit the potential
damage. Some risk management processes may be built into the code, while others require a human presence to ensure a failure-safe operation.
Coding of trading and risk-management infrastructure: 40 percent
Coding trading and risk-management signals comprises the primary focus of
HFT development. High-frequency execution systems tend to be complex entities that detect and react to a variety of market conditions. Most HFT systems
today are built to be “platform independent”—that is, to incorporate flexible interfaces to multiple broker-dealers, electronic communication networks (ECNs),
and exchanges.This independence is accomplished through the use of the Financial
Information eXchange (FIX) language, a special sequence of codes optimized for
financial trading data. With FIX, at the flip of a switch the routing can be changed
from one executing broker to another or to several brokers simultaneously. Best
coding practices are described in Chapter 16.
FIX can be quite cumbersome, as discussed in Chapter 2. To counteract the delay in speed induced by the complexities of FIX, several providers have rolled out
proprietary communication protocols and application programming interfaces
(APIs). The proprietary structures also have the effect of making it difficult for
traders to switch platforms, thus capturing the audience. The extent of work required to adapt to a given platform can be extensive, however, and some providers
even offer monetary incentives for traders interested in building out connectivity.
Some divisions of Deutsche Börse, for example, may offer as much as $65,000 to
prospective traders to defray the interface implementation costs.
System testing: 20 percent
System testing is another critical component, discussed in detail in Chapter
16. To ensure thorough testing, the system is run through various scenarios, or
“scripts.” Professional software testers are typically deployed to examine each
block of code, to compare its performance with its stated mandate, and to document all discrepancies, known as “bugs.” Testers are often compensated about one
third as much as coders. Separating coding and testing duties also ensures proper
testing, free of face-saving whitewashing gaffes that can ultimately cost the business significant money.

■

THE BusInEss oF HIgH-FrEquEnCy TrAdIng

120

run-time monitoring: 5 percent
run-time monitoring is another HFT task requiring personnel. The task of
monitoring a well-defined HFT system with clear risk management parameters
and escalation procedures is not particularly involved, but requires close attention
to detail. separate personnel are typically tasked with the duty of watching the
systems and ensuring that run-time performance remains within acceptable
limits. Best practices for HFT monitoring are discussed in Chapter 16.
Compliance and other administrativia: 10 percent
Compliance and other administrative tasks are a function of all trading businesses. Keeping track of regulatory guidelines, documentation, and all other related activities is a full-time job.

The proportion of time spent on each task outlined here varies with the stage
of HFT business development, as shown in Figure 7.2. In the start-up phase, HFT
businesses tend to be data and programming centered. In the ramp-up stage, testing,
risk management, and monitoring take the majority of effort. Finally, in steady-state
production, it is monitoring, compliance, and other administrative tasks that take the
majority of time.
In the traditional broker-dealer world, where the word technology is often associated only with new shiny gadgets provided by technology teams far removed from
business, tasks such as system testing and policy development may seem like an unnecessary expense. By separating technology from the business, the management
creates an impression that traders need not feel accountable for the systems they
are using. real-life examples, such as the Knight Capital fiasco that occurred in the
summer of 2012, have shown that thorough testing, compliance, and monitoring of
HFT systems are key to the long-term profitability of the business. These functions
follow directly from the best practices of software development, discussed in detail
in Chapter 16.
As Figure 7.2 illustrates, development of an HFT business follows a process unusual for most traditional trading desks. designing new HFT strategies is costly;
executing and monitoring finished high-frequency products costs close to nothing.
By contrast, a traditional proprietary trading businesses incurs fixed costs from the
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%

Quant model
development
Risk management
Coding of trading and
infrastructure
System testing
Run-time monitoring
Start-up

Ramp-up

Steady-state

Compliance and other
administrativia

FIGURE 7.2 Allocation of Man-Hours during different Phases of HFT development

Cost
High-frequency
trading

Traditional
trading

Start-up

Ramp-up

Steady state
Time in development and use

FIGURE 7.3 The Economics of High-Frequency versus Traditional Trading Businesses

■ Financial Markets Suitable for HFT
A wide range of securities and market conditions fit the profile for trading at high
frequencies. some securities markets, however, are more appropriate than others.
To be appropriate for this type of trading, two requirements must be met: the
ability to quickly move in and out of positions and sufficient market volatility to
ensure that changes in prices exceed transaction costs. The volatilities of different
markets have been shown to be highly interrelated and dependent on the volume of
macroeconomic news reaching the markets. The ability to quickly enter into positions as well as to close them is in turn determined by two factors: market liquidity
and availability of electronic execution.
Liquid assets are characterized by readily available supply and demand. Liquid
securities such as major foreign exchange pairs are traded 24 hours a day, 5 days a
week. Less liquid securities, such as penny stocks, may trade only once every few
days. Between trades, the prices of illiquid assets may change substantially, making
less liquid securities more risky as compared with more liquid assets.

121
THE BusInEss oF HIgH-FrEquEnCy TrAdIng

moment an experienced senior trader with a proven track record begins running the
trading desk and training promising young apprentices, through the time when the
trained apprentices replace their masters.
Figure 7.3 illustrates the cost curves for rolling out computerized and traditional
trading systems. The cost of traditional trading remains fairly constant through time.
With the exception of trader “burnouts” necessitating hiring and training new trader
staff, costs of staffing the traditional trading desk do not change. developing computerized trading systems, however, requires an up-front investment that is costly in
terms of labor and time. one successful trading system takes on average 36 months
to develop. The costs of computerized trading decline as the system moves into production, ultimately requiring a small support staff that typically includes a dedicated
systems engineer and a performance-monitoring agent. Both the systems engineer
and a monitoring agent can be responsible for several trading systems simultaneously, driving the costs closer to zero.

The Business of High-Frequency Trading

122

High-frequency strategies focus on the most liquid securities; a security requiring
a holding period of 10 minutes may not be able to find a timely reasonably-priced
counterparty in illiquid markets. While longer-horizon investors can work with either liquid or illiquid securities, Amihud and Mendelson (1986) show that longerhorizon investors optimally hold less liquid assets. According to these authors, the
key issue is the risk/return consideration; longer-term investors (already impervious to the adverse short-term market moves) will obtain higher average gains by
taking on more risk in less liquid investments.
A perfectly liquid market is the one where the quoted bid or ask price can
be achieved irrespective of the quantities traded (see Bervas, 2006, for detailed
treatment of the subject). Market liquidity depends on the presence of limit-order
traders in the market, as well as the counterparties’ willingness to trade. The
market participants’ willingness to trade in turn depends on their risk aversions and expectations of impending price movements, along with other market
information.
One way to compare the liquidity of different securities is to use the average daily
volume of each security as the measure of liquidity. In terms of daily average trading volume, foreign exchange is the most liquid market, followed by recently issued
U.S. Treasury securities, then equities, options, commodities, and futures. Swaps,
traditionally traded over the counter (OTC), but entering the electronic era under
the Dodd-Frank Act, are on their way to become the most liquid and optimal market
for HFT.
■■ Economics of HFT

Costs of Doing HFT Business
The cost drivers in an HFT business are data, labor, equipment and software, trading
costs, administrative and legal costs, and, most important, trading losses. Effective
risk management, monitoring, and compliance frameworks, discussed in Chapters
14 and 16 are required to limit the latter. This section describes the costs of doing
business that are not attributable to risk.

Costs of Data
Data tend to be either very expensive or entirely free. Multiple companies, like
Reuters and Bloomberg, offer tick data for sale for a significant premium. Brokerdealers and trading venues may offer quality tick data free of charge to prospective
traders. Start-up HFT firms will need to obtain at least two years of historical data
in the instrument of choice to generate initial trading models.
As discussed in Chapter 2, hardware costs are the least prominent component of HFT operating expenses. The most basic, yet effective, HFT setup involves computers commonly available at retail stores. A professional operating system, like Windows 7 or Red Hat Linux, is necessary for thorough configuration and
Hardware

remote access. It is wise to purchase separate machines for development, testing,
and production, to minimize incidents of unintentional code manipulation and overloads of processing power.
Connectivity is important for any successful HFT operation: a fast
connection with a sufficient bandwidth ensures that the trading operation receives
the fullest set of quotes and trades: as described in Chapter 2, quotes in particular
can be lost in cyberspace congestion. Connectivity options involve

Connectivity

■■
■■
■■

Co-location
Proximity
Run-of-the-mill connections

HFT operations deploy the following software that may or may not be
built in-house:

Software

■■

Computerized generation of trading signals is the core functionality of an
HFT system. The generator accepts and processes tick data, generates portfolio allocations and trade signals, and records profit and loss (P&L). Generators are most often built in-house and kept in utmost secrecy. The secrecy
requirement stems from purely competitive business considerations: every
investment strategy has a finite capacity, and a competitor armed with a generator code is bound to significantly diminish or outright destroy profitability
of an HFT strategy.
Computer-aided analysis is done with financial modeling software deployed by
HFT operations to build new trading models. MatLab and R have emerged as the
industry’s most popular quantitative modeling choices. MatLab can be pricey, but
is well known in the industry. R, however, is free: it is an open-source software
that is efficient, and, best of all, can be extended with proprietary libraries. Citigroup, for example, now runs almost all of its modeling in R.

123
The Business of High-Frequency Trading

Co-location or “colo” is offered by exchanges and other trading venues in their
dedicated facilities, and typically includes a secure “cage” for the HFT server, a power
source, and an actual network “wire” connecting the HFT and the exchange servers,
most often via a dedicated line. High-frequency traders are free to configure the
server anyway they like, and may include remote accessibility.
Proximity services are similar to co-location, except they are run by third-party
companies with access to facilities located close to trading venues, but not in the
same facility as trading venues. Like co-location, proximity offers a cage for servers,
a power source, and a fast wire (typically, a fiber-optic hookup). The wire, however,
connects to the exchange via the general Internet, making proximity less secure than
co-location.
Finally, a shoestring HFT start-up can survive on a premium cable network as well
until its systems become consistently profitable. The common network, however, is
subject to extreme congestion, resulting in serial quote losses and information and
trading delays.

■■

The Business of High-Frequency Trading

124

■■

Internet-wide information-gathering software facilitates high-frequency fundamental pricing of securities. Promptly capturing rumors and news announcements
enhances forecasts of short-term price moves. Thomson Reuters, Dow Jones, and
newcomers like RavenPack, SemLab and AbleMarkets.com offer a range of products that deliver real-time news in a machine-readable format.
Trading software incorporates optimal execution algorithms for achieving the
best execution price within a given time interval. This software enables traders
to time trades, decide on market aggressiveness, and size orders into optimal
lots. Development and per-trade licensing of best execution algorithms is now
the bread and butter of many broker-dealers. Yet independent companies have
sprung up to help investors distribute their orders in the most efficient manner.
For example, the New York–based MarketFactory provides a suite of software
tools to help automated traders get an extra edge in the foreign exchange market.
Furthermore, an increasing number of traditional buy-side investors, like large
pension funds and hedge funds, have developed their own suites of best execution
algorithms in a bid to bypass broker-dealers altogether. Chapter 15 discusses the
latest developments in best execution.
Run-time risk management applications ensure that the system stays within
pre-specified behavioral and P&L bounds, as discussed in detail in Chapter
14. Such applications may also be known as system-monitoring and faulttolerance software and are often built in-house, but are generic enough to
buy off the shelf. The advantage of buying third-party risk software is the reliability of the modules. The third-party software undergoes diligent review by
multiple customers and, as a result, may be more sound than anything built
in-house.
Desktop and mobile applications designed for monitoring performance of HFT
systems are a must for all modern HFT organizations. Any issues, breaches of risk
limits, power outages, or any other problems should be immediately related to
responsible parties. Like risk-management systems, performance monitoring and
compliance systems tend to be generic enough to warrant purchasing well-tested
third-party software.
Real-time third-party research can stream advanced information and forecasts.
Sometimes, these forecasts can be incorporated into a trading system in a useful
manner. For example, a forecast that warns of an imminent crash can be used to
enhance a liquidity provision HFT system. AbleMarkets.com and HFTindex.com
provide this kind of information.

Electronic Execution HFT practitioners may rely on their executing brokers and ECNs to quickly route and execute their trades. Goldman Sachs and
Credit Suisse are often cited as broker-dealers dominating electronic execution.
UBS, Barclays and Quantitative Brokers have been the go-to venues for foreign
exchange and fixed income.
Execution providers typically charge a per-trade fee, known in advance. The total
costs may, however, include other unobservable components that vary from broker to broker, as Chapter 5 describes in detail. Understanding the cost structure of

execution is especially important in high-frequency settings where the sheer number
of transactions can eliminate gains.
Custody and Clearing In addition to providing connectivity to exchanges,
broker-dealers typically offer special “prime” services that include safekeeping of
trading capital (known as custody) and trade reconciliation (known as clearing). Both
custody and clearing involve a certain degree of risk. In a custody arrangement,
the broker-dealer takes the responsibility for the assets, whereas in clearing, the
broker-dealer may act as insurance against the default of trading counterparties.
Broker-dealers and trading venues charge custody and clearing fees.

Initial development of high-frequency systems is both risky and
pricey, and the staff required to design trading models needs to understand PhD-level
quantitative research in finance and econometrics. In addition, programming staff
should be experienced enough to handle complex issues of system interoperability,
computer security, and algorithmic efficiency.

Staffing Costs

Administrative and Legal Costs Like any business in the financial sector, highfrequency traders need to make sure that “all i’s are dotted and all t’s are crossed” in
legal and accounting departments. Qualified legal and accounting assistance is therefore indispensable for building a capable operation.

As with any other form of trading, an HFT firm can be capitalized with equity and
leverage. The initial equity normally comprises contributions from the founders of
the firm, private equity capital, private investor capital, or capital of the parent company. The amount of the initial equity required depends on many factors, but can be
approximated using the following variables:
■■
■■
■■
■■

Profitability of the HFT strategy to be traded with live capital.
Cost structure of the trading operation.
Sharpe ratio of the strategy.
Maximum drawdown of the strategy.

The profitability of the HFT strategy describes the “gross” return on every
dollar invested. The gross return does not account for trading costs and presents a high-level picture of potential profitability. During the earliest stages of
investment, back-test performance can be used as potential future performance.
Great caution, however, should be used: back-tests often fail to account for basic
costs and market impact of the strategy itself, reducing production profitability.
Worst of all, back-tests can be simply wrong, either due to unrealistic assumptions or coding mistakes that may not be exposed until the code is transferred
into production.
Strategies that do well in gross performance terms are subject to significant
costs. In high-frequency settings, per-trade gains are typically small compared to

125
The Business of High-Frequency Trading

Capitalization of HFT

The Business of High-Frequency Trading

126

the transaction costs, which can easily annihilate any semblance of profitability. This
is particularly true in the start-up phases of operation, when the traded notional is
often small. As described in Chapter 5, trading costs are often larger when the traded
amount is small and vice versa. For example, a common retail brokerage charges $20
per every leg of the trade with notional of $40,000 and less, or more than 0.05 percent of the notional. And every trade has two legs: one to open a position, and one
to close, emptying a retail trader of 0.1 percent per every round-trip trade. At the
same time, a large institution faces costs of as little as $3 or $5 for every $1 million
traded—just 0.0005 percent of the notional, a cost 100 times smaller than the one
offered to the retail investors.
When the available capital is small, it often can be “levered.” Leverage most often refers to borrowed funds collateralized by the traded financial instruments.
Thus, with a 1:9 leverage, a $100,000 investment becomes $1 million trading notional, possibly obtaining lower transaction costs and retaining better profitability.
In addition, leverage helps multiply gains of the strategy. A 0.1 percent return on
$100,000 is $100 without leverage. When the strategy is traded with a 1:9 leverage,
the $0.1 percent return becomes a $1 million × 0.1 percent = $1,000 or 1 percent
return on the $100,000 investment, a significant improvement. Of course, when the
strategy loses money, its losses are also multiplied accordingly: what is a $100 loss in
an unlevered $100,000 notional extends to a $1,000 loss with a 1:9 leverage.
Broker-dealers are the most natural providers of leverage: they can observe the
trader’s positions in real time and ensure return of their capital by liquidating said
trader’s positions. Liquidation happens when the trader’s account value falls below
a safety collateral value known as margin. Margin requirements vary from broker
to broker, but typically designate a certain percentage of the traded notional to be
in the account at all times. Margin requirements are not, however, written in stone
and can be negotiated on an account-by-account and even situation-by-situation
basis.
To avoid liquidation, traders can optimize the leverage that works best for each
strategy. Maximum drawdown and Sharpe ratio metrics help traders determine how
much leverage the trader can afford given the volatility of his strategy and the maximum downside recorded in historical data.
In addition to leverage, later-stage equity can be a source of trading capital, and it
can be obtained from established institutions, such as bank asset management divisions, fund-of-funds, pension funds, large hedge funds interested in boosting their
performance, and the like.
From the perspective of a large institutional investor, possibly looking to invest
into a high-frequency operation, most HFT tends to fall into the category of “alternative” investments. The term alternative investments describes most strategies under a broader hedge fund umbrella; the term is used to distinguish strategies from
“traditional” investments, such as long-only mutual funds and bond portfolios. As a
result of its alternative status, HFT strategies are candidates for inclusion in larger
institutional portfolios. To qualify for institutional investment, HFT managers need
to deliver a one- to three-year auditable performance track record of 8 to 12 percent
per annum, with as little volatility as possible.

The compensation of HFTs then follows the hedge fund model: HFT managers
are paid management and performance fees. Management fees are typically fixed
percentages of the notional amount invested. The performance fees are percentages
of the gain above the previous highest value of the fund shares, known as high water
mark. Just as with any other hedge fund manager, the performance fee is paid to a
high-frequency manager only when the manager increases (or has increased) the
value of the fund shares, creating an incentive to outperform.
Due to its relative novelty, HFT is often treated as an “emerging manager” business. The “emerging” label typically results in higher perceived risk as far as strategy
longevity is concerned, from the institutional investor’s point of view. This, in turn,
translates into higher performance, but lower management fees. Where an arbitrary
hedge fund may command 2 percent management fee and 20 percent performance
fee (the classic “2-and-20” model), high-frequency traders often offer a “1-and-30”
model, with 1 percent of all assets under management serving as a compensation for
administrative activity, and 30 percent of above-the-highest-water mark gains paid as
a performance incentive.

Leverage of HFT

SR HFT =

[Rannualized ] = E [Rannualized ] × L
σ [ Rannualized ] σ [ Rannualized ] × L
E

(1)

The expected return of the high-frequency operation must take into account the
costs of doing business, so the Sharpe ratio of an HFT business is adjusted for expenses:
SR HFT Ops =

[Rannualized ] × L × (Capital ) − ( Annualized Expenses )
σ [ Rannualized ] × L ×(Capital )

(2)

or, using daily data, and assuming 250 trading days per year:
E  Rdaily  × L × ( Capital ) − ( Daily Expenses )

SR HFT Ops = 
250
σ Rdaily  × L × ( Capital )

(3)

127
The Business of High-Frequency Trading

How much leverage can an HFT business sustain and remain viable? The quick answer to this question depends on two performance variables characteristic to each
HFT strategy: Sharpe ratio and maximum drawdown. The beauty of the Sharpe ratio
lies in its invariance with respect to leverage: a Sharpe ratio of an unlevered HFT
strategy is exactly the same as the Sharpe ratio of an HFT strategy levered 100 times.
This is due to the structure of the high-frequency Sharpe ratio: no levered HFT positions are held overnight, so the HFT Sharpe ratio does not include the risk-free rate
in the numerator, as pointed out in Chapter 6. When the Sharpe ratio increases, the
expected return in the numerator and the volatility in the denominator of the ratio
increase proportionally by the amount of leverage, L:

Expressions in equations (2) and (3) have to be positive for a profitable business, yet the leverage value L cannot be increased infinitely. Annualized volatility
is only the average measure of return variability. The actual realizations of losses
can be much more severe. To determine the minimum Sharpe ratio SRHFT Ops
required for a stable operation, a maximum drawdown comes in as a convenient
metric.
Assuming that the historical maximum drawdown can occur in 10 percent of
worst-case scenarios, the required Sharpe ratio SRHFT Ops is related to the number
of standard deviations the historical maximum drawdown lies away from the mean
of returns:
Max$$Drawdown
> SR HFT Ops ×σ [ Rannualized ] × L − 1.645×⋅σ [ Rannualized ] × L (4)
Capital
from where the minimum SRHFT Ops can be obtained as
SR HFT Ops min =

The Business of High-Frequency Trading

128

Max$$Drawdown Capital + 1.96 × σ [Rannualized ] × L

σ [Rannualized ] × L

(5)

For a levered strategy to remain solvent, the Sharpe ratio takes into account operating costs SRHFT Ops that have to exceed SRHFTOpsmin determined by equation (5).
Figure 7.4 presents gross cumulative performance of a sample high-frequency strategy. The strategy delivers a gross Sharpe ratio of 2.78 with a maximum drawdown
of 0.93 percent incurred in July 2012, and daily volatility of 0.15 percent computed over the sample history of the strategy. The minimum operational Sharpe ratio
SRHFT Ops this strategy delivers when levered has to exceed SRHFTOpsmin of equation (5),
computed to be 1.41. If this particular strategy is allocated $10 million in capital
and allowed a nine-to-one leverage, L = 10, then the maximum daily spending of the
operation cannot exceed $13,730, or $3,432,729 for 250 trading days per year. This
number is considerably smaller than the number computed from the daily average
return: if the risk of going bankrupt via maximum drawdown is ignored completely,
then the expected levered performance is computed as the annualized average daily
return multiplied by capital and leverage:
E [Gainnaive ] = E Rdaily  × 250 × Capital × Leverage

(6)

If computed using equation (6), the naïve gain works out to be nearly $6,959,034– a
misleading number to spend when the risk of drawdown is taken into account.
If a stricter performance measure is required, whereby the observed maximum
drawdown occurs in less than 5 percent of all cases, equation (5) can be rewritten as
SR HFT Ops min =

MaxDrawdown Capital + 1.96 × σ [ Rannualized ] × L

σ [ Rannualized ] × L

(7)

where number of standard deviations where maximum drawdown is located has
changed from 1 to 3. For the $10 million capital deployed in strategy with the

FIGURE 7.4 HFT Industry Participants

minimum operational sharpe ratio of 2.41, for example, the maximum allowable
annual expense is $931,801.
An HFT operation is more likely to survive and prosper if it has leverage and high
sharpe ratios. High leverage increases the likelihood of covering costs, and the high
sharpe ratio reduces the risk of a catastrophic loss.
129

Like any other industry, HFT is subject to outside forces and influences. Figure 7.4
summarizes the playing field of HFT. The remainder of the section discusses market
participants in detail.

Competitors
HFT firms compete with other, more traditional, investment management firms,
as well as market-making broker-dealers. The competition with traditional mutual and hedge funds centers on attracting investment. The rivalry with quantitative
hedge funds and other high-frequency trading firms also includes recruitment of
talented and experienced strategists and technologists, as well as direct contest for
market inefficiencies. Likewise, the battle with traditional non-HFT broker-dealers
involves turf wars over “first dibs” access to profit opportunities in the traditional
market-making arena.

Investors
Investors in HFT include funds-of-funds aiming to diversify their portfolios, hedge
funds eager to add new strategies to their existing mix, and private equity firms seeing a sustainable opportunity to create wealth. Most investment banks offer leverage
through their “prime” services.

THE BusInEss oF HIgH-FrEquEnCy TrAdIng

■ Market Participants

Services and Technology Providers
Like any business, a high-frequency trading operation requires specific support services. Most common and, in many cases, critical providers to the high-frequency
business community include providers of data, hardware, connectivity, software, execution, custody, clearing, staffing, and administrative and legal services, described
in more detail earlier in this chapter.

Government
Several regulatory initiatives were under way around the world at the time this book
was written. Chapter 13 summarizes the latest regulatory thought.
■■ Summary

The Business of High-Frequency Trading

130

Developing a high-frequency business involves challenges that include issues surrounding the “gray box” or “black box” nature of many systems.The low transparency
of fast and complex algorithm decisions requires diligent risk management and monitoring processes, and constant human supervision. The deployment and execution
costs decrease considerably with time, leaving the profit-generating engines operating consistently, with no emotion, sickness, or other human factors. Well-designed
and -executed high-frequency systems, capitalizing on multiple short-term moves of
security prices, are capable of generating solid profitability in all types of electronic
markets.
■■ End-of-Chapter Questions
1. What are the key steps in algorithm development?
2. How much time is spent on monitoring in a stable HFT operation?
3. What kind of operational costs can an HFT with $100 million in capital and a net
(after transaction costs) Sharpe ratio of 1.5 carry?
4. What is the minimum capital needed for a breakeven of an HFT with the following characteristics:
a. Net (after transaction costs) Sharpe ratio of 2.8
b. Three full-time officers earning $150,000 per year each
c. Office overhead (office space, networking and computer expenses) of
$72,000 per year
d. Co-location of $36,000 per year
5. Who are the HFT industry participants?

Chapter 8

Statistical Arbitrage
Strategies
L

ike human trading, high-frequency trading (HFT) strategies can be broken down
into three major categories (per Harris, 1998):

1. Statistical arbitrage or stat-arb, also known as value-motivated strategies. Stat-arb traders
wait for security prices to become cheap relative to their proprietary valuations
of security based on fundamental or purely statistical indicators. These traders
run models to determine the fair value of each financial instrument. Stat-arb
traders might be traditional, low-frequency institutional money managers, as
well as high-frequency managers, arbitraging short-term valuation discrepancies. Stat-arb traders may deploy market orders for fast-dissolving price discrepancies as well as limit orders to capture slowly evolving misvaluations (see
Kaniel and Liu, 2006; and Angel, 1994).
2. Directional strategies, also known as informed trading. Directional traders successfully estimate the direction of an impending market move. Directional traders
are often high-frequency money managers and other proprietary traders with
superior access to information and skill in assessing immediate market situations. Their information can include analyses from paid-for news sources, like
Bloomberg, not yet available to the general public; forecasts based on market
microstructure; and other sources.
Directional traders’ forecasts tend to be time sensitive. Forecasts may be related to an event scheduled to occur at a specific time, after which the forecasts
cease to be useful. Information obtained from premium sources may soon be
distributed to the public, reducing its potency. As a result, directional traders are
impatient and typically execute using market orders or “aggressive” limit orders
set at prices close to market (see Vega, 2007). Directional event-based strategies
are discussed in Chapter 9.

131

3. Market-making, also known as liquidity trading. Market makers have no material
market insights and aim to profit from providing liquidity. When using highfrequency algorithms, liquidity traders deploy automated market-making strategies, discussed in Chapters 10 and 11. Market makers are most likely to use limit
orders, although selected situations may call for market orders as well.

STATISTICAL ArBITrAge STrATegIeS

132

Figure 8.1 illustrates distributions of order aggressiveness and trader types relative to the market price in the limit order book.
Statistical arbitrage (stat-arb) exploded on the trading scene in the 1990s, with
traders reaping double-digit returns using simple statistical phenomena.This chapter
discusses common stat-arb strategies deployed in the HFT space.
Stat-arb is named after its primary function: detection of statistically persistent
phenomena, most often, with fundamental roots. Such statistically persistent relationships may exist between the current price level of equity and the recently reported earnings of the traded company. The relationships may also be between price
levels of multiple financial instruments, linked by some fundamental variables, the
price level of one financial instrument and the volatility of another, and many other
values.
The critical point in the identification process of financial instruments suitable for
stat-arb is that the relationship among the variables has to hold with at least 90 or
higher percent statistical confidence. This level of statistical confidence is observed
when the numerical variation in the tested relationship remains within two standard
deviations from its average value. Thus, in a way, stat-arb is a modern and sophisticated cousin of a technical analysis strategy utilizing “Bollinger bands” that showed
a two-standard-deviation envelope around the simple moving average of the price,
suggesting the likely near-term price path bounds.
Stat-arb models measuring statistical persistence of shown economic phenomena tend to have higher profitability and longer staying power than models detecting statistical persistence based on data mining alone. An example of stat-arb
based on solid economic principles is the exchange-traded fund (eTF) or index
arbitrage: by the Law of One Price of finance, a traded index or eTF should have
the same price as a basket of individual financial instruments comprising the eTF

Order
aggressiveness

Value traders
Low price (bids)

Liquidity traders
(Uninformed)

Informed
traders

Market price

Liquidity traders
(Uninformed)

Value traders
High price (asks)

FIGURE 8.1 graphical representation of Order Aggressiveness and Trader Type Distributions in
the Limit Order Book

and weighed accordingly. If a mismatch between the do-it-yourself basket and the
traded ETF exists, a trader can profitably arbitrage the mismatch, as discussed
later in this chapter.
By contrast, a statistical relationship observed between prices of two completely
unrelated stocks may be purely random, or “spurious.” While the relationship produces a highly significant statistical dependency, it can hardly be used to make meaningful predictions about future values of the stocks under consideration. From a
trading strategy point of view, such a relationship is not too different from the statistical relationships shown by Challe (2003), who illustrates the following outrageous
spurious relationship: a statistically significant link between the occurrence of sunspots and the predictability of asset returns.
This chapter explores techniques developed for detecting stat-arb relationships,
as well as presents specific cases of proven dependencies.
■■ Practical Applications of Statistical Arbitrage

General Considerations

Equities
Examples of successful statistical arbitrage strategies involving fundamental equities models abound. This section reviews the following popular equity stat-arb trading strategies: pairs, different equity classes of the same issuer, market-neutral pairs
trading, liquidity arbitrage, and large-to-small information spillovers.

133
Statistical Arbitrage Strategies

The prices of two or more financial instruments traded in stat-arb models often will
be fundamentally related in some fashion or other, but they can nevertheless span a
variety of asset classes and individual names. In equities, the companies issuing securities may belong to the same industry and will therefore respond similarly to changes in the broad market. Alternatively, the securities may actually be issued by the
same company. Companies often issue more than one class of shares, and the shares
typically differ by voting rights. Even shares of the same class issued by the same
company but trading on different exchanges may have profitable intraday deviations
in prices. In foreign exchange, the pair of instruments chosen can be a foreign exchange rate and a derivative (e.g., a futures contract) on the same foreign exchange
rate. The same underlying derivative trading strategy may well apply to equities and
fixed-income securities. Passive indices, such as infrequently rebalanced ETFs, can
be part of profitable trades when the index and its constituents exhibit temporary
price deviations from equilibrium. In options, the pair of instruments may be two
options on the same underlying asset but with different times to expiration.
This section discusses numerous examples of statistical arbitrage applied to various financial instruments. Table 8.1 itemizes the strategies discussed subsequently.
The selected strategies are intended to illustrate the ideas of fundamental arbitrage.
The list is by no means exhaustive, and many additional fundamental arbitrage opportunities can be found.

Table 8.1 Summary of Fundamental Arbitrage Strategies by Asset Class Presented in This
Section
Asset Class

Fundamental Arbitrage Strategy

Equities

Pairs trading

Equities

Different equity classes of the same issuer

Equities

Risk arbitrage

Equities

Liquidity rbitragea

Foreign exchange

Triangular arbitrage

Foreign exchange

Uncovered interest parity (UIP) arbitrage

Indices and ETFs

Index composition arbitrage

Options

Volatility curve arbitrage

Cross-asset

Futures basis trading

Cross-asset

Futures/ETF arbitrage

Pairs trading is the simplest and most commonly used stat-arb
strategy. Mathematically, the steps involved in the development of stat-arb trading
signals are based on a relationship between price levels or other variables characterizing any two financial instruments. A relationship based on price levels Si,t and
Sj,t for any two instruments i and j can be can be arrived at through the following
procedure:

Pairs Trading

Statistical Arbitrage Strategies

134

1. Identify the universe of liquid financial instruments: instruments that trade at
least once within the desired trading frequency unit. For example, for hourly
trading frequency choose securities that trade at least once every hour.
2. Measure the difference between prices of every two securities, i and j, identified
in step (1) across time t:
∆Sij,t = Si,t − S j,t , t ∈ [1,T ]

(1)

where T is a sufficiently large number of daily observations. According to the central limit theorem (CLT) of statistics, 30 observations at selected trading frequency
constitute the bare minimum. The intra-day data, however, may have high
seasonality—that is, persistent relationships can be observed at specific hours of
the day. Thus, a larger T of at least 30 daily observations is strongly recommended.
For robust inferences, a T of 500 daily observations (two years) is desirable.
3. For each pair of securities, select the ones with the most stable relationship—
security pairs that move together.To do this, Gatev, Goetzmann and Rouwenhorst
(1999) perform a simple minimization of the historical differences in returns between every two liquid securities:
T

min ∑ ( ∆Sij,t )2
i, j

t =1

(2)

The stability of the relationship can also be assessed using cointegration and
other statistical techniques.
Next, for each security i, select the security j with the minimum sum of
squares obtained in equation (2).

4. Estimate basic distributional properties of the difference as follows.
Mean or average of the difference:
E[ ∆St ] =
Standard deviation:

σ [ ∆St ] =

1 T
∑ ∆St
T t =1

1 T
( ∆St − E[ ∆St ])2
∑
T − 1 t =1

5. Monitor and act upon differences in security prices:
At a particular time t, if
∆Sτ = Si,τ − S j,τ > E[ ∆Sτ ] + 2σ [ ∆Sτ ]
sell security i and buy security j. However, if

∆Sτ = Si,τ − S j,τ < E[ ∆Sτ ] − 2σ [ ∆Sτ ]
buy security i and sell security j.
6. Once the gap in security prices reverses to achieve a desirable gain, close out the
positions. If the prices move against the predicted direction, activate stop loss.

It is reasonable to
expect stocks corresponding to two common equity classes issued by the same company to be trading within a relatively constant price range from each other. Different classes of common equity issued by the same company typically diverge in the
following two characteristics only: voting rights and number of shares outstanding.

Arbitraging Different Equity Classes of the Same Issuer

135
Statistical Arbitrage Strategies

Instead of detecting statistical anomalies in price levels, statistical arbitrage can be
applied to other variables, such as correlation between two securities and traditional fundamental relationships. The details of implementation of statistical arbitrage
based on fundamental factors are discussed in detail in the following text.
Pairs-trading strategies can be trained to dynamically adjust to changing market
conditions. The mean of the variable under consideration, to which the identified
statistical relationships are assumed to tend, can be computed as a moving weighted
average with the latest observations being given more weight than the earliest observations in the computation window. Similarly, the standard deviation used in computations can be computed using a limited number of the most recent observations,
reflecting the latest economic environment.
Statistical relationships validated by academic research in economics and finance
may consistently produce positive results for many traders. Thorough understanding
of economic theory helps quantitative analysts distinguish between solid and arbitrary relationships and, in turn, improves the profitability and reduces risk of trading
operations that use stat-arb methodology.
In addition to the issues embedded in the estimation of statistical relationships,
statistical arbitrage strategies are influenced by numerous adverse market conditions.

Statistical Arbitrage Strategies

136

Shares with superior voting rights are usually worth more than the shares with
inferior voting rights or nonvoting shares, given that shares with wider voting
privileges allow the shareholders to exercise a degree of control over the direction of the company—see Horner (1988) and Smith and Amoako-Adu (1995), for
example. Nenova (2003) shows that the stock price premium for voting privileges
exists in most countries. The premium varies substantially from country to country and depends on the legal environment, the degree of investor protection, and
takeover regulations, among other factors. In countries with the greatest transparency, such as Finland, the voting premium is worth close to zero, whereas in South
Korea, the voting premium can be worth close to 50 percent of the voting stock’s
market value.
Stocks with a higher number of shares outstanding are usually more liquid, prompting actively trading investors to value them more highly (see Amihud and Mendelson,
1986, 1989; Amihud, 2002; Brennan and Subrahmanyam, 1996; Brennan, Chordia,
and Subrahmanyam, 1998; and Eleswarapu, 1997). At the same time, the more liquid class of shares is likely to incorporate market information significantly faster than
the less liquid share class, creating opportunities for information arbitrage.
A typical trade may work as follows: if the price range widens to more than two
standard deviations of the average daily range without a sufficiently good reason, it
may be a fair bet that the range will narrow within the following few hours.
The dual-class share strategy suffers from two main shortcomings and may not
work for funds with substantial assets under management (AUM).
1. The number of public companies that have dual share classes trading in the open
markets is severely limited, restricting the applicability of the strategy. In January
2009, for example, Yahoo! Finance carried historical data for two equity classes for just eight companies trading on the New York Stock Exchange (NYSE):
Blockbuster, Inc.; Chipotle; Forest City Entertainment; Greif, Inc.; John Wiley
& Sons; K V Pharma; Lennar Corp.; and Moog, Inc.
2. The daily volume for the less liquid share class is often small, further restricting
the capacity of the strategy. Table 8.2 shows the closing price and daily volume
for dual-class shares registered on the NYSE on January 6, 2009. For all names,
Class B daily volume on January 6, 2009, does not reach even one million in
shares and is too small to sustain a trading strategy of any reasonable trading size.
Table 8.2 Closing Price and Daily Volume of Dual-Class Shares on NYSE on January 6, 2009
Company Name

Ticker Class A

Blockbuster, Inc.

BBI

Chipotle

CMG

Forest City Entertainment

FCE-A

Greif, Inc.

GEF

John Wiley & Sons

JW-A

K V Pharma

KV-A

Lennar Corp.
Moog, Inc.

Class A Close

Class A Volume
(MM Shares)

Ticker
Class B

Class B
Close

Class B Volume
(MM Shares)

1.59

2.947

BBI-B

0.88

0.423

60.38

0.659

CMG-B 55.87

0.156

8.49

1.573

FCE-B

8.41

0.008

35.42

0.378

GEF-B

35.15

0.016

36.82

0.237

JW-B

36.63

0.005

3.68

0.973

KV-B

3.78

0.007

LEN

11.17

8.743

LEN-B

8.5

0.074

MOG-A

37.52

0.242

MOG-B 37.9

0.000

Risk arbitrage or market-neutral arbitrage refers to a class of trading models that are based on classical equilibrium finance literature. At core, most
market-neutral models are built on the capital asset pricing model (CAPM) developed by Sharpe (1964), Lintner (1965), and Black (1972).
The CAPM is based on the idea that returns on all securities are influenced by
the broad market returns. The degree of the co-movement that a particular security
may experience with the market is different for each individual security and can vary
through time. For example, stocks of luxury companies have been shown to produce positive returns whenever the broad market produces positive returns as well,
whereas breweries and movie companies tend to produce higher positive returns
whenever the overall market returns are downward sloping.
The CAPM equation is specified as follows:

Risk Arbitrage

ri,t − r f ,t = α i + β i ( rM,t − r f ,t ) + ε t

(3)

∆βˆ = βˆi − βˆ j

σˆ ∆β =

σ β2 i
ni

σ β2 j
nj

(4)

(5)

where ni and nj are the numbers of observations used in the estimation of equation
(3) for security i and security j, respectively.
The standard t-ratio statistic is then determined as follows:
∆βˆ
Studenttβ =
(6)
σˆ
∆β

137
Statistical Arbitrage Strategies

where ri,t is the return on security i at time t, rM,t is the return on a broad market
index achieved in time period t, and rf,t is the risk-free interest rate, such as Fed
Funds rate, valid in time period t. The equation can be estimated using ordinary
least squares (OLS) regression. The resulting parameter estimates, α̂ and β̂ , measure the abnormal return that is intrinsic to the security ( α̂ ) and the security’s comovement with the market ( β̂ ).
The simplest example of CAPM-based pair arbitrage in equities is trading pairs
with the same response to the changes in the broader market conditions, or beta,
but different intrinsic returns, or alpha. This type of strategy is often referred to as
a market-neutral strategy, with the idea that going long and short, respectively, in
two securities with similar beta would neutralize the resulting portfolio from broad
market exposure.
Often, the two securities used belong to the same or a similar industry, although
this is not mandatory. The alpha and beta for two securities i and j are determined
from the CAPM equation (3). Once the point estimates for alphas and betas of the
two securities are produced, along with standard deviations of those point estimates,
the statistical significance of difference in alphas and betas is then determined using
the difference in the means test, described here for betas only:

The difference test for alphas follows the same procedure as the one outlined for
betas in equations (4) through (6).
As with other t-test estimations, betas can be deemed to be statistically similar if
the t statistic falls within one standard deviation interval:
 − σ ∆β , ∆ β
 + σ ∆β ]
tβ ∈[∆ β

(7)

At the same time, the difference in alphas has to be both economically and statistically significant. The difference in alphas has to exceed trading costs, TC, and the
t-ratio has to indicate a solid statistical significance, with 95 percent typically considered the minimum:

Statistical Arbitrage Strategies

138

∆α̂ > TC

(8)

tα > [ ∆α + 2σ ∆α ]

(9)

Once a pair of securities satisfying equations (7) through (9) is identified, the
trader goes long in the security with the higher alpha and shorts the security with
the lower alpha. The position is held for the predetermined horizon used in the
forecast.
Variations on the basic market-neutral pair trading strategy include strategies accounting for other security-specific factors, such as equity fundamentals. For example, Fama and French (1993) show that the following three-factor model can be
successfully used in equity pair trading:
ri,t = α i + β iMKT MKTt + β iSMB SMBt + β iHML HMLt + ε t

(10)

where ri,t is the return on stock i at time t, MKTt is the time-t return on a broad market index, SMBt (small minus big) is the time-t difference in returns between market
indices or portfolios of small and big capitalization stocks, and HMLt (high minus
low) is the return on a portfolio constructed by going long in stocks with comparatively high book-to-market ratios and going short in stocks with comparatively low
book-to-market ratios.
In classical asset pricing literature, a financial security that offers some inconvenience to the prospective investors should offer higher returns to
compensate investors for the inconvenience. Limited liquidity is one such inconvenience; lower liquidity levels make it more difficult for individual investors to
unwind their positions, potentially leading to costly outcomes. On the flip side, if
liquidity is indeed priced in asset returns, then periods of limited liquidity may offer
nimble investors highly profitable trading opportunities.
In fact, several studies have documented that less liquid stocks have higher average
returns: see Amihud and Mendelson (1986); Brennan and Subrahmanyam (1996);
Brennan, Chordia, and Subrahmanyam (1998); and Datar, Naik, and Radcliffe
(1998). Trading the illiquid stocks based exclusively on the information that they are
illiquid, however, delivers no positive abnormal returns. The relatively high average

Liquidity Arbitrage

returns simply compensate prospective investors for the risks involved in holding
these less liquid securities.
Pastor and Stambaugh (2003), however, recognize that at least a portion of the
observed illiquidity of financial securities may be attributed to market-wide causes.
If the market-wide liquidity is priced into individual asset returns, then market illiquidity arbitrage strategies may well deliver consistent positive abnormal returns
on the risk-adjusted basis.
Pastor and Stambaugh (2003) find that in equities, stocks whose returns have
higher exposure to variability in the market-wide liquidity indeed deliver higher
returns than stocks that are insulated from the market-wide liquidity. To measure
sensitivity of stock i to market liquidity, Pastor and Stambaugh (2003) devise a metric g that is estimated in the following OLS specification:
rie,t +1 = θ + β ri,t + γ sign( rie,t ).v i,t + τ t +1

(11)

Large-to-Small Information Spillovers Equity shares and other securities with
relatively limited market capitalization are considered to be “small.” The precise
cutoff for “smallness” varies from exchange to exchange. On the NYSE in 2002,
for example, “small” stocks were those with market capitalization below $1 billion;
stocks with market capitalization of $1 billion to $10 billion were considered to be
“medium,” and “large” stocks were those with market cap in excess of $10 billion.
Small stocks are known to react to news significantly more slowly than large
stocks. Lo and MacKinlay (1990), for example, found that returns on smaller stocks
follow returns on large stocks. One interpretation of this phenomenon is that large
stocks are traded more actively and absorb information more efficiently than small
stocks. Hvidkjaer (2006) further documents “an extremely sluggish reaction” of
small stocks to past returns of large stocks and attributes this underreaction to the
inefficient behavior of small investors.
A proposed reason for the delay in the response of small stocks is their relative
unattractiveness to institutional investors who are the primary source of the information that gets impounded into market prices. The small stocks are unattractive
to institutional investors because of their size. A typical size of a portfolio of a
midcareer institutional manager is $200 million; if a portfolio manager decides
to invest into small stocks, even a well-diversified share of an institutional portfolio will end up moving the market for any small stock significantly, cutting into
profitability and raising the liquidity risk of the position. In addition, ownership

139
Statistical Arbitrage Strategies

where ri,t is the return on stock i at time t, vi,t is the dollar volume for stock i at time
t, and ri,te is the return on stock i at time t in excess of the market return at time t:
rie,t = ri,t − rm,t . The sign of the excess return ri,te proxies for the direction of the order
flow at time t; when stock returns are positive, it is reasonable to assume that the
number of buy orders in the market outweighs the number of sell orders, and vice
versa. The prior time-period return ri,t is included to capture the first-order autocorrelation effects shown to be persistent in the return time series of most financial
securities.

of 5 percent or more of a particular U.S. stock must be reported to the Securities
and Exchange Commission (SEC), further complicating institutional investing in
small stocks. As a result, small stocks are traded mostly by small investors, many
of whom use daily data and traditional “low-tech” technical analysis to make trading decisions.
The market features of small stocks make the stocks illiquid and highly inefficient, enabling profitable trading. Llorente, Michaely, Saar, and Wang (2002)
studied further informational content of trade volume and found that stocks of
smaller firms and stocks with large bid-ask spreads exhibit momentum following
high-volume periods. Stocks of large firms and firms with small bid-ask spread,
however, exhibit no momentum and sometimes exhibit reversals following highvolume time periods. Profitable trading strategies, therefore, involve trading small
stocks based on the results of correlation or cointegration with lagged returns of
large stocks as well as the volume of large and small stocks’ records during preceding periods.

Foreign Exchange

Statistical Arbitrage Strategies

140

Foreign exchange has a number of classic models that have been shown to work
in the short term. This section summarizes statistical arbitrage applied to triangular arbitrage and uncovered interest rate parity models. Other fundamental foreign
exchange models, such as the flexible price monetary model, the sticky price monetary model, and the portfolio model can be used to generate consistently profitable
trades in the statistical arbitrage framework.
Triangular arbitrage exploits temporary deviations from
fair prices in three foreign exchange crosses. The following example illustrates
triangular arbitrage of EUR/CAD, following a triangular arbitrage example described by Dacorogna et al. (2001). The strategy arbitrages mispricings between
the market prices on EUR/CAD and “synthetic” prices on EUR/CAD that are
computed as follows:
Triangular Arbitrage

EUR/CADSunthetic,bid = EUR/USDMarket,bid × USD/CADMarket,bid

(12)

EUR/CADSunthetic,ask = EUR/USDMarket,ask × USD/CADMarket,ask

(13)

If market ask for EUR/CAD is lower than synthetic bid for EUR/CAD, the strategy is to buy market EUR/CAD, sell synthetic EUR/CAD, and wait for the market and synthetic prices to align, then reverse the position capturing the profit. The
difference between the market ask and the synthetic bid should be high enough to
at least overcome two spreads—on EUR/USD and on USD/CAD. The USD-rate
prices used to compute the synthetic rate should be sampled simultaneously. Even
a delay as small as one second in price measurement can significantly distort the relationship as a result of unobserved trades that affect the prices in the background;
by the time the dealer receives the order, the prices may have adjusted to their noarbitrage equilibrium levels.

The uncovered interest parity (UIP) is just
one such relation. Chaboud and Wright (2005) find that the UIP best predicts changes in foreign exchange rates at high frequencies and daily rates when the computation
is run between 4:00 p.m. ET and 9:00 p.m. ET. The UIP is specified as follows:

Uncovered Interest Parity Arbitrage

1 + it = (1 + it* )

Et [St +1 ]

(14)

where it is the one-period interest rate on the domestic currency deposits, it* is the
one-period interest rate on deposits denominated in a foreign currency, and St is the
spot foreign exchange price of one unit of foreign currency in units of domestic currency. Thus, for example, if domestic means United States–based and foreign means
Swiss, the UIP equation, equation (14), can be used to calculate the equilibrium
CHF/USD rate as follows:
1 + it,USD = (1 + it*,CHF )

Et [St +1,CHF /USD ]
St,CHF /USD

(15)

The expression can be conveniently transformed to the following regression form
suitable for linear estimation:
In(St +1,CHF /USD ) − In(St,CHF /USD ) = α + β (In(1 + it,USD ) − In(1 + it*,CHF )) + ε t +1

(16)

Indices and ETFs
Index arbitrage is driven by the relative mispricings of indices and their underlying
components. Under the Law of One Price, index price should be equal to the price
of a portfolio of individual securities composing the index, weighted according to
their weights within the index. Occasionally, relative prices of the index and the
underlying securities deviate from the Law of One Price and present the following
arbitrage opportunities. If the price of the index-mimicking portfolio net of transaction costs exceeds the price of the index itself, also net of transaction costs, sell
the index-mimicking portfolio, buy index, hold until the market corrects its index
pricing, then realize gain. Similarly, if the price of the index-mimicking portfolio is
lower than that of the index itself, sell index, buy portfolio, and close the position
when the gains have been realized.
Alexander (1999) shows that cointegration-based index arbitrage strategies deliver consistent positive returns and sets forth a cointegration-based portfolio management technique step by step:
1. A portfolio manager selects or is assigned a benchmark. For a portfolio manager
investing in international equities, for example, the benchmark can be a European,
Asian, or Far East (EAFE) Morgan Stanley index and its constituent indices. Outperforming the EAFE becomes the objective of the portfolio manager.

141
Statistical Arbitrage Strategies

A statistical arbitrage of this relationship would look into the statistical deviations of
the two sides of equation (16) and make trading decisions accordingly.

2. The manager next determines which countries lead EAFE by running the errorcorrecting model (ECM) with log(EAFE) as a dependent variable and log prices
of constituent indices in local currencies as independent (explanatory) variables:
EAFEt = α + β1x1,t + ... + β n x n,t + ε t

(17)

where the statistically significant b1…bn coefficients indicate optimal allocations pertaining to their respective country indices x1…xn, and a represents
the expected outperformance of the EAFE benchmark if the residual from the
cointegrating regression is stationary. b1…bn can be constrained in estimation,
depending on investor preferences.
An absolute return strategy can further be obtained by going long in the indices
in proportions identified in step 2 and shorting EAFE.

Options
In options and other derivative instruments with a nonlinear payoff structure, statistical arbitrage usually works between a pair of instruments written on the same
underlying asset but having one different characteristic. The different characteristic
is most often either the expiration date or the strike price of the derivative.The strategy development proceeds along the steps noted in the previous sections.
Statistical Arbitrage Strategies

142

Cross-Asset
Statistical arbitrage is not limited to a single asset class. Instead, statistical arbitrage
can apply to pairs consisting of a financial instrument and its derivative, or two financial instruments sharing fundamental values.
Futures are financial instruments of choice in many cross-market
stat-arb models. Futures prices are linear functions of the underlying asset and are
easy to model:

Basis Trading

Ft=St exp[rt(T - t)]

(18)

where Ft is the price of a futures contract at time t, St is the price of the underlying
asset (e.g., equity share, foreign exchange rate, or interest rate) also at time t, T is
the time the futures contract expires, and r t is the interest rate at time t. For foreign
exchange futures, rt is the differential between domestic and foreign interest rates.
The statistical arbitrage between a futures contract and the underlying asset is
known as “basis trading.” As with equity pairs trading, the basis-trading process follows the following steps: estimation of the distribution of the contemporaneous
price differences, ongoing monitoring of the price differences, and acting upon those
differences.
Lyons (2001) documents results of a basis-trading strategy involving six currency pairs: DEM/USD, USD/JPY, GBP/USD, USD/CHF, FRF/USD, and
USD/CAD. The strategy bets that the difference between the spot and futures

prices reverts to its mean or median values. The strategy works as follows: sell
foreign currency futures whenever the futures price exceeds the spot price by
a certain predetermined level or more, and buy foreign currency futures whenever the futures price falls short of the spot price by at least a prespecified difference. Lyons (2001) reports that when the predetermined strategy trigger
levels are computed as median basis values, the strategy obtains a Sharpe ratio
of 0.4 to 0.5.
In response to macroeconomic news announcements, futures markets have been shown to adjust more quickly than spot markets. Kawaller,
Koch, and Koch (1993), for example, show that prices of the S&P 500 futures react
to news faster than prices of the S&P 500 index itself, in the Granger causality specification. A similar effect was documented by Stoll and Whaley (1990): for returns
measured in 5-minute intervals, both S&P 500 and money market index futures led
stock market returns by 5 to 10 minutes.
The quicker adjustment of the futures markets relative to the equities markets
is likely due to the historical development of the futures and equities markets. The
Chicago Mercantile Exchange, the central clearinghouse for futures contracts in
North America, rolled out a fully functional electronic trading platform during the
early 1990s; most equity exchanges still relied on a hybrid clearing mechanism that
involved both human traders and machines up to the year 2005. As a result, faster
information-arbitraging strategies have been perfected for the futures market, while
systematic equity strategies remain underdeveloped to this day. By the time this book
was written, the lead-lag effect between futures and spot markets had decreased
from the 5- to 10-minute period documented by Stoll and Whaley (1990) to a 1- to
2-second advantage. However, profit-taking opportunities still exist for powerful
HFT systems with low transaction costs.

Futures/ETF Arbitrage

P1,t = α + β P2,t + ε t

(19)

where P1,t is the price of the first financial instrument, P2,t is the price of the second financial instrument under consideration, and α and β are coefficients in a
simple OLS regression. Instruments 1 and 2 and said to be cointegrated whenever
the generated error term ε t is stationary, that is, mean reverting. Several tests for
stationarity of error terms exist. Perhaps the simplest test works as follows: if at least
90 percent of error observations, ε t , lie within two standard deviations of ε t away
from the mean of ε t , the error series ε t can be considered stationary.

Statistical Arbitrage Strategies

Cointegration of Various Financial Instruments/Asset Classes Stat-arb models can also be built on two or more financial instruments, potentially from drastically different asset classes. Often, such multi-instrument multiasset models are
developed using cointegration. Cointegration refers to a condition whereby prices of
two or more financial instruments move in tandem according to a simple specification, parameterized on historical data. A two-instrument cointegration model can
be specified as follows:

143

To further fine-tune statistical dependencies between any two securities, a stat-arb
researcher may include lagged realizations of price changes in a vector-autoregressive
framework to detect stat-arb relationships several time periods ahead of trading time:
P1,t = α + β 0 P2,t + β1( P2,t − P2,t −1 ) + β2 ( P2,t −1 − P2,t −2 ) +  + β k ( P2,t −k +1 − P2,t −k ) + ε t

(20)

P2,t = γ + δ 0 P1,t + δ1( P1,t − P1,t −1 ) + δ 2 ( P1,t −1 − P1,t −2 ) +  + δ k ( P1,t −k +1 − P1,t −k ) + ωt
(21)

The number of lags, k, used in the regressions (20) and (21), is typically determined based on statistical significance of the coefficients β k and δ k . As a rule of
thumb, if the absolute value of t-ratios accompanying β k and δ k drop off to less than
two, the of the kth lag is considered nonexistent, and the kth lag becomes the terminal lag in the regressions.
Yet another common way to enhance performance of stat-arb models is to extend
the regression of equation (19) with additional financial instruments:
P1,t = α + β P2,t + γ P3,t +  + δ Pn,t + ε t

Statistical Arbitrage Strategies

144

(22)

As in equation (19), the key stat-arb criterion of the multi-instrument cointegration is the stationarity of the error terms, ε t . Similar to equations (20) and (21),
equation (22) can be extended to include lagged observations of prices.
■■ Summary
Statistical arbitrage is powerful in high-frequency settings as it provides a simple
set of clearly defined conditions that are easy to implement in a systematic fashion
in high-frequency settings. Statistical arbitrage based on solid economic theories is
likely to have longer staying power than strategies based purely on statistical phenomena.
■■ End-of-Chapter Questions
1. What are the three types of traders present in financial markets? How do they
differ and coexist?
2. What are the key principles behind statistical arbitrage? Discuss.
3. You are considering trading SPY and E-mini futures on the S&P 500 contracts in
a stat-arb model. According to equation (18), prices of SPY and E-mini futures
are theoretically linked by a mathematical relationship. Suppose that the shortterm estimate of the cointegration models of equations (20) and (21) generates
negative and statistically significant coefficients b1 and δ1. How can SPY and Emini futures on the S&P 500 be arbitraged in this scenario?

4. Suppose that, over a long range, high-frequency returns on two stocks are linked
by the market-neutral framework of equations (3) through (10) (same b, different α: α1 > α2). In the short term, however, this relationship has reversed, and
now α2 > α1 over the past 30 minutes. How can one statistically arbitrage such
an occurrence?
5. A particular ETF is updated daily. Suppose you are interested in arbitraging the
ETF against the basket of securities it comprises. To do so, you run cointegration models pitching the high-frequency ETF returns against returns of a large
universe of stocks and pick up some statistically significant dependencies. How
do you arbitrage your findings?

145
Statistical Arbitrage Strategies

Chapter 9

Directional Trading
Around Events
M

any traditional low-frequency quantitative models assume several idealized
market conditions. The following condition is assumed particularly often:
markets instantaneously incorporate all relevant public information as soon as the
information is available. Fair long-term quantitative valuation, the theory goes, is
feasible only when the prices always reflect all fundamental information (see rational
expectations of Muth, 1961, and the efficient markets hypotheses, Fama, 1970, for
details).
Anyone who has watched the evolution of real-life financial prices surrounding
a major news release has noted that the price adjustment to news is hardly instantaneous. In fact, the news “impoundment” into prices can be described as follows:
volatile swings of the price that eventually settle within a certain range. The price
never settles on a constant price level because a degree of volatility, however small,
accompanies all market conditions. The process of the market finding its optimal
postannouncement price band is often referred to as tâtonnement, from the French
for “trial and error.”
The tâtonnement toward a new optimal price happens through the implicit negotiation among buyers and sellers that is occurring in the order flow.
With news reported instantly and trades placed on a tick-by-tick basis, high-frequency traders are ideally positioned to profit from the impact of
announcements on markets. By arbitraging price fluctuations surrounding each news
release, HFTs high-frequency strategies further deliver a common good: they bring
real-life markets ever closer to their idealized state whereby all prices are instantaneously updated with the latest news.The high-frequency strategies presented in this
chapter trade on the market movements surrounding market-wide events, such as
news announcements and other occurrences.

147

■■ Developing Directional Event-Based Strategies

Directional Trading Around Events

148

Directional event-based strategies refer to the group of trading strategies that place
trades on the basis of the markets’ reaction to events. The events may be economic,
industry, or even instrument-specific occurrences that consistently affect the
instrument(s) of interest time and time again. For example, unexpected increases
in the Fed Funds rates consistently raise the value of the U.S. dollar, simultaneously
raising the rate for USD/CAD and lowering the rate for AUD/USD. The announcements of the U.S. Fed Funds decisions, therefore, are events that can be consistently
and profitably arbitraged.
The goal of event arbitrage strategies is to identify portfolios that make positive
profit over the time window surrounding each event. The time window is typically
a time period beginning just before the event and ending shortly afterwards. For
events anticipated ex-ante, such as scheduled economic announcements, the portfolio positions may be opened ahead of the announcement or just after the announcement. The portfolio is then fully liquidated shortly after the announcement.
Trading positions can be held anywhere from a fraction of a second to several
hours and can result in consistently profitable outcomes with low volatilities. The
speed of response to an event often determines the trade gain; the faster the response, the higher the probability that the strategy will be able to profitably ride the
momentum wave to the post-announcement equilibrium price level. As a result,
event arbitrage strategies are well suited for high-frequency applications and are
most profitably executed in fully automated trading environments.
Developing an event arbitrage trading strategy harnesses research on equilibrium
pricing and leverages statistical tools that assess tick-by-tick trading data and events
the instant they are released. Further along in this chapter, we will survey academic
research on the impact of events on prices; now we investigate the mechanics of
developing an event arbitrage strategy.
Most event arbitrage strategies follow a three-stage development process:
1. For each event type, identify dates and times of past events in historical data.
2. Compute historical price changes at desired frequencies pertaining to securities
of interest and surrounding the events identified in step 1.
3. Estimate expected price responses based on historical price behavior surrounding past events.
The sources of dates and times for specified events that occurred in the past can
be collected from various Internet sites. Most announcements recur at the same
time of day and make the job of collecting the data much easier. U.S. unemployment announcements, for example, are always released at 8:30 a.m. Eastern time.
Some announcements, such as those of the U.S. Federal Open Markets Committee
interest rate changes, occur at irregular times during the day and require greater
diligence in collecting the data. Firms such as Reuters, Dow Jones, RavenPack,
SemLab, HFTIndex.com and AbleMarkets.com distribute news and other tradeable data in machine-readable formats, further simplifying automation of eventdriven trading strategies.

■■ What Constitutes an Event?

149
Directional Trading Around Events

The events used in event arbitrage strategies can be any releases of news about economic
activity, market disruptions, and other events.The key requirement for event suitability
is that the chosen events are repetitive. The recurrence of events allows researchers to
estimate historical impact of the events and project the effect into the future.
All events do not have the same magnitude. Some events may have positive and
negative impacts on prices, and some events may have more severe consequences
than others. The magnitude of an event can be measured as a deviation of the realized event figures from the expectations of the event. In economics, the deviation is
frequently referred to as a “surprise.” The price of a particular stock, for example,
should adjust to the net present value of its future cash flows following a higher- or
lower-than-expected earnings announcement. However, if earnings are in line with
investor expectations, the price should not move. Similarly, in the foreign exchange
market, the level of a foreign exchange pair should change in response to an unexpected change—for example, in the level of the consumer price index (CPI) of the
domestic country. If, however, the domestic CPI turns out to be in line with market
expectations, little change should occur.
Market participants form expectations about event figures well before the formal
statistics are announced. Many financial economists are tasked with forecasting inflation, earnings, and other figures based on other continuously observed market and
political variables, as well as pure news. When event-related forecasts become available, market participants trade securities on the basis of the forecasts, impounding
their expectations into prices well before the formal announcements occur.
One of the key steps in the estimation of news impact is separating the unexpected change, or news, from the expected and priced-in component. The earliest
macroeconomic event studies (see Frenkel, 1981, and Edwards, 1982, for example)
assumed that most economic news developed slowly over time, and the trend observed during the past several months or quarters was the best predictor of the value
to be released on the next scheduled news release day. The news, or the unexpected
component of the news release, was then the difference between the value released in
the announcement and the expectation formed on the basis of autoregressive analysis.
Later researchers such as Eichenbaum and Evans (1993) and Grilli and Roubini
(1993) have been using such a framework to predict the decisions of the central
bankers, including the U.S. Federal Reserve. Once again, the main rationale behind
the autoregressive predictability of the central bankers’ actions is that the central
bankers are not at liberty to make drastic changes to economic variables under their
control, given that major changes may trigger large-scale market disruptions. Instead, the central bankers adopt and follow a longer-term course of action, gradually
adjusting the figures in their control, such as interest rates and money supply, to lead
the economy in the intended direction.
The empirical evidence of the impact of news defined in the autoregressive fashion shows that the framework indeed can be used to predict future movements of
securities.Yet the impact is best seen in shorter terms. Almeida, Goodhart, and Payne
(1998) documented a significant effect of macroeconomic news announcements on

the USD/DEM exchange rate sampled at five-minute intervals. The authors found
that news announcements pertaining to the U.S. employment and trade balance
were particularly significant predictors of exchange rates, but only within two hours
following the announcement. However, U.S. non-farm payroll and consumer confidence news announcements caused price momentum lasting 12 hours or more
following an announcement.
Surprises in macroeconomic announcements can be measured relative to published averages of economists’ forecasts. For example, every week Barron’s and the
Wall Street Journal publish consensus forecasts for the coming week’s announcements,
as do Bloomberg and Reuters. The forecasts are developed from a survey of field
economists.
■■ Forecasting Methodologies
Development of forecasts involves event studies on very specific trading data surrounding event announcements of interest. Event studies measure the quantitative
impact of announcements on the returns surrounding the news event and are usually
conducted as follows:

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150

1. The announcement dates, times, and “surprise” changes are identified and recorded. To create useful simulations, the database of events and the prices of
securities traded before and after the event should be very detailed, with events
categorized carefully and quotes and trades captured at high frequencies. The
surprise component can be measured in two ways:
■■ As the difference between the realized value and the prediction based on autoregressive analysis.
■■ As the difference between the realized value and the analyst forecast consensus.
2. The returns corresponding to the times of interest surrounding the announcements are calculated for the securities under consideration. For example, if
the researcher is interested in evaluating the impact of CPI announcements
on the 1-second change in USD/CAD, the one-second change in USD/CAD
is calculated from 8:30:00 to 8:30:01 a.m. on historical data on past CPI
announcement days. (The U.S. CPI announcements are always released at
8:30 a.m. ET.)
3. The impact of the announcements is then estimated in a simple linear regression:
Rt=α+β∆Xt+εt
where Rt is the vector of returns surrounding the announcement for the security of interest arranged in the order of announcements ∆Xt is the vector of
“surprise” changes in the announcements arranged in the order of announcements; εt is the idiosyncratic error pertaining to news announcements; a is the
estimated intercept of the regression that captures changes in returns due to
factors other than announcement surprises; and, finally, b measures the average
impact of the announcement on the security under consideration.

Changes in equity prices are adjusted by changes in the overall market prices to
account for the impact of broader market influences on equity values. The adjustment is often performed using the market model of Sharpe (1964):
Rta = Rt − Rˆt

(1)

where the “hat” notation expresses the average estimate and R̂t is the expected equity
return estimated over historical data using the market model:
Rt = α+βRm,tεt

(2)

A Practical Example
The latest figures tracking U.S. inflation are released monthly at 8:30 a.m. on prespecified dates. On release, USD/CAD spot and other USD crosses undergo an
instantaneous one-time adjustment, at least in theory. Identifying when and how
quickly the adjustments happen in practice, we can construct profitable trading strategies that capture changes in price levels following announcements of the latest inflation figures.
The first step in identification of profitable trading opportunities is to define
the time period from the announcement to the end of the trading opportunity,
known as the event window. We select data sample windows surrounding the recent
U.S. inflation announcements in the tick-level data from January 2002 through
August 2008. As all U.S. inflation announcements occur at 8:30 a.m. EST, we
define 8:00 to 9:00 a.m. as the trading window and download all of the quotes

151
Directional Trading Around Events

The methodology was first developed by Ball and Brown (1968), and the estimation
method to this day delivers statistically significant trading opportunities.
During a typical trading day, numerous economic announcements are made
around the world. The news announcements may be related to a particular company,
industry, or country; or, like macroeconomic news, they may have global consequences. Company news usually includes quarterly and annual earnings releases,
mergers and acquisitions announcements, new product launch announcements, and
the like. Industry news comprises industry regulation in a particular country, the
introduction of tariffs, and economic conditions particular to the industry. Macroeconomic news contains interest rate announcements by major central banks, economic indicators determined from government-collected data, and regional gauges
of economic performance.
With the development of information technology such as RSS feeds, alerts, press
wires, and news aggregation engines such as Google, it is now feasible to capture
announcements the instant they are released. A well-developed automated event arbitrage system captures news, categorizes events, and matches events to securities
based on historical analysis. Various companies offer machine-readable streams of
data that can be readily parsed by a computer and used as an input to event-driven
strategies. The companies with machine-readable offerings include Thomson Reuters, Dow Jones, and a large number of smaller players.

Directional Trading Around Events

152

and trades recorded during that time. We partition the data further into 5-minute,
1-minute, 30-second, and 15-second blocks. We then measure the impact of
the announcement on the corresponding 5-minute, 1-minute, 30-second, and
15-second returns of USD/CAD spot.
According to the purchasing power parity (PPP), a spot exchange rate between
domestic and foreign currencies is the ratio of the domestic and foreign inflation
rates. When the U.S. inflation rate changes, the deviation disturbs the PPP equilibrium and the USD-based exchange rates adjust to new levels. When the U.S. inflation rate rises, USD/CAD is expected to increase instantaneously, and vice versa. To
keep matters simple, in this example we will consider the inflation news in the same
fashion as it is announced, ignoring the market’s preannouncement adjustment to
expectations of inflation figures.
The sign test then tells us during which time intervals, if any, the market properly
and consistently responds to announcements during our “trading window” from 8
to 9 a.m. The sample includes only days when inflation rates were announced. The
summary of the results is presented in Table 9.1.
Looking at five-minute intervals surrounding the U.S. inflation announcements,
it appears that USD/CAD reacts persistently only to decreases in the U.S. inflation rate and that reaction is indeed instantaneous. USD/CAD decreases during
the five-minute interval from 8:25 to 8:30 a.m. in response to announcements of
lower inflation with 95 percent statistical confidence. The response may potentially support the instantaneous adjustment hypothesis; after all, the U.S. inflation
news is released at 8:30 a.m., at which point the adjustment to drops in inflation
appears to be completed. No statistically significant response appears to occur following rises in inflation.
Higher-frequency intervals tell us a different story—the adjustments occur in
short-term bursts. At one-minute intervals, for example, the adjustment to increases
in inflation can now be seen to consistently occur from 8:34 to 8:35 a.m.This postannouncement adjustment, therefore, presents a consistent profit-taking opportunity.
Splitting the data into 30-second intervals, we observe that the number of tradable opportunities increases further. For announcements of rising inflation, the price
adjustment now occurs in four 30-second postannouncement intervals. For the announcements showing a decrease in inflation, the price adjustment occurs in one
30-second postannouncement time interval.
Examining 15-second intervals, we note an even higher number of time-persistent
trading opportunities. For rising inflation announcements, there are five 15-second
periods during which USD/CAD consistently increased in response to the inflation
announcement between 8:30 and 9:00 a.m., presenting ready tradable opportunities. Six 15-second intervals consistently accompany falling inflation announcements
during the same 8:30 to 9:00 a.m. time frame.
In summary, as we look at shorter time intervals, we detect a larger number of
statistically significant currency movements in response to the announcements. The
short-term nature of the opportunities makes them conducive to a systematic (i.e.,
black-box) approach, which, if implemented knowledgeably, reduces risk of execution delays, carrying costs, and expensive errors in human judgment.

Table 9.1 Number of Persistent Trading Opportunities in USD/CAD Following the U.S.
Inflation Rate Announcements
Estimation Frequency

U.S. Inflation Up

U.S. Inflation Down

5 minutes

1 minute

30 seconds

15 seconds

■■ Tradable News
This section summarizes various event types and their impact on specific financial
instruments. The impact of events is drawn from various academic sources. The time
frames for the impact of the news may have shrunk considerably since the studies were first published due to proliferation of machine-readable news and general
interest in this set of trading strategies. The described impact is, however, based on
strong fundamental factors, and is likely to persist, even if for shorter periods of
time. Some of the included studies estimate impact using low-frequency data; the
high-frequency response of the variables used in studies tends to be comparable or
even more pronounced.

Corporate News

∞

E[Earningst ]
t
t =1 (1 + Rt )

Equity price = ∑

(3)

where E[Earningst] are the expected cash flows of the company at a future time t, and
Rt is the discount rate found appropriate for discounting time t dividends to present. Unexpected changes to earnings generate rapid price responses whereby equity
prices quickly adjust to new information about earnings.
Significant deviations of earnings from forecasted values can cause large market
movements and can even result in market disruptions. To prevent large-scale impacts

153
Directional Trading Around Events

Corporate activity such as earnings announcements, both quarterly and annual, significantly impacts equity prices of the firms releasing the announcements. Unexpectedly positive earnings typically lift equity prices, and unexpectedly negative earnings
often depress corporate stock valuation.
Earnings announcements are preceded by analyst forecasts. The announcement
that is materially different from the economists’ consensus forecast results in a rapid
adjustment of the security price to its new equilibrium level. The unexpected component of the announcements is computed as the difference between the announced
value and the mean or median economists’ forecast. The unexpected component is
the key variable used in estimation of the impact of an event on prices.
Theoretically, equities are priced as present values of future cash flows of the
company, discounted at the appropriate interest rate determined by the capital asset
pricing model (CAPM), the arbitrage pricing theory of Ross (1977), or the investorspecific opportunity cost:

of earnings releases on the overall market, most earnings announcements are made
after the markets close.
Other firm-level news also affects equity prices.The effect of stock splits, for example, has been documented by Fama, Fisher, Jensen, and Roll (1969), who show that the
share prices typically increase following a split relative to their equilibrium price levels.
Event arbitrage models incorporate the observation that earnings announcements
affect each company differently. The most widely documented firm-level factors for
evaluation include the size of the firm market capitalization (for details, see Atiase,
1985; Freeman, 1987; and Fan-fah, Mohd, and Nasir, 2008).

Industry News

Directional Trading Around Events

154

Industry news consists mostly of legal and regulatory decisions along with announcements of new products. These announcements reverberate throughout the entire
sector and tend to move all securities in that market in the same direction. Unlike
macroeconomic news that is collected and disseminated in a systematic fashion, industry news usually emerges in an erratic fashion.
Empirical evidence on regulatory decisions suggests that decisions relaxing rules
governing activity of a particular industry result in higher equity values, whereas the
introduction of rules constricting activity pushes equity values down. The evidence
includes the findings of Navissi, Bowman, and Emanuel (1999), who ascertained that
announcements of relaxation or elimination of price controls resulted in an upswing
in equity values and that the introduction of price controls depressed equity prices.
Boscaljon (2005) found that the relaxation of advertising rules by the U.S. Food and
Drug Administration was accompanied by rising equity values.

Macroeconomic News
Macroeconomic decisions and some observations are made by government agencies
on a predetermined schedule. Interest rates, for example, are set by economists at
the central banks, such as the U.S. Federal Reserve or the Bank of England. On the
other hand, variables such as CPIs are typically not set but are observed and reported
by statistics agencies affiliated with the countries’ central banks.
Other macroeconomic indices are developed by research departments of both forprofit and nonprofit private companies.The ICSC Goldman store sales index, for example, is calculated by the International Council of Shopping Centers (ICSC) and is actively
supported and promoted by the Goldman Sachs Group.The index tracks weekly sales at
sample retailers and serves as an indicator of consumer confidence: the more confident
consumers are about the economy and their future earnings potential, the higher is their
retail spending and the higher is the value of the index. Other indices measure different
aspects of economic activity ranging from relative prices of McDonald’s hamburgers in
different countries to oil supplies to industry-specific employment levels.
Table 9.2 shows an ex-ante schedule of macroeconomic news announcements for
Tuesday, March 3, 2009, a typical trading day. European news is most often released in
the morning of the European trading session while North American markets are closed.

Table 9.2 Ex-Ante Schedule of Macroeconomic Announcements for March 3, 2009
Prior Value

Consensus
Forecast

Time (ET)

Event

1:00 a.m.

Norway Consumer Confidence

1:45 a.m.

GDP Q/Q

0.0%

–0.8%

Switzerland

1:45 a.m.

GDP Y/Y

1.6%

–0.1%

Switzerland

2:00 a.m.

Wholesale Price Index M/M

–3.0%

–2.0%

Germany

2:00 a.m.

Wholesale Price Index Y/Y

–3.3%

–6.3%

Germany

3:00 a.m.

Norway PMI SA

40.8

40.2

Norway

4:30 a.m.

PMI Construction

34.5

34.2

United Kingdom

7:45 a.m.

ICSC Goldman Store Sales

8:55 a.m.

Redbook

9:00 a.m.

Bank of Canada Rate

1.0%

0.5%

10:00 a.m.

Pending Home Sales

6.3%

–3.0%

1:00 p.m.

Four-Week Bill Auction

2:00 p.m.

Total Car Sales

9.6M

United States

2:00 p.m.

Domestic Car Sales

6.8M

6.9M

United States

5:00 p.m.

ABC/Washington Post Consumer Confidence

5:30 p.m.

AIG Performance of Service Index

7:00 p.m.

Nationwide Consumer Confidence

7:30 p.m.

GDP Q/Q

0.1%

Australia

7:30 p.m.

GDP Y/Y

1.9%

1.1%

Australia

9:00 p.m.

ANZ Commodity Prices

–13.3

Country

Norway

United States
United States
Canada
United States
United States

v48

–4.3%

–47

United States
Australia

United Kingdom

New Zealand

Most macroeconomic announcements of the U.S. and Canadian governments are distributed in the morning of the North American session that coincides with afternoon
trading in Europe. Most announcements from the Asia Pacific region, which includes
Australia and New Zealand, are released during the morning trading hours in Asia.
Many announcements are accompanied by “consensus forecasts,” which are
aggregates of forecasts made by economists of various financial institutions. The
consensus figures are usually produced by major media and data companies, such
as Bloomberg LP, that poll various economists every week and calculate average
industry expectations.
Macroeconomic news arrives from every corner of the world. The impact on currencies, commodities, equities, and fixed-income and derivative instruments is usually estimated using event studies, a technique that measures the persistent impact of
news on the prices of securities of interest.
■■ Application of Event Arbitrage
Event trading is applicable to many asset classes, yet the impact of each event may be
different for every financial instrument. This section considers documented persistent impact of events on various financial instruments.

155
Directional Trading Around Events

SA = seasonally adjusted; NSA = non–seasonally adjusted data.

Foreign Exchange Markets

Directional Trading Around Events

156

Market responses to macroeconomic announcements in foreign exchange were
studied by Almeida, Goodhart, and Payne (1997); Edison (1996); Andersen,
Bollerslev, Diebold, and Vega (2003); and Love and Payne (2008), among many
others.
Edison (1996) finds that foreign exchange reacts most significantly to news
about real economic activity, such as nonfarm payroll employment figures. In
particular, Edison (1996) shows that for every 100,000 surprise increases in
nonfarm payroll employment, USD appreciates by 0.2 percent on average.
At the same time, the author documents little impact of inflation on foreign
exchange rates.
Andersen et al. (2003) conducted their analysis on foreign exchange quotes
interpolated based on timestamps to create exact five-minute intervals. The
authors show that average exchange rate levels adjust quickly and efficiently
to new levels according to the information releases. Volatility, however, takes
longer to taper off after the spike surrounding most news announcements. The
authors also document that bad news usually has a more pronounced effect than
good news.
Andersen et al. (2003) use the consensus forecasts compiled by the International
Money Market Services (MMS) as the expected value for estimation of surprise component of news announcements. The authors then model the five-minute changes in
spot foreign exchange rate Rt as follows:
I

Rt = β 0 + ∑ β i Rt −i + ∑ ∑ β kj Sk,t − j + ε t , t = 1,...,T
i =1

k =1 j =0

(4)

where Rt-i is i-period lagged value of the five-minute spot rate, Sk,t-j is the surprise
component of the kth fundamental variable lagged j periods, and et is the time-varying
volatility that incorporates intraday seasonalities. Andersen et al. (2003) estimate the
impact of the following variables:
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■

GDP (advance, preliminary, and final figures)
Nonfarm payroll
Retail sales
Industrial production
Capacity utilization
Personal income
Consumer credit
Personal consumption expenditures
New home sales
Durable goods orders
Construction spending
Factory orders
Business inventories

■■
■■
■■
■■
■■
■■

■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■

Government budget deficit
Trade balance
Producer price index
Consumer price index
Consumer confidence index
Institute for Supply Management (ISM) index (formerly the National Association
of Purchasing Managers [NAPM] index)
Housing starts
Index of leading indicators
Target Fed Funds rate
Initial unemployment claims
Money supply (M1, M2, M3)
Employment
Manufacturing orders
Manufacturing output
Trade balance
Current account
CPI
Producer prices
Wholesale price index
Import prices
Money stock M3

Equity Markets
A typical trading day is filled with macroeconomic announcements, both domestic
and foreign. How do the macroeconomic news impact equity markets?

Directional Trading Around Events

Andersen, Bollerslev, Diebold, and Vega (2003) considered the following currency pairs: GBP/USD, USD/JPY, DEM/USD, CHF/USD, and EUR/USD from
January 3, 1992, through December 30, 1998. The authors document that all currency pairs responded positively, with 99 percent significance, to surprise increases
in the following variables: nonfarm payroll employment, industrial production, durable goods orders, trade balance, consumer confidence index, and the National Association of Purchasing Managers (NAPM) index. All the currency pairs considered
responded negatively to surprise increases in the initial unemployment claims and
money stock M3.
Love and Payne (2008) document that macroeconomic news from different countries affects different currency pairs. Love and Payne (2008) studied the impact of the
macroeconomic news originating in the United States, the Eurozone, and the United
Kingdom on the EUR/USD, GBP/USD, and EUR/GBP exchange-rate pairs. The
authors find that the U.S. news has the largest effect on the EUR/USD, while GBP/
USD is most affected by the news originating in the United Kingdom. Love and
Payne (2008) also document the specific impact of the type of news from the three
regions on their respective currencies; their findings are shown in Table 9.3.

157

Table 9.3 Effect of Region-Specific News Announcements on the Respective Currency,
per Love and Payne (2008)
News Announcement Type

Directional Trading Around Events

158

Region of News Origination

Increase in prices or money Increase of output

Eurozone, Effect on EUR

Appreciation

Increase in trade balance

United Kingdom, Effect on GBP

Appreciation

United States, Effect on USD

Depreciation

Appreciation

According to classical financial theory, changes in equity prices are due to two
factors: changes in expected earnings of publicly traded firms, and changes in the
discount rates associated with those firms. Expected earnings may be affected by
changes in market conditions. For example, increasing consumer confidence and
consumer spending are likely to boost retail sales, uplifting earnings prospects for
retail outfits. Rising labor costs, however, may signal tough business conditions and
decrease earnings expectations as a result.
The discount rate in classical finance is, at its bare minimum, determined by the
level of the risk-free rate and the idiosyncratic riskiness of a particular equity share.
The risk-free rate pertinent to U.S. equities is often proxied by the three-month bill
issued by the U.S. Treasury; the risk-free rate significant to equities in another country is taken as the short-term target interest rate announced by that country’s central
bank. The lower the risk-free rate, the lower is the discount rate of equity earnings
and the higher are the theoretical prices of equities.
How does macroeconomic news affect equities in practice? Ample empirical evidence shows that equity prices respond strongly to interest rate announcements
and, in a less pronounced manner, to other macroeconomic news. Decreases in both
long-term and short-term interest rates indeed positively affect monthly stock returns with 90 percent statistical confidence for long-term rates and 99 percent confidence for short-term rates. (See Cutler, Poterba, and Summers,1989, for example.)
Anecdotal evidence suggests that most adjustments of prices occur within seconds
or minutes of the announcement time.
Stock reaction to nonmonetary macroeconomic news is usually mixed. Positive
inflation shocks tend to induce lower stock returns independent of other market
conditions (see Pearce and Roley, 1983, 1985, for details). Several other macroeconomic variables produce reactions conditional on the contemporary state of the
business cycle. Higher-than-expected industrial production figures are good news
for the stock market during recessions but bad news during periods of high economic activity, according to McQueen and Roley (1993).
Similarly, unexpected changes in unemployment statistics were found to cause
reactions dependent on the state of the economy. For example, Orphanides (1992)
finds that returns increase when unemployment rises, but only during economic expansions. During economic contractions, returns drop following news of rising unemployment. Orphanides (1992) attributes the asymmetric response of equities to
the overheating hypothesis: when the economy is overheated, increase in unemployment actually presents good news. The findings have been confirmed by Boyd, Hu,

159
Directional Trading Around Events

and Jagannathan (2005). The asymmetric response to macroeconomic news is not
limited to the U.S. markets. Löflund and Nummelin (1997), for instance, observe
the asymmetric response to surprises in industrial production figures in the Finnish
equity market; they found that higher-than-expected production growth bolsters
stocks in sluggish states of the economy.
Whether or not macroeconomic announcements move stock prices, the announcements are always usually surrounded by increases in market volatility.
While Schwert (1989) pointed out that stock market volatility is not necessarily
related to volatility of other macroeconomic factors, surprises in macroeconomic
news have been shown to significantly increase market volatility. Bernanke and
Kuttner (2005), for example, show that an unexpected component in the interest rate announcements of the U.S. Federal Open Market Committee (FOMC)
increase equity return volatility. Connolly and Stivers (2005) document spikes in
the volatility of equities comprising the Dow Jones Industrial Average (DJIA) in
response to U.S. macroeconomic news. Higher volatility implies higher risk, and
financial theory tells us that higher risk should be accompanied by higher returns.
Indeed, Savor and Wilson (2008) show that equity returns on days with major U.S.
macroeconomic news announcements are higher than on days when no major announcements are made. Savor and Wilson (2008) consider news announcements
to be “major” if they are announcements of consumer price index (CPI), producer
price index (PPI), employment figures, or interest rate decisions of the FOMC.
Veronesi (1999) shows that investors are more sensitive to macroeconomic news
during periods of higher uncertainty, which drives asset price volatility. In the
European markets, Errunza and Hogan (1998) found that monetary and real macroeconomic news has considerable impact on the volatility of the largest European
stock markets.
Different sources of information appear to affect equities at different frequencies.
The macroeconomic impact on equity data appears to increase with the increase in
frequency of equity data. Chan, Karceski, and Lakonishok (1998), for example, analyzed monthly returns for U.S. and Japanese equities in an arbitrage pricing theory
setting and found that idiosyncratic characteristics of individual equities are most
predictive of future returns at low frequencies. By using factor-mimicking portfolios, Chan et al. (1998) show that size, past return, book-to-market ratio, and dividend
yield of individual equities are the factors that move in tandem (“covary”) most with
returns of corresponding equities. However, Chan et al. (1998, p. 182) document
that “the macroeconomic factors do a poor job in explaining return covariation” at
monthly return frequencies. Wasserfallen (1989) finds no impact of macroeconomic
news on quarterly equities data.
Flannery and Protopapadakis (2002) found that daily returns on the U.S. equities
are significantly impacted by several types of macroeconomic news. The authors estimate a generalized autoregressive conditional heteroskedasticity (GARCH) return
model with independent variables and found that the following macroeconomic announcements have significant influence on both equity returns and volatility: CPI,
PPI, monetary aggregate, balance of trade, employment report, and housing starts
figures.

Ajayi and Mehdian (1995) document that foreign stock markets in developed
countries typically overreact to the macroeconomic news announcements from the
United States. As a result, foreign equity markets tend to be sensitive to the USDbased exchange rates and domestic account balances. Sadeghi (1992), for example,
notes that in the Australian markets, equity returns increased in response to increases
in the current account deficit, the AUD/USD exchange rate, and the real gross domestic product (GDP); equity returns decreased following news of rising domestic
inflation or interest rates.
Stocks of companies from different industries have been shown to react differently to macroeconomic announcements. Hardouvelis (1987), for example, pointed
out that stocks of financial institutions exhibited higher sensitivity to announcements
of monetary adjustments. The extent of market capitalization appears to matter as
well. Li and Hu (1998) show that stocks with large market capitalization are more
sensitive to macroeconomic surprises than are small-cap stocks.
The size of the surprise component of the macroeconomic news impacts equity
prices. Aggarwal and Schirm (1992), for example, document that small surprises,
those within one standard deviation of the average, caused larger changes in equities
and foreign exchange markets than did large surprises.

Fixed-Income Markets
Directional Trading Around Events

160

Jones, Lamont, and Lumsdaine (1998) studied the effect of employment and PPI
data on U.S. Treasury bonds. The authors find that while the volatility of the bond
prices increased markedly on the days of the announcements, the volatility did not
persist beyond the announcement day, indicating that the announcement information is incorporated promptly into prices.
Hardouvelis (1987) and Edison (1996) note that employment figures, PPI, and
CPI move bond prices. Krueger (1996) documents that a decline in the U.S. unemployment causes higher yields in bills and bonds issued by the U.S. Treasury.
High-frequency studies of the bond market responses to macroeconomic announcements include those by Ederington and Lee (1993); Fleming and Remolona
(1997, 1998, 1999); and Balduzzi, Elton, and Green (2001). Ederington and Lee
(1993) and Fleming and Remolona (1998) show that new information is fully incorporated in bond prices just two minutes following its announcement. Fleming
and Remolona (1999) estimate the high-frequency impact of macroeconomic announcements on the entire U.S.Treasury yield curve. Fleming and Remolona (1999)
measure the impact of 10 distinct announcement classes: CPI, durable goods orders,
GDP, housing starts, jobless rate, leading indicators, nonfarm payrolls, PPI, retail
sales, and trade balance. Fleming and Remolona (1999) define the macroeconomic
surprise to be the actual number released less the Thomson Reuters consensus forecast for the same news release.
All of the 10 macroeconomic news announcements studied by Fleming and
Remolona (1999) were released at 8:30 a.m. The authors then measure the
significance of the impact of the news releases on the entire yield curve from
8:30 to 8:35 a.m., and document statistically significant average changes in yields in

Table 9.4 Effects of Macroeconomic News Announcements Documented by Fleming and
Remolona (1999)
Announcement

3-Month Bill

2-Year Note

30-Year Bond

CPI

0.593*

1.472**

1.296**

Durable goods orders

1.275**

2.180**

1.170**

GDP

0.277

0.379

0.167

Housing starts

0.670**

1.406**

0.731**

Jobless rate

–0.939*

–1.318**

–0.158

Leading indicators

0.411**

0.525*

0.271*

Nonfarm payrolls

3.831**

6.124**

2.679*

PPI

0.768**

1.879**

1.738

Retail sales

0.582*

1.428**

0.766**

Trade balance

–0.138

0.027

–0.062

The table shows the average change in percent in the yields of the 3-month U.S. Treasury bill, the 2-year U.S. Treasury note,
and the 30-year U.S. Treasury bond, corresponding to a 1 percent “surprise” in each macroeconomic announcement. *
and ** indicate statistical significance at the 95 percent and 99 percent confidence levels, respectively. The estimates were
conducted on data from July 1,1991, to September 29,1995.

Futures Markets
The impact of the macroeconomic announcements on the futures market has been
studied by Becker, Finnerty, and Kopecky (1996); Ederington and Lee (1993); and
Simpson and Ramchander (2004). Becker, Finnerty and Kopecky (1996) and Simpson and Ramchander (2004) document that news announcements regarding the
PPI, merchandise trade, nonfarm payrolls, and the CPI move prices of bond futures.
Ederington and Lee (1993) find that news-induced price adjustment of interest rate
and foreign exchange futures happens within the first minute after the news is released.
News-related volatility, however, may often persist for the following 15 minutes.

Emerging Economies
Several authors have considered the impact of macroeconomic news on emerging
economies. For example, Andritzky, Bannister, and Tamirisa (2007) study how macroeconomic announcements affect bond spreads. The authors found that the U.S.
news had a major impact, whereas domestic announcements did not generate much
effect. However, Nikkinen, Omran, Sahlström, and Äijö (2006) conducted similar
analysis on equity markets and found that while mature equity markets respond
almost instantaneously to U.S. macroeconomic announcements, emerging equity
markets are not affected. Kandir (2008) estimated macroeconomic impact on the

161
Directional Trading Around Events

response to a 1 percent positive surprise change in the macro variable. The results
are reproduced in Table 9.4. As Table 9.4 shows, a 1 percent “surprise” increase in the
jobless rate led on average to a 0.9 percent drop in the yield of the 3-month bill with
95 percent statistical confidence and a 1.3 percent drop in the yield of the 2-year
note with 99 percent confidence. The corresponding average drop in the yield of the
30-year bond was not statistically significant.

Istambul Stock Exchange, and found that the Turkish lira/USD exchange rate, the
Turkish interest rate, and the world market returns significantly affect Turkish equities, while domestic variables such as industrial production and money supply had
little effect. Muradoglu, Taskin, and Bigan (2000) found that emerging markets were
influenced by global macroeconomic variables, depending on the size of the emerging market under consideration and the degree of the market’s integration with the
world economy.
Association of Southeast Asian Nations (ASEAN) countries, however, appear to
be influenced predominantly by their domestic variables. Wongbangpo and Sharma
(2002) find that local gross national products (GNPs), CPIs, money supplies, interest
rates, and the USD-based exchange rates of ASEAN countries (Indonesia, Malaysia,
Philippines, Singapore, and Thailand) significantly influence local stock markets. At
the same time, Bailey (1990) found no causal relation between the U.S. money supply and stock returns of Asian Pacific markets.

Commodity Markets

Directional Trading Around Events

162

Empirical evidence in the commodity markets includes the findings of Gorton and
Rouwenhorst (2006), who document that both real activity and inflation affect
commodity prices. The effect of the news announcements, however, can be mixed;
higher-than-expected real activity and inflation generally have a positive effect on
commodity prices, except when accompanied by rising interest rates, which have a
cooling impact on commodity valuations. See Bond (1984), Chambers (1985), and
Frankel (2006) for more details on the relationship between commodity prices and
interest rates.

Real Estate Investment Trusts
Equity real estate investment trusts (REITs) are fairly novel publicly traded securities, established by the U.S. Congress in 1960. The market capitalization
of all U.S.-based REITs was about $9 million in 1991 and steadily grew to
$300 billion by 2006. A REIT is traded like an ordinary equity, but it is required
to have the following peculiar structure: at least 75 percent of the REIT’s assets
should be invested in real estate, and the REIT must pay out at least 90 percent
of its taxable earnings as dividends. Because of their high payout ratios, REITs
may respond differently to macroeconomic news announcements than would
ordinary equities.
The impact of inflation on REIT performance has been documented by Simpson, Ramchander, and Webb (2007). The authors found that the returns on REITs
increase when inflation unexpectedly falls as well when inflation unexpectedly
rises. Bredin, O’Reilly, and Stevenson (2007) examine the response of REIT returns to unanticipated changes in U.S. monetary policy. The authors find that
the response of REITs is comparable to that of equities—increase in the Federal
Funds rates increases the volatility of REIT prices while depressing the REIT
prices themselves.

■■ Summary
Directional trading around events generates profitability in narrow windows immediately following the news and preceding the reaction of other market participants.
Estimation of the impact of historical announcements enable profitable trading decisions surrounding market announcements.
■■ End-of-Chapter Questions

163
Directional Trading Around Events

1. Which of the following is/is not a tradable event in the HFT sense? Why?
a. The S&P 500 registers a positive gain on market open relative to previous
close.
b. Announcement of the QE3 (quantitative easing led by the U.S. Fed).
c. Regular announcement of employment figures.
2. What financial instruments can be traded on events in HFT setting?
3. Suppose a particular stock usually rises within 15 minutes of an announcement
of positive changes to the U.S. nonfarm payroll.The latest announcement figures
have just been released, and the change is negative. How can your system trade
on the announcement?
4. Intuitively, why does something like a change in CPI affect futures prices in the
short term?
5. Does high-frequency directional trading on events make markets more or less
efficient?

Chapter 10

Automated Market
Making—Naïve
Inventory Models
M

ost high-frequency trading (HFT) systems are deployed to provide automated
market-making services. Some 30 years ago, this activity was entirely human,
but is now moving to a nearly fully computerized mode. This chapter considers the
basic principles behind the successful market-making models.
■■ Introduction
Every veteran trader can recount a story of a dominant human market maker who
“owned” transactions in a particular financial instrument. These kingpins of financial
markets generated heavy transaction-based profits for their employers, commanded
extensive bonuses and lived luxurious lifestyles.
With rare exceptions, nearly all stories about these once-potent human traders
end on the same sour note: “and then one day, the market turned against him, he
suffered a major loss, and was fired the next day.” An example of such a “burnout”
was a trader in USD/CAD foreign exchange futures at a certain bank, who made
markets for a long time and periodically enhanced his profitability and bonus by taking directional bets at his personal discretion. Once, the trader’s bet fell radically off
its mark, resulting in nearly instantaneous multimillion-dollar losses to his employer.
The trader was immediately dismissed following the incident and was prohibited
from ever again setting a foot on any trading floor.
Automated market making provides several advantages to the market-making
institution as well as other market participants. First, automated market makers
stay on script. Unlike human traders, properly programmed and tested computer systems do not deviate into discretionary actions. As a result, automated

165

Automated Market Making—Naïve Inventory Models

166

market makers reduce the incidence of market crashes and negative surprises for
market makers’ bottom line. Second, execution of automated market making
is cost efficient: once the human-intensive programming and testing stages are
completed (see Chapter 16 for details of HFT development processes), automated market makers require little compensation. The savings from head-count
reductions are significant and are passed directly to the automated market makers’ shareholders and clients in the form of enhanced profitability and reduced
transaction costs.
Perhaps the best feature of market-making strategies is their scalability across various markets. Almost any market-making strategy running on an exchange equipped
with a centralized limit order book can be run on another exchange, another financial instrument and even another asset class, provided that the new trading venue
also deploys centralized limit order book methodology (see Chapter 3 for limit order book definitions and description). Most of today’s exchanges in the world deploy the centralized limit order book model, making market-making technology
extremely portable.
A market-making process works as follows: a market maker, whether human or
computerized, posts limit buy and limit sell orders. Depending on market conditions and positions in the market maker’s current portfolio, the market maker may
choose to post only limit buy or only limit sell orders. Some market participants,
however, consider market making to refer strictly to a continuous activity with
open limit orders placed simultaneously on both sides of the market. Liquidity
provision is a more general term describing market making as well as most limit
order trading.
When the market price reaches the market maker’s limit buy order with the highest price, this price becomes the best bid on that market, and is distributed to other
market participants as a Level I “quote.” Similarly, when the market maker’s limit sell
order is the lowest-priced limit sell order in the market, his order becomes a best
offer or best ask, and is quoted to other market participants.
Market makers’ orders are executed by virtue of being matched with incoming
market orders of the opposite direction. The market maker’s bids are said to be “hit”
by market sell orders, and the market maker’s ask or offer limit orders are said to
be “lifted” by incoming market buy orders. With every executed limit order, the
market maker accumulates or divests quantities of the traded financial instrument
in his account. These quantities are known as inventory. Immediately upon acquiring
the inventory, the market maker begins to manage it, to reduce risk and enhance
profitability.
The two broad functions of a market maker are therefore:
■■
■■

Manage inventory to ensure sufficient profitability.
Keep track and respond to information in order to avoid being “run over” or
“picked over” by the markets.

Too little inventory may be insufficient to generate a profit; too much inventory
makes the trader risk inability to quickly liquidate his position and face a certain loss.

■■ Market Making: Key Principles
In a nutshell, “market-making” describes placement of limit orders on both sides
of the market price. A market maker placing a limit buy order just below the market price and a limit sell order just above the market price creates or “makes” the
“market.” When a market buy order arrives from another market participant, it is
matched with the market maker’s limit sell order, and the limit sell order is executed
(i.e., a short position is recorded in the market maker’s account). Similarly, if a market sell order arrives from yet another market participant, it is matched with the
market maker’s limit buy order, and a long position is added to the market maker’s
account. If the size of the long position neutralizes the size of the short position in
the market maker’s portfolio, the market maker collects the spread as a compensation for providing limit orders, or liquidity, to traders placing market orders. The
market order traders are known as liquidity takers.
Of course, market making is subject to risk. As soon as the market maker places
his limit orders, he immediately faces two types of risk:
■■

Inventory risk

■■

Risk of adverse selection

■■ Simulating a Market-Making Strategy
Trading with limit orders generates nonlinear payoffs; sometimes limit orders execute and sometimes they do not. As a result, limit orders are difficult to model. This
section delves into the logistics of limit-order modeling.

167
Automated Market Making—Naïve Inventory Models

Inventory risk describes the potential loss the market maker might incur when
the value of his inventory declines in price due to natural market movements. Thus,
a market maker accumulating a long position (buying) in a downward-trending market is likely to experience a loss on his position, at least in the short term. In addition, inventory risk is incurred when the market maker wishes to close his positions,
as the market maker may face competition from other parties looking to sell their
positions at the same time, resulting in difficulties liquidating his inventory. Inventory risk also includes the opportunity costs reflecting the gains the market maker
misses while waiting for execution of his limit orders.
The risk of adverse selection measures potential loss due to informational differences
between the market maker and a market taker. When the market taker possesses better
information set than the market maker, the market maker is likely to be entering the
losing end of the trade. For example, when a market maker’s limit buy order is matched
with a market sell order, it is possible that the seller has better information than the
market maker about the imminent direction of the market – in this case, down, and that
the market maker is about to commit to a losing trade. Per Copeland and Galai (1983),
all limit orders suffer from an informational disadvantage, whereby they are picked off
by better-informed investors. While the risks of inventory and adverse selection can
produce significant losses for the market makers, the risks can be profitably controlled.

Limit buy order is “placed”

Price
Limit buy order
is “executed”

Simulated
Limit buy
Order
Price
Last trade price or best ask quote
“crosses” the price of the limit buy order

FIGURE 10.1 Mechanics of Simulating limit Order Execution

AUTOMATED MArkET MAkINg—NAïvE INvENTOry MODElS

168

Strategies that deploy market orders can be simulated with an assumption that each
order is executed near the latest trade price observed in data at the time the simulated order is placed. By contrast, simulating execution of limit orders requires additional work.
Most solid simulations consider a given limit order executed only when the best opposing
quote reaches or crosses the limit order, in a process shown in Figure 10.1. A limit buy order is considered executed when the last trade price or the best ask quote falls below the
price of the simulated limit order. A limit sell order can be marked processed whenever
the last trade price or the best bid quote exceeds the price of the simulated limit order.
■ Naïve Market-Making Strategies
This section explains the details of practical market-making strategies that concern
themselves only with effective management of inventory. Enhancements based on
short-term directional market forecasts are discussed in Chapter 11.

Fixed Offset
The most naïve market-making strategy is continuously placing limit orders at a predetermined number of ticks away from the market price, on both sides of the market. Naturally, the probability of limit orders being executed depends on the limit
order price proximity to the current market price. limit orders placed at current
market quotes are likely to be executed, whereas the probability of execution for
passive limit orders, those far away from the market price, is close to zero. In most
financial instruments, market makers are allowed to place limit orders only within
10 percent of the current market price, to prevent so-called “stub quotes” far away
from the market from executing at times of extreme volatility.
The smaller the offset of a limit order from the market price in a naïve strategy,
the higher the probability of order execution, and the more frequent the resulting

Volatility-Dependent Offset
To improve the fixed-offset strategy, one may vary the offset of limit orders with market conditions. One intuitive way to change the offset is to make it a function of volatility: in high-volatility conditions, limit orders farther away from the market are likely
to be hit, generating higher premium for market makers. In low-volatility conditions,
however, limit orders may need to be placed closer to the market to be executed. A
sample determination of volatility-dependent offset is shown in equation (1):
1 t −T
offsett = round  ∑τ =t −1( Pτ − Pτ −1 )2 
T


(1)

Offset Is a Function of Order-Arrival Rate
Still another way to improve the naïve market making is to make the offset dependent on the arrival frequency of market orders. As Parlour and Seppi (2008) point

169
Automated Market Making—Naïve Inventory Models

reallocation of the market maker’s capital. Frequency of trading has been shown to
be key to market makers’ profitability. The higher the number of times the market
maker can “flip” his capital, the higher the cumulative spread the market-maker can
capture, and the lower the risk the market maker bears waiting for execution of his
orders. A study of market making on actively traded stocks on the Stockholm Stock
Exchange, for example, found that the expected profit on limit orders increases
when they are matched more frequently. The study, written by Sandas (2001), shows
that market makers’ profitability is not proportional to the time they spend providing liquidity; instead, market makers’ profit is directly tied to the frequency with
which their orders are executed.
By contrast, early market-making theories presumed that market makers were
content to be compensated for time spent providing liquidity. The longer the waiting
time until order execution, the thought went, the higher was the expected compensation to liquidity providers who did not change their limit order specifications once
they submitted the orders. Such ideas were known as static equilibrium models and
included Rock (1996), Glosten (1994), and Seppi (1997).
The assumptions of static equilibrium models reflected early exchange conditions. Changing the details of a limit order and canceling orders was prohibitively
costly, and market makers indeed expected a tidy compensation for bearing the risk
of ending up in an adverse position once their limit orders were hit. Limit order
cancellations and revisions could be performed free of charge on most markets at the
time this book was written. As a result, today’s high-frequency market makers enjoy
better profitability than their human market-making counterparts.
The ability to place orders at the best bid and best ask prices, however, may be
limited by the speed of the HFT market maker’s technology. Super-fast technology
allows market makers to continually cancel and resubmit their limit orders to ensure their spot on the top of the book, high execution rates, and high profitability.
Slower technology can still deliver profitable market-making strategies via larger
offsets away from the going market price.

out, limit orders compete with other limit orders, both existing and those submitted
in the future. Furthermore, all limit orders execute against future market orders.
The market order arrival rate, therefore, is an important determinant of marketmaking profitability.
The market orders can be assumed to arrive independently of one another,
and with a great degree of randomness. Much like the arrival of subway trains
or street cars, though, the randomness of order arrivals can be modeled using
well-specified statistical distributions. Under the assumptions of exponentiallydistributed inter-arrival times, for example, the market orders arrive to “hit the
bid” and to “lift the ask” with a certain average rate, m. The limit orders can be
assumed to repopulate the top of the limit order book at an average rate l. Probability of a top-of-the-book limit order being matched can then be expressed as
a function of λ = 1/l, µ = 1/µ and a given interval of time, ∆t:
 λ 
P( hit, ∆t ) = 1 − P ( not hit, ∆t ) = 1 − exp  − ∆t 
 µ 

Automated Market Making—Naïve Inventory Models

170

(2)

Parameters λ and µ can be calibrated on recent tick data. Level I data can be used
to calibrate parameters for minimal time intervals, ∆t = 1. When the best bid moves
up or the size at the best bid increases, a new limit buy order is assumed to have
arrived. When the best ask moves up or the size at the best ask decreases, a market
buy order is recorded. Avellaneda and Stoikov (2008) present an example of strategy
deploying arrival rates.
Another analytical model for determining the optimal offset of limit orders is due
to Foucault, Kadan, and Kandel (2005). This model explicitly suggests whether a
trader should place a passive or an aggressive limit order, and how many ticks away
from the market price should the trader place his limit order. The model makes the
following key assumptions:
■■
■■

All other execution parameters have been selected.
All traders in the market are free to switch from passive to aggressive execution,
and vice versa.

The determining factor in whether or not a trader decides to place a passive or an
aggressive order, is the so-called “reservation spread,” defined as follows:
δ 
jR = ceiling  
 µ∆ 

(3)

where
■■

δ is the market-maker’s expected dollar-cost of execution that may incorporate
expectations about market impact.

■■

∆ is the minimal tick size, say $0.01 for equities.

■■

m is the arrival rate of matching market orders per unit of time; with 1⁄ m rep-

resenting the average time between two sequential order arrivals. If the model

is used to determine levels of aggressiveness of limit buy orders, m is the rate
of arrival of market sell orders, computed as a number of market sell orders
recorded per unit of time. In Foucault et al. (2005), all orders, both market and
limit, are assumed to be of the same size.
Foucault et al. (2005) use the reservation spread jR to establish a short-run equilibrium, where all traders achieve their optimality. To do so, Foucault et al. (2005)
consider three different types of markets:
1. A market with identical (homogenous) traders.
2. A market with two different types of traders, facing diverging transaction costs.
3. A market with q different types of traders, with heterogeneous transaction
costs.

■■

Fees: Large institutional traders are likely to face lower fees than smaller traders.

171
Automated Market Making—Naïve Inventory Models

The main intuition behind the model works as follows: The trader’s reservation spread is the cost of executing the given order slice. If the current market
spread is smaller than the trader’s reservation spread, the trader can avoid additional costs associated with the risk of nonexecution, placing a market order. When the trader’s execution costs per rate of arrival of opposing orders
are smaller than the market spread, the trader places an aggressive limit order,
shrinking the spread and further improving his cost structure by avoiding crossing the spread.
In a market with identical traders, all traders [1 . . . q] have the same transaction
costs, and face common arrival rates for opposing orders, resulting in equal reservation spreads: j1R = j2R = ... = jqR = jR . In such a market, each trader would submit
a limit order jR ticks away from the market whenever the inside market spread s is
greater than jR, and submit a market order otherwise. Such a market is characterized by a highly competitive outcome, with traders shrinking market spreads to the
minimum tick size.
In a market with two traders facing different transaction costs, similar dynamics
take place. Trader 1 places a limit order j1R ticks away from the market whenever
the market spread s is larger than j1R. Similarly, trader 2 places a limit order j2R
ticks away from the market whenever the market spread s is larger than j2R. Yet,
when the market inside spread s exceeds j1R and S< j2R, trader 2 places a market
order, while trader 1 places a limit order j1R ticks away from the market price,
potentially shrinking the spread. In this market with identically sized orders, no
trader ever places a limit order “behind” the market or farther away from the market than the spread.
In a market with [1 … q] heterogeneous traders, j1R Pr(Loss).
Garman (1976) applies the Gambler’s Ruin Problem to the market-making business in the following two ways:
1. The market maker fails if he runs out of cash.
2. The market maker fails if he runs out of inventory and is unable to satisfy client
demand.

Gain = 1
Loss = 1
In the case of equity, this unit may be a share of stock. In the case of foreign exchange,
the unit may be a clip. Then, from the market maker’s perspective, the probability
of “losing” one unit of inventory is the probability of selling a unit of inventory, and
it equals the probability λa of a buyer arriving. By the same logic, the probability of
gaining one unit of inventory is λb, the probability of a seller arriving. The Gambler’s
Ruin Problem equation (9) now becomes
λ 
lim PrFailure (t ) ≈  a 
t →∞
 λb 

InitialWealth / E0 ( Pa ,Pb )

= 1, otherwise.

, if λb > λa
(10)

where E0(Pa, Pb) is the initial average price of an underlying unit of inventory and
Initial Wealth
is the initial number of units of the financial instrument in possession
E0 ( pa , pb )
of the market maker.

177
Automated Market Making—Naïve Inventory Models

In modeling the Gambler’s Ruin Problem for the market maker’s ruin through
running out of inventory, we assume that both the Gain and Loss variables are single
units of the underlying financial asset. In other words,

The Gambler’s Ruin Problem is further applied to the market maker’s probability
of failure due to running out of cash. From the market maker’s perspective, gaining a
unit of cash—say a dollar—happens when a buyer of the security arrives. As before,
the arrival of a buyer willing to buy at price Pa happens with probability λa. As a result,
the market maker’s probability of gaining a dollar is Pa. Similarly, the market maker’s
probability of “losing” or giving away a dollar to a seller of the security for selling the
security at price Pb is λb. The Gambler’s Ruin Problem now takes the following shape:
λ p 
lim PrFailure (t ) ≈  b b 
t →∞
 λa pa 

InitialWealth

= 1, otherwise.

, if λaPa > λaPb

(11)

For a market maker to remain in business, the first conditions of equations (10)
and (11) need to be satisfied simultaneously. In other words, the following two inequalities have to hold contemporaneously:
λb > λa and
λa pa > λapb

Automated Market Making—Naïve Inventory Models

178

For both inequalities to hold at the same time, the following must be true at all
times: pa > pb, defining the bid-ask spread. The bid-ask spread allows the market
maker to earn cash while maintaining sufficient inventory positions. The reverse,
however, does not hold true: the existence of the bid-ask spread does not guarantee
that the market maker satisfies profitability conditions of equation (11).
■■ Summary
Market making and any liquidity provision is a service to the markets and deserves
compensation. Profitable automated market making is feasible with very simple
models that only take into account inventory on the market maker’s books. While
Level II data is informative, and, therefore, desirable, the information delivered by
Level II data can be extracted out of Level I data using simple techniques like technical analysis.
■■ End-of-Chapter Questions
1.
2.
3.
4.
5.

What is market making? How does it differ from liquidity provision?
Why is market making inherently profitable?
What is the core market-making strategy? What are the common extensions?
What are the common measures of liquidity?
What are the minimum profitability conditions of market-making strategies?

Chapter 11

Automated Market
Making II
I

nventory market-making models, discussed in Chapter 10, explain and help manage transitory variations in prices resulting from the imbalances in a dealer’s book,
or portfolio. The models usually start with a “sweet spot” inventory, an inventory
level sufficient to satisfy immediate client demand, and proceed to adjust the inventory according to client demand and the market’s conditions. Such models do not
consider actions and information available to other market participants.
By contrast, information-based market-making models addressed in this chapter carefully evaluate the trading patterns of various market participants, deduce
the news available to them, and optimize market-making process by responding to
available supply and demand in the markets. The models account for present and
expected future trading, including the shape of limit order book, order flow, as well
as histories of orders and trading outcomes.
■■ What’s in the Data?

Publicly available data carries information that is sufficient to detect short-term
price movements and manage one’s positions accordingly. This section presents four
cases for illustration. The figures accompanying the cases show sample market situations observable by all market participants subscribing to Level I data from a given
trading venue. The cases apply to all trading venues that deploy a centralized limit
order book for its matching operation.
In all figures, the horizontal axis is time. The solid lines are the best bid and the
best ask, a.k.a. best offer, observed at the given point in time, and the dashed line
shows the midquote: the simple average between the best bid and the best ask. The
stars indicate the price and timing of trades: some trades occur at ask, some at bid,
and some may occur in the vicinity of either bid or ask.

179

Ask

Mid
Bid

*
t

t+1

t+2

Time

FIGURE 11.1 The Market does not Move in response to Trades

Case 1: Market Does Not Move

AuToMATed MArkeT MAkIng II

180

In Figure 11.1, the trades are recorded in the following sequence: the first trade occurred
at the best bid, then at the best ask, and finally at the best bid again. neither the best bid
nor the best ask moved.What is the dynamic at work in the market shown in Figure 11.1?
A short answer to this question is “none.” In the market shown in Figure 11.1,
nothing interesting or unusual is happening. The first order that arrived and resulted
in the trade was a market sell—the trade was recorded at the bid, as market sell
orders would be. The market sell order was smaller in size than the size at the best
bid at the time the order arrived—following the trade, the best bid did not move.
The order did not carry any information, at least not from the broader market perspective: the best bid and the best ask quotes remained at their original levels. Had
other market participants been concerned about the specialized knowledge of the
trader or the imminent movement of the market, they would have likely revised
their quotes to minimize their risk.
Following the first sell order, Figure 11.1 shows that two additional orders are executed shortly afterward: a market buy order and a market sell order. The buy order
is identified as such because it is recorded at the best ask—market buy orders would
be matched with the ask side of the limit order book. The next trade is recorded at
the best bid and, therefore, must be a sell. once again, Figure 11.1 shows no changes
in prices following either order, implying that
■

■

The size of both orders was small in comparison with aggregate sizes at the best
bid and the best ask.
The orders were not perceived to have any special informational advantages.

Case 2: Market Moves and rebounds
Figure 11.2 presents a different scenario: a trade is recorded at the bid. Following
the bid, the quotes drop lower, yet gradually recovers over time.
The trade in Figure 11.2 occurred at the bid, and was, therefore, triggered by a
market sell order. The subsequent drop in the quotes that was followed by gradual
recovery suggests that:
1. The trade size was large relative to the size available at the best bid; the market
sell order had to “sweep” through the book to be fully matched.

Ask
Mid
Bid

*
Time
t

FIGURE 11.2 The Market Moves and Shortly rebounds Following a Trade

2. despite its large size, the trade did not move the fundamentals that drive the
price—the quotes slowly recovered to their original levels; the trade carried no
information.
In Figure 11.2, the best ask quote also drops following the sell. This may be due
to the market makers’ activity seeking to disgorge the inventory just acquired via
the sell trade. By lowering the best ask quote, a market maker can promptly sell the
newly purchased inventory, realizing a quick profit.

Case 3: a trade Moves Markets

Ask
Mid
Bid

FIGURE 11.3 A Trade Moves Markets

Time

181
AuToMATed MArkeT MAkIng II

The trade in Figure 11.3 also occurred at the bid. unlike Case 2 above, where the
quotes recovered following the trade, in Figure 11.3 the trade substantially shifted
both bid and ask quotes downward. no immediate recovery of quotes is observed.
The most likely explanation of market activity in Figure 11.3 is information. The
trade once again came in at the bid and was hence a sell. The markets interpreted
the sell, however, as a trade containing enough information to warrant a permanent
price decline. unlike Case 2 above, the quotes did not recover to their original levels, but instead remained at their new lows. The new persistent price level is most
likely the result of fundamental information carried by the sell trade.
The market makers may determine that the sell trade possessed information in
several ways. often, the broker-dealer of the trader who placed the sell market
order may observe that the trader possesses superior research skills and routinely
places profitable orders ahead of other traders. In such situations, the trader’s broker-dealer may be the first to adjust the quotes after the trade is executed to protect

Ask
Mid
Bid

Time

FIGURE 11.4 The Quotes Widen Following a Trade

himself against accepting further trades with a losing counterparty. Such activity is
perfectly legal, and is often referred to as prehedging. Alternatively, the broker-dealer
and other market participants may determine the probabilistic presence of informed
traders through information-extracting models described later in this chapter.

Case 4: the Quotes Widen

AuToMATed MArkeT MAkIng II

182

Figure 11.4 illustrates yet another scenario: a case where spreads widen following a trade.
The scenario depicted in Figure 11.4 is most often a result of increased uncertainty in the markets. An example of such uncertainty can be the time preceding a major
scheduled news announcement, where the news, once released, is likely to move
the markets considerably one way or the other. Market makers’ natural response is
to avoid being run over by better-informed traders and to pull orders closest to the
market price, a practice known as quoting wide, shown in Figure 11.4.
Cases 1 through 4 illustrate predictable market maker behavior following distinct situations. other scenarios are also possible. Market makers’ behavior following specific market events, observable in public quote data, helps automated trading
systems to extract information available solely to other market makers.
■ Modeling Information in Order Flow
The remaining sections of the chapter describe four classes of techniques that have
been developed to identify impending market moves based on the behavior of other
market participants. The described models take into account:
■
■
■
■

order flow autocorrelation
order flow aggressiveness
Shape of the order book
Sequential evolution of quotes

autocorrelation of Order Flow as a
predictor of Market Movement
order flow is a result of end customers receiving and acting on information. Information models are trained to observe order flow and extract and then trade upon
information available to various market participants.

Order flow is the difference in trade volume between trades initiated with market
buy orders and trades triggered by market sell orders, all noted within a predetermined period of time. Trades begun with a market buy order are known as buyer
initiated. Similarly, trading volume caused by market sell orders is referred to as seller
initiated. Equation (1) illustrates the definition of order flow:
xt = vta − vtb

(1)

where vta is the trading volume resulting from market buy orders being matched
with the ask side of the order book, and vtb is the trading volume triggered by market
sell orders hitting the bid side of the order book.
According to academic research, order flow is directly responsible for at least
50 percent of information impounded into market prices. Around news releases,
order flow becomes highly directional. For example, Love and Payne (2008) estimate that following a major Eurozone and the U.S. news announcement, the order
flow surrounding the EUR/USD exchange rate closely follows the directionality of
the announcement. Thus, “good” U.S. news, expected to lift the U.S. dollar, is dominated by “buy U.S. dollar” or “sell Euro” orders. Other studies with similar findings
about various securities include Lyons (1995), Perraudin and Vitale (1996), Evans
and Lyons (2002a), and Jones, Kaul, and Lipson (1994).
According to Lyons (2001), order flow is informative for three reasons:
183
Automated Market Making II

1. Order flow can be thought of as market participants exposing their equity to
their own forecasts. Market orders are irrevocable commitments to buy or sell,
and therefore carry most powerful information. Limit orders can also be executed and be costly and, as a result, carry information. Order flow therefore
reflects market participants’ honest beliefs about the upcoming direction of the
market.
2. Order flow data is decentralized with limited distribution. Brokers can directly
observe the order flow of their clients and interdealer networks. End investors
seldom see any direct order flow at all, but can partially infer the order flow
information from market data, as described in this section. Exchanges possess
order flow data they receive from brokers and other market participant. The
exchange data may, however, miss significant numbers of investor orders, as
broker-dealers increasingly seek to match orders internally, in the process called
internalization of the order flow. The internalization is presently viewed as a necessary function to contain broker costs by avoiding exchanges whenever possible.
Because the order flow is not available to everyone, those who possess full order
flow information or successfully model it are in a unique position to exploit it
before the information is impounded into market prices.
3. Order flow shows large and nontrivial positions that will temporarily move the
market regardless of whether the originator of the trades possesses any superior
information, due to market impact. Once again, the traders observing or modeling the order flow are best positioned to capitalize on the market movements
surrounding the transaction.

Lyons (2001) further distinguishes between transparent and opaque order flows, with
transparent order flows providing immediate information, and opaque order flows failing
to produce useful data or subjective analysis to extract market beliefs. According to Lyons
(2001), order flow transparency encompasses the following three dimensions:
■■
■■
■■

Pretrade versus posttrade information
Price versus quantity information
Public versus dealer information

Brokers observing the customer and interdealer flow firsthand have access to the
information pretrade, can observe both the price and the quantity of the trade, and
can see both public and dealer information. End customers can generally see only the
posttrade price information by the time it becomes public or available to all customers. Undoubtedly, dealers are much better positioned to use the wealth of information embedded in the order flow to obtain superior returns, given the appropriate
resources to use the information efficiently.

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184

Order Flow Is Directly Observable As noted by Lyons (1995), Perraudin and Vitale
(1996), and Evans and Lyons (2002b), among others, order flow was previously dispersed among market participants but can be viewed centrally by the broker-dealer
or a trading venue. Order flow for a particular financial security at any given time is
formally measured as the difference between buyer-initiated and seller-initiated trading interest. Order flow is sometimes referred to as buying or selling pressure. When the
trade sizes are observable, the order flow can be computed as the difference between
the cumulative size of buyer-initiated trades and the cumulative size of seller-initiated
trades. When trade quantities are not directly observable (as is often the case in foreign exchange), order flow can be measured as the difference between the number of
buyer-initiated trades and seller-initiated trades in each specific time interval.
Both trade-size-based and number-of-trades-based measures of order flow have
been used in the empirical literature. These measures are comparable since most
orders are transmitted in “clips,” or parcels of a standard size, primarily to avoid
undue attention and price run-ups that would accompany larger trades. Jones et al.
(1994) actually found that order flow measured in number of trades predicts prices
and volatility better than order flow measured in aggregate size of trades.
The importance of order flow in arriving at a new price level following a news
announcement has been verified empirically. Love and Payne (2008), for example,
examine the order flow in foreign exchange surrounding macroeconomic news announcements and find that order flow directly accounts for at least half of all the
information impounded into market prices.
Love and Payne (2008) studied the impact of order flow on three currency pairs:
USD/EUR, GBP/EUR, and USD/GBP.The impact of the order flow on the respective
rates found by Love and Payne (2008) is shown in Table 11.1.The authors measure order
flow as the difference between the number of buyer-initiated and the number of sellerinitiated trades in each one-minute interval. Love and Payne (2008) document that at
the time of news release from Eurozone, each additional buyer-initiated trade in excess
of seller-initiated trades causes USD/EUR to increase by 0.00626 or 0.626 percent.

taBle 11.1 average Changes in One-Minute Currency returns Following a Single trade
Increase in the Number of Buyer-Initiatedtrades in excess of Seller-Initiatedtrades
USD/eUr return

GBp/eUr return

USD/GBp return

Flowt at a time coinciding with a news
release from eurozone

0.00626*

0.000544

0.00206

Flowt at a time coinciding with a news
release from the united kingdom

0.000531

0.00339***

0.00322***

Flowt at a time coinciding with a news
release from the united States

0.00701***

0.00204

0.00342**

***, ** and * denote 99.9 percent, 95 percent, and 90 percent statistical significance, respectively.

Order Flow Is Not Directly Observable order flow is not necessarily transparent
to all market participants. For example, executing brokers can directly observe
buy-and-sell orders coming from their customers, but generally the customers can
see only the bid and offer prices, and, possibly, the depth of the market.
As a result, various models have sprung up to extract order flow information from
the observable data. The most basic algorithm tests autocorrelation of trade signs.
First, the algorithm separates all trades recorded over the past period of time T, say,
30 minutes, into buys and sells. The identification of trades can be performed using
the Lee-ready or volume clock rule described in Chapter 4 of this book. Trades
identified as buys are assigned “trade direction value” of +1, and each sell trades is
noted as –1. next, the algorithm computes the autocorrelation function (ACF) for
lagged trade direction variable, xt :

Trade sign ACF for BEAM
on 2011.10.31

1.0

0.8

Autocorrelation

Trade sign ACF for MSFT
on 2011.10.31

0.6
0.4
0.2

0.6
0.4
0.2
0.0

0.0
0

Trade (log)

FIGURE 11.5 Autocorrelation of order Flow observed for Microsoft (MSFT) and Sunbeam

(BeAM) on october 31, 2011
Source: Sotiropoulos, 2012.

AuToMATed MArkeT MAkIng II

1 N
(2)
∑ xt xt +τ
N t =1
where t is the sequential number of a given trade tick in the chosen evaluation interval T, and N is the total number of ticks within the time interval. An ACF plot, linking the computed autocorrelation ρt,t +τ with a lag τ, reveals trade dependencies.
Figure 11.5 shows comparative autocorrelation figures for two financial instruments.

ρt,t +τ =

185

Hasbrouck (1991), in estimating order autocorrelation, adjusts for returns caused
by previously placed orders as well as effects of the time of day:
K

k =1

m =1

t =1

xt = α x ∑ β k rt −k + ∑ γ m xt −m + ∑ δ Dt + ε t

Automated Market Making II

186

(3)

where xt is the order flow observed at time t, set to +1 when the given trade was
estimated originate from a market buy order and –1 otherwise; rt is a one-trade return; and Dt is the dummy indicator controlling for the time of day into which time
t falls.
Ellul, Holden, Jain, and Jennings (2007) interpret short-term autocorrelation in
high-frequency order flows as waves of competing order flows responding to current market events within liquidity depletion and replenishment. Ellul et al. (2007)
confirm strong positive serial correlation in order flow at high frequencies, but find
negative order firm correlation at lower frequencies. Other studies of order autocorrelation include Hedvall, Niemeyer, and Rosenqvist (1997); Ranaldo (2004);
Hollifield, Miller, and Sandas (2004); Foucault, Kadan, and Kandel (2005); Rosu
(2005); and Biais, Hillion, and Spatt (1995).
Order flow information is easy to trade profitably. A disproportionately large
number of buy orders will inevitably push the price of the traded security higher;
placing a buy order at the time a large buy volume is observed will result in positive
gains. Similarly, a large number of sell orders will depress prices, and a timely sell
order placed when the sell order flow is observed will generate positive results.

Order Aggressiveness as a Predictor of
Market Movement
To extract the market information from the publicly available data, Vega (2007) proposes monitoring the aggressiveness of trades. Aggressiveness refers to the percentage of orders that are submitted at market prices, as opposed to limit prices. The
higher the percentage of market orders, the more aggressive is the trader in his bid
to capture the best available price and the more likely the trader is to believe that the
price of the security is about to move away from the market price.
The results of Vega (2007) are based on those of Foster and Viswanathan (1996),
who evaluate the average response of prices in a situation where different market
participants are informed to a different degree. For example, before an expected
economic announcement is made, it is common to see “a consensus forecast” that
is developed by averaging forecasts of several market analysts. The consensus number is typically accompanied by a range of forecasts that measures the dispersion of
forecasts by all analysts under consideration. For example, prior to the announcement of the January 2009 month-to-month change in retail sales in the United
States, Bloomberg LP reported the analysts’ consensus to be –0.8 percent, while
all the analysts’ estimates for the number ranged from –2.2 percent to 0.3 percent
(the actual number revealed at 8:30 a.m. on February 12, 2009, happened to
be +1.0 percent).

Difft = β 0 + β1Sizet + β2 Aggressivenesst + β3Institutionalt + D1t + .... + Dn −1,t + ε t (4)

where t is the time of the order submission, n equals 5 and then 60 minutes after
order submission. Size is the number of shares in the particular order divided by the
mean daily volume of shares traded in the particular stock over the sample period.
For buy orders, Aggressiveness is a dummy that takes the value 1 if the order is placed
at or better than the standing quote and zero otherwise. Institutional is a dummy variable that takes the value 1 for institutional orders and 0 for individual orders. D1 to
Dn-1 are stock-specific dummies associated with the particular stock that was traded.
Table 11.2, from Anand et al. (2005), summarizes the results of robustness regressions testing for a difference in the performance of institutional and individual
orders. The regression equation controls for stock selection by institutional and individual traders. The dependent variable in the regression is the change in the bid-ask
midpoint 5 and then 60 minutes after order submission.

187
Automated Market Making II

Foster and Viswanathan (1996) show that the correlation in the degree of informativeness of various market participants affects the speed with which information
is impounded into prices, impacts profits of traders possessing information, and also
determines the ability of the market participants to learn from each other. In other
words, the narrower the analysts’ forecast range, the faster the market arrives at fair
market prices of securities following a scheduled news release. The actual announcement information enters prices through active trading. Limit orders result in more
favorable execution prices than market orders; the price advantage, however, comes at
a cost—the wait and the associated risk of nonexecution. Market orders, on the other
hand, are executed immediately but can be subject to adverse pricing. Market orders
are used in aggressive trading, when prices are moving rapidly and quick execution
must be achieved to capture and preserve trading gains. The better the trader’s information and the more aggressive his trading, the faster the information enters prices.
As a result, aggressive orders may themselves convey information about the impending direction of the security price move. If a trader executes immediately instead of waiting for a more favorable price, the trader may convey information about
his beliefs about where the market is going. Vega (2007) shows that better-informed
market participants trade more aggressively. Mimicking aggressive trades, therefore,
may result in a consistently profitable trading strategy. Measures of aggressiveness
of the order flow may further capture informed traders’ information and facilitate
generation of short-term profits.
Anand, Chakravarty, and Martell (2005) find that on the New York Stock Exchange
(NYSE), institutional limit orders perform better than limit orders placed by individuals, orders at or better than market price perform better than limit orders placed inside
the bid-ask spread, and larger orders outperform smaller orders. To evaluate the orders, Anand et al. (2005) sampled all orders and the execution details of a three-month
trading audit trail on the NYSE, spanning November 1990 through January 1991.
Anand et al. (2005) use the following regression equation to estimate the impact
of various order characteristics on the price changes measured as Difft, the difference
between the bid-ask midpoints at times t and t + n:

Table 11.2 Summary of Robustness Regressions Testing for a Difference in the Performance
of Institutional and Individual Orders
Intercept

Size

Aggressiveness

Institutional

5 min after order placement

0.005

0.010*

0.016*

0.004*

60 min after order placement

0.020**

0.020*

0.012*

0.006*

Panel A: 97 stocks

Panel B: 144 stocks
5 min after order placement

0.006

0.012*

0.014*

0.004*

60 min after order placement

0.021**

0.023*

0.012*

0.004*

*t-test significant at 1 percent; **t-test significant at 5 percent.
Reprinted from Amber Anand, Sugato Chakravarty, and Terrence Martell, “Empirical Evidence on the Evolution of Liquidity:
Choice of Market versus Limit Orders by Informed and Uninformed Traders,” Journal of Financial Markets (August 3, 2005):
21, with permission from Elsevier.

According to several researchers, market aggressiveness exhibits autocorrelation
that can be used to forecast future realizations of market aggressiveness. The autocorrelation of market aggressiveness is thought to originate from either of the following sources:
■■

■■

Automated Market Making II

188

Large institutional orders that are transmitted in smaller slices over an extended
period of time at comparable levels of market aggressiveness
Simple price momentum

Research into detecting autocorrelation of market aggressiveness was performed
by Biais et al. (1995), who separated orders observed on the Paris Bourse by the
degree of aggressiveness—from the least aggressive market orders that move prices
to the most aggressive limit orders outside the current book. The authors found that
the distribution of orders in terms of aggressiveness depends on the state of the market and that order submissions are autocorrelated. The authors detected a “diagonal
effect” whereby initial orders of a certain level of aggressiveness are followed by
other orders of the same level of aggressiveness. Subsequent empirical research confirmed the findings for different stock exchanges. See, for example, Griffiths, Smith,
Turnbull, and White (2000) for the Toronto Stock Exchange; Ranaldo (2004) for
the Swiss Stock Exchange; Cao, Hansch, and Wang (2004) for the Australian Stock
Exchange; Ahn, Bae, and Chan (2001) for the Stock Exchange of Hong Kong; and
Handa et al. (2003) for the CAC40 stocks traded on the Paris Bourse.

Shape of the Order Book as a Predictor of
Market Direction
Several studies have considered how the limit order book can be used to predict
short-term price moves. Cao et al. (2004), for example, find that a liquidity peak
close to the market price, for example, tends to push the market price away from the
peak. However, a liquidity peak away from the market price tends to “pull” the market price toward the peak. Cohen, Maier, Schwartz, and Whitcomb (1981), call this
phenomenon a “gravitational pull” of quotes. Figure 11.6 shows the sample evolution
of the market depth and the associated liquidity.

Market price

FIGURE 11.6 An Asymmetric Liquidity Peak near the Market Price Tends to Push the Market

Price Away from the Peak

rosu (2005) determines that the shape of the limit order book depends on the
probability distribution for arriving market orders. High probabilities of large market orders lead to hump-shaped limit order books. Foucault, Moinas, and Theissen (2005) find that the depth of the limit order book can forecast future volatility
of asset prices: the lower the depth, the lower the expected volatility. Berber and
Caglio (2004) find that limit orders carry private information around events such as
earnings announcements: a concentration of limit orders far away from the current
market price is likely to reflect someone’s postannouncement valuation of the traded
instrument.
Cont, kukanov, and Stoikov (2011) suggest that even Level I data can be used to
generate successful predictions of the impending price movements. To predict the
price movement, Cont et al. (2011) define a new variable, order flow imbalance
(oFI):
N ( tk )

k −1)+1

(5)

where en represents an instantaneous change in the top-of-the-book liquidity, and is
defined as follows:
e n = I{P

B
n

B
≥ PnB−1 }qn

− I{P

B
n

B
A
≤ PnB−1 }qn −1 − I{PnA ≤ PnA−1 }qn

+ I{P

A
n

A
≥ PnA−1 }qn −1

(6)

where I is the indicator function, equal to 1 when the bracketed condition is true,
and 0 otherwise, and qB and qA are the sizes at the best bid and the best ask,
respectively.
equations (5) and (6) can be interpreted as follows: order Flow Imbalance depends on the instantaneous change in the top-of-the-book liquidity, which in turn
depends on the tick-to-tick change in best bid and best offer prices. If the best bid
price increased, the order Flow Imbalance increases by the size at the new best bid. If
the best bid price decreases from one tick to the next, the associated oFI is reduced
by the best bid size recorded at the previous tick. Similarly, if the ask price decreases,
the oFI is decremented by the size at the new best ask. If the ask price increases from
last tick to the present tick, the oFI is increased by the size recorded at the previous
best ask.
To ascertain predictive power of the oFI, Cont et al. (2011) next map the oFI
figures vis-à-vis short-term price changes, and obtain a linear relationship, as shown
in Figure 11.7.

AuToMATed MArkeT MAkIng II

OFLk = ∑ n =N (t

189

∆Pk

3
T = 0.005x – 0.002
R3 = 0.091
–300

–200

–100

2
1
0
–1

OFIk
0

100

200

300

–2
–3
–4

FIGURE 11.7 order-Flow Imbalance versus Short-Term Price Changes

Source: Cont, kukanov, and Stoikov (2011)

evolution of tick Data as a predictor of
Market Movement

AuToMATed MArkeT MAkIng II

190

The advanced class of information models specifically addresses the intent and future actions of various market participants. Such models include game-theoretic approaches to reverse-engineer quote and trade flows to discover the information a
market maker possesses. Information models also use observed or inferred order
flow to make informed trading decisions.
At their core, information models describe trading on information flow and possible informational asymmetries arising during the dissemination of information.
differences in information flow persist in different markets. Information flow is
comparably faster in transparent centralized markets, such as most equity markets
and electronic markets, and slower in the opaque markets, such as foreign exchange
and over-the-counter (oTC) markets in bonds and derivatives.
Asymmetric information present in the markets leads to adverse selection, or the
ability of informed traders to “pick off ” uninformed market participants. According
to dennis and Weston (2001) and odders-White and ready (2006), the following
measures of asymmetric information have been proposed over the years:
■
■
■
■
■

Quoted bid-ask spread
effective bid-ask spread
Information-based impact
Adverse-selection components of the bid-ask spread
Probability of informed trading

The quoted bid-ask spread is the crudest, yet most readily
observable measure of asymmetric information. First suggested by Bagehot (1971) and
later developed by numerous researchers, the bid-ask spread reflects the expectations
of market movements by the market maker using asymmetric information. When the
quoting dealer receives order flow that he suspects may come from an informed trader
and may leave the dealer at a disadvantage relative to the market movements, the dealer
increases the spread he quotes in order to compensate himself against potentially adverse uncertainty in price movements. As a result, the wider the quoted bid-ask spread,

Quoted Bid-Ask Spread

the higher is the dealer’s estimate of information asymmetry between his clients and
the dealer himself. Given that the dealer has the same access to public information as
do most of the dealer’s clients, the quoted bid-ask spread may serve as a measure of
asymmetric information available in the market at large at any given point in time.
Effective Bid-Ask Spread The effective bid-ask spread is computed as twice the
difference between the latest trade price and the midpoint between the quoted bid
and ask prices, divided by the midpoint between the quoted bid and ask prices:


 4S
Ste =  a t b − 1
 St + St


(7)

The effective spread measures how far, in percentage terms, the latest realized
price fell away from the simple midquote. When markets are balanced and no information streams through, the true midquote is the natural trading price. When the
limit order book is skewed or imbalanced in some other way, the traded price moves
closer to the side with excess limit orders located at or near the top of the book.
Information-Based Impact The information-based impact measure of asymmetric information is attributable to Hasbrouck (1991). Brennan and Subrahmanyam
(1996) specify the following vector autoregressive (VAR) model for estimation of
the information-based impact measure, l:
M

k =1

m =1

Vi,t = θ i,0 + ∑ β i,k ∆Pi,t −k + ∑ γ i,mVi,t −m + τ i,t

(8)

∆Pi,t = φi,0 + φi,1sign( ∆Pi,t ) + λτ
i i,t + ε i,t

(9)

where ∆Pi,t is the change in price of security i from time t–1 to time t, Vi,t=sign(∆Pi,t). vi,t,
and vi,t is the volume recorded in trading the security i from time t – 1 to time t. Brennan
and Subrahmanyam (1996) propose five lags in estimation of equation (8): K = M = 5.
The adverse selection
components of the bid-ask spread is attributable to Glosten and Harris (1988). The
model separates the bid-ask spread into the following three components:

Adverse Selection Components of the Bid-Ask Spread

■■
■■
■■

Adverse selection risk
Order-processing costs
Inventory risk

Models in a similar spirit were proposed by Roll (1984); Stoll (1989); and
George, Kaul, and Nimalendran (1991). The version of the Glosten and Harris
(1988) model popularized by Huang and Stoll (1997) aggregates inventory risk and
order-processing costs and is specified as follows:
∆Pi,t = (1 − λi )

Si,t
2

sign( ∆Pi,t ) + λi

Si,t
2

sign( ∆Pi,t ).v i,t + ε i,t

(10)

191
Automated Market Making II

where ∆Pi,t is the change in price of security i from time t – 1 to time t, Vi,t=sign(∆Pi,t).
vi,t, vi,t is the volume recorded in trading the security i from time t – 1 to time t, Si,t is
the effective bid-ask spread as defined previously, and li is the fraction of the traded
spread due to adverse selection.
Easley, Kiefer, O’Hara, and Paperman (1996)
propose a model to distill the likelihood of informed trading from sequential quote
data.The model reverse-engineers the quote sequence provided by a dealer to obtain
a probabilistic idea of the order flow seen by the dealer.
The model is built on the following concept. Suppose an event occurs that is
bound to impact price levels but is observable only to a select group of investors.
Such an event may be a controlled release of selected information or a research finding by a brilliant analyst. The probability of such an event is a. Furthermore, suppose
that if the event occurs, the probability of its having a negative effect on prices is d
and the probability of the event’s having a positive effect on prices is (1 – d). When
the event occurs, informed investors know of the impact the event is likely to have
on prices; they then place trades according to their knowledge at a rate m. Thus,
all the investors informed of the event will place orders on the same side of the
market—either buys or sells. At the same time, investors uninformed of the event
will keep placing orders on both sides of the market at a rate w. The probability of
informed trading taking place is then determined as follows:
Probability of Informed Trading

Automated Market Making II

192

αµ

(11)
αµ + 2ω
The parameters a, m and w are then estimated from the following likelihood function
over T periods of time:
PI =

L( B, S α , µ,ω,δ ) = ∏ ( B, S,t α , µ,ω,δ )
t =1

(12)

where ( B, S,t α , µ,ω,δ ) is the likelihood of observing B buys and S sells within a
specific period of time:


(ωT )B  
(ωT )S 
( B, S,t|α , µ,ω,δ ) = (1 − α ) exp( −ωT )
exp(
ω
T
)
−


B!  
S! 


((ω + µ )T )B  
(ωT )S 
exp(
ω
T
)
+ α (1 − δ ) exp( −(ω + µ )T )
−
(13)


B!
S! 



(ωT )B  
((ω + µ )T )S 
exp(
(
ω
µ
)
T
)
+ αδ exp( −ωT )
−
+


B!  
S!



■■ Summary
Understanding the type and motivation of each market participant can unlock profitable trading strategies. For example, understanding whether a particular market
participant possesses information about impending market movement may result in
immediate profitability from either engaging the trader if he is uninformed or following his moves if he has superior information.
■■ End of Chapter Questions
1. If the quotes widen following a trade, and then revert to their original levels,
what can be said about the informational content of the trade? Explain.
2. What is order flow? How is it measured? How can it be estimated from tick data?
3. Does the order-flow imbalance metric developed by Cont, Kukanov, and Stoikov
(2011) increase when the size at the best bid increases? Explain.
4. Suppose you observe a high autocorrelation of order flow in MSFT. Who is most
likely trading and why? How can your algorithm utilize the information to generate positive gains?
5. What is adverse selection? When the risk of adverse selection falls, what does
this mean for a market-making algorithm?
193
Automated Market Making II

Chapter 12

Additional HFT
Strategies, Market
Manipulation, and
Market Crashes
195

s Chapters 8 through 11 illustrate, high-frequency trading (HFT) by and large
automates human trading. The opponents of HFT, however, perceive a range of
adverse HFT outcomes that have the potential to negatively impact market dynamics. This chapter discusses these perceived threats in detail, along with methods that
enable detection of high-frequency market manipulation and future market crashes.
Opinions on HFT continue to run the gamut. On one end of the spectrum we find
employers in the financial services industry. Just open the “Jobs” page in “Money and
Investment” section in the Wall Street Journal, and you will mostly find job postings
seeking talent for HFT roles. The advertising employers are the whitest shoe investment banks like Morgan Stanley. These careful firms generally invest resources into
something they deem worthwhile and legitimate. The extent of their hiring (often
the only hiring advertised in the Wall Street Journal) implies that the industry is enormously profitable and here to stay.
At the other extreme we find individuals such as Mark Cuban, a successful
Dallas-based businessman, who recently proclaimed that he is afraid of high-frequency traders. Mr. Cuban’s fears are based on his belief that high-frequency traders are
nothing more than “hackers,” seeking to game the markets and take unfair advantage
of systems and investors.
So how can Mr. Cuban and Morgan Stanley have such divergent views of the highfrequency world? For one, Mr. Cuban has likely fallen prey to some unscrupulous
uncompetitive financial services providers making a scapegoat out of high-frequency

traders. Opponents of high-frequency traders identify a range of purported HFT
strategies that are supposedly evidence of how HFT destroys the markets. Purportedly malicious HFT strategies compiled by one of the workgroups of the Commodity
Futures Trading Commission’s (CFTC) subcommittee on HFT included such ominous names as spread scalping, market ignition, and sniping, just to name a few.
As this chapter shows, strategies thought to be malicious and often associated with
HFT fall into one of the following categories:
■■
■■

■■

Legitimate strategies serving price discovery.
Strategies not feasible in “lit” markets–regulated exchanges; the same strategies
can be feasible in dark pools.
Strategies that are a direct consequence of pump-and-dump activity, a market
manipulation technique that is banned in most financial markets.

The CFTC subcommittee on HFT tasked with identifying undesirable HFT strategies identified the following instances:
■■
■■
■■
■■
■■

Additional HFT Strategies

196

■■
■■
■■
■■
■■
■■

Latency arbitrage
Spread scalping
Rebate capture
Quote matching
Layering
Ignition
Pinging/Sniping/Sniffing
Quote stuffing
Spoofing
Pump-and-dump manipulation
Machine learning

Each of the proposed activities is discussed in detail in the following sections.
While some market participants claim that HFTs can also manipulate markets via
special front-running order types, such advanced orders typically carry a heavier
price tag that annihilates any excess profitability of such orders in the long term,
rendering the orders unprofitable to HFT. This chapter also discusses methodologies
for detection of pump-and-dump activity.
■■ Latency Arbitrage
Latency arbitrage is often pinpointed by the opponents of HFT as the most direct
example of the technological arms race, and one without obvious consequences. To
succeed in latency arbitrage, unlike other HFT strategies discussed in Chapters 8
through 11, deployment of the fastest technology is pivotal. Contrary to the belief of
some, however, latency arbitrage has a well-defined market benefit, described next.
An important concept of financial theory is the Law of One Price. The Law states
that in well-functioning markets, a given financial instrument always has the same
price, regardless of the characteristics of markets where the financial instrument

trades. The Law of One Price then serves to assure low-frequency investors that
their trading will always be at the fair market price, no matter in which market they
decide to trade. In other words, in ideal theoretical market conditions, the price of
the IBM stock in London should always be the same as the price of IBM in NewYork,
after adjusting for foreign exchange.
When prices of the same financial instrument in different markets diverge for
whatever reason, high-frequency latency arbitrageurs jump in and trade away the
price discrepancies. For example, HF latency traders sell IBM in the market where
the stock is temporarily overpriced, while simultaneously buying it where the stock
trades too cheaply. In the process, the demand and supply produced by the highfrequency traders serves to equilibrate the market prices in previously divergent
markets. The high-frequency trader then quickly reverses his position to capture the
gain, and investors of all frequencies can be assured that prices on traded financial
instruments are consistent across the globe, upholding the Law of One Price.
Latency arbitrage is an example of a trading strategy that is based on taking advantage of high speeds. A question commonly asked by market participants and regulators alike is how much speed is enough? When does the race end? Should there be a
limit on how much speed is acceptable in the markets? From the economic point of
view, the race for speed will end as soon as there is equilibrium between increasing
technological capacity and trading profitability: when an additional dollar spent on
technology no longer generates extra return. Until that time, competition among
high-frequency traders will continue to foster innovation in the area of trading.

High-frequency spread scalping often refers to an automated market-making activity
that some market participants think is simple: a continuous two-sided provision of
liquidity that generates or “scalps” the spread value for the account of the HFT. As
discussed in Chapter 10, such activity is subject to extensive inventory and adverse
selection risks and can hardly be profitable in its simplest incarnation. Even in a nearly
stagnant market, market making is subject to inventory risk, whereby the market maker’s accumulated positions rise and fall with variations in the markets. In the absence
of opposing market orders, the market maker may not be able to profitably liquidate
his positions. Significant analysis of market conditions, presented in Chapters 10 and
11, is necessary to ensure profitability of seemingly naïve spread-capturing strategies.
As discussed in Chapter 11, even in their normal state, markets are fraught with
informational asymmetries, whereby some traders know more than the market
maker. Better-informed traders may have superior information about industry
fundamentals or just superior forecasting skills. In such situations, better-informed
traders are bound to leave the market maker on the losing end of trades, erasing all
other spread-scalping profits the market maker may have accumulated.
For a specific example, consider a news announcement. Suppose an alleggedly
spread-scalping HFT has positions on both sides of the market, ahead of the impending
announcement on the jobs figures—information on how many jobs were added or lost

Additional HFT Strategies

■■ Spread Scalping

197

during the preceding month. A better-informed trader, whether of the low- or highfrequency variety, may have forecasted with reasonable accuracy that the jobs number
is likely to have increased. Suppose the better-informed trader next decides to bet on
his forecast, sending a large market buy order to the market. The presumed spreadscalping market maker then takes the opposite side of the informed-trader’s order,
selling large quantities in the market that is just about to rise considerably on the news
announcement. In a matter of seconds, and due to activity of lower-frequency traders,
our high-frequency market maker may end up with a considerable loss in his portfolio.
In summary, spread scalping may seem like a predatory strategy to some market
participants, yet it is hardly profitable in its most naïve incarnation. Spread scalping
enhanced with inventory and informational considerations is what most market participants call market making, a legitimate activity that is the integral part of market
functionality. Without limit orders sitting on either side of the spread, traders desiring immediacy would not be capable of executing their market orders. Compensation of a spread is a tiny profit comparable to the amount of work required to be able
to provide the limit orders on both sides of the market on the daily basis.
■■ Rebate Capture

Additional HFT Strategies

198

Another strategy often put forth as an example of the dangers of HFT is the rebate
capture. Under this strategy, high-frequency traders are presumed to generate profit
simply by arbitraging the costs and benefits of limit and market orders on various
exchanges. The strategy is thought to be an empty exercise with no economic value,
and a frequent example of what is wrong with market fragmentation. In reality, as
this section illustrates, rebates help improve the profitability of trading strategies,
but cannot deliver profitability without other forecasting methodologies, such as the
ones presented in Chapters 8 through 11.
To be profitable, a high-frequency trader needs to execute an order and hold a
position long enough to realize a gain. As outlined in Chapter 3, rebates for limit and
market orders presently exist only in equities, where a myriad of exchanges seek to
differentiate them from the rest of the pack. The minimum gain per trade in most
U.S. equity markets is currently $0.01. In normal rebate markets, the exchanges pay
rebates to traders posting limit orders, and providing liquidity by doing so. The New
York Stock Exchange (NYSE), for example, pays $0.13 to $0.30 for every 100 shares
to traders posting limit orders. Consider a trader who estimates ahead of each trade
the directional probability of a stock going up 1 tick or $0.01 is pup. In the current
NYSE environment, a rational high-frequency trader will post a limit buy order only
when the marginal cumulative rebate value exceeds the trader’s expected return:
$0.01 pup – $0.01(1 – pup) – $(transaction costs) ≥ – $rebate

(1)

where $rebate is the value of the rebate per share, and $(transaction costs) represents
the costs the trader needs to pay per share to execute his trades. Transaction costs in
equities may include a clearing fee, a transaction fee, a FINRA pass-through fee, and
a NYSE pass-through fee, in addition to broker-dealer commissions.

Equation (1) is equivalent to
$transaction costs -$rebate
(2)
+ 50%
$0.02
As the inequality (2) shows, in the absence of rebates, a limit order–posting
trader has to predict direction of the price correctly with probability greater than
50 percent. A broker-dealer advertises that transaction costs for selling 30 million
shares without considering NYSE rebates run about $50,000, or $0.0016 per share.
When executed as a market order, the 30 million shares incur the additional NYSE
fee, a negative rebate, for removing liquidity of about $70,000 or another $0.0023
per share. To be profitable under such cost structure, a rational high-frequency trader needs to have forecasting that reliably predicts probability of market movement,
pup, to be at least 70 percent:
Pup ≥

$0.0016 − ( −$0.0023)
+ 50% = 70%
(3)
$0.02
When posting the same 30 million shares as limit orders, the trader receives
$60,000 in rebates or $0.0020 per share, offsetting the nonrebate transaction costs
and generating about $10,000 or $0.0003 in profit per trade. This rebate-driven
profitability allows the high-frequency trader to lower his required probability of
correct directional forecasting, but just to 48 percent:
Pup ≥

■■ Quote Matching
In a so-called quote-matching strategy, a high-frequency trader is thought to mimic
the limit orders of another trader. A high-frequency trader is then thought to ride the
market impact the original orders generate. If feasible, such a strategy could negatively
impact block trades of a large investor by amplifying the market impact and worsening
the pricing the investor obtains on subsequent child trades. The strategy assumes that
the high-frequency trader is capable of identifying which limit orders always move the
markets in the certain direction in the short term, allowing the high-frequency trader
to quickly take advantage of the move, reversing positions and capturing the profit.
Specifically, the success of the strategy is predicated on the high-frequency trader’s ability to foresee which limit orders generate positive or negative market impact.
The key assumption of the strategy is the primary reason for its infeasibility. Most
of today’s exchanges are anonymous:They protect the identity of traders, disallowing

199
Additional HFT Strategies

$0.0016 − ( −$0.0020)
(4)
Pup ≥
+ 50% = 48%
$0.02
In other words, while rebates decrease the required accuracy of high-frequency
forecasts, and the respective probability of forecast correctness, the rebates do not allow random trading strategies to be profitable. As with the spread-scalping strategy, a
successful rebate capture is a complex market-making operation, with rebates serving
as a minor improvement of performance, and not as a primary source of profitability.

the HFTs the ability to tag and follow orders of a specific entity. Furthermore, as discussed in Chapter 5, while many buy orders are followed by a positive price movement in the short term, the movement is by no means guaranteed. In the case of
limit orders, while the market impact following a limit buy order is positive on
average, it is very small even for top-of-the-book orders, and can be mostly negative
or not statistically persistent for orders behind the market price. As a result, a quote
matching strategy solely relying on copying other trader’s limit orders is likely to be
a disappointment.
■■ Layering

Additional HFT Strategies

200

In layering, a high-frequency trader enters limit orders at different price levels away
from the market price, often to cancel the orders in the near future, and then to resubmit the orders again. The objectives of layering often confound casual observers,
who in turn suspect wrongdoing.
Some layering may indeed be manipulative. The manipulative layering is one-sided:
a market participant “layers” either buy or sell side of the order book with limit orders
and then promptly cancels the orders with the intent of changing other traders’ inferences about available supply and demand, The Securities and Exchange Commission
(SEC) penalized such layering in highly publicized cases in September 2012.
Much of layering, however, is a legitimate strategy, practiced by many executing
brokers as well as market makers in limit order books with price-time priority, described in Chapter 3. In most layering, a broker or a market maker leaves “placeholder” limit orders at different price points with the intent of securing a time priority in
a given price queue of a limit order book. When the market price reaches a broker’s
order, the broker may pursue one of two paths:
■■

■■

The broker may use his priority to execute a slice of an order, securing a preferential price for his customer.
In the absence of customer orders, the broker may simply cancel the placeholder
order.

Similarly, a market maker may decide to execute on the order or cancel it, depending on his estimates of inventory and information risks.
As such, most incarnations of the layering strategy are not manipulative but do
create unwanted noise in the markets by clogging the networks and the matching
engine with order cancellations. A successful solution implemented by the Chicago
Mercantile Exchange (CME), for example, changes the execution of the matching
engine from the price-time priority to a pro-rata schedule. As described in Chapter
3, under the pro-rata schedule, all limit orders posted at a given price level are executed at the same when the price level becomes the best bid or the best ask. Each
limit order in the given price queue is matched partially, proportional to the size
of each limit order. Such strategy eliminates the need to secure the time priority in
the given queue, and, as a result, entirely removes the need for layering as means of
securing priority of execution.

■■ Ignition
In an ignition strategy, a high-frequency trader is thought to detect the location of
long-term investors’ stop-loss orders and match against them, or “ignite” them.
Next, the strategy assumes that large stop-loss positions will have a substantial impact on the market, allowing the high-frequency trader to ride the market impact
wave, swiftly closing out his positions, all the while capturing small gains at the expense of long-term investors’ losses.
In today’s exchanges and other “lit” trading venues, such a strategy may work only as
a result of market manipulation, such as pump-and-dump. To match against someone’s
orders placed well away from the market price, one needs to move the market price
substantially in the direction of said stop loss orders. Market manipulation has always
been illegal and can be screened using methodology described later in the chapter.
While a manipulation-free ignition strategy is not feasible in lit trading venues,
such as all regulated exchanges, it can be deployed in dark pools. The dark pools,
however, have been created for sophisticated institutional investors, explicitly without regulatory protection, and operate under the “buyer beware” principle.
■■ Pinging/Sniping/Sniffing/Phishing

■■ Quote Stuffing
Quote stuffing refers to a purported high-frequency strategy whereby a trader intentionally clogs the networks and the matching engine with a large number of limit orders
and order cancellations. Unlike layering, where the high-frequency trader is seeking to
ensure execution priority in the order book queues, quote-stuffing traders are thought
to send in rapid orders and cancellations with the expressed purpose of slowing down

201
Additional HFT Strategies

Pinging, sniping, sniffing, and phishing monikers typically refer to the same general type
of strategy.The pinging strategy, much like the ignition strategy, identifies hidden pools
of limit orders and matches against those orders, creating and riding temporary market
impact for small gains. Much like the ignition strategy, such a strategy is often observed
in dark pools. Some dark pools, for example, Citibank’s Automated Trading Desk, have
designed ways to screen for pingers and charge them for pinging behavior. Such charges render pinging unprofitable and discourage pingers with market mechanisms.
While pinging is feasible in dark pools, it is not generally possible in lit markets, such
as exchanges, unless it is accompanied by illegal market manipulation. Just as in the
case of ignition strategies, in lit markets traders cannot selectively execute at random
price levels away from the present market price, unless they expressly move the price
away from the market first. Such price movements construe market manipulation.
As discussed later in this chapter, some market conditions are more conducive to
market manipulation than others. Avoiding conditions favorable to market manipulation may help traders to eliminate risks associated with ignition and other variants
of pinging strategies.

other traders, and thus manipulating markets. Quote-stuffing traders are further
thought to do so to delay other traders, ensure quote stuffers’ priority access to the
matching engine and the quote stream, and then effectively front-run other traders.
The idea of the quote-stuffing strategy contains one critical flaw: as any network
engineer will confirm, an individual network account cannot selectively slow down
network communication for some participants, while still receiving high-speed access to the trading venue. When a matching engine gets clogged with orders and
cancellations, it is equally clogged for all market participants, irrespective of who
caused the problem. Obviously, such network-clogging exercises do little for traders
equipped with fast technology; if anything, network clogging only voids the benefits
of fast technology. However, the network-clogging maneuver may be advantageous
for low-frequency traders, those who indeed desire to slow down matching capabilities. If anyone can be suspected of intentionally clogging up the lines (a market
manipulation), the natural trail leads to low-frequency culprits unequipped with fast
technology, for whom such manipulation may indeed result in increased profitability.
■■ Spoofing

Additional HFT Strategies

202

The spoofing strategy is similar to layering but executed with a radically different intent. In spoofing, the trader intentionally distorts the order book without execution;
in the process, the trader changing other traders’ inferences about available supply and
demand, and resulting prices. In principle, spoofing can be screened for and detected
in most lit markets: while layering calls for fairly balanced entry of limit orders across
all price ranges, spoofing would show one-sided peaks of limit orders in selected trading accounts. Spoofing has been made expressly illegal in the United States under the
Dodd-Frank Act, and has been actively prosecuted. In 2011, for example, the U.S.
CFTC fined Bunge Global Markets $550,000 for spoofing at the market’s open.
In summary, most strategies considered to be illicit HFT activity and reasoned
to be the cause for which HFTs should be banned do not exist or are a direct consequence of already illegal activity, such as market manipulation. Identification of
market manipulation activity and the market conditions conducive to market manipulation are discussed in the following section.
■■ Pump-and-Dump
Pump-and-dump is a truly adverse activity, whether implemented at high or low frequencies. The low-frequency pump-and-dump was well portrayed in the film Boiler
Room, where unscrupulous brokers “pumped” or raised the value of a particular financial instrument just to dump it at the first opportunity, realizing a profit at the expense
of other investors. The flip side of the pump-and-dump is the bear raid, whereby the
trader artificially depresses the price of a financial instrument, only to close his position
at a profit at the first available opportunity, all while leaving other investors in the dust.
In the high-frequency pump-and-dump, computer-assisted traders are thought
to momentarily drive up or down the prices of securities, only to promptly

Price

∆Pt (Vt)

∆Pt (−Vt)
Time

PnD PnD
buy buy

PnD PnD
sell sell

FIGURE 12.1 Market Impact that rules Out High-Frequency Pump-and-Dump Manipulation

Event: a market order (buy or sell) is
submitted for execution
t–3

t–2

t–1

FIGURE 12.2 Sequence of events Used in Market Impact Computation

t+1

203
ADDITIOnAl HFT STrATegIeS

reverse their positions and capitalize on false momentum at the expense of other
traders. Huberman and Stanzl (2004) and gatheral (2010) have developed necessary conditions for the absence of high-frequency pump-and-dump opportunities: the posttrade permanent market impact function should be symmetric in
size for buyer-initiated and seller-initiated trades. When the posttrade permanent
market impact for buyer-initiated trades exceed that for seller-initiated trades,
for example, a high-frequency trader could “pump” the security price through repeated purchases to a new high level and then “dump” the security, closing out his
positions at a profit. The gain would originate solely from the asymmetric market
impact: the absolute value of market impact following buy trades would differ
from that following sell trades. On the other hand, when pump-and-dump is not
feasible, the price change following a sell-initiated trade of size V is equal to the
negative of the price change following a buy-initiated trade of size V, as shown in
Figure 12.1. A pump-and-dump arbitrage opportunity exists when the “no-pumpno-dump” condition is violated.
Aldridge (2012e) formally describes pump-and-dump strategies using a measure of permanent market impact f(Vt) of a trade of size Vt processed at time t,
where Vt>0 indicates a buyer-initiated trade and Vt<0 describes a seller-initiated
trade. If f(V) > −f(−V), a trader could artificially pump and then dump by first
buying and then selling at the same trade size V. Conversely, if f(V) < −f(−V), the
trader could manipulate the markets by first selling and then buying the securities back.
To examine the evolution of market impact over time, we consider market impact within different event windows, where the length of the window is determined
by a number of trade ticks before and after the market order event, as shown in
Figure 12.2.

Denoting market impact function f, we obtain the following specification:
ft +1 = ln[ Pt +1 ] − ln[ Pt −1 ]

ft +τ = ln[ Pt +τ ] − ln[ Pt −1 ]
To evaluate the feasibility of the pump and dump, we use a linear specification
for the market impact as a function of trading volume, V, consistent with Breen,
Hodrick, and Korajczyk (2002); Kissell and Glantz (2002); and Lillo, Farmer, and
Mantegna (2003), following Huberman and Stanzl (2004) and Gatheral (2010):
ft +τ (Vt ) = ατ + βτ Vt + ε t +τ

(5)

where Vt is the size of trade executed at time t, βτ is the trade size–dependent market impact, and ατ is the trade size–independent impact of each trade recorded at time t. If the
high-frequency pump-and-dump is feasible, βτ for buyer-initiated trades will be different
from –βτ estimated for seller-initiated trades.The null hypothesis, that pump-and-dump
exists in trading activity of a financial instrument, can then be specified as follows:

Additional HFT Strategies

204

H 0 : βτ

buyer − initiated trades

≠ − βτ

seller − initiated trades

(6)

And the alternative hypothesis ruling out pump and dump can be specified as:
H − A.:,, β − τ . − buyer − initiated trades = −,, β − τ . − seller − initiated trades (7)
The framework above allows for straightforward screening for market manipulative activity in various financial instruments.
What does pump-and-dump detect? The example in Figure 12.3 illustrates the
analysis on a sequence of Eurex Eurobund futures (symbol FGBL) trades, recorded
sequentially and time-stamped with millisecond granularity. In addition to the timestamp, the data includes the trade price and trade size. The data is the “official” copy
of the Eurex trading tape, and is commercially distributed to traders. The data does
not contain best bid/offer information or identification of whether the trades were
initiated by the buyer or seller. To identify whether the trade was initiated by a market buy or a market sell, a tick rule discussed in Chapter 3 is used.
In computing market impact (MI), overnight returns are treated as missing observations, ensuring that the MI on a specific day is a function of data recorded on
that day only.
Table 12.1 reports estimates of equation (5) for trades of all sizes by month of
2009–2010 period. Figure 12.3 graphically illustrates the relationship of volume
coefficients for buy and sell trades. Figure 12.4 shows the results of the difference
tests of volume coefficients observed for buy and sell trades.

2.00E-07
1.50E-07
1.00E-07
5.00E-08
Buys, all sizes

0.00E+00

Sells, all sizes

-5.00E-08
-1.00E-07

201011

201009

201007

201005

201003

201001

200911

200909

200907

200905

200901

-2.00E-07

200903

-1.50E-07

FIGURE 12.3 Volume Coefficients of Market Impact of Buy-and-Sell Trades, FgBl Futures,

2009–2010
taBLe 12.1 estimation of Size-Dependent Market Impact for Large and Small trades in
eurobund Futures, by Month
Buys, all trade Sizes

α5

t-stat

β5

t-stat # obs

α5

t-stat

373631
332584
400829
319454
298859
348640
310745
284896
331673
337226
283547
249533
247741
298294
295452
297115
413507
393351
314054
299741
422772
345432
447795
305279

1.6e-5
1.4e-5
1.5e-5
1.0e-5
1.2e-5
1.2e-5
7.5e-6
8.6e-6
9.5e-6
7.2e-6
7.5e-6
8.6e-6
5.7e-6
6.5e-6
6.6e-6
6.4e-6
1.1e-5
1.1e-5
6.3e-6
7.1e-6
1.3e-5
8.7e-6
1.1e-5
1.4e-5

50.7
37.4
54.8
39.5
37.1
32.4
20.8
23.1
43.5
35.6
35.1
23.2
14.9
16.9
26.4
23.1
33.5
41.1
18.5
17.4
61.0
41.6
55.6
45.2

1.6e-7
1.3e-7
3e-8
1.8e-7
1.1e-7
3.8e-8
1.4e-7
1.2e-7
1.8e-8
8.4e-8
7.6e-8
1.4e-8
9.9e-8
8.1e-8
2.9e-8
8.3e-8
1.1e-7
2.5e-8
1.2e-7
9.9e-8
2.5e-8
1.0e-7
1.0e-7
2.2e-8

24.1
20.0
11.8
37.3
23.3
11.9
22.8
20.1
12.4
32.4
29.6
6.4
21.0
19.8
16.4
26.2
22.9
11.8
23.9
18.6
15.5
35.5
33.8
8.8

–2e-5
–1.7e-5
–1.6e-5
–1.4e-5
–1.4e-5
–1.5e-5
–1.2e-5
–1.3e-5
–1.1e-5
–8.1e-6
–9.6e-6
–1.3e-5
–1.1e-5
–1.1e-5
–9.5e-6
–8.3e-6
–1.3e-5
–1.4e-5
–1.1e-5
–1.2e-5
–1.4e-5
–9.6e-6
–1.3e-5
–1.8e-5

–50.5
–46.0
–55.5
–46.2
–41.4
–38.5
–29.3
–30.3
–42.5
–38.2
–39.2
–36.1
–22.7
–29.5
–34.8
–31.7
–45.1
–45.8
–29.4
–26.9
–55.0
–42.2
–52.9
–49.3

367857
334078
402137
318556
300020
341341
303278
285690
325211
330927
281327
248061
247258
295019
297502
298106
409226
387231
307322
296117
419480
328033
426999
302936

β5
–1.4e-7
–1.1e-7
–4.8e-8
–1e-7
–1.2e-7
–2.6e-8
–1.1e-7
–1.2e-7
–2.9e-8
–8.3e-8
–5e-8
–1.1e-8
–6.9e-8
–5.4e-8
–1.9e-8
–7.3e-8
–8e-8
–2.1e-8
–1.1e-7
–6.6e-8
–2.9e-8
–1.1e-7
–9.3e-8
–3e-8

t-stat
–18.6
–17.6
–17.4
–21.8
–23.4
–7.7
–17.1
–17.0
–15.0
–28.9
–18.6
–5.1
–12.1
–14.1
–11.9
–24.6
–20.3
–9.0
–20.4
–12.4
–17.0
–35.2
–27.8
–9.3

Note: Coefficients for the entire sample, large trades and small trades, were estimated using the following linear regressions:
MIt+τ (V)=ατ +βτVt+εt+τ, where the observations were separated into buys and sells.

205
ADDITIOnAl HFT STrATegIeS

200901
200902
200903
200904
200905
200906
200907
200908
200909
200910
200911
200912
201001
201002
201003
201004
201005
201006
201007
201008
201009
201010
201011
201012

Sells, all trade Sizes

# obs

1.00E-07

14.00
12.00

8.00E-08

10.00

4.00

Difference in volumeattributable market impact,
buyer-initiated less sellerinitiated trades

2.00E-08

2.00

Associated t-statistic

0.00E+00

0.00

6.00E-08

8.00
6.00

4.00E-08

-2.00

-2.00E-08

201011

201009

201007

201005

201003

201001

200911

200909

200907

200905

200903

200901

-4.00E-08

-4.00
-6.00

FIGURE 12.4 Difference in Volume-Attributable Market Impact, of Buyer-Initiated Trades less

That of Seller Initiated Trades

ADDITIOnAl HFT STrATegIeS

206

The observed differences in buyer-initiated and seller-initiated market impact change from month to month and lack statistical significance. Based on the
results, the FgBl futures data does not support the possibility of high-frequency
pump-and-dump.
The results presented in Table 12.1 indicate another interesting phenomenon:
trade-size-related MI does not begin to register until the trade size rises to about
100 contracts. The unexplained variation, intercept α, in the market impact equation is large (on the order of 10–5), and the trade-related MI is on the order of 10–7, a
single trade of up to 100 contracts may incur as much impact as a trade of 1 contract.
This is great news for institutions and other large fund managers who are concerned
about the impact of their trades—in the FgBl futures market, a single trade of a size
considerably larger than the median trading size on average leaves no trace. Unlike
the equities markets, the eurex FgBl market is resilient to a much larger capacity.
To check whether the results are robust, several auxiliary explanatory variables
can be added to the analysis: volatility, spread, and intertrade duration. Other studies
found such additional explanatory variables for temporary market impact.
For example, in futures, Burghardt, Hanweck, and lei (2006) show that posttrade
MI is also dependent on liquidity characteristics, such as the market depth. Other studies have focused on equities. Breen, Hodrick, and Korajchyk (2002); lillo,
Farmer, and Mantegna (2003); and Almgren, Thum, Hauptmann, and li (2005)
showed that the permanent MI function in equities is dependent on stock-specific liquidity characteristics. Dufour and engle (2000) find that longer intertrade duration
leads to lower MI, and vice versa. Ferraris (2008) reports that several commercial
models for equity MI use volatility and bid-ask spread prevailing at the time of the
trade as predictive inputs to forecasts of MI of the trade. In the current study, we find
that volatility, spread, and intertrade duration help explain market impact in futures
as well. none of the auxiliary variables, however, change the symmetry between
the volume-dependent MI coefficient created by buyer-initiated and seller-initiated

trades. The auxiliary variables also do not alter the value or the statistical significance
of the trade size–independent component, the intercept, leaving the dominant sizeindependent market impact unexplained.
■■ Machine Learning

Yt=G(Xt,θ)+et

(8)

Next, the boosting error term is computed as follows:
E = ∑Wt I st <>0

(9)

where Ist<>0 is the indicator function taking on value of 0 when G(Xt, θ) matches
Yt precisely, and 1 when et is not equal to 0. The time series wt represents boosting
weights assigned to each observation time, with all weights in the first iteration set to
1, and weights in later iterations recomputed according to the following calculation:
wt′ = wt exp(α t I st <>0 )

(10)

207
Additional HFT Strategies

Machine learning is often cited as one of the most worrisome event accompanying
HFT. A CNBC commentator, Doug Kass, for example, in the conversation about
HFT proposed that investors should shut down machines before machines attack
investors. The belief that machines are capable of independent reasoning and intelligence similar to Arnold Schwarzenegger’s Terminator film character resonates among
some traditional market participants with little exposure to the fundamentals of
technology. Machine learning is then cited as evidence of such machine intelligence.
In reality, machine learning originates in control theory and is often a series of
nested analyses. Each analysis can be parametric, as basic as a simple linear regression, or nonparametric, a set free-form functional estimators. Independent of the
type of the analysis used, the nature of machine learning remains the same: uncover
patterns in data. As a result, machine learning is less threatening intelligence, and
more basic data mining.
Machine learning can be broken down into two major categories: supervised
learning and unsupervised learning. Supervised learning is the iterative estimation of
data relationships, whereby each subsequent iteration seeks to minimize the deviations from the previous analysis. Models used to fit data in supervised learning models may range from regression to neural networks to boosting algorithms discussed
below. Unsupervised learning seeks to identify patterns in so-called unstructured
data, devoid of any relationships. Techniques used to distill information under an unsupervised learning umbrella include identification of important signals by observing clustering of data points.
A supervised boosting algorithm, for example, works as follows: a dependent
variable Y, for instance, a time series of returns on a particular financial instrument,
is fitted with a function G, expressing dependence of Y on returns of another financial instrument, X, and parameters θ:

where

 1 − st 
α = log 

 st 

(11)

This machine learning methodology ultimately produces a function G(Xt, θ) that
closely fits Yt. Human researchers running the machine learning simulation select
the parameters such window sizes for training and testing, additional predictors, etc.
Machine learning algorithms may suffer from a critical flaw: data mining devoid of
economic underpinnings may produce relationships that may have been stable in the
past, but are not stable in the long term. Such accidental relationships are known as
spurious inferences, and are not reliable predictors for future behavior of dependent
variables. At the time this book was written, no machine learning algorithm was capable of intelligence beyond its immediate trading application and was certainly not
threatening to humans.
■■ Summary

Additional HFT Strategies

208

This chapter discusses algorithms often presented as evidence of adverse outcomes
from HFT. As the chapter illustrates most of the fears surrounding HFT strategies are
unwarranted. Some strategies, however, are a direct consequence of high-frequency
market manipulation, yet even those strategies can be screened for, greatly reducing
the risks to all market participants.
■■ End-of-Chapter Questions
1. What is latency arbitrage?
2. Suppose a stock of IBM is simultaneously trading at 125.03 on the NYSE and at
125.07 in Tokyo. Does latency arbitrage deliver positive or negative impact on
the price of IBM from the market efficiency point of view?
3. What is spread scalping? What is rebate capture?
4. What kind of layering is manipulative? What kind of layering is benign?
5. How can one detect pump-and-dump high-frequency manipulation?
6. What is machine learning?

Chapter 13

Regulation
A

t the time this book was written, high-frequency trading (HFT) was already a
heavily regulated market activity, tracked at the broker-dealer level. Current
regulation of HFT follows much the same rules as other forms of trading in a given
financial instrument. Indeed, as this book shows, HFT is little more than automation
of traditional trading processes and should be regulated as such. Proponents of HFT
regulation, however, call for stricter monitoring of machines, citing examples of
market failures such as the flash crash of May 6, 2010; the botched initial public offering (IPO) of electronic ATS BATS (Best Alternative Trading System) on March 23,
2012; and the spectacular $10-million-per-minute loss of Knight Capital Group on
August 1, 2012. This chapter discusses modern legislation relevant to HFT, traditional and current approaches, and likely imminent directions.
■■ Key Initiatives of Regulators Worldwide

Currently, main issues on the regulatory table include:
■■

Jurisdiction

■■

Stability of systems

■■

Investor protection

■■

Efficient trade matching

■■

Market structure
This section considers each of the issues in detail.

Jurisdiction
The long shadow cast by market regulators covers HFT as part of their mandate to provide legal oversight to markets at large. Roles and objectives of market regulators have
evolved on a regional basis due to philosophies and histories of individual jurisdictions.

209

Regulation

210

Most of U.S. regulation represents a rule-based approach, in which regulators
prescribe specific remedies as well as punishments for certain behaviors observed
in the markets. By contrast, regulators of the European Union have established a
principle-based regulatory system, whereby each regulatory case is evaluated in its
conformance with the general principles of desired market systems. The differences
between the U.S. and EU regulatory models can be traced to the philosophical differences that exist between regulatory systems in the two regions. In the United
States, the objective of regulation has been to level the playing field, allowing equal
access to the markets for large investors and for “widows and orphans” alike. Behaviors blocking fair access are considered to go against the grain of the U.S. markets.
Such behaviors are actively identified, documented, and dealt with. In the European
Union, however, the main tenet of regulation can be distilled to fairness of gains—an
action that is deemed unfair to a contingent of traders may run afoul of European
regulators.
Other countries have developed their own regulatory styles. The key objective
of Australian regulators, for example, tends to be market integrity. The U.K. government has taken more of a forward-looking approach to regulation, working to
anticipate future developments and then assessing the resulting impact. Canadian
regulators seek to conform to the international standards of financial regulation,
and, specifically those promulgated by the International Organization of Securities
Commissions (IOSCO).
Jurisdictional issues arise within each country, as well. In the United States, for
example, regulatory rules for various markets are developed and adopted by several
agencies. The Securities and Exchange Commission (SEC) oversees trading in equities and related products, like equity options, exchange-traded funds, and so on. The
Commodity Futures Trading Commission (CFTC) deals with futures contracts and
related markets, such as options on futures. Swaps and futures on fixed income and
foreign exchange also fall under the jurisdiction of the CFTC, even though foreign
exchange itself is not regulated outside of basic common investor frameworks. In
addition to the SEC and CFTC, the U.S. regulatory system includes industry selfregulatory organizations (SROs). Financial Industry Regulatory Authority (FINRA)
navigates the world of equities. In this role, FINRA administers industry licensing
examinations and maintains first-level supervision of market abuses. Potential cases
of market manipulation detected by FINRA are next sent over to the SEC for further examination. The Futures Industry Association (FIA) is the futures equivalent to
FINRA and promotes best practices among futures traders.
Regulatory approaches can vary dramatically from one asset regulator to the next.
The U.S. equities, for example, have been subject to three groundbreaking regulations in the past 15 years. The 1997 Order Display Rule required exchanges to display limit orders of all customers, no matter how small. The rule for the first time
allowed all sorts of trading entities, including individuals, to make markets. Previously, such privileges were bestowed only on members of the exchange and selected
broker-dealers paying dearly for such ability. Regulation Automated Trading Systems
(Reg ATS), that went into force in 1998, further mandated electronization of exchanges and has led to the ability to receive, process and store quotes electronically,

211
Regulation

bringing in great transparency of prices at tick levels. Regulation National Market
Systems (Reg NMS), enacted in 2005, further enhanced an investor’s ability to track
a broker-dealer’s execution. In the 1980s, a client executing a market order had only
the daily open, high, low, and close quotes, printed in the next day’s newspaper, as a
reference for the price given by the broker. Under Reg NMS, all investors can be assured of validity of their execution prices within a minute from trade prints recorded
in the centralized ticker-data tape, Securities Information Processor (SIP). The oneminute window for submitting quotes into SIP under Reg NMS may seem too large
by now. After all, most broker-dealers in the United States can guarantee the execution of a market order in as little as one-hundredth of a second (10 milliseconds) or
faster, while selected U.S. exchanges can receive a market order, match it, and send
back the acknowledgment in as little as a quarter of a one-thousandth of a second
(250 microseconds). Still, even with a 1-minute window Reg NMS delivers investors and end traders much needed execution benchmark prices.
Reg NMS has introduced another structure peculiar to equities: the National Best
Bid and Offer rule (NBBO). Under NBBO, all equity exchanges may only execute at
the price distributed in SIP or better. If a given exchange does not have enough limit
orders on hand to execute an incoming market order at the NBBO, the exchange
must route the market order to another exchange.
The order-forwarding rule of the Reg NMS created a new line of differentiation
for exchanges: flash orders. When a U.S. exchange does not possess limit orders
satisfying the NBBO, the exchange may choose to broadcast or “flash” the incoming
and instantly departing market orders to the subscribers of the exchange data. At
present, most exchanges have voluntarily banned flash orders, yet some exchanges,
such as DirectEdge, persist in flash order executions. The flashing is really a negotiation tactic for traders choosing to place their orders on the DirectEdge exchange:
when DirectEdge does not have NBBO, the traders flash their intent to execute, and
invite matching limit orders with potential price improvements over contemporary
NBBO to the table. Most orders from DirectEdge are typically forwarded to Boston
OMX, where flash order observers at DirectEdge can immediately direct their orders, should they be inclined to take on the orders flashing on DirectEdge. While the
flash order system as a whole is not set up for investors with slow communication,
the system is fair as it is based on voluntary participation: only the traders desiring
to flash or be flashed trade at DirectEdge, rendering DirectEdge a special negotiation
venue and separating the exchange from the pack. A study by Brodsky (2011), for
example, confirms that flash orders result in price improvements, yet disincentivize
liquidity provision on flashing exchanges, reducing the traded volume.
The U.S. SEC has also taken steps to ban naked access, also known as sponsored access and direct market access (DMA). Under DMA, broker-dealers would lend traders
their identification information and allow traders to use the information to access
exchanges directly, without any risk checks. DMA makes complete sense to sophisticated traders, who can develop their own execution systems (discussed in Chapter
15 of this book) and avoid paying fees to broker-dealers. At present, however, most
exchanges use broker-dealer identification to stamp the trades. When many traders
use the same broker-dealer’s ID without a broker-dealer’s checks and records under

Regulation

212

DMA, the exchanges or the ID-lending broker-dealers are unable to discern which
trader caused which type of market reaction, complicating existing surveillance. The
legal entity identifier (LEI), discussed in the following section, is likely to resolve
this issue by granting the exchanges the ability to track and measure risks of end
traders numbered with individual LEIs. Once implemented, the LEI initiative may
lead to reinstatement of DMA privileges, this time with even smaller involvement
by broker-dealers.
The U.S. CFTC has also taken on co-location and proximity services. As discussed
in Chapter 2, co-location implies that the location of a trader’s machine in the same
facility as the exchange’s servers. Proximity hosting, however, leaves traders’ machines in a building in the proximity of the exchange, but not in the same exact
facility. To ensure transparent pricing and fair access, in June 2010 the CFTC recommended that all co-location and proximity hosting facilities implement uniform fees
to all their customers, and to disclose their longest, shortest, and average latencies
to all current and prospective clients.1
Following the flash crash, the SEC and CFTC introduced clear rules under which
erroneous trades can be corrected or “busted.” The new rules were successfully applied in the Knight Capital fiasco of August 2012.
European regulators have generally followed the U.S. model; they have voted
against naked access, flash orders, and quote stuffing, discussed in Chapter 12. They
have also called for risk and error controls for algorithmic systems, minimum quote
life, and equal access to co-location services. Overall, however, the Europeans have
treaded lightly on the HFT. In light of European financial woes, HFT has been viewed
by some as the source of free money for all. A transaction taxation proposal, introduced by Greek parliamentarians and recently ratified by the broader EU Parliament, calls for a small tax on all trading activity. The proposal finds substantial riches
in the European financial markets and considers that the trading activity will shrink
little in response to the tax.
Given today’s mobility of international capital, however, such a tax is likely to
backfire. Most of today’s trading systems communicate using Financial Information
eXchange (FIX), a computer mark-up language discussed in detail in Chapter 6.
Changing from trading in one country to trading in another takes as little as changing a few lines in FIX code; after such a minute change, the trader can execute in a
jurisdiction free of transaction taxes. Even if all the countries around the world agree
1 At

the time this book was finalized, the U.S. Senate Committee on Banking was weighing in on
disallowing co-location altogether, with the idea that co-location offers unfair data advantage to technologically savvy market participants. The Senate hearings tend to focus only on the negative aspects
of co-location and ignore most positives. As detailed in Chapter 2, however, co-location provides
an enormous benefit to all market participants: security of trading communications. In co-located
operations, the trader’s machine has a dedicated private line to the exchange’s computer. Most of
the trading traffic in today’s markets is sent in plain text; sending it over co-located networks ensures
secrecy of communications. Without co-location, one can imagine an outright attack on financial
markets: a computer bandit may intercept trading communication, redirecting funds to his personal
accounts and outright annihilating trading venues, broker-dealers, and traders in the process. A ban
on co-location, therefore, would create a tremendous gap in market security and stability of financial
systems worldwide.

to impose an identical transaction tax, the measure would likely fail as the temptation and the instantaneous benefits from breaking the agreement would be just too
high—the first jurisdiction to defect the agreement would collect all the global trading activity that can move quickly, generating great trading and settlement premia.
The u.K. regulators have taken a most proactive approach, that of creating rules
for envisioned future of computer trading. The u.K. government has identified the
following four dimensions of instability potentially caused by computer trading:
1. nonlinear sensitivities to change, whereby small perturbations in code of trading systems or matching engines have large system-wide impact.
2. Incomplete information, where some market participants are able to assemble a
more accurate picture of the markets than others.
3. normalization of variance, where unexpected and risky events can be seen increasingly as normal.
4. Internal risks amplified by system-wide feedback loops that include risk-management systems, changes in market volatility, market news, and a delay in obtaining reference data, as illustrated in Figure 13.1.

Stability of Systems: Detecting error-prone algorithms
The stability of systems refers to the ideal operational scenario of markets: trading
free of inadvertent algorithmic errors. nothing in recent memory illustrates the
host of issues surrounding erroneous algorithms better than the recent “incident”

Sale of stocks in
delta-hedge holding

Synchronized
selling of risk

Adjust
delta-hedge

Initial
Losses

Capital hit,
Risk increases

Prices
adversely
affected

Prices fall
Investor
decides
to sell

Investor algo
sells on increased
volume

Losses on
positions,
“Halrcuts” go up

HFTs
“pass-the-parcel”

HFT Sells
Volume increases
Volatility Up
Incoming market
orders move prices
more

HFT “microprice”
revised down below
true market price

Bids and asks
become more
dispersed

NYSE falls,
NYSE quotes delayed

Sell orders
routed to NYSE

NYSE shows
best bid prices

Delay worsened

Newsfeed reports sale,
HFT news listener pick
up the story

ETF market
affected by
illiquidity
Volatility
up

Single-stock
volatility up,
factors mispriced

HFTs reduce linkage
between markets for
ETFs and single stocks

Market making
of single stocks
affected

FIGURE 13.1 Key Findings of the u.K. Foresight Initiative on Computerized Trading: Problem-

Amplifying Feedback loops
Source: Zigrand, Cliff, Hendershott (2011)

REGulATIOn

Index falls

213

Regulation

214

of Knight Capital Group, when a poorly tested and ill-operated algorithm wreaked
havoc in the markets. A whopping 45 minutes after the start of trading, employees
at the New York Stock Exchange noticed that Knight Capital’s system was losing on
average US$10 million every minute. (Employees at Knight Capital still appeared to
be oblivious to the fact at that moment.)
In the case of Knight Capital, it was the portfolio of Knight Capital itself that bore
the brunt of the incident. However, it is easy to imagine how a similar scenario could
have affected other market participants.To limit or eliminate the occurrences of such
rampant algo issues, regulators are naturally mulling ways to police markets with the
goal of ensuring stability, much like the highway patrol polices roads for errant drivers who may present dangers to themselves and others.
The surveillance for erroneous algos is best performed in real time. As the example of Knight Capital shows, even a 45-minute delay before pinpointing Knight’s
problem cost Knight’s shareholders US$440 million. Modern regulators, however,
are ill equipped for such a task. In the United States, both FINRA and CFTC currently collect volumes of tick data from every executed transaction the following
business day, or “on the T+1 basis.”2 While the T+1 data is perfectly suitable for
identification of market manipulation or other activity requiring multiday recurrence, as discussed in the next subsection, next-day data cannot detect algorithmic
problems in real time.
Instead of implementing complex data screening systems for real-time surveillance at their offices, however, regulators may be much more productive in the field.
At the level of clearing firms, for example, regulators can observe all the counterparties and their trades.Yet, most clearing happens at the end of the trading day, and
such surveillance would be tardy for many fast-moving markets. Surveillance at the
executing firm level, that is, broker-dealers, is also feasible, yet can be complicated,
as many traders utilize services of multiple brokers, and aggregating trades across
brokers in real time can be a challenge. Surveillance at the matching level may prove
to be the best solution, with exchanges best positioned to observe and detect market
irregularities across multiple accounts in real time. After all, in the case of the Knight
Capital Group debacle, it was the exchange, NYSE, that was first to sound an alarm
about unusual behavior of Knight’s trading. While it took the NYSE 45 minutes to
establish erroneous trading patterns on the exchange, modern technology can detect
patterns in much shorter time frames.
Still, unresolved issues surrounding exchange-level surveillance persist: for example, how to aggregate data among exchanges to track cross-asset trading strategies. Some proposed synchronizing timestamps of exchanges using equipment used
in global positioning systems (GPSs). The opponents of time synchronization, however, cite market participants’ reluctance to forfeit freedom to deploy technology
of choice. In addition, the opponents point to the latency inherent in GPS-based
2

The SEC does not obtain tick data and is commonly cited as lacking funds to do so. Part of the reason behind the SEC’s reluctance to build the data capability is the agency’s implicit agreement with
FINRA. At present, FINRA detects potential instances of market manipulation and forwards them to
the SEC. The SEC on average prosecutes every eighth case forwarded by FINRA.

synchronization: depending on the location of the exchange, even GPS-wound clocks
may differ by several microseconds—an issue in today’s fast-paced markets.

Currently Deployed Measures for System Stability
At present, most exchanges have already enabled some forms of real-time surveillance. All exchanges today, for example, are required to implement circuit breakers
that halt trading in a selected financial instrument for several minutes following an
intraday price drop of several percentage points. Futures exchanges like the CME
and the Intercontinental Commodity Exchange (ICE) have also introduced the following measures described in detail next:
■
■
■
■
■
■
■
■

Interval price limits
no-cancel range
Protection points
Cancel orders on system disconnect
Message throttle limits
Maximum quantity limits
Real-time position validation
Price reasonability

■
■

The price reverts to a higher level above the lower IPl.
The IPl computational period shifts and the new IPl is lower than the previous
limit, allowing trading.
Reasonability limit
No cancel range
Average price

Interval
price
Limit
(Hi/Lo)

FIGURE 13.2 Illustration of Interval Price limits

Source: ICE

Halt

215
REGulATIOn

Interval price limits (IPls) are circuit breakers that are triggered by extreme short-term moves. The IPl-based halts work as follows. For each
traded financial instrument, the exchange computes a moving average price level and
a “normal” variation determined on the highs and lows evidenced in the moving data
window used in computation.The moving average price plus and minus the variation
parameter define the upper and lower IPls, illustrated in Figure 13.2. As shown in
Figure 13.2, when the price falls below the lower IPl, the trading is halted until one
of the two following situations occur:

Interval Price Limits

The width of the window used for computing the price bands is determined by
the trading frequency of the financial instrument: the price bands for a frequently
traded instrument will be recomputed more often than those for the instrument
with little activity.
No-cancel range refers to the depth of quotes in the limit order
book, where the limit orders cannot be cancelled for a predetermined period of time.
When the no-cancel range comprises only the best bid and the best ask, the measure
is also known as the minimum quote life (MQL). At the foreign exchange interdealer
broker EBS, for example, limit orders placed at the best bid and the best ask cannot
be canceled for 250 milliseconds (ms) from the time the order was placed. As a result, within the quarter of a second, the best bid and best ask quotes may change only
when the limit orders are matched with an incoming market order. The ICE has also
instituted a measure whereby limit orders falling in the no-cancel range may not be
canceled altogether. In the case of both EBS and ICE, the limit orders can be canceled
as soon as they fall out of the no-cancel range due to natural price movements.
Introduction of MQL appears to be of little consequence to the markets. A study
by Chaboud (2012), for example, showed that the markets were much more impacted by overhaul in the EBS matching algorithm than the introduction of MQL.
The no-cancel range may gain popularity with other exchanges or be mandated in
the near future.
No-Cancel Range

Regulation

216

Protection points stipulate the maximum number of price levels
or ticks a large incoming market order can sweep through in the limit order book.
When a market buy order sweeps through the maximum number of price levels and
is still not filled in its entirety, the unfilled remainder of the order is automatically
converted into a limit buy order. Protection points are currently in use on the CME.
Protection points were created in response to a previously common occurrence in
the futures markets—large market orders that could sweep as many as 100 ticks of
the order book at once. The sweeps disadvantaged the traders and the markets alike:
traders received poor average prices on their large orders, and markets were left
bare, with little or no liquidity, as a result of the sweeps. Today, protection points are
welcomed by the trading community.

Protection Points

Exchanges and broker-dealers alike
continuously monitor “heartbeat” messages from their clients, as described in
Chapter 16. When a client fails to check in with the regular heartbeat, and then
misses further scheduled “pings,” the client connection is assumed to have been terminated. Exchanges such as CME take cancel limit orders of disconnected clients as
a protective measure. The cancellation of limit orders is performed to ensure that
the clients do not execute orders when they are unable to monitor their positions,
reducing the incidence of unwanted trade executions.

Cancel Orders on System Disconnect

Message Throttle Limits The message throttle limits, also known as minimum fill ratios,
dictate the maximum ratio of order cancellations to order executions. For example,

a trader may be required to execute at least 1 order for every 10 canceled orders. At
the ICE, the message throttle limits are determined on a case-by-case basis in consultation with each trader. Appropriate message throttle limits ensure that the limits
detect algorithmic problems without impacting properly operating trading strategies.
Maximum quantity limits help prevent human and algorithmic “fat finger” errors by enforcing the maximum order sizes and trading positions. Maximum quantities are often determined in consultation with algorithm
designers, in order to take into account optimal operation of the trading system.

Maximum Quantity Limits

Real-Time Position Validation At present, futures markets are uniquely positioned
to withstand blow-ups of clients’ trading systems, like the one incurred by Knight
Capital. The secret to stable futures markets is the continuous real-time check of position market values vis-à-vis credit worthiness of trading account. When the market
value in a given account exceeds the critical margin limit, the client’s trading algorithm is prohibited from entering into new positions. In extreme situations, some of
the account holdings may be liquidated to satisfy margin requirements. In most equity
markets, similar checks are performed only at the end of each trading day.

Near-Term Surveillance Measures Both regulators and exchanges are seeking
to further improve market surveillance and stability with the following measures,
expected to be rolled out in the near future:
■■
■■

Kill switches
Legal entity identifiers

Kill switches are designed to automatically block and unblock order
entry at the following levels:

Kill Switches

■■
■■
■■
■■
■■
■■

Execution firm
Account
Asset class
Side of market
Product
Exchange

217
Regulation

Price Reasonability Under price reasonability, exchanges allow orders only at price
levels within a predetermined range away from the market price. On most U.S. exchanges, traders may not place limit orders higher or lower than 10 percent away from
the prevailing market price. The rule was instituted after the flash crash to prevent
market orders in crisis from executing at unreasonably low prices, known as stub quotes.
Overall, many existing exchange measures are robust in catching errant algorithms. Wider proliferation of measures, as well as additional near-term measures,
described next, will ensure that the markets identify and deter errant algorithms
before problems occur.

At the execution firm’s level, a kill switch allows termination of all flow from
a broker-dealer whose algorithms are determined to be corrupt. In the Knight
Capital case, an execution-firm-level kill switch would have stopped all Knight’s
trading upon detection of irregularities. An account-level kill switch disables
trading by a specific account, while the asset-class kill switch disallows trading in
a specific type of financial instrument, for instance, options, potentially allowing trading in other markets. The side-of-market kill switch turns off buying or
selling capability. The product kill switch bars trading in one particular financial
instrument, while the exchange kill switch takes away ability to trade on a given
execution venue.
Kill switches may be operated by exchanges following some specific risk guidelines. In addition, API-based kill switches may be programmed directly into a client’s
algorithm, shutting down trading ability whenever the algorithm’s particular risk
tolerance conditions are exceeded. Various risk-tolerance metrics are described in
Chapter 14.
Real-time regulatory surveillance at the exchange level
is further likely to be aided by one of the key new regulatory initiatives: legal entity
identifiers (LEIs). An LEI is a unique identifier assigned to all market participants:

Legal Entity Identifiers

■■
■■

Regulation

218

■■
■■
■■
■■
■■
■■
■■
■■

Financial intermediaries
Banks
Finance companies
All listed companies
Hedge funds
Proprietary trading organizations
Pension funds
Mutual funds
Private equity funds
Other entities

There are expected to be no thresholds (capitalization or other) required to obtain an LEI. Such configuration will extend the LEI-based surveillance to all trading
entities, except for natural persons.
Presently proposed LEIs are composed of 20 alphanumeric characters, with special sequencing of digits that can be validated using a check character system. Each
LEI will be associated with the official name of the legal entity or with the fund
manager for pooled investments, the address of the headquarters, the country of
incorporation, the date of the first LEI assignment, the date of last update of LEI
information, and the date of expiry, if any.
The LEI system will be administered by the International Organization for
Standardization (ISO). The ISO will take on validation of LEI applications, assignment of LEIs, maintenance of LEI registry, as well as the annual review of LEI records. The LEI system is expected to operate on an international level; in addition
to the U.S. regulators, authorities in Canada, Hong Kong, and Australia have already
expressed intention to apply the LEI system in their respective jurisdictions.

The LEIs are expected to phase in by asset class, beginning with over-the-counter
(OTC) derivatives, like credit default swaps, and later extending to all asset classes.
The U.S. CFTC already requires the use of LEIs for all dealers executing OTC derivative transactions.

Investor Protection
Investor protection is one of the explicit goals of several regulators, like the U.S.
SEC. The SEC and most other regulators seek to safeguard traders and investors by
minimizing the following activities in the markets:
■■
■■
■■

Market manipulation
Front-running
Market crashes
This section considers each of these issues.

Detecting Intentional Market Manipulation Whole classes of strategies attributed to high-frequency market distortions often prove ill thought through, as discussed
in Chapter 12. Having said that, HFT market manipulation is as feasible in principle
as is the screening and detection of such manipulation.
From the regulatory perspective, establishing credible market manipulation requires two principles:

In other words, to credibly detect market-manipulating activity, regulators need
to establish a pattern of intentional market manipulation. To do so, after observing
an instance of potentially harmful activity, regulators need to consider previous and
subsequent market activity by the same entity and detect a sequence of actions along
the same trajectory.
Manipulation can be detected following the blueprints discussed in Chapter 12.
As shown in the previous section on stability of systems, the extent of market manipulation can be measured by the symmetry of a market impact following buy-and-sell
market orders of equal size. Investors and regulators alike can successfully monitor markets for high-frequency manipulation by screening markets in real-time for
asymmetric market impact. Account-level trading in asymmetric markets can next
be examined for high-frequency manipulation.
Naturally, unscrupulous brokers possessing order-flow data may
choose to front-run their own clients whenever they detect a large impending price
move. The regulation has tried to deal with this problem. Under the Volcker rule,
for example, banks were forced to dispose of their proprietary trading operations,
with the intent of minimizing incentives for using client order-flow information, to
ensure stability of the banking sector. In some banks, however, the proprietary trading operations of high-frequency nature were not shut down. Instead, the HFT was

Front-Running

Regulation

1. The activity should be recurrent.
2. The activity was performed with the intent of manipulating markets.

219

moved directly into the execution area with a new moniker of prehedging function,
where the same HFT strategies are now executed with clients’ money on the banks’
behalf. The Dodd-Frank rule further complicates the problem by proposing to exempt brokers from their obligation to execute in customer interests first, essentially
creating a front-running bonanza at any broker-dealer’s execution desk. To prevent
front-running, clients can take matters into their own hands and diversify brokers,
effectively limiting the information each broker has about the client’s order flow.
Small traders are at a disadvantage, however, as few have enough capital to establish
positions with various brokers.
The Australian regulators have placed the goal of market integrity above all other
issues. One of the key initiatives on the table of the Australian regulators is the requirement for pretrade transparency, designed to stem front-running. The Australian
Securities and Investment Commission (ASIC) has specifically concerned itself with
detecting shifts in liquidity in response to orders, moving market prices before traders obtained execution but after they placed their orders.
Following the flash crash of May 6, 2010, a considerable body of research focused on advanced prediction of such events going forward.
Two main streams of crash predictability have emerged:

Predicting Market Crashes

1. Based on asymmetry of liquidity in the limit order books.
2. Based on abnormal trading patterns.
Regulation

220
Crash Prediction Based on Asymmetry of Liquidity in the Limit Order
Books The first stream of research first developed by Easley, Lopez de Prado, and
O’Hara (2011) takes root in the observation that the May 6, 2010, crash was a direct
result of asymmetric liquidity in the markets: the limit orders on the bid side of
E-minis, for example, were “eaten up” by incoming market sell orders a few hours
before the market activity precipitated into a full-blown crash.
To estimate the incidence of a crash, the authors develop a volume-based probability of informed trading, or VPIN metric:

V S − VτB
∑
τ =1 τ
VPIN ≈
n

(1)
nV
where VτS and VτB are volumes initiated by sell and buy market orders, respectively,
computed within each volume-based clock unit. Easley, Lopez de Prado, and O’Hara
(2011) consider volume clocks where each “time” unit corresponds to 50 E-mini
S
B
contracts: within each volume-clock unit τ, then, Vτ + Vτ = 50 contracts. The
authors show that extreme asymmetry in trading volume as measured by VPIN is
capable of predicting extreme crashes a few hours ahead of crash time. Tudor Investment Corporation has applied for a patent in VPIN, and may require fees for utilization of the methodology.
A separate stream of
literature considers “normal” patterns in trading and uses deviations from those

Crash Prediction Based on Abnormal Trading Patterns

normalities as the predictors of crashes. Normal market movements are calibrated
to fit the Mandelbrot-like growth parameter, known as the Hurst exponent. A Hurst
exponent of returns of 0.5 describes the market where the returns evolve in a completely random manner. A lower Hurst coefficient indicates a mean-reverting market,
while a higher Hurst value points to a trending market. Florescu et al. (2012) shows
that in most normal real-life markets, the Hurst exponent value has been shown to
be about 0.6. A heightened value of Hurst exponent is likely to precede a crash. For
example, Florescu et al. (2012) shows that ahead of financial services mini-crash
of March 2008, Hurst exponent values in financial services stocks reached 0.85.
Aldridge 2012f develops a separate crash-predicting methodology that can be shown
to identify onset of market crashes hours and sometimes days ahead of the events.

Efficient Trade Matching
Regulators are actively encouraging internalization, seeking to minimize the situations where broker-dealers execute trades against their own orders. Such incidents
are known as wash trades. An example of a wash trade may consist of a broker-dealer’s
placing an order for one customer at the best bid of the exchange, only to match
it with a market sell order for another customer. Wash trades have been deemed
feasible for money laundering and are closely monitored and discouraged.

Market Structure

Following the Dodd-Frank regulation, swaps are a
new asset class to be traded electronically in the United States The newly established
computerized swap trading falls under the jurisdiction of the CFTC, and will trade
in specialized swap-execution facilities (SEFs) that will have a new market structure,
are bound to attract high-frequency traders due to their electronic nature, and will
require new regulatory rules.
Swap Execution Facilities

Regulation Alternative Trading Systems (Reg ATS) introduced by the SEC in 1998 streamlined definitions and applicability of lit and dark
pools. The term pool refers to a trading venue attracting or “pooling” trading capital
for matching less formal than a regulator-supervised exchange. The terms lit pool
and, more often, lit market usually refer to a traditional exchange-like trading venue,
where the limit order book is observable by all engaged market participants. While
the transparency of the lit order book may induce confidence in some investors,
it may disadvantage others, particularly those desiring to trade large volumes and
seeking to avoid order-related market impact and other information leakage. As discussed in Chapter 11, lit order books contain information about impending directions of the market price and order flow, items many market participants prefer to
retain in secret.
“Lit” and “Dark” Pools

221
Regulation

Regulatory dimensions surrounding market structure presently span two main areas:
new markets, such as swap execution facilities, and “lit” versus “dark” pools. This section briefly considers the issues on the table.

To lit markets whenever:
- Too few market makers
- Rents are high

To dark pools whenever:
- Informational advantages
are cost effective
- Rents in lit markets are
low

FIGURE 13.3 Market-Making Equilibrium between Dark and lit Trading Venues

REGulATIOn

222

Dark pools are largely unregulated trading venues that do not disclose their limit
order books. By keeping their order books “in the dark,” dark pools create advantages
to large investors and market makers. large investors are enticed by limited information signaling associated with their orders. The orders are revealed only when
executed—trade prints are disseminated to all participants of a given market.
large investors are not the only group benefiting from dark pools. Market makers
also tend to earn more in dark pools than in lit markets. According to the research
of Boulatov and George (2011), for instance, market makers are able to hide informational revisions to their quotes, discussed in Chapter 11, trading longer on their
information. Examples of dark pools include Citigroup’s Automated Trading Desk
(ATD) and liquidnet’s offerings.
Even though dark pools tend to offer higher profitability to market participants
than do lit venues, an equilibrium controls proportion of market makers engaged in
dark pools versus lit trading operations. Once the majority of market makers’ moves
to the dark pools, lit venues become less competitive and market makers in these lit
venues earn higher rents. When the value of the market makers’ rents in the lit markets exceeds the informational advantages in the dark markets, more market-makers
moves from dark to lit venues, until an equilibrium is reached. Figure 13.3 illustrates
the mechanism by which the equilibrium between the dark and lit markets is achieved.
Canadian regulators have singled out dark pools as trading venues suitable only to
large investors trading amounts greater than a cut-off “Dark Order Size Threshold.”
In the united States, the nYSE went the opposite direction and created a segregated
dark pool for small investors, the success of which is yet to be determined.
■ Summary
Regulators worldwide are proactively tackling issues relating to HFT. new ideas
have emerged to monitor markets in real time and screen for issues such as market
manipulation and market crashes. Expanding monitoring activity at the exchange
level will likely deliver most substantial improvements of current enforcement; the
legal entity identifier initiative is bound to be helpful in the process.

■■ End-of-Chapter Questions
1. What are the latest key regulatory developments in the United States? In the
United Kingdom? In Canada? In Australia?
2. What kind of HFT protection mechanisms are already deployed in selected U.S.
markets?
3. What is the interval price limit? How does it work?
4. What is the message throttle limit? How is it determined?
5. What is a legal entity identifier?

223
Regulation

Chapter 14

Risk Management of
HFT
M

edia coverage of risks accompanying high-frequency trading (HFT) tends to focus on and overstate the risks of market manipulation, as detailed in Chapter 12.
However, little or no attention is paid to the real risks inherent in many HFT strategies
and the ways to mitigate or minimize said risks. These risks include those incurred by
high-frequency traders themselves and their trading venues and clearing parties. Chapters 14 through 16 describe the nature of such risks and existing strategy for dealing
with them. Chapter 14 covers the risks facing high-frequency traders. Chapter 15 discusses mitigation of risks associated with market impact (MI) that can be used by both
HFTs and other market participants, such as institutional investors. Chapter 16 covers
best practices in development of HFT with specific consideration placed on minimizing
risks embedded in technology implementation. Chapter 16 also discusses minimization of operational risks, and suggests best practices for execution of HFT.
■■ Measuring HFT Risk
As recent problems on Nasdaq and the Best Alternative Trading Systems (BATS)
illustrate, the risks from poorly executed HFT systems alone may result in
multimillion-dollar losses, incurred almost instantaneously. Understanding and
management of risks embedded in HFT therefore is critical to ensuring operational
success of HFT enterprises.
The following sections detail the quantification and management of risk exposure
for different types of risk. Chapter 16 documents best practices for ongoing oversight of risk exposure. The methodology for measuring risk depends on the type of
risk under consideration. All risk can be broken down into the following categories:
■■
■■

Regulatory and legal risk
Credit and counterparty risk

225

■■
■■
■■

Market risk
Liquidity risk
Operational risk

Regulatory and legal risk, credit and counterparty risk, market risk, and liquidity
risks are discussed in the sections below. Chapter 15 describes mitigation of market
impact. Chapter 16 focuses on operational risk.

Regulatory and Legal Risk
Regulatory and legal risk comprises the demands of new legislations that may affect
the operation of HFT systems. As discussed in Chapter 13, recent regulatory reforms
strengthened risk controls surrounding HFT, and are therefore beneficial to both the
markets and the HFTs themselves. As the latest U.S. Senate hearings indicate, however, the risks of adverse to HFT regulatory reform, such as the ill-thought-through
idea of banning co-location, still exist. (As discussed in footnote 1 in Chapter 13,
co-location is imperative for computer security and therefore stability of market
systems.)

Credit and Counterparty Risk
Risk Management of HFT

226

Credit risk specifies potential issues in a high-frequency trader’s ability to secure leverage. Leverage refers to the trader’s ability to borrow capital for his trading needs.
HFTs generally have leverage abilities comparable to those of other traders. In equities, for example, HFTs can generally borrow and trade three or more times as much
capital as the amount of cash available in their account, on a three-to-one or greater
margin, at the discretion of the margin-advancing broker-dealer. Because most HFTs
do not need to hold positions overnight, their leverage is considerably cheaper than
that of long-term investors. From the broker-dealers’ perspective, it is the typically unsupervised overnight changes in market value of long-term investors that are
subject to blow-ups and defaults on broker’s leverage. The intraday margin of HFTs
is tightly monitored along with HFT positions by the responsible HFT oversight
employee, at least in the best practices configurations. In futures markets, margin
positions are automatically monitored and enforced by the exchanges in real time.
Counterparty risk reflects the probability of financial loss should the high-frequency trader’s partners in the trading equation not live up to their obligations. An example of losses due to a counterparty failure is a situation in which
a fund’s money is custodied with a broker-dealer, and the broker-dealer goes
bankrupt. The collapse of Lehman Brothers in October 2008 was the most spectacular counterparty failure in recent memory. According to Reuters, close
to $300 billion was frozen in bankruptcy proceedings as a result of the bank’s
collapse, pushing many prominent hedge funds to the brink of insolvency. The
high-frequency traders may prevent similar conditions by tracking the creditworthiness of their brokers, as well as diversifying their exposure among different brokers and trading venues.

Market Risk
Market risk is the risk of loss of capital due to an adverse price movement of the traded financial instrument. A long position in E-mini futures following a buy order at
1446.02 begins incurring market risk as soon as the order is executed. Even before
any market movement takes place, instantaneous liquidation of the position will cost
the trader money: to immediately close down the position, the trader or the trading
system will need to pay the bid-ask spread.
The proliferation of automated trading has not changed the nature of market risk
carried by market makers and other intraday trading strategies. However, on the
per-trade basis and due to their ability to read every tick of market data and react in
the matter of nanoseconds, high-frequency traders face considerably lower market
risks than do their human counterparts.
The bulk of high-frequency market risk management focuses on the following
four key aspects:
1.
2.
3.
4.

First order: Stop losses
Second order: Volatility cutouts
Third and fourth order: Short-term value-at-risk (VaR)
Higher order: Hedging with other instruments

First-Order Risk Management: Stop Losses Stop losses denote hard loss limits for
each position and can be fixed or variable, absolute or trailing. Fixed stop losses outline
the absolute maximum each position can potentially lose and are same for each trade
within a given trading strategy. Variable stop losses can be determined for each trade
within a strategy and can be a strategy-specific function of market volatility and other
related variables. Absolute stop losses specify the hard amount a strategy can afford to
lose relative to the price level at which the position was opened. The trailing stop loss,
however, stipulates the hard price an amount a strategy can lose relative to the price at
which the strategy has achieved the highest gain after the position was opened. Figure
14.1 illustrates the difference between fixed and trailing stop losses.
Determining Stop-Loss Parameters

The optimal stop-loss parameter should sat-

isfy the following three requirements:
1. The stop loss should limit losing trades without affecting the winning trades.
2. A stop loss should not be triggered due to natural market volatility alone.
3. Stop losses should be executed immediately.

227
Risk Management of HFT

The order of the risk management methodologies previously noted refers to the
methodology relationship with the price of the traded financial instrument. Stop
losses are linear in price, and are therefore “first-order” functions of price. Volatility
is computed from squared price deviations and is referred to as a “second-order”
metric. VaR takes into account skewness and kurtosis of the trading returns, the
third- and fourth-order distributional parameters. Finally, hedging may be related to
any functional shape of price, and is therefore “higher-order.”
Each order of risk management is discussed in detail next.

Buy here

Max gain
Stop loss

1.2067

Max gain
Stop loss

1.2067

0.0050

1.2017
1.2000
1.1950

0.0050

1.2000

12:00 12:15 13:15

12:00 12:15 12:40

FIGURE 14.1 Difference between Simple (Fixed) and Trailing Stop-Loss Thresholds

The preceding requirements translate into the following mathematical conditions
for stop losses:
E[Profit] > 0
where E[Profit]
=E(Gain) * Pr(Gain) + E(Loss|Loss > StopLoss)
* Pr(Loss|Loss > StopLoss)
+ E(Loss|Loss ≤ StopLoss)
* Pr(StopLoss|Loss ≤ StopLoss)
RISk MANAgeMeNT oF HFT

228

Probability of gain, Pr(Gain), as well as the cumulative probability of loss,
Pr(Loss|Loss > StopLoss) + Pr(StopLoss|Loss ≤ StopLoss), can be estimated from the
simulation, as can be the average gain, E(Gain), and average losses above and below
the stop loss values, E(Loss|Loss > StopLoss) and E(Loss|Loss ≤ StopLoss).
During periods of high volatility, natural oscillations of the market price may trigger “false” stop losses, adversely affecting performance of trading strategies. The simplest way to account for variable volatility is via the following analysis:
■

■

In the in-sample back-test, estimate the volatility parameter over a rolling window. Within each time window, the volatility parameter can be estimated as a
simple standard deviation, or (better) weighted toward later observations using
a triangular or exponential weighting function. The duration of the window can
match the average position holding time of the strategy.
Distribution of the volatility parameters obtained in the previous step can be used
to create a multiplier for the stop-loss parameter: higher volatility should result
in larger absolute value of the stop loss.
An out-of-sample back-test should confirm higher profitability of the stop-lossenabled strategy.

Volatility cutouts refer to
rules surrounding market conditions during which the HFT systems are halted. Some
HFT strategies work better in high-volatility conditions, while others work best in
low volatility. To optimize capital performance, volatility cutouts “pass through” orders of some strategies when one set of conditions takes place and allow orders of

Second-Order Risk Management: Volatility Cutouts

other strategies when a different state of the world is realized. Volatility “states of
the world” can be determined empirically by computing a rolling volatility estimate,
such as the standard deviation of short-term returns of the underlying asset or a
market index over a certain past window of data. Such backward-looking volatility
estimates are risky, as they are assuming that the past volatility conditions will persist
into the future (volatility tends to “cluster” or persist for long periods of time, so the
assumption is plausible if not bulletproof). Alternatively, volatility cutouts can be
tied to a variable measuring forward-looking volatility, such as the volatility index
(VIX) or an implied volatility derived from the options on the traded security. Since
volatility cutouts are tied to the squared changes in the value of the traded security,
volatility cutouts can be considered a “second-order” risk metric.
Many trading strategies perform better in certain volatility conditions independent of the stop-loss parameters. To enhance performance of a strategy, it may be desirable to limit execution of such strategies in
adverse volatility conditions. To determine the volatility conditions optimal for strategy execution, one may use the following technique:

Determining Volatility Cutouts

where Rt represents the gain of the last completed round-trip trade realized at
time t, and σˆ t is the moving volatility estimate obtained in the previous step.
Instead of realized strategy returns, the Rt on the left-hand side of the regression
can be mark-to-market strategy gain sampled at regular time intervals.
3. If the estimate of b is positive (negative) and statistically significant, the strategy performs better in high (low) volatility conditions. A median of volatility
estimates obtained in step 1 above can be used as a turn-on/turn-off volatility
switch for the strategy.
A successful risk management process should establish the risk budget that the
operation is willing to take in the event that the operation ends up on the losing
side of the equation. The risks should be quantified as worst-case scenario losses
tolerable per day, week, month, and year and should include operational costs, such
as overhead and personnel costs. Examples of the worst-case losses to be tolerated
may be 10 percent of organizational equity per month or a hard dollar amount—for
example, $15 million per fiscal year.
Forecasting volatility is important
in many trading applications. In addition to option-based strategies that directly
Determining Volatility Cutouts Ex-Ante

229
Risk Management of HFT

1. In the in-sample back-test, estimate the volatility parameter over a rolling window. Within each time window, the volatility parameter can be estimated as a
simple standard deviation, or (better) weighted toward later observations using
triangular or exponential weighting function. The duration of the window can
match the average position holding time of the strategy.
2. Regress strategy gains on the obtained volatility estimates using the following
equation:
Rt = α + βσˆ t + ε t

Risk Management of HFT

230

arbitrage volatility, some spot and futures strategies may work better in some volatility conditions than in others. Many risk management models also call for volatilitydependent treatment of the strategies: stop losses may be “tighter” in low-volatility
conditions and “looser” in high-volatility ones.
Forecasting volatility can be simple in principle. Volatility has been shown to “cluster” in time: volatility “builds up” into peaks and reverses into valleys gradually, resulting in clusters of high-volatility observations. As a result, volatility is straightforward
to predict: high-volatility observations are usually followed by more or less high observations, while low-volatility cases are surrounded by similarly low volatility figures.
Popular tools for measuring volatility are quite simple: a standard deviation of returns
(a simple average of square deviations from the mean) presents the most basic metric of
volatility calculations. Since most recent observations can be more relevant than observations in the past, some researchers weigh later observations by computing a weighted
average of square deviations from the mean. The weights can be either linear or exponential. Another popular metric of volatility is the average of squared intraperiod
returns; it has been shown to be superior to standard deviation–based computations.
Given the tendency of volatility to cluster, it is reasonable to assume that the next
period’s volatility will be the same as the last period’s volatility. Alternatively, one
may calculate if the latest volatility observations form a trend, and then extrapolate
the trend into the future. A popular trending volatility forecasting tool is called the
generalized autoregressive conditional heteroskedasticity (GARCH) estimator and is
built into many software packages.
Yet, when the key research question is whether the volatility is high or low, another technique, known as Markov state dependency, developed by Aldridge (2011),
may work best. The Markov technique divides historical observations into high and
low volatility states, and then assesses probabilities of transition from high to low
probability and vice versa. Specifically, the technique can be used as follows:
1. Run a linear regression of price changes on past price changes.
2. Examine the distribution of error terms; separate them into two groups: low
and high errors, based on the arbitrary yet appropriate cutoff point.
3. Estimate historical “transition probabilities” based on the sequential changes
from low to high states and vice versa:
a. For each sequential error observation, determine whether the error was a
change from low to high, a change from high to low, a stay in the low state, or
a stay in the high-volatility state.
b. Count the totals and express them in a percentage probability form.
4. During run-time, assess whether the current volatility level is high or low. Given
the probabilities of transition determined in step 3, assess the likelihood of a
volatility change in the next period. Adjust the trading accordingly.
Markov switching models can be very fast and effective in HFT applications and
many other models.
Value-at-risk (VaR)
is a probabilistic metric of potential loss that takes into consideration distributional

Third- and Fourth-Order Risk Management: Value-at-Risk

1. Compute daily net (after transaction costs) historical returns of the strategy
either live or simulated (back-tested) returns.
2. Determine the cut-off corresponding to the worst 5 percent of strategy returns.

α = 1%

α = 5%

FIGURE 14.2 The 99 Percent VaR (a = 1 Percent) and 95 Percent VaR (a = 5 Percent)

Computed on the Sample Return Population

231
RISk MANAgeMeNT oF HFT

properties of returns of the HFT. Intraday VaR is typically used in HFT applications
to set the ceiling for the intraday market exposure and the floor for the intraday
mark-to-market loss. If the strategy hits the intraday VaR threshold, the strategy is
moved into paper trading for review of its stability until further notice. VaR considers the entire historical distribution of the traded security, including skewness and
kurtosis of the security returns, the third and fourth moments of returns. As a result,
VaR represents a “fourth-order” risk measure.
The concept of VaR has by now emerged as the dominant metric in market risk
management estimation. The VaR framework spans two principal measures—VaR
itself and the expected shortfall (eS). VaR is the value of loss in case a negative scenario with the specified probability should occur. The probability of the scenario
is determined as a percentile of the distribution of historical scenarios that can be
strategy or portfolio returns. For example, if the scenarios are returns from a particular strategy and all the returns are arranged by their realized value in ascending
order from the worst to the best, then the 95 percent VaR corresponds to the cutoff
return at the lowest fifth percentile. In other words, if 100 sample observations are
arranged from the lowest to the highest, then VaR corresponds to the value of the
fifth lowest observation
The eS measure determines the average worst-case scenario among all scenarios
at or below the prespecified threshold. For example, a 95 percent eS is the average return among all returns at the 5 percent or lower percentile. If 100 sample
observations are arranged from the lowest to the highest, the eS is the average of
observations 1 through 5. Figure 14.2 illustrates the concepts of VaR and eS.
To compute VaR, the trader or risk manager may use the following steps:

3. Set the shutdown threshold equivalent to the lowest 5 percentile of strategy
returns, place the strategy “on probation” in paper trading until the cause of the
low return is ascertained and the strategy is adjusted.

RISk MANAgeMeNT oF HFT

232

An analytical approximation to true VaR can be found by parameterizing the sample
distribution.The parametric VaR assumes that the observations are distributed in a normal fashion. Specifically, the parametric VaR assumes that the 5 percent in the left tail of
the observations fall at m−1.65σ of the distribution, where m and s represent the mean
and standard deviation of the observations, respectively.The 95 percent parametric VaR
is then computed as m−1.65σ, while the 95 percent parametric eS is computed as the
average of all distribution values from –∞ to m−1.65σ. The average can be computed
as an integral of the distribution function. Similarly, the 99 percent parametric VaR is
computed as m−2.33σ, while the 99 percent parametric eS is computed as the average
of all distribution values from –∞ to m−2.33σ. The parametric VaR is an approximation of the true VaR; the applicability of the parametric VaR depends on how close the
sample distribution resembles the normal distribution. Figure 14.3 illustrates this idea.
While the VaR and eS metrics summarize the location and the average of many
worst-case scenarios, neither measure indicates the absolute worst scenario that can
destroy entire trading operations, banks, and markets. Most financial return distributions have fat tails, meaning that the very extreme events lie beyond normal
distribution bounds and can be truly catastrophic.
The limitations of VaR methodology have hardly been a secret. In a NewYork Times
article published on January 2, 2009, David einhorn, the founder of the hedge fund
greenlight Capital, stated that VaR was “relatively useless as a risk-management tool
and potentially catastrophic when its use creates a false sense of security among senior managers and watchdogs. This is like an air bag that works all the time, except
when you have a car accident.” The article also quoted Nassim Nicholas Taleb, the
best-selling author of The Black Swan, as calling VaR metrics “a fraud.” Jorion (2000)
points out that the VaR approach both presents a faulty measure of risk and actively
pushes strategists to bet on extreme events. Despite all the criticism, VaR and eS
have been mainstays of corporate risk management for years Most recently, daily VaR
has made forays into risk management of active trading, quickly becoming a tool of
choice on many trading floors.

µ − 2.33σ
a = 1%

µ−
1.65σ

FIGURE 14.3 The 95 Percent Parametric VaR Corresponds to m – 1.65σ of the Distribution,
While the 99 Percent Parametric VaR Corresponds to m – 2.33σ of the Distribution

To alleviate the shortcomings of the VaR, many quantitative outfits began to parameterize extreme tail distributions to develop fuller pictures of extreme losses.
once the tail is parameterized based on the available data, the worst-case extreme
events can be determined analytically from distributional functions, even though no
extreme events of comparable severity were ever observed in the sample data.
The parameterization of the tails is performed using the extreme value theory
(eVT). EVT is an umbrella term spanning a range of tail modeling functions.
Dacorogna et al. (2001) note that all fat-tailed distributions belong to the family of
Pareto distributions. A Pareto distribution family is described as follows:
0
x≤0

G( x ) = 
(1)
−α
exp( − x ) x > 0, α > 0
where the tail index a is the parameter that needs to be estimated from the return data.
For raw security returns, the tail index varies from financial security to financial security. even for raw returns of the same financial security, the tail index can vary from one
quoting institution to another, especially for really high-frequency estimations.
When the tail index a is determined, we can estimate the magnitude and probability of all the extreme events that may occur, given the extreme events that did occur
in the sample. Figure 14.4 illustrates the process of using tail parameterization:

The tail index approach allows us to deduce the unobserved return distributions
from the sample distributions of observed returns. Although the tail index approach

Probability

Tail index function is fitted
for observations of the
bottom 5% of the entire
sample distribution

Sample return observations
(back test and/or production)
0.5%
–11%

–7%

–4% –3% –1%

Return

FIGURE 14.4 Using Tail Index Parameterization to Predict extreme events

233
RISk MANAgeMeNT oF HFT

1. Sample return observations obtained from either a back-test or live results are
arranged in ascending order.
2. The tail index value is estimated on the bottom 5 percentile of the sample return
distribution.
3. Using the distribution function obtained with the tail index, the probabilities of
observing the extreme events are estimated. According to the tail index distribution function, a –7 percent return would occur with a probability of 0.5 percent
while a return of –11 percent would register with a probability of 0.001 percent.

is useful, it has its limitations. For one, the tail index approach “fills in” the data for
the observed returns with theoretical observations; if the sample tail distribution is
sparse (and it usually is), the tail index distribution function may not be representative of the actual extreme returns. In such cases, a procedure known as parametric
bootstrapping may be applicable.
Parametric bootstrap simulates observations based on the properties of the sample
distribution. The technique “fills in” unobserved returns based on observed sample
returns. The parametric bootstrap process works as follows:
The sample distribution of observed returns delivered by the manager is decomposed into three components using a basic market model:
1. The manager’s skill, or alpha.
2. The manager’s return due to the manager’s portfolio correlation with the
benchmark.
3. The manager’s idiosyncratic error.
The decomposition is performed using the standard market model regression:
Ri,t=ai+bi,xRx,t+et

Risk Management of HFT

234

(2)

where Ri,t is the manager’s raw return in period t, Rx,t is the raw return on the
chosen benchmark in period t, ai is the measure of the manager’s money management skill or alpha, and bi,x is a measure of the dependency of the manager’s
raw returns on the benchmark returns.
4. Once parameters α̂ i and βˆi,x are estimated using equation (2), three pools of data
are generated: one for α̂ i (constant for given manager, benchmark, and return
sample), βˆi,x Rx,t , and ei,t.1 For example, if α̂ i and βˆi,x were estimated to be 0.002
and –0.05, respectively, then the component pools for a sample of raw returns
and benchmarked returns may look as shown in Table 14.1.
5. Next, the data is resampled as follows:
a. A value ε iS, t is drawn at random from the pool of idiosyncratic errors, {ei,t}.
S
b. Similarly, a value βˆi,x Rx,t is drawn at random from the pool of {bi,xRx,t}
c. A new sample value is created as follows:
RˆiS,t = αˆ i + βˆi,x RxS,t + ε tS

(3)

S
The sampled variables ε i,t and βˆi,x RxS,t are returned to their pools (not eliminated from the sample).

Table 14.1 Examples of Generated Bootstrap Components
Observation No.

Ri,t

Rx,t

bi,xRx,t

ei,t

0.015

–0.001

0.002

0.00005

0.01295

0.0062

0.002

–0.00017

0.00403

0.0034

on variables, as in ai and bi,x, denotes that the parameters were estimated from a
sample distribution, as opposed to comprising the true distribution values.
1 The “hat” notation

The resampling process outlined in steps a–c is then repeated a large number of
times deemed sufficient to gain a better perspective on the distribution of tails.
As a rule of thumb, the resampling process should be repeated at least as many
times as there were observations in the original sample. It is not uncommon for
the bootstrap process to be repeated thousands of times. The resampled values RˆiS,t
can differ from the observed sample distribution, thus expanding the sample data
set with extra observations conforming to the properties of the original sample.
6. The new distribution values obtained through the parametric process are now
treated as were other sample values and are incorporated into the tail index,
VaR, and other risk management calculations.
The parametric bootstrap relies on the assumption that the raw returns’ dependence on a benchmark as well as the manager’s alpha remain constant through time.
This does not have to be the case. Managers with dynamic strategies spanning different asset classes are likely to have time-varying dependencies on several benchmarks.
Despite this shortcoming, the parametric bootstrap allows risk managers to glean
a fuller notion of the true distribution of returns given the distribution of returns
observed in the sample.
To incorporate portfolio managers’ benchmarks into the VaR framework,
Suleiman, Shapiro, and Tepla (2005) propose analyzing the “tracking error” of the
manager’s return in excess of his benchmark. Suleiman et al. (2005) define tracking
error as a contemporaneous difference between the manager’s return and the return
on the manager’s benchmark index:
(4)

where Ri,t is the manager’s return at time t and Rx,t is return on the manager’s benchmark, also at time t. The VaR parameters are then estimated on the tracking error
observations.
In addition to VaR, statistical models may include Monte Carlo simulation–
based methods to estimate future market values of capital at risk. The Monte Carlo
simulations are often used in determining derivatives exposure. Scenario analyses
and causal models can be used to estimate market risk as well. These auxiliary types
of market risk estimation, however, rely excessively on qualitative assessment and
can, as a result, be misleading in comparison with VaR estimates, which are based on
realized historical performance.
Higher-Order Risk Management: Hedging The objective of hedging is to create
a portfolio that maximizes returns while minimizing risk—downside risk in particular. Hedging can also be thought of as a successful payoff matching: the negative
payoffs of one security “neutralized” by positive payoffs of another.
Hedging can be passive or dynamic. Passive risk hedging is most akin to insurance.
The manager enters into a position in a financial security with the risk characteristics that offset the long-term negative returns of the operation. For example, a
manager whose main trading strategy involves finding fortuitous times for being
long in USD/CAD may want to go short the USD/CAD futures contract to offset

Risk Management of HFT

TEt = In(Ri,t ) − In(RX,t )

235

his exposure to USD/CAD. As always, detailed analysis of the risk characteristics of
the two securities is required to make such a decision.
Dynamic hedging is most often done through a series of short-term, potentially
overlapping, insurance-like contracts. The objective of the short-term insurance
contracts is to manage the short-term characteristics of trading returns. In the case
of market risk hedging, dynamic hedging may be developed for a particular set of recurring market conditions, when behaviors of the trading systems may repeat themselves. It may be possible to find a set of financial instruments or trading strategies the
returns of which would offset the downside of the primary trading strategy during
these particular market conditions. For example, during a U.S. Fed announcement
about the level of interest rates, the USD/CAD exchange rate is likely to rise following a rise in the U.S. interest rates, while U.S. bond prices are likely to fall following
the same announcement. Depending upon return distributions for USD/CAD and
U.S. bonds, it may make sense to trade the two together during the U.S. interest
rate announcements in order to offset the negative tail risk in either. Mapping out
extensive distributions of returns as described previously in this chapter would help
in determining the details of such a dynamic hedging operation.
High-frequency portfolio management can be applied to manage market risks of
instruments used in HFT strategies as well as to extend capacity of strategies by carrying it over to other instruments.
Hedging can be further broken down into the following categories:
Risk Management of HFT

236

■■
■■

Delta hedging
Portfolio hedging

In delta hedging HFT in a particular financial instrument, the portfolio system enters and closes positions in a liquid related instrument.The related instrument for a single stock or a spot commodity can be a near-term futures contract
written on that stock or commodity. Delta hedging instruments related to stocks,
commodities or futures may be a liquid option. Most liquid options tend to be with
near expiration dates and “at-the-money,” with strike prices close to the present
price of the underlying instrument.
In delta hedging, for every unit of the HF-traded instrument, the system purchases a specific quantity of the hedging instrument. This hedging quantity is determined
by the average relative changes in the prices of the HF-traded instrument and the
hedging instrument:

Delta Hedging

Q hedging,t =

∆PHFT ,t
∆Phedging,t

(5)

where ∆PHFT,t is the average return on the HF-traded instrument computed per
chosen unit of time, and ∆Phedging,t represents the return on the selected hedging
instrument computed over the same unit of time. To standardize the units of HFtraded and hedging instruments, both returns need to be time-based; the volume
and tick clocks are inappropriate for the hedging application. In dynamic hedging,

the quantity of the hedging instrument, Q hedging,t, needs to be recalculated continuously in the moving-window specification to ensure the average price changes are
accurately captured.
In dynamic hedging, after the latest quantity of the hedging instrument, Q hedging,t,
is estimated, a new challenge arises: executing the trades in the primary and the
hedging instruments. The situation becomes particularly demanding in cases when
the high-frequency trading strategy relies on limit orders, as the risk of non-execution in either instrument may compromise hedging activity altogether. A possible
solution involves always trading the hedging instrument using market orders, and
only after the trades in the principal instrument were completely executed. Care
should be taken to ensure that such solution does not destroy profitability of the HFT
strategy.
Portfolio Hedging The main challenge of dynamic hedging of high-frequency strategies is speed: computation of risk-minimizing allocations takes time, during which
the markets move and render the just-computed allocations stale. The hedging problem becomes a moving target in fast-paced markets, as illustrated in Figure 14.5.
To overcome the challenge described in Figure 14.5, trading systems can deploy
fast portfolio optimization algorithms discussed in detail below.
A classic portfolio hedging strategy, developed by Markowitz (1952), solves the
following optimization problem:

237

max x E[R ] − Ax ′Vx
(6)

where xi is the portfolio weight of security i, i∈[1,…,I], E[R] is a vector of expected
returns of I securities, V is an I×I variance-covariance matrix of returns, and A is the

…

Optimal portfolio for data
observed at t = 0
t=0

Observe price and
volatility of securities
of interest: upload
recent history of prices
[P1...PK ]

t=1

Calculate optimal
portfolio allocation
based on the data
observed at t = 0

Time
t=2

Observe changes in market
prices; in fast-moving
markets, calculations
performed at t =1 may no
longer be valid

FIGURE 14.5 The High-Frequency Hedging as a Perpetually Moving Target

RISk MANAgeMeNT oF HFT

s.t.∑ x i = 1

coefficient reflecting the risk aversion of the trading operation. A is commonly assumed to be 0.5 to simplify the solution. A dynamic state-dependent hedging would
repeat the process outlined in equation (6), but only for returns pertaining to a
specific market state.
The solution to equation (6) calls for an inversion of the variance-covariance matrix V, a computationally demanding operation the execution time of which has been
shown to grow as a square of number of financial instruments considered.
Several classes of algorithms have been proposed to simplify and speed up setting
the optimal portfolio weights:
■■
■■
■■
■■
■■

Risk Management of HFT

238

Simultaneous equations
Nonlinear programming
Critical-line optimizing algorithms
Discrete pairwise (DPW) optimization
Genetic algorithms
The following sections describe each of the algorithms in detail.

Simultaneous Equations The simultaneous equations framework is the algorithm that directly follows the Markowitz (1952) specification. It has been
shown to be inefficient for optimization if the portfolio exceeds 10 strategies,
and it may produce highly erroneous forecasts when 20 or more assets are involved. The forecast errors are due to the estimation errors that occur when
the average returns and variances are computed. The Bayesian error-correction
framework, discussed later in this chapter, can be used to alleviate some of the
input estimation errors. Still, in addition to the issues of forecast errors, the
estimation time of this algorithm grows exponentially with the number of trading strategies involved, making this method hardly suitable for high-frequency
trading of many assets. Tsagaris, Jasra, and Adams (2010) show that computational speed improvement can be improved by updating portfolio weights using
eigenvalue decomposition, instead of recalculating portfolio weights afresh with
each new tick of data.
Nonlinear Programming Nonlinear programming is a class of optimizers popular in commercial software. The nonlinear algorithms employ a variety of techniques
with the objective of maximizing or minimizing the target portfolio optimization
function given specified parameters such as portfolio allocation weights. Some of
these algorithms employ a gradient technique whereby they analyze the slope of the
objective function at any given point and select the fastest increasing or decreasing
path to the target maximum or minimum, respectively. The nonlinear programming
algorithms are equally sensitive to the estimation errors of the input means and variances of the returns. Most often, the algorithms are too computationally complex
to be feasible in the high-frequency environments. A recent example of a nonlinear
optimizer is provided by Steuer, Qi, and Hirschberger (2006).
The Critical Line–Optimizing Algorithm
The critical line–optimizing
algorithm was developed by Markowitz (1959) to facilitate the computation of his

own portfolio theory. The algorithm is fast and comparatively easy to implement. Instead of providing point weights for each individual security considered in the portfolio allocation, the critical line optimizer delivers a set of portfolios on the efficient
frontier, a drawback that has precluded many commercial companies from adapting this method. A recent algorithm by Markowitz and Todd (2000) addresses some
of the issues. According to Niedermayer and Niedermayer (2007), the Markowitz
and Todd (2000) algorithm outperforms the algorithm designed by Steuer, Qi, and
Hirschberger (2006) by a factor of 10,000 when at least 2,000 assets considered
simultaneously.

1. Candidates for selection into the overall portfolio are ranked using Sharpe ratios
and sorted from the highest Sharpe ratio to the lowest. This step of the estimation utilizes the fact that the Sharpe ratio itself is a measure of where each individual strategy lies on the efficient frontier.
2. An even number of strategies with the highest Sharpe ratios are selected for inclusion into the portfolio. Half of the selected strategies should have historically
positive correlations with the market, and half should have historically negative
correlations with the market.
3. After the universe of financial instruments is selected on the basis of the Sharpe
ratio characteristics, all selected strategies are ranked according to their current liquidity. The current liquidity can be measured as the number of quotes or
trades that have been recorded over the past fixed number of seconds or even
minutes of trading activity.
4. After all the strategies have been ranked on the basis of their liquidity, the
pairs are formed through the following process: the two strategies within
each pair have opposite historical correlation with the market. Thus, strategies historically positively correlated with the market are matched with
strategies historically negatively correlated with the market. Furthermore,
the matching should occur according to the strategy liquidity rank. The most

239
Risk Management of HFT

Discrete Pairwise (DPW) Optimization The existing algorithms, whatever the complexity and accuracy of their portfolio allocation outputs, may not be
perfectly suited to the high-frequency trading environment. First, in environments
where a delay of one microsecond can result in a million-dollar loss, the optimization algorithms in their current form still consume too much time and system
power. Second, these algorithms ignore the liquidity considerations pertinent to the
contemporary trading settings; most of the transactions occur in blocks or “clips”
of a prespecified size. Trades of larger-than-normal sizes as well as trades of smaller
blocks incur higher transaction costs that in the high-frequency environment can put
a serious strain on the system’s profitability.
A simple high-frequency alternative to the complex optimization solutions is a
discrete pairwise (DPW) optimization developed by Aldridge (2010). The DPW
algorithm is a fast compromise between the equally weighted portfolio setting and
a full-fledged optimization machine that outputs portfolio weights in discrete clips
of the prespecified sizes. No fractional weights are allowed. The algorithm works as
follows:

Risk Management of HFT

240

liquid strategy positively correlated with the market should be matched with
the most liquid strategy negatively correlated with the market, and so on
until the least liquid strategy positively correlated with the market is matched
with the least liquid strategy negatively correlated with the market. The
liquidity-based matching ensures that the high-frequency dynamic captured
by correlation is due to idiosyncratic movements of the strategy rather than
the illiquidity conditions of one strategy.
5. Next, for each pair of strategies, the high-frequency volatility of a portfolio of
just the two strategies is computed for discrete position sizes in either strategy.
For example, in foreign exchange, where a common transactional clip is
$1 million, the discrete position sizes considered for the pairwise optimization
may be –$3 million, –$2 million, –$1 million, 0, $1 million, $2 million, and
$3 million, where the minus sign indicates the short position. Once the volatility
for the various portfolio combinations is selected within each pair of strategies,
the positions with the lowest portfolio volatility are selected.
6. The resulting pair portfolios are subsequently executed given the maximum allowable allocation constraints for each strategy. The maximum long and short
allocation is predetermined and constrained as follows: the cumulative gross
position in each strategy cannot exceed a certain size, and the cumulative net
position cannot exceed another, separately set, limit that is smaller than the aggregate of the gross limits for all strategies. The smaller net position clause ensures a degree of market neutrality.
The DWP algorithm is particularly well suited to high-frequency environments
because it has the following properties:
■■

■■

The DPW algorithm avoids the brunt of the impact of input estimation errors by
reducing the number of strategies in each portfolio allocation decision.
The negative historical correlation of input securities ensures that within each
pair of matched strategies, the minimum variance will result in long positions
in both strategies most of the time. Long positions in the strategies are shown to
historically produce the highest returns per unit of risk, as is determined during
the Sharpe ratio ranking phase.The times that the system results in short positions
for one or more strategy are likely due to idiosyncratic market events.
The algorithm is very fast in comparison with other portfolio optimization
algorithms. The speed of the algorithm comes from the following “savings” in
computational time:
■■

■■

If the total number of strategies selected in the Sharpe ratio ranking phase is
2K, the DPW algorithm computes only K correlations. Most other portfolio
optimization algorithms compute correlation among every pair of strategies
among the 2K securities, requiring 2K(K−1) correlation computations instead.
The grid search employed in seeking the optimal portfolio size for each strategy within each portfolio pair optimizes only between two strategies, or in
two dimensions. A standard algorithm requires a 2K-dimensional optimization.

Finally, the grid search allows only a few discrete portfolio weight values. In
the main example presented here, there are seven allowable portfolio weights:
–$3 MM, –$2 MM, –$1 MM, 0, $1 MM, $2 MM, and $3 MM. This limits the
number of iterations and resulting computations from, potentially, infinity, to
72 = 49.
Alexander (1999) notes that correlation and volatility are not sufficient to ensure
long-term portfolio stability; both correlation and volatility are typically computed
using short-term returns, which only partially reflect dynamics in prices and necessitate frequent portfolio rebalancing. Instead, Alexander (1999) suggests that in
portfolio optimization more attention should be paid to cointegration of constituent
strategies. Auxiliary securities, such as options and futures, can be added into the
portfolio mix based on cointegration analysis to further strengthen the risk-return
characteristics of the trading operation. The cointegration-enhanced portfolios can
work particularly well in trading operations that are tasked with outperforming specific financial benchmarks.
■■

241
Risk Management of HFT

Genetic Algorithms Genetic algorithms “learn” from past forecasts via the socalled Bayesian approach. Specifically, the Bayesian self-correction model compares
the realized performance of portfolio with forecasted values, and adjusts future forecasts on the basis of errors retrieved from the comparison. Bayesian methodology
continuously recalculates the trajectory of prices of portfolio instruments and updates the optimal portfolio weights. In many cases, genetic algorithms adjust, but
do not fully recalculate portfolio weights, saving considerable computational time.
In the Bayesian approach, the average return estimate of a particular security is
considered to be a random variable and is viewed probabilistically in the context of
previously obtained information, or priors. All expectations are subsequently developed with respect to the distribution obtained for the estimate. Multiple priors,
potentially representing multiple investors or analysts, increase the accuracy of the
distribution for the estimate.
Under the Bayesian specification, all mean and variance-covariance estimates are
associated with a confidence interval that measures the accuracy of the forecast.
An accurate forecast has a tight confidence interval, while the inaccurate forecast
has a wide confidence interval. After the accuracy of the previous forecast has been
determined, the portfolio weight of a security is scaled depending on the width of
the confidence intervals of these securities. The wider the confidence intervals for
parameter estimates, the smaller is the portfolio weight for that security. When the
confidence intervals approach zero, the weights are similar to those of the classic
mean-variance optimization.
The traditional Bayesian approach, applied to mean-variance optimization by
Jorion (1986), works as follows: both mean and variance estimates of a portfolio
computed on a contemporary data sample are adjusted by lessons gleaned from
historical (prior) observations.
The dispersion of the distributions of the true mean and variance of the distributions shrinks as more observations are collected and analyzed with time. If Rp,t
is the portfolio return following the mean-variance optimization of equation (7)

from time t – 1 to time t, and Eˆ[Ri,t ] is the average return estimate for security i,
t
ˆE[R ] = 1 ∑ R , the “Bayes-Stein shrinkage estimators” for expected return and
i,t
i,τ
t
τ =1

variance of an individual security i to be used in the mean-variance optimization for
the next period t + 1, are computed as follows:
E[Ri,t +1 ]BS = (1 − φi,BS )E [Ri,t ] + φi,BS Rp,t
1 
v
+
V [Ri,t +1 ]BS = V [Ri,t ] 1 +
V [Ri,t ]

 t + v  t(t + 1 + v )
where v is the precision of the mean estimates: v =

N is the number of observations in the sample at time t, and φBS is the shrinkage
v
. The case of zero precision (v = 0) corresponds to
factor for the mean: φBS =
t +v
completely diffuse estimates.
Despite the computational complexities of high-frequency hedging, HFT hedging
can be very effective due to the following feature of high-frequency data: low correlations between any two financial instruments. Figure 14.6 illustrates the point
with empirical correlations observed on the S&P 500 eTF and iShares MSCI Index (eFA). Trade correlations are particularly low, just 3 percent when the data is
sampled every 45 seconds, and decrease to zero as data sampling frequency increases
to 200 ms. Quote correlations are much higher, around 30 percent when sampled
every 45 seconds. The quote correlations also decrease dramatically with sampling
frequency, to about 7 percent with 200-ms sampling. Relatively higher correlations of quote data may illuminate relative informativeness of tick data: quote data
likely reflects market makers’ information unavailable in trade data. The daily close
35%
Trade Data
Mid Quote
SW Mid Quote

30%
Empirical Correlations

RISk MANAgeMeNT oF HFT

242

V [Ri,t ]
(N − 2)
,
t (Rp,t − E [Ri,t ])2

25%
20%
15%
10%
5%
0%

200mss

1ss
15ss
Sampling Frequency

FIGURE 14.6 Correlations in High-Frequency Data.

Source: Aldridge (2010).

45ss

correlation of the Standard & Poor’s (S&P) 500 ETF and iShares MSCI Index (EFA)
often reaches 65 percent.

Liquidity Risk

VaRL=VaR+Liquidity Adjustment=VaR - (mS+zaσS)

(7)

where VaR is the market risk value-at-risk discussed previously in this chapter, mS is
the mean expected bid-ask spread, s S is the standard deviation of the bid-ask spread,
and za is the confidence coefficient corresponding to the desired a–percent of the
VaR estimation. Both mS and s S can be estimated either from raw spread data or
from the Roll (1984) model.
Using Kyle’s l measure, the VaR liquidity adjustment can be similarly computed
through estimation of the mean and standard deviation of the trade volume:
VaRL=VaR+Liquidity Adjustment=VaR - (a+λ(mNVOL+zaσNVOL))

(8)

where a and λ are estimated using OLS regression following Kyle (1985):
∆Pt=a+λNVOLt+et

(9)

243
Risk Management of HFT

Liquidity risk may affect high-frequency traders during the normal intraday trading
or during the end-of-day liquidation. Liquidity risk measures the firm’s potential
inability to unwind or hedge positions in a timely manner at current market prices.
The inability to close out positions is normally due to low levels of market liquidity
relative to the position size. The lower the market liquidity available for a specific
instrument, the higher the liquidity risk associated with that instrument. Levels of
liquidity vary from instrument to instrument and depend on the number of market participants willing to transact in the instrument under consideration. Bervas
(2006) further suggests the distinction between the trading liquidity risk and the
balance sheet liquidity risk, the latter being the inability to finance the shortfall in
the balance sheet either through liquidation or borrowing.
In mild cases, liquidity risk can result in minor price slippages due to the delay
in trade execution and can cause collapses of market systems in its extreme. For
example, the collapse of Long-Term Capital Management (LTCM) in 1998 can be
attributed to the firm’s inability to promptly offload its holdings.
To properly assess the liquidity risk exposure of a portfolio, it is necessary to take
into account all potential portfolio liquidation costs, including the opportunity costs
associated with any delays in execution. While liquidation costs are stable and are
easy to estimate during periods with little volatility, the liquidation costs can vary
wildly during high-volatility regimes. Bangia et al. (1999), for example, document
that liquidity risk accounted for 17 percent of the market risk in long USD/THB
positions in May 1997, and Le Saout (2002) estimates that liquidity risk can reach
over 50 percent of total risk on selected securities in CAC40 stocks.
Bervas (2006) proposes the following measure of liquidity risk:

∆Pt is the change in market price due to market impact of orders, and NVOLt is the
difference between the buy and sell market depths in period t.
Hasbrouck (2005) finds that the Amihud (2002) illiquidity measure best indicates
the impact of volume on prices. Similar to Kyle’s λ adjustment to VaR, the Amihud
(2002) adjustment can be applied as follows:
VaRL =VaR+Liquidity Adjustment =VaR−(mγ+zaσγ)

(10)

where mγ and σγ are the mean and standard deviation of the Amihud (2002) illiquid1 D rd,t
ity measure g, γ t = ∑
, Dt is the number of trades executed during time
Dt d =1 vd,t
period t, rd,t is the relative price change following trade d during trade period t, and
vd,t is the trade quantity executed within trade d.
The liquidity risk also applies in multiasset HFT upon entering positions. When
the strategy calls for simultaneous acquisition of multiple instruments via limit orders, the less liquid instruments may compromise the strategy as they may be difficult to acquire. In such cases, the limit orders for the illiquid instruments are sent
first; if executed, orders for the liquid instruments are placed.
t

■■ Summary
Risk Management of HFT

244

Competent risk management protects deployed capital, reduces risk and often
enhances overall performance of high-frequency strategies. The risk management
framework of HFT should take into account all aspects of HFT operation, including
HFT suppliers and the government.
■■ End-of-Chapter Questions
1. What are the key types of risk faced by a high-frequency trading operation?
2. How to measure and mitigate market risk?
3. What is the credit and counterparty risk from a high-frequency trading
perspective?
4. What are the key problems in high-frequency portfolio optimization?
5. What is liquidity risk? How to measure it?

Chapter 15

Minimizing Market
Impact
A

lgorithmic execution, also known as algo execution or smart order routing, refers to a set
of programmatic computer methodologies used to determine the optimal way to
parcel and execute an order. An ideal execution algo would consistently execute the
customer’s buy order at the lowest price available during a given period of time and
transmit the sell when the price is at its peak, delivering “best execution.” Given the
difficulties of precisely pinpointing the price lows and the highs within a period of time,
a good algo produces a certain price improvement according to prespecified optimality conditions. The optimality conditions may be based on the trader’s risk aversion,
concurrent market state, the benchmark chosen by the trader, and a range of other
features, discussed in detail for the remainder of this part of the book. The execution
algorithms can be built “in-house” by a buy-side trader, purchased “off-the-shelf ” from
the algorithm provider, or licensed on a one-off execution basis from the trader’s broker. The brokers may provide algos for a commission or in exchange for a portion of
the cost savings delivered by the algorithm relative to some executional benchmark.
Algo execution evolved naturally from human-driven best execution practice.
For decades, brokers competed for client order flow by promising unique ability
to pinpoint market highs and lows, and to negotiate preferred terms for the clients.
Algorithmic execution builds on the human broker practice in developing an automated human-free approach.
From the point of view of classical finance and the quantitative portfolio management, best execution algorithms exist to smooth out natural market imperfections.
■■ Why Execution Algorithms?
Execution algorithms have become essential for all investors, as execution algos help
traders accumulate or liquidate large positions by breaking up orders into pieces,
and reducing market impact and visibility of orders. To avoid being “picked off ” in

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the markets, algos deploying limit orders cancel many of the orders when the orders
fail to execute. The orders are then resubmitted almost immediately, often at a price
closer to the market.
Different algorithms have been shown to substantially lower execution costs, in
different ways. Execution costs comprise exchange and broker-dealer fees, bid-ask
spread, opportunity cost associated with nonexecution of a limit order, and market
impact (MI), to name a few. According to Engle, russell, and Ferstenberg (2007),
for example, the costs delivered by an algorithm depend on the level of order aggressiveness the algo produces: passive orders “save” investor capital by avoiding the
spread, yet may aggravate costs whenever passive orders fail to execute. Other design aspects of the algo, such as the timing of the order parcels and size of each parcel
relative to the market depth, also impact the obtained execution costs.
In addition to net execution costs, traders may consider the costs associated with
the risk of the algorithms. The risk of nonexecution can be the largest risk component in algorithmic execution, but can be minimized with market orders at the
expense of higher execution costs, resulting from crossing the spread, higher MI,
transaction costs, and so on. Other risk metrics used in algo execution may include
variability of the execution price of order slices, and value-at-risk (Var) measure
designed to contain execution costs below certain maximum limit.
To compare the performance of several algorithms, Almgren and chriss (2000) proposed the concept of an efficient trading frontier. Like the efficient markets frontier developed in the framework of the capital asset pricing model (cApM), the efficient trading
frontier provides a convenient graphical representation of performance of various execution algorithms per unit of risk incurred by each algorithm. A sample efficient trading
frontier is shown in Figure 15.1. Analytically, it can be described as in equation (1):
min Cost(α)+λRisk(α)

(1)

where
■

α is a measure of order aggressiveness, for example, counting the number of ticks

away from the market each child order is placed.
■

■

Cost(α) is the aggregate expected execution cost, including expected market impact, for all child orders of the strategy executed at the aggressiveness level α.
Risk(α) is the cumulative risk associated with all the child orders placed at aggressiveness level α.
Cost of MI

Efficient strategies

FIGURE 15.1 Illustration of the Efficient Trading Frontier

Risk

■■

λ is the degree of risk aversion, specific to the trader. A risk aversion level λ=0

indicates a trader who does not care about the execution risk. A risk aversion level
λ=0.5 indicates a fairly risk-averse trader.
■■ Order-Routing Algorithms
Order-routing algorithms are designed to seamlessly navigate various issues differences between securities markets and deliver investors a cost-effective execution
schedule that would fit the investors’ risk profile. As such, the order-routing algorithms target the following objectives:
■■

Minimize execution costs

■■

Obtain best price

■■

Maximize execution speed

■■

Maximize trading size

■■

Minimize trade footprint

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Minimizing Market Impact

To minimize costs, algorithms select appropriate venues and market conditions.
Venue selection can reduce the fee structure, and picking the right time to execute
a trade can pick periods of low bid-ask spreads, and help reduce or eliminate slippage and subsequent market impact (more on these later). To obtain best price, sophisticated algorithms perform short-term forecasting to ensure the sell orders are
processed during times with higher market prices and vice versa. To maximize the
execution speed for clients desiring to capture present market conditions, the algos
seek venues with appropriate market participation and minimal trade impact. To
maximize trading size and minimize trade footprint, the algos slice the order into
a series of smaller parcels or “child orders,” all according to the latest scientific advances and investor’s preferences. Large trading size can be particularly important
to funds with large positions or strategy capacity. Minimal footprint of the trade
ensures minimal detection of the order by outside parties, and helps thwart traders
attempting to infer the informational content of orders.
Performance of execution algorithms is typically measured relative to some
benchmarks. A benchmark may be the closing price observed at the end of the trading day, an average of the daily open, high, low, and close prices, the daily open, or
other, more complex metrics, such as several commonly used execution algorithms.
Algorithmic benchmarks and the daily close are most common algo benchmarks.
The daily close is an easy reference for any investor building his forecasting models
on daily data, as is often the case with low-frequency quantitative modelers. Daily
data analysis is nearly always performed on daily closing prices, and the developed
forecasts usually predict future daily closes, too. As a result, algos that consistently
outperform the daily close are in high demand by traders of daily close–based
models, who are willing to pay a portion of their execution algo-induced gains to the
algorithm provider.

Yet the betterment of the closing price is notoriously difficult to achieve. Unlike other benchmarks, closing prices are not at all known in advance, and the only
way to approximate them ahead of time is to deploy short-term price-forecasting
models. Short-term forecasting utilizes the high-frequency trading models discussed
in Chapters 8-11, and requires thorough understanding of the complexities of
HFT modeling. is difficult As a consequence, traders often deploy other common
algorithms as suitable algo performance benchmarks.
The following sections discuss each of the objectives of algo execution in detail.

Minimize Execution Costs
Trading costs comprise several major components:

Minimizing Market Impact

248

■■

Broker commissions, both fixed and variable

■■

Exchange fees

■■

Taxes

■■

Bid-ask spread

■■

Slippage

■■

Opportunity cost

■■

Market impact

Obtain Best Price
The core principle of the best price trading is “buy low, sell high.” Due to the natural price moves, the direction of the price can be difficult to predict, and advanced
short-term forecasting models are required for the purpose.
The best price execution is further complicated by additional factors. Consider
the following example. It is 9:30 a.m., and a client wants to buy 10,000 shares of
IBM at most at the closing price recorded at 4:00 p.m. later that day. The naturally
arising issues create the following questions:
■■
■■

■■

Given the market uncertainty, what will the execution price be at 4:00 p.m. that day?
The client’s desired execution size is considerably bigger than normal trading size.
Should the order be broken into smaller parcels? If so, how should the order be split?
If the client’s 10,000-share order is broken into smaller child orders, how frequently are the child orders executed?
Each buy trade (sell trade) will deplete some of the liquidity on the offer side (bid
side). The resulting liquidity gaps will lead to adverse prices for subsequent child
orders. Can this effect, known as market impact, be eliminated or minimized?
Other market participants may observe trading footprint of the client, and decide
to trade in the same direction, further moving the price in an adverse direction.
Can the trading footprint be minimized?

Maximize execution Speed

A market
order

Exchange 1:
2,000

Exchange 2:
3,000

Exchange 3:
500

FIGURE 15.2 Maximizing Execution Speed

A limit
order

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Fast execution helps capture current market conditions. Market orders can be executed most rapidly in the most liquid markets. To maximize the speed of execution
of market orders, therefore, investors may poll various exchanges for their available
liquidity, and send their orders to the exchange with the most liquidity first. Limit
orders, however, are executed most rapidly in the least liquid conditions. As a result,
limit orders are best executed on the markets with the fewest limit orders available. Figure 15.2 illustrates a sample process of polling multiple exchanges for their
liquidity levels and selecting the proper exchange for a given order or order slice.
In the example shown in Figure 15.2, there are three exchanges: Exchange 1
has available bid-side liquidity of 2,000 trading units (shares, contracts, and so on,
available at the best bid); Exchange 2 has liquidity of 3,000 units; and Exchange 3
has available liquidity off 500 units only. To minimize his trading footprint, a trader
placing market sell orders would first go to Exchange 2 and place an order for 3,000
or fewer units there. placing an order equal to or smaller than the top-of-the book
matching liquidity available at the exchange ensures that the market order does not
move or only slightly moves the market, leaving little or no footprint.
After exhausting the top-of-the-book liquidity on Exchange 2, the market order trader would turn to the next most liquid exchange: in our example, this is
Exchange 1, with the top-of-the-book bid-side liquidity equal to 2,000 units. The
trader would then place his order on Exchange 1 for 2,000 units or less, and then
proceed to Exchange 3 and trade against the available liquidity there.
A trader desiring to execute limit buy orders, however, would first place a limit order
with Exchange 3, as that exchange has the lowest aggregate size of buy limit orders available at the best bid. The trader next would place a limit buy order at Exchange 1, the
exchange with the next lowest number of aggregate limit buy orders available at the top
of the book. At this point, the limit order trader may or may not proceed to place a buy
limit order at Exchange 2, currently the most competitive exchange for buy limit orders.
The underlying rationale for selection of the exchange is this: place limit orders
wherever the limit orders are fewest, and place market orders wherever the limit

orders are most numerous. Such process ensures that the orders have the highest
probability of fast execution. The process is known as the minimal impact algorithm.

Minimize Footprint
In addition to maximizing execution speed, the MI algorithm can be used to minimize trading footprint, or the disturbance registered in the markets following an
order. The exact causes of the disturbance are discussed in chapter 5. The intuition
behind the disturbance can be explained as follows: every order is a credible signal
as it reveals the trader’s true beliefs committed to trader’s capital. As a result, every
order carries information about the current views of the trader. Other market participants may desire to trade on these views as well, without necessarily knowing the
information content beyond the observed action of placing an order. In such situations, placing child orders of sizes comparable to the sizes available at the best bid
or offer at different exchanges minimizes the resulting change in market quotes, and
reveals the least information associated with each order slice.

Maximize trading Size

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The ability to process large trading volume is critical to investors deploying sizable
capital in their strategies. For example, a large pension fund needs to be able to buy
and sell large quantities of securities without incurring much additional cost in order
to successfully reallocate pension fund’s positions. To maximize the trading size, the
large trader may use a combination of market and limit orders in processing each
individual order. To do so, a trader seeking to execute a large buy order may first
exhaust the top-of-the-book ask liquidity on all accessible markets by sequentially
polling for the best ask size available, and placing the market buy orders matching or
smaller than the best ask liquidity at each exchange, beginning with the most liquid
one. Subsequently, the trader may switch to limit orders and increase the bid-side

Market orders

Exchange 2:
3,000

Exchange: 1
2,000

Exchange 3:
500

Limit
orders

Exchange 2:
3,000

Exchange 1:
2,000

Exchange 3:
500

FIGURE 15.3 Maximizing Trading Size Implementation of Execution Algorithms

liquidity by placing the best top-of-the-book buy orders at all the exchanges, beginning with the least liquid and rotating among the exchanges in the direction of
increasing bid-liquidity. Figure 15.3 illustrates such strategy.
Most researchers develop execution algorithms in the following sequence:
1. Researchers explore published and not-yet-published academic research in the
area of optimal execution algorithm design and implementation. Some traders may be skeptical of using publicly available research, fearing that all known
research has been arbitraged in the markets. In reality, a change in parameterization of the algorithm may result in an algo with an entirely different, yet still
valuable, output.
2. The researchers model the algorithm in econometric languages such as MatLab
or R and, as a result, transition their code to faster programming languages like
C++ or optimized Java.
3. The algorithm is tested on historical tick data utilizing assumptions and predictions about price movement generated by the algorithms, own orders.
4. If the previous step results in a satisfactory execution schedule and price, cost,
and risk outcome, the algorithm is moved into production, where it is enabled
to communicate in real time using quote-receiving and -sending languages such
as FIX, ITCH, OUCH, FAST, and the like.

■■

■■
■■

How to slice the order: What is the general rule behind the algo’s order slicing
mechanism?
When the algo should trade: How frequently and at what time of the day should
be algo initiate its child trades?
In what size the algo should trade: How large should each child order be?
For how long the algo should trade: What is the horizon of the algo? When does
the algo stop?

The second layer, which can be described as the micro trader, defines additional
properties for each child order. In particular, the micro trader is responsible for deciding whether to execute the child order as a limit or market order, and, for limit
orders, what price to set.
Finally, the smart order router decides to which venues to send the child orders.
Over the past two years, significant progress has been made in developing mathematical solutions for best execution. The decisions of the macro trader, the micro

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Minimizing Market Impact

Slicing large orders is imperative: research of Chan and Lakonishok (1995),
for example, shows that if a typical institutional trade size were executed all at
once, it would account for about 60 percent of the daily trading volume, making
simultaneous execution of the order expensive and difficult, if not impossible.
The smaller “child” orders are then executed one slice at a time over a certain
time period.
According to Gatheral, Schied, and Slynko (2012), algorithmic execution can be
broken down into three distinct layers, as shown in Figure 15.4.The first layer, called
the macro trader, allows us to answer the following questions:

The macrotrader:
How to slice the
order?
When should the
algo trade?
In what size should
the algo trade?
For how long should
the algo trade?

The microtrader:
For each order slice
(a.k.a., child order):
Make it a market or
limit order?
If limit, at what price
relative to market
(aggressiveness)?

The smart order
router:
Which venue to
send each market
or limit order to?

FIGURE 15.4 Layers of Algorithmic Execution

Source: Gatheral, Schied and Slynko (2012)

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trader, and the smart order router can all be tailored with great precision to the
given market conditions. Optimal execution solutions can be classified into static
and dynamic strategy groups. A static strategy is completely determined ahead of
trading: it is based on past market conditions. A volume-weighted average price
(VWAp) is an example of a static strategy. In contrast, a dynamic strategy is determined and refined during the course of execution. As such, dynamic strategies
depend on contemporary market conditions. A simple delta hedge is an example of a
dynamic strategy. At first glance, dynamic strategies may seem to always outperform
static strategies, since dynamic strategies respond to current market conditions and
static strategies do not. In reality, certain static strategies perform well, but only
under specific market assumptions.
The performance of both static and dynamic strategies is often compared using
benchmarks, for example, the following simple metrics:
■

Average realized price compares the actual prices per unit traded received under
different algos:
P=

■
■

1
∑Vj Pj ∀ j ∈ J
∑Vj

(2)

where Pj is the realized price for slice or child order j, and Vj is the size of child
order j.
pretrade price P0 is the market price prevailing at the time the order j was placed.
posttrade price Pj,post is the price of the security after the temporary liquidity
effects, induced by trading stream, have disappeared. To identify Pj,post, Almgren
et al. (2005) regress ∆Pt on ∆t, and pinpoint the time ∆tpost when dependency of
∆Pt on ∆t ceases to be statistically significant. Then, the price P recorded at tpost is
the Pj,post.

■■

Total trade size V=ΣVj allows comparison of algorithms used to process large
trading volumes relative to available liquidity. In such conditions, some algorithms
may perform better than others.
Similarly, volume-adjusted trade size V/VDaily, where VDaily is the total trading volume on a particular day, allows comparison of algorithms’ ability to take advantage of available liquidity.

In addition, common benchmarks for evaluating performance of execution algos include other common execution algos, such as time-weighted average price
(TWAP), percentage of volume (POV), MI, VWAP, implementations shortfall, and
various intraday price benchmarks, discussed in subsequent sections of this chapter.
According to Kissell and Glantz (2005), order execution benchmarks can be
grouped into three broad categories: pretrade, intratrade, and posttrade. Table 15.1
summarizes this classification. The pretrade category includes benchmarks known
ahead of execution, such as:
■■

■■

■■
■■

Trading decision price, the price at which the trader or portfolio manager decided
was advantageous for trading.
Previous day’s close price, which can be used as a benchmark for traders working
with daily.
Daily open price.

The intratrade category includes the following benchmarks:
■■

VWAP, determined using intraday prices.

■■

TWAP, also determined on the basis of prices throughout the day.

■■

The average of daily open, high, low, and close prices (OHLC)
The posttrade category includes the future close, the price not known in advance.

TWAP
TWAP attempts to conceal the order flow by breaking a large order into equally
sized parcels, which are then sent out at equally spaced time intervals. Mathematically, TWAP executes a fixed portion 1/T of the order every predetermined unit of
Table 15.1 Order Execution Benchmarks
Pretrade

Intratrade

Posttrade

Decision price

VWAP

Future close

Previous close

TWAP

Opening price

OHLC

Arrival price
Source: Kissel and Glantz (2005)

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Minimizing Market Impact

Arrival price, the price that was prevalent when the executing broker received
the order.

Start with one large order of size S

1. How many “slices,” N?

Decide:

2. What is the total execution time, T?

Execute N trades:
Send one order of size S/N every1/T units of time

Compute execution statistics

FIGURE 15.5 TWAp process

time. The resulting TWAp price is the arithmetic average of prices sampled at the
regular unit time intervals:
1 T
(3)
∑ Pt
T 1
The TWAp algorithm is illustrated in Figure 15.5. When a trader chooses to execute a large order of size S using TWAp, the trader also needs to decide on the total
number N of child orders or slices to execute, and the total execution time T. next,
an order slice of size S/N is sent to the market every T/N seconds, until the entire
order of size S is processed. The total number of slices N and the execution time
T are best determined using characteristics specific to the traded security. These
characteristics may include historical variation in volume throughout the trading
day, market depth at the beginning of execution, and a host of other variables. The
overarching objective is to select slices small enough so that each child order does
not significantly move the market, yet large or frequent enough so that the entire
large order can be executed within a reasonable time T. The resulting TWAp order
flow can be represented as in Figure 15.6, with each child order drawn as an arrow.
TWAP =

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VWap
The VWAp algorithm is currently one of the most popular execution methodologies.
The principle of VWAp is straightforward: break up a large order in such a way that
S/T S/T

S/T

2
∆t

∆t

S/T

… T–1

∆t

FIGURE 15.6 Diagram of resulting TWAp Order Flow

S/T

T
∆t

Time

Pct of
Daily Volm
9

1000

1100

1200

1300

1400

1500

1600

Time of day (hours)

FIGURE 15.7 Map of Historical Volume Averages for Futures

Source: Almgren and chriss (2000)

Start with one large order of size S
Decide : use volatility or volume base?
Determine number of trade slices, N

Execute N trades:

∑

Given historical metrics, send one order of size ∑

every t =1/T

units of time

Compute execution statistics

FIGURE 15.8 VWAp process

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VWAp child orders are larger when the trading volume is higher, and child orders are
smaller when trading volume is lower. Higher trading volume is likely to provide larger
pool of matching orders and result in faster and more cost-effective execution.
To determine the execution schedule, the VWAp algorithm uses a map of historical averages of intraday volume variations, such as the one shown for equities in Figure 15.7. The map is often computed using preceding month of trading data: for every 15-minute (or other duration) interval of the trading day, the VWAp map shows
the average volume over the past trading month. With the VWAp map in hand, the
sizes of the child orders are determined as follows: for every trading period throughout the day, the total order size S is scaled by the VWAp proportion of volume historically observed during that time period, as shown in equation (3). Figure 15.8
diagrams the VWAp algorithm.
Vt
st = S
(4)
∑τ ∈TVτ

The resulting benchmark VWAp price can be determined as follows:
VWAP =

∑τ ∈TVτ pτ
∑τ ∈TVτ

(5)

The VWAp map is based solely on historical data and does not accurately reflect
concurrent market conditions. Even so, on average, a VWAp algorithm can deliver
an allocation of child orders that efficiently utilizes the intraday liquidity. Such relative success of VWAp is based on persistence of the intraday volume patterns: specific markets possess their own intraday volume variations that change little from
one month to the next. For example, Figure 15.9 illustrates the hourly VWAp map
for Eurobund futures, computed using data for April 2009 and April 2010.While the
average hourly trading volumes in the Eurobund futures have grown from 2009 to
Intraday Volume Averages, April 2009

70
60

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256

FGBL Contracts

50
40
30
20
10
0

10 11 12 13 14 15 16 17 18 19 20 21 22
Trading Hours
Intraday Volume Averages, April 2010

70
60

FGBL Contracts

50
40
30
20
10
0

10 11 12 13 14 15 16 17 18 19 20 21 22
Trading Hour

FIGURE 15.9 persistence of Intraday Volume Distribution, Eurobund futures (FGBL) pOV

2010, the shape of the VWAp map remained largely the same: an uptick in volume at
the open of the European and the U.S. trading sessions, followed by a lull post–U.S.
lunchtime, followed by a spike of activity at the market close.
According to the joint U.S. commodity Futures Trading commission (cFTc) and
Securities and Exchange commission (SEc) report on the causes of the flash crash
(2010), it was the pOV algorithm that created the mayhem in the markets on May 6,
2010. The examination discovered that the significant volatility in market prices first
started to occur when “a large fundamental trader” initiated a trade of $4.1 billion of
E-minis with pOV set at 9 percent of volume over the previous minute.
Figure 15.10 illustrates the algorithm behind the pOV. Like TWAp and VWAp,
the pOV algorithm sends child orders at regular time intervals. Unlike TWAp and
VWAp, the size of each pOV child order is determined dynamically and set to a fixed
percentage of the trading volume recorded during a previous predefined period of
time, for example, 10 minutes. The execution next continues until the entire large
order is processed. The previous period’s trading volume used in calculation of pOV
child order should exclude the volume generated by the pOV trader himself:
SPOV,t = (Vt−1 − SPOV,t−1)(POV)

(6)

Start with one large order of size S

Observe the external trade volumevt during the last
period t

Execute POV* vt

Compute execution statistics

FIGURE 15.10 pOV process

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While the joint SEc and cFTc report did not mention whether the pOV algorithm used by the large fundamental trader accounted for the volume generated
by the trader himself, failure to account for his own volume would generate exponentially increasing child orders, and could have caused the crisis of flash crash
proportions.
When properly programmed, pOV has one distinct advantage over TWAp and
VWAp: pOV dynamically adjusts to present market conditions, instantaneously responding to such events as shifts in liquidity.

■■ Issues with Basic Models
TWAP, VWAP, and POV execution models discussed in the previous sections were
developed in the 1990s and are still widely popular, but suffer from serious shortcomings:
1. These models can be shown to be optimal only in specific, not-very-common
market conditions.
2. The models are easy to spot with advanced mathematical tools.

Optimality Conditions for Earlier Models
Under limited assumptions about market dynamics, like martingale pricing or arithmetic Brownian motion (ABM),TWAP, and VWAP can be shown to be optimal. Both
martingales and ABM, however, assume that the market does not trend, a hardly
realistic condition. One can also show that VWAP is optimal in rapidly trending
markets, where the trend completely dominates short-term noise-induced volatility.
In most market conditions where both the trend and the volatility are sizable, however, these models lose their optimality. The later sections of this chapter describe
the latest advanced execution models applicable to most market conditions.

Security of Earlier Models
Minimizing Market Impact

258

Popular models like TWAP, VWAP, and POV also lack security. The models’ primary
mission is to break up and hide the order flow in general markets. Due to the regular
nature of the child orders these strategies send, their child orders can be surprisingly
easy to spot with simple tools like autocorrelation and advanced tools like Fourier
analysis.
TWAP, for example, does little to hide the order flow from anyone familiar with
the basics of digital signal processing, a core study of electrical engineering that is often deployed to remedy scratched CDs. As shown in Figure 15.6, TWAP comprises
the regularly spaced orders of identical size. To detect market TWAP orders in the
stream of tick data, therefore, one needs to:
1. Tag all recent market trade tick data as either buys and sells as discussed in Chapter 4.
2. Separate all buy trade ticks into virtual “buckets” by trade size; do the same for
sell ticks.
3. Within each bucket, identify trades that occurred at identical time intervals
from one another.
This process can be continuously repeated in real time, allowing systems to predict the time and size of the next TWAP installment, and thereby eliminating the
original purpose of TWAP orders.
VWAP may seem more secure as the trades are not uniform in size; instead, the
VWAP trades are scaled by the time-specific trade volume or volatility observed
during the previous trading day or averaged over the previous week or month. While
such scaling may appear to prevent reverse-engineering of VWAP order flow, in reality, VWAP flow can be just as transparent as TWAP.

…
Time

FIGURE 15.11 Sample VWAp Order Flow in Equities

f (x) =

∞

∫ F (k)e

2π ikx

−∞

F (k) =

∞

∫

−∞

f ( x )e −2π ikx dx

(7)

(8)

where x represents a time-based variable, and F(k) is a frequency-domain function. Figures 15.12 through 15.15 illustrate the capabilities of Fourier analysis.

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To see the limitations of security VWAp, consider an equity VWAp process as
shown in Figure 15.11. Descaling all the trade ticks observed by the same scaling volume or volatility function as the one used in the VWAp-generating process
of Figure 15.8 transforms VWAp into TWAp, and subsequently enables TWAp-like
identification of the order flow.
VWAp scaling functions used by different traders may differ by the number of
days used in averaging either volume or volatility, as well as by the width of time
bars over which the intraday averages are computed. Even so, repeating the descaling analysis over the complete order flow several times using different precomputed
scaling functions will identify orders sent in with a given scaling function.
The order flow sent via pOV algorithms can be similarly identified. regular spacing of orders, coupled with predictable functional form of order sizes, gives away the
order flow. In the case of pOV, the functional form of order flow is dependent on the
volume executed during the time elapsed since the previous pOV order.
In response to such security issues, some market participants and broker-dealers randomize sizes and timing of orders to reduce transparency of the basic algos.
While the randomization may restrict other market participants’ ability to observe
the order flow with the basic methodology described earlier, the orders will still be
traceable with advanced digital signal processing techniques, such as Fourier analysis.
Fourier analysis is often used to identify repetitive signals “buried” in the noise.
Digital Fourier analysis models are routinely used to restore scratched music cDs or
to “correct” the slightly off-key voice of pop singers. Likewise, Fourier analysis can be
used to detect slightly randomized order flow of basic algorithms.
The key concept in Fourier analysis is Fourier transform, a mathematical construct connecting time and frequency domains. continuous (as opposed to digital)
forms of the Fourier transform are specified as follows:

1
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1
0

100

200

300

400

500

600

700

FIGURE 15.12 Sample recurrent process

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260

Figure 15.12 shows a simple continuous cyclical process that can be generated by
a time-dependent sinusoid function with frequency of 50 Hz (hertz, or repetition
of 50 cycles per second). Figure 15.13 shows the same process transformed with
Fourier analysis. The perfectly repeating cycles in time domain become a single clear
spike in frequency domain. Furthermore, the spike falls directly onto the frequency
of the cycles: 50 Hz.
Frequency content of y

80
70
60
50
40
30
20
10
0

100

150

200
250
300
frequency (Hz)

350

400

450

FIGURE 15.13 Fourier representation of the process Shown in Figure 15.12

500

Signal Corrupted with Zero-Mean Random Noise
8
6
4
2
0
–2
–4
–6

20
25
30
time (milliseconds)

FIGURE 15.14 Signal corrupted with zero-Mean random noise

Single-Sided Amplitude Spectrum of y (t)
1
0.9
0.8
0.7

|Y(f)|

0.6
0.5
0.4
0.3
0.2
0.1
0

100

150

200
250
300
Frequency (Hz)

FIGURE 15.15 Single-Sided Amplitude Spectrum of y(t)

350

400

450

500

261
MInIMIzInG MArkET IMpAcT

Figure 15.14 shows a different time-based function: two sinusoids generated at
50 Hz and 120 Hz corrupted by noise. The noise may represent a random stream of
data, such as other traders’ orders mixed in with the TWAp or VWAp. The cycles
in Figure 15.14 are hard to identify just by eyeballing the chart. However, a pass
through the Fourier transform delivers a clear representation of the periodicity,

shown in Figure 15.15: clear peaks at 50 Hz and 120 Hz dominate the frequency domain of this example. Similar ideas extend to identification of periodic order flow in
the sea of “noise” orders, placing the usefulness of TWAP and VWAP into question.
Over the past few years, advanced models have been developed to overcome
issues embedded in TWAP, VWAP, and POV algorithms. The latest algorithms are
discussed in the next section.
■■ Advanced Models

Minimizing Market Impact

262

To use realistic market assumptions and to avoid transparency of order flow
induced by the basic TWAP, VWAP, and POV algorithms, researchers have developed advanced models that work under normal market conditions with a
mixture of trend and volatility. Under these conditions, it can be shown that the
optimal trading strategy is the one that induces a constant rate of order book
replenishment.
The order book replenishment refers to the process of repopulation of the book
following a market order. Figure 15.16 illustrates an example of replenishment in a
limit order book.
Stylized replenishment function assumes that the order book possesses a “shadow”
form, a structure to which the book reverts after some liquidity has been taken away.
The shadow order book is assumed to exist independent of the current price level—
the shadow book slides up and down the price axis with the movement of the price.
The reversion of liquidity in the order book to the book’s shadow form is referred
to as resilience of the book.
The order book’s resilience, h(Es), is a function of the trading process and is specified as follows:
t

Et = Xt − ∫ h(Es )ds
0

(9)

where Et is the aggregate size of limit orders available at p ticks away from prevailing
market price P at time t, Xt is the aggregate order flow, E0 = 0, and ∆Xt=∆Et for 0 ≤ t
≤ T. The function h(Es) measures how fast the order book p ticks away from the market recovers following an order of size ∆Xt , and satisfies the following properties:
■■
■■

The function is strictly increasing in X, and
The function is a locally Lipschitz function on [0,∞): |h(x)-h(y)|≤C|x-y| for all
x and y, where C is a constant independent of x and y, and the function has a
bounded first derivative dh < ∞ . The trader’s execution strategy X measures the
dX
amount of the total order still left to be processed in the market. As such, x0 = X
and xT = 0. The trader’s rate of trading is defined as
∂x
vt = − t
(10)
∂t

Price

A large market sell order
sweeps the bids in the book,
realizes lower aggregate price,
changes best bid

Bid-ask spread

Best ask = best offer

FIGURE 15.16 replenishment in a Limit Order Book

Step 2

Best bid

Step 1

Wider bid-ask spread

Price

A few more stochastic limit buy orders arrive, order book recovers

Step 4

Step 3

New limit buy order arrives

Price process of the traded instrument, St, can be assumed to follow any continuous process. Independent of the shape of the price process St, the expected impact
inflicted by strategy X on price S can always be measured as cost C:
T

C = ∫ St dxt
0

(11)

The expected value of MI cost can be expressed via integration by parts as follows:
T



T
E [C ] = E  ∫ St dxt  = E ST xT − S0 x0 − ∫ xt dSt 

(12)



 0
0
The most recent stream of research on best execution has focused on developing
optimal execution algorithms under the following rigorous assumptions:

1. Geometric Brownian motion, the specification most commonly used in modern
asset pricing.
2. Generalized price functions that can be used to describe any empirically observed price evolutions in an MI framework.
This section reviews the latest models developed under the two price evolution
models.

Minimizing Market Impact

264

When Price Follows Geometric Brownian Motion
Most security pricing models assume that prices follow geometric Brownian motion
with price increments dSt exhibiting dependency on the contemporary price level St,
as well as incurring drift μ:
dSt = μStdt + σStdZt

(13)

The vanilla execution cost function, not incorporating any risk optimization measures, can then be specified as follows (see Forsyth et al., 2011):
T

C = η ∫ vt dt + λσ ∫ St2 xt2dt
0

(14)

∂xt
. Under the assumption
∂t
of geometric Brownian motion, the costs and the resulting optimal solution of the
cost minimization problem are dependent on the price of the price path. However,
as Forsyth et al. (2011) show, many strategies lead to the almost identical outcome.
Euler-Lagrange equations produce the following closed-form solution for optimal cost-minimizing trading strategy:

where, as before, the optimal rate of execution is vt = −

xt * =

t

λT
T −t 
Su du 
X −
∫
T 
4 0


(15)

* 2
*
The resulting expected minimal cost, E[Cmin ( x )] = E[ ∫ ((vt ) + λ xt St )dt ]
0
becomes
*

E Cmin ( x * ) =

X 2 λTXS0 λ 2 2  σ T
σ 4T 2 
+
− 6 S0  e − 1 − σ 2T −

T
2
4 
8σ

2

(16)

See Forsyth et al. (2011) for derivation.

When Price Follows a Generalized Market
Impact–Based Function
While most now-traditional asset-pricing models, such as Black-Scholes, assume
Geometric Brownian motion as the model accurately describing evolution of security
prices, a new breed of models proposes to model short-term price changes closer to
their empirical roots. In such models, the price level at time t is expected to evolve
as follows (see Gatheral, 2011):
(17)

St = S0 + impact of prior trading + risk (noise)
t

where the risk or noise component is the price-level independent ∫ σ dZ s . The im0

E[C ] =

T t

1
h(Es )dX s dXt
2 ∫0 ∫0

(18)

To minimize expected cost [C], one is required to solve the following equation:
∂ ∂E [C ]
=0
∂t ∂ut

(19)

which can be interpreted as follows: the optimal value of cost requires cost invariance with trading rate. Since the cost is directly dependent on volume impact Et, the
optimality condition requires that volume impact stays constant:
(20)

Et = const

See Obizaeva and Wang (2005), Alfonsi and Schied (2010), and Gatheral (2011)
for details.

Case 1: Exponential Market Resiliency
When the market resiliency can be assumed to follow exponential form, h(Et)=e-pt,
the equation (20) then can be rewritten as:
t

St = S0 + η ∫ us e
0

− ρ (t − s )

ds + ∫ σ dZ s
0

(21)

265
Minimizing Market Impact

pact of prior trading is quantified using the execution strategy X trading rate dydx
namics ut ≡ − and the function measuring resiliency of the order book h(Et). The
dt
expected execution cost can next be expressed as

from where the expected execution cost of a trading strategy X can be expressed as
T

E[C ] = η ∫ ut ∫ e − ρ (t − s )ds dt

(22)

To derive suitable conditions for Et, Obizhaeva and Wang (2005) note that Et can be
expressed as
t

Et = ∫ E0+ e − ρ (t − s )ds
0

(23)

where E0 measures the residual impact of trading prior to the chosen time 0. Integration by parts then yields:
t

Et = E0 e − ρ t + ρ ∫ e − ρ (t − s )ds

(24)

Normalizing E0 by E0 = 1, the optimality condition with constant volume impact
becomes
(25)
Et = E0 = 1
Equation (25) then translates into
t

e − ρ t + ρ ∫ e − ρ (t − s )ds = 1

Minimizing Market Impact

266

(26)

The original optimality condition for the execution cost [equation (21)] can then be
expanded
∂E [C ]
= η ∫ us e − ρ (t − s )ds + η ∫ us e − ρ (t − s )ds = η ∫ us e − ρ|t − s|ds = const
∂ut
0
0
t
t

Substituting the volume impact component
equation (26) produces the following result:

∫ us e

(27)

− ρ|t − s|

ds from equation (27) into

e − ρ t + ρ ∫ e − ρ (t − s )ds = ∫ us e − ρ|t − s|ds

(28)

The optimal trading rate ut can then be determined as
(29)
ut * = δ ( t ) + ρ + δ (t − T )
Equation (29) can be interpreted as follows: when the market resiliency function can
be assumed to be exponential, the optimal execution strategy is composed of:
■■

A large block trade of size δ at the beginning of execution process.

■■

A large block trade of size δ at the end of execution horizon, T.

■■

A continuum of TWAP-like small orders placed at trading rate ρ, where ρ is the
parameter in the exponential market resiliency function, h(Et)=e-ρt.

u (s)
0.0

0.2

0.4
0.6
Time (s)

0.8

1.0

FIGURE 15.17 Optimal Execution in a Market with Linear permanent Market Impact and
Exponential Decay of Temporary Impact
Source: Gatheral, Shied and Slynko (2011)

The resulting optimal execution strategy for T=1 and exponential market resiliency with ρ = 0.1 is illustrated in Figure 15.17. Figure 15.18 illustrates optimal
execution strategies for different trading frequencies.

267

Trade Profiles for Different N

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1
N=25

24697

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1
N=100

23899

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

FIGURE 15.18 Optimal Execution with Exponential resiliency for Different Trading
Frequencies
Source: Obizhaeva and Wang (2005)

MInIMIzInG MArkET IMpAcT

N=10
26317

Case 2: power-law Market resiliency
When the market resiliency can be assumed to fit the power-law function, h(Et)=t-γ,
the optimal strategy can once again be derived via the constant volume impact requirement, equation (30):
T

Et = ∫ u( s )|t − s |−γ ds = const

(30)

The optimal trading rate is then
ut*=δ[t(Τ−t)]−(1−γ)/2

(31)

with γ representing a parameterized constant from h(Et)=t-γ, and δ analytically determined from equation (32):
1+ γ 
Γ 
T   2 

X = ∫ u ( t )dt = δ π  
 2  Γ 1 + γ 
0


 2
γ

where gamma function is defined as Γ( n) = ( n −1)! for discrete n, and
∞
Γ( z) = ∫ e −t t z −1dt for continuous z. The resulting optimal strategy is continuous
0
with large singular block trades at the beginning and the end of execution times 0
and T. The optimal execution schedule is illustrated in Figure 15.19.

Case 3: linear Market resiliency
When the market resiliency fits a straight line until the markets are restored, the
market resiliency function is described as h(Et)=(1 - ρt)+, and the optimal strategy
can yet again be deduced via the constant volume impact requirement, equation (33):
T

Et = ∫ u( s )(1 − ρ t − s )+ ds = const

(33)

u (s)

MInIMIzInG MArkET IMpAcT

268

(32)

0.0

0.2

0.4

0.6

0.8

1.0

FIGURE 15.19 Optimal Execution in a Market with Linear permanent Market Impact and
power-Law Decay of Temporary Impact
Source: Gatheral, Shied and Slynko (2011)

u (s)
0

Time (s)

FIGURE 15.20 Optimal Execution in a Market with Linear permanent Market Impact and
Linear Decay of Temporary Impact
Source: Gatheral, Shied and Slynko (2011)

The optimal trading strategy comprises harmonic block trades with no-trading
intervals between the blocks, as shown in Figure 15.20.
The aggregate execution schedule is broken down into 2N trades each of the size
269
(34)

■ Practical Implementation of Optimal Execution

Strategies

To determine the optimal order slices per the framework presented in the previous
section, the execution trader can go through the following steps:
1. Estimate the empirical MI function.
2. Fit distributions of temporary and permanent MI of the traded security.
3. Derive optimal allocation on the basis of step 1.
4. Back test the execution strategy.
5. put the strategy to use in real-life production environment.
The resulting strategies perform well in chosen market conditions.
■ Summary
Algorithmic order execution is inseparable from today’s markets. It is a necessary function that delivers considerable value to all investors, large and small.With plummeting
technology costs, most investors today can afford to build and use advanced order routing and best execution algos, previously available only to a select few market participants. Services such as co-location provide added benefits of security and speed.

MInIMIzInG MArkET IMpAcT

i 
δ 1 −
 , so that the total trading size X satisfies
 N +1
T
N
i 
X = ∫ u ( t ) dt = δ ∑2 1 −

N +1
i =0 
0

■■ End-of-Chapter Questions
1. The best offer on exchange A contains 300 units of instrument X, the best offer
on exchange B contains 500 units, and the best offer on exchange C contains just
100 units.Your customer wants you to buy 550 units on his behalf. How would
you break up the customer’s order and send them to exchanges under the minimal impact algorithm?
2. What is TWAP? VWAP? POV? Explain.
3. What are the main shortcomings of TWAP, VWAP, and POV?
4. How can the disadvantages of TWAP, VWAP, and POV be remedied?
5. What is resilience of the order book?

Minimizing Market Impact

270

Chapter 16

Implementation
of HFT Systems
H

igh-frequency trading (HFT) systems tend to be “mission-critical applications,”
comparable with software piloting NASA shuttle launches and having little
room for error. This chapter describes best practices of implementing accurate and
reliable HFT systems.
■■ Model Development Life Cycle
HFT systems, by their nature, require rapid hesitation-free decision making and execution. Properly programmed computer systems typically outperform human traders
in these “mission-critical” trading tasks, particularly under treacherous market conditions—see Aldridge (2009b), for example. As a result, computer trading systems are
rapidly replacing traditional human traders on trading desks around the world.
The development of a fully automated trading system follows a path similar to
that of the standard software development process. The typical life cycle of a development process is illustrated in Figure 16.1.
A sound development process normally consists of the following five phases:
1.
2.
3.
4.
5.

Planning
Analysis
Design
Implementation
Maintenance

The circular nature of the process illustrates the continuous quality of system development. When a version of the system appears to be complete, new issues demand
advanced modifications and enhancements that lead to a new development cycle.
The purpose of the planning phase is to determine the goals of the project as well
as to generate a high-level view of what the completed project may look like. The

271

Planning

Maintenance

Analysis

Design
Implementation

FIGURE 16.1 Typical Development Cycle of a Trading System

IMPleMeNTATIoN oF HFT SySTeMS

272

planning is accompanied by a feasibility study that evaluates the project in terms of
its economics, operating model, and technical requirements. The economical considerations explore whether the project has a sufficient profit-and-loss (P&l) potential, whereas operational and technical issues address the feasibility of the project
from the compliance, human resources, and other day-to-day points of view. The
outputs of the planning phase include concrete goals and targets set for the project,
established schedules, and estimated budgets for the entire system.
During the analysis stage of the process, the team aggregates requirements for
system functionality, determines the scope of the project (which features are in and
which features are out of the current release), and solicits initial feedback from users
and management.The analysis stage is arguably the most critical stage in the development process, because it is here that stakeholders have the ultimate ability to shape
the functionality of the system given the allocated budget.
The design phase incorporates detailed specifications of functionality, including
process diagrams, business rules, and screenshots, along with other output formats
such as those of daily reports and other documents. An objective of the design stage
is to separate the whole project into discrete components subsequently assigned
to teams of software developers; the discrete components will have well-specified
interfaces that can lock in seamlessly with other components designed by different teams of software developers. Such early specification of software packaging
of internal computer modules streamlines future communication among different
software development teams and enables smooth operation of the project going forward. The design phase also outlines test cases—that is, the functionality paths that
are later used as blueprints to verify the correctness of the completed code.
The implementation phase, finally, involves actual programming; the software
teams or individual programmers develop software modules according to the specifications defined in the design stage. The individual modules are then tested by the
development teams themselves against the predefined test cases. When the project
management is satisfied that the individual modules have been developed according
to the specifications, the project integration work begins. Integration, as its name implies, refers to putting together the individual modules to create a functional system.
While successfully planned projects encounter little variance or problems in the
integration stage, some work still remains. Scripts may have to be written to ensure
proper communication among various system components, installation wrappers

may have to be developed, and, most important, the system has to be comprehensively tested to ensure proper operation. The test process usually involves dedicated
personnel other than the people who developed the code. The test staff diligently
monitors the execution of each functionality according to testing procedures defined
in the design stage. The test personnel then documents any “bugs”—that is, discrepancies between the prespecified test case performance and observed performance.
The bugs are then sent back over to the development team for resolution and are
subsequently returned to the testing teams.
Successful implementation is followed by the deployment and subsequent maintenance phase of the system. The maintenance phase addresses system-wide deviations
from planned performance, such as troubleshooting newly discovered bugs.
■ System Implementation

Key Steps in Implementation of high-Frequency
Systems
Most systematic trading platforms are organized as shown in Figure 16.2. This section discusses each component of the process in detail.
Electronic

273

Broker-Dealer or
Trading Venue

Run-Time Processor
Proprietary software
technology

Services:
Live Quotes

Quotes
Order Processing
Trade
Reconciliation

Buy/Sell
Orders

Process real-time quotes
Perform run-time
econometrics
Develop buy and sell
signals
Calculate run-time P&L,
Risk management based on
pre-defined parameters

Run-time performance monitoring
Innovation in strategy
development/enhancement

Archive all quotes
received

USD/CAD

Order Ack

Human Element

Generate order and fulfillment record
for future reconciliation

Simulation Engine

Post-Trade Analysis

Proprietary software technology

Generates and tests new
strategies
Enhances current trading
strategies based on the results
generated in the post-trade
analysis

Reconciles daily trades with
simulation results based on
archived data

FIGURE 16.2 Typical High-Frequency Process

Identifies slippages, anomalies
and other discrepancies

IMPleMeNTATIoN oF HFT SySTeMS

Interface

Step 1: The Core Engine The core engine is composed of one or several run-time
processors that contain the core logic of the trading mechanism and perform the
following functions:
■■

Receive, evaluate, and archive incoming quotes.

■■

Perform run-time econometric analysis.

■■

Implement run-time portfolio management.

■■

Initiate and transmit buy and sell trading signals.

■■

Listen for and receive confirmation of execution.

■■

Calculate run-time P&L.

■■

Implementation of HFT Systems

274

Dynamically manage risk based on current portfolio allocations and market
conditions.

Most of the high-frequency production-bound systems are written in C++, although
some high-frequency trading firms are known to use Java and Q, a commercial hybrid
of language syntax and database organization distributed by Kx Systems. The matching
engine of Nasdaq OMX, for example, is said to be written in Java, yet the code disables
“garbage collection,” a core functionality of Java that distinguishes it from C++, but
also slows down the systems. C++ is often considered to be “lighter” and “faster” than
Java, meaning that C++ programs do not have the processing power overhead required
by Java; as a result, C++ systems often work faster than Java-based systems.
The core engine and the portfolio management framework then initiate and
transmit orders to the broker-dealer. Upon receiving and executing an order, the
broker-dealer sends back the order status and order-filling price and size to the client. The system then calculates the P&L and assesses risk management parameters
that feed back into the portfolio management piece.
The design and implementation of run-time portfolio management reflects the
core econometric engine. In addition to the raw quote inputs, the portfolio management framework incorporates inputs from the econometric model, current position
sizes, and other information relevant to portfolio diversification and maximization
of portfolio returns, while minimizing portfolio risk.
Incoming quotes, along with outgoing orders and any other communication between a broker-dealer and a client or an exchange, are most often transmitted via
the Financial Information eXchange (FIX) protocol specifically designed for transmission of real-time financial information. Other protocols, like FAST and Nasdaq’s
proprietary ITCH and OUCH, are also used.
According to the FIX industry web site (www.fixprotocol.org), FIX emerged in
1992 as a bilateral communications framework for equity trading between Fidelity
Investments and Salomon Brothers. It has since become the dominant communication method among various broker-dealers, exchanges, and transacting customers.
In fact, according to a survey conducted by fixprotocol.org, FIX was used for systematic trading by 75 percent of buy-side firms, 80 percent of sell-side firms, and
over 75 percent of exchanges in 2006.

[Field #] = [data]
For example, to communicate that the message carries the status of an order, the
following sequence is used:
35 = 8|
All field sequences are terminated with a special character that has a computer value
of 0x01. The character looks like “|” when seen on-screen.
The body of the message contains the details of the message, whether it is a quote
request, a quote itself, or order and trade information. The message body further
specifies the exchange of interest, a timestamp that includes milliseconds, a security
symbol, and other necessary transaction data. Like the header, all fields in the body
are included in the following format:
[Field #] = [data]

275
Implementation of HFT Systems

FIX is best described as a programming language that is overseen by a global steering
committee, consisting of representatives from banks, broker-dealers, exchanges, industry utilities and associations, institutional investors, and information technology providers from around the world. Its standard is open and free. Implementation of a communication process via FIX, however, requires careful planning and dedicated resources
and may demand significant expense, much like any other system development process.
A typical FIX message is composed of a header, a body, and a trailer. The header
always contains the following three fields: a string identifying the beginning of a message (FIX field # 8), the number of characters in the body of the message to follow
the message header (FIX field # 9), and the type of the message (FIX field # 35).
Among many message types are quotation and order execution directives and acknowledgments as well as housekeeping messages designed to ensure that the system
remains up and running.
For example, MsgType = 0 is the “Heartbeat” message—a message is sent to the
other communication party to ensure that the communication connection remains
operational and has not been lost as a result of any unforeseen technical problems.
The heartbeat message is typically sent after a prespecified number of seconds of
inactivity. If either communication party has not received a heartbeat message from
the other party, it sends a TestRequest message (MsgType = 1) to “poll” the other
communication party. If no heartbeat message is received following a TestRequest
message, the connection is considered lost and steps are taken to restart it.
MsgType = 6 is known as “Indication of Interest.” Exchanges and broker-dealers
use Indication of Interest messages to transmit their interest in either buying or selling in either a proprietary or an agency capacity. MsgType = R indicates a “Quote
Request” message with which a client of a broker-dealer requests a quote stream.
Under normal circumstances, the broker-dealer responds to the Quote Request
message with a continuous stream of Quote messages (MsgType = S) that carry actual quote information, such as bid or ask prices.
Other message types include orders such as single-name orders, list orders, day
limit orders, multiday orders, various cancellation requests, and acknowledgments.
All fields in the body are included in the following format:

and each field sequence is terminated by a special computer character 0x01.
Finally, at the end of the body of every message is the “checksum”—a sum of digital
values of all the characters in the message included as a verification of whether the message has arrived in full. An example of a FIX message is shown in Chapter 2 of this book.
The risk management functionality can include the following components: tracking the basic components of the system performance and generating warning messages should the performance limits be breached. Appropriate risk management
parameters may include message count limits per unit time, P&L parameters, and
other variables discussed in detail later in this chapter.
Most quotes are accepted and archived using proprietary
FIX engines that are tested with various message scenarios. The quotes are next archived for reconciliation and simulation purposes.
As discussed in Chapter 2, quote delivery over the public networks can be unreliable: the User Datagram Protocol (UDP) over which some quotes are broadcast
does not guarantee point-to-point delivery. As a result, an HFT without co-location
may lose quotes. Furthermore, variations in quote-receiving technology from one
entity to the next do not guarantee that each entity’s recorded datastream will be
identical to that of the next entity. In some cases, purchased tick data may not be
completely representative of the quote process archived by the data buyer from his
own quote interface.While purchased historical data fills an important informational
void when a researcher has no data, best practices suggest that each trading entity
will benefit most from the internally archived data as such data will be most representative of the data received by the system during production.
Most firms with serious HFT needs archive all received and sent messages in text
or binary file formats. The text file, known as a flat file in the industry, is the simplest form of storage. The flat file is readable by humans without special translation.
The fields in the file can be comma or tab separated, and can be easily loaded into
Excel or opened with Notepad on PCs or plain text editors on LINUX. Binary files,
commonly referred to as Large Binary OBjects, or BLOBs, are recorded in hexadecimal (Hex) characters readable by machines. At the expense of readability, BLOBs
are faster and much more compact than flat files. Interdealer broker ICAP’s foreign
exchange matching engine, for example, records all ticks in a continuous weekly
BLOB. Along with foreign exchange markets, each ICAP’s BLOB begins on Sunday
night and ends on Friday night, NewYork time. Each such BLOB can occupy as much
as a terabyte of storage space. Such storage requirements could have been prohibitively expensive just 10 years ago, yet today such storage is very reasonable. Various
incarnations of Storage Area Networks (SANs) allow seamless access to stored data.
Many databases have attempted to crack the market for archiving real-time highfrequency data, and replace flat files with their products. Most databases are unsuitable to HFT because in HFT the most time-sensitive functionality is data archival.
Slow input/output operation delays execution of the trading engine, compromising
performance of the HFT system. Retrieval of tick data occurs only at the simulation
level where execution time is not a critical parameter. Most databases, however,
are optimized to efficiently retrieve data, and not to enter it into the system. KDB,
Step 2: Quote Archival

Implementation of HFT Systems

276

distributed by Kx Systems, however, has been shown to be a promising tool, adopted
by several firms.
Step 3: Posttrade Analytics The best HFT systems do not stop there. A posttrade
analysis engine reconciles production results with simulation results run with the
same code on the same data and updates distributions of returns, trading costs, and
risk management parameters to be fed back into the main processing engine, portfolio optimization, and risk management components.

Simulation refers to a make-belief execution of a trading strategy.
Simulation is important for one key reason: it allows researchers to test a strategy within a short time span, without risking actual capital. A strategy that works well in simulation has a chance on actual money, in “production.” Conversely, a strategy that fails in
simulation will be hard-pressed to deliver positive results in a real trading environment.
The simulation engine is an independent module that tests new trading ideas on
past and run-time data without actually executing the trades. Unlike ideas that are
still in the early stages of development that are often coded in MatLab or even Excel,
ideas tested in the simulation engine are typically coded in the production language
(C++ or Java).
Simulation produces an approximation of real-life trading, and only if the execution part of simulation is programmed correctly. Specifically, execution of market and
limit orders requires different treatment. A market order submitted in simulation can
be assumed to be executed at the prevailing quote at the time the market order is
submitted. Thus, a market buy order can be assumed to be filled at the best ask, providing that the size of the market order is smaller than the size of the best ask queue.
Similarly, a small market sell order can be assumed to be executed at the best bid.
The best-quote assumptions about execution of market orders, however, will
most of the time overstate performance of the trading system. In live trading, market orders will incur MI or slippage, resulting in worse prices than predicted by the
best bid and best offer (for more details on market impact, please see Chapter 5). To
better approximate the live trading results, the HFT researcher can estimate the average MI per unit trade size, and then adjust the best quotes by the estimated values
of the MI. The market buy orders will then be considered executed at the prevailing
ask plus the expected size-dependent MI, closer reflecting real-market conditions
and applying a great degree of conservatism to simulation. Similarly, the market sell
orders will be expected to execute at the best bid less MI estimation.
Simulation of execution of limit orders is also complex. A limit order can be
considered to be executed only when the market price “crosses” the order price, as
shown in Figure 10.1. When the market price equals the limit order price, the limit
order may or may not to be executed in live trading. As a result, simulations of limit
order trading generally consider a limit order to be executed when the market price
drops below the price of the buy limit order, or when the market price rises above
the price of the limit sell order, and the limit order execution is guaranteed.
Simulation of strategies can be performed in-sample and out-of-sample. In-sample
simulation runs the strategy on the same sample of data on which the strategy was

Step 4: Simulation

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Implementation of HFT Systems

first developed. Natural issues dog the in-sample process: the data can be overfitted,
and the results may not hold up in normal market conditions.
To make sure that the strategy has a chance in real-life trading, the strategy needs
to be tested out-of-sample. Out-of-sample testing involves running the strategy on
a copious amount of previously unused data. The out-of-sample testing is usually
performed in the following order:
1. Back-test
2. Paper trading
3. Production

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278

Back-Test A strategy run on historical data is called a back-test. The back-test typically utilizes at least two years of most recent tick data. The two-year minimum for
the test is likely an overhang from low-frequency monthly performance evaluation
days: 24 months provides a number of monthly observations nearly sufficient for
making statistically significant inferences under the central limit theorem in statistics.
In theory, the minimum number of days sufficient to prove the performance of
a strategy is determined by the Sharpe ratio it is thought to produce, as discussed
in Chapter 6. In practice, however, a larger number of observations is preferred
to the smaller set because the larger the number of observations, the more opportunities to evaluate the strategy performance, and the more confidence in the
strategy results.
A large reserve of historical data (at least two years of continuous tick data) also
ensures that the model minimizes the data-snooping bias, a condition that occurs
when the model overfits to a nonrecurring aberration in the data. Running the backtest on a fresh set of historical data unused in the model development is known as
making out-of-sample inferences.
A back-test is also useful in estimation of risk of a given trading system. The preferred distributions of returns used as inputs into HFT risk quantification models
are obtained from running the system on live capital. Still, a back-test distribution
of trade returns obtained from running the model over at least two years of tick data
can also be used in risk management applications, even though the back-test distribution may generate misleading results: back-tests may fail to account for all the
extreme returns and hidden costs that occur when the system is trading live.
To mitigate the unexpected and low probability extreme returns, known as
black swans (Taleb, 2007), the HFT researcher may consider running the HFT code
through historical or simulated data representing made-up “stress-test scenarios.”
The data surrounding the flash crash of May 6, 2010, represents a historical example
of a stress event. However, data corresponding to some hypothetical simultaneous
failure of global financial markets can be simulated.
The out-of-sample back-test results need to be evaluated. At a minimum, the
evaluation process should compute basic statistical parameters of the trading idea’s
performance: cumulative and average returns, Sharpe ratio, and maximum drawdown, as explained in Chapter 6.
Once a strategy is determined to perform satisfactorily in the back-test, the strategy is moved into paper trading, discussed next.

A strategy run in real time on live data, but without placing the
actual trades, is known as paper trading. The paper-trading stage records all orders in
a text file. The orders and trades records at a minimum should include:

Paper Trading

■■

A granular timestamp of the order, with a minimum of 1 ms or finer precision.

■■

A code of the traded financial instrument.

■■

Last observed best bid price, best bid size, best ask price, and best ask size, for
end-of-day reconciliation of orders and data.

■■

Order quantity.

■■

Assumed execution price.

A strategy running in real time on live capital is usually referred to live
trading or as production. Production orders are sent to live trading venues via FIX or
other messaging protocols. An HFT system running in production will still need to
locally archive all orders, as for the paper trading discussed above. The paper trading
records and the live trading records will help generate order fulfillment and reconciliation analysis, as well as assess executional performance of the strategy.
The difference in performance of the live strategy and paper trading is formally
known as implementation shortfall. Implementation shortfall provides the most reliable measures of slippage and other latent costs by allowing direct observation of
prices obtained in real markets and their simulated counterparts.

Production

Step 5: Human Supervision Continuous human supervision of the system is required to ensure that the system does not fall victim to some malicious activity such
as a computer virus or a market event unaccounted for in the model itself. The
role of the human trader, however, should normally be limited to making sure that
the performance of the system falls within specific bounds. Once the bounds are
breached, the human trader should have the authority to shut down trading for the
day or until the conditions causing the breach have been resolved.

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Implementation of HFT Systems

The main difference between the live trading model and the back-test model
should be the origin of the quote data; the back-test system includes a historical
quote-streaming module that reads historical tick data from archives and feeds it
sequentially to the module that has the main functionality. In the paper trading system, a different quote module receives real-time tick data from trading venues and
broker-dealers.
Except for differences in receiving quotes, paper-trading and back-test systems
should be identical; they can be built simultaneously and use the same code for
core functionality. This chapter reviews the systems implementation process under the assumption that both back-testing and paper-trading engines are built and
tested in parallel. The following sections summarize key steps in the process of
developing high-frequency systems, detail the system development process, including common pitfalls,as well as discuss the best practices for testing developed
trading systems.

Common Pitfalls in Systems Implementation
Message Acknowledgment Loops

A market order communication process in-

cludes the following steps:

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280

■■

The client sends a market order to the broker or a trading venue.

■■

The venue receives the order/the broker forwards the order to the exchange.

■■

The trading venue sends out an order acknowledgment.

■■

The client receives the order acknowledgment.

■■

The order is executed.

■■

The trading venue sends out the execution acknowledgment.

■■

The client receives the execution acknowledgment.

Time elapses from the instance the client sends an order to the moment the client
receives an order execution acknowledgment. In the United States, the round-trip
execution speed of a market order is 10 ms or less; in Europe, this number may grow
to 50 to 100 ms, and in Asia the round-trip time may still take a whole minute or
two. Regardless of the speed of the execution process, the finite time that elapses
between the order origination and confirmation of execution is sufficient to produce
wildly runaway algos.
A frequent rookie cause for the runaway condition is an ill-programmed position counter. Consider the following logic: a trading algorithm sends out orders in
response to specific market conditions and until the total portfolio reaches a certain
position limit. When the position counter is adjusted only upon receiving execution
acknowledgments, the system keeps spewing out orders during the time the order
is being executed, potentially resulting in an extreme quantity of executions, well
above the set position limit. The mistake is common and is easy to fix. One solution
involves keeping two position counters: one for sent-in orders, and the other for
executed positions. The idea, however, does not occur easily to someone lacking
HFT experience.
Time Distortion The simulation runs in its own time using quotes collected and
stored during a run time of another process. The frequency of the quotes recorded
by the process that collected the data that is now historical data can vary greatly,
mostly because of the following two factors:

1. The number of financial instruments for which the original process collected
quotes.
2. The speed of the computer system on which the original process ran.
Their impact is due to the nature of the quote process and its realization in most
trading systems. Most systems comprise a client (the quote collecting and/or trading application) that is geared to receive quotes and the server (a broker-dealer application supplying the quotes). The client is most often a “local” application that

runs “locally”: on computer hardware over which the trader has full control. The
broker-dealer server is almost always a remote application, meaning that the client
has to communicate with the server over a remote connection, such as the Internet.
To receive quotes, the client application usually has to perform the following communication with the server process:

281
Implementation of HFT Systems

1. The client sends the server a message or a series of messages with the following
information:
a. Client identification (given to the client by the broker-dealer that houses the
server).
b. Names of financial securities for which the quotes are requested.
2. The server will respond, acknowledging the client’s message. The server’s response will also indicate whether the client is not allowed to receive any of the
quotes requested for any reason.
3. The server will begin to stream the quotes to the client. The quotes are typically
streamed in an “asynchronous” manner—that is, the server will send a quote
to the client as soon as a new quote becomes available. Some securities have
higher-frequency quotes than others. For example, during high-volatility times
surrounding economic announcements, it is not unusual for the EUR/USD exchange rate to be accompanied by as many as 300 quotes per second. At the same
time, some obscure option may generate only one quote per trading day. It is
important to keep in mind the expected frequency of quotes while designing the
quote-receiving part of the application.
4. Quote distortion often happens next. It is the responsibility of the client to collect and process all the quotes as soon as they arrive at the client’s computer.
Here, several issues can occur. On the client’s machine, all incoming quotes are
placed into a queue in the order of their arrival, with the earliest quotes located
closest to the processor. This queue can be thought of as a line for airport checkin. Unlike the airport line, however, the queue often has a finite length or capacity; therefore, any quote arrivals that find the queue full are discarded, hence the
first issue: quote time series may vary from client to client if the client systems
have queues of varying lengths, all other system characteristics being equal.
Once the quotes are in the queue, the system picks the earliest quote arrival
from the queue for processing; then all the quotes in the queue are shifted closer
to the processing engine. As noted previously, the quotes may arrive faster than the
client is able to process them, filling up the queue and leading the system to discard
new quote arrivals until the older quotes are processed. Even a seemingly simple
operation such as copying a quote to a file or a database stored on the computer
system takes computer time. While the quote-storing time may be a tiny fraction
of a second and thus negligible by human time standards, the time can be significant by computer clock and slow down the processing of incoming quotes.
A client system may assign the quote an arrival time on taking the quote from
its arrival queue. The timestamp may therefore differ from the timestamp given
to the quote by the server. Depending on the number of securities for which
the quotes are collected and the market’s volatility at any given time of day, the

t imestamp distortion may differ significantly as a result of the quote-processing
delay alone. If the quotes are further mathematically manipulated to generate
trading signals, the distortions in timestamps may be even more considerable.
5. Naturally, systems running on computers with slower processing power will
encounter more timestamp distortion than systems running on faster machines.
Faster machines are quicker at processing sequential quotes and drop fewer
quotes as a result. Even the slightest differences in system power can result in
different quote streams that in turn may produce different trading signals.
The reliability of quote delivery can be improved in the following four ways:
1. Time-stamping quotes immediately when each quote arrives before putting the
quote into the queue.
2. Increasing the size of the quote queue.
3. Increasing system memory to the largest size feasible given a cost/benefit analysis.
4. Reducing the number of securities for which the quotes are collected on any
given client.

Implementation of HFT Systems

282

These four steps toward establishing greater quote reliability are fairly easy to implement when the client application is designed and built from scratch, and in particular
when using the FIX protocol for quote delivery. However, many off-the shelf clients,
including those distributed by executing brokers, may be difficult or impossible to customize. For firms planning to use an off-the-shelf client, it may be prudent to ask the
software manufacturer how the preceding issues can be addressed in the client.
Duration of execution can make or break HFT models. Most
strategies for arbitraging temporary market mispricings, for example, depend on the
ability to get the orders posted with lightning speed.Whoever detects the mispricing
and gets his order posted on the exchange first is likely to generate the most profit.
Speed of execution is controlled by the following components of trading platforms:

Speed of Execution

■■

The speed of applications generating trading signals.

■■

The proximity of applications generating trading signals to the executing broker.

■■

The speed of the executing broker’s platform in routing execution requests.

■■

The proximity of the executing broker to the exchange.

■■

The speed of the exchange in processing the execution orders.

Figure 16.3 illustrates the time-dependent flow of execution process.
To enhance message security and to alleviate delays due to the physical transmission
of trading signals between clients and the broker or the exchange, clients dependent on
the speed of execution often choose to co-locate or house their servers in proximity
centers. Co-location and proximity hosting services typically employ systems administration staff that are capable of providing recovery services in case of systems or power
failure, making sure that the client applications work at least 99.999 percent of the time.
Co-location and proximity hosting are discussed in detail in Chapter 2 of the book.

Trading signal
generation

Order processing
and routing

(Buy-side Client)

(Executing
broker)

Factors
influencing speed:
•

Complexity
of trading
signals

•

Processing
power of
hardware

Order Execution
(Exchange)

Signal travel
speed

signal travel
distance

Factors
influencing speed:
•

Optimization
of routing
algorithms

•

Capacity to
process large
number of
orders in
parallel

signal travel
distance

Factors
influencing speed:
•

Optimization
of order
matching
algorithms

•

Capacity to
process large
number of
orders in
parallel

FIGURE 16.3 execution Process

■ Testing Trading Systems

■

Data set testing

■

Unit testing

■

System testing

■

Integration testing

■

Regression testing

■

Automation testing

Data Set testing
Data set testing refers to testing the validity of the data, whether historical data used
in a back-test or real-time data obtained from a streaming data provider. The objective of data testing is to ascertain that the system minimizes undesirable influences
and distortions in the data and to ensure that the run-time analysis and trading signal
generation work smoothly.
Data set testing is built on the premise that all data received for a particular security should fall into a statistical distribution that is consistent throughout time.
The data should also exhibit consistent distributional properties when sampled at

IMPleMeNTATIoN oF HFT SySTeMS

The costs of rolling out a system that contains programmatic errors, or bugs, can be
substantial. Thorough testing of the system, therefore, is essential prior to wide rollout of the model. Testing has the following stages:

283

d ifferent frequencies: one-minute data for USD/CAD, for example, should be consistent with historical one-minute data distribution for USD/CAD observed for the
past year. Naturally, data set testing should allow for distributions to change with
time, but the observed changes should not be drastic, unless they are caused by a
large-scale market disruption.
A popular procedure for testing data is based on testing for consistency of autocorrelations. It is implemented as follows:
1. A data set is sampled at a given frequency—say, 10-second intervals.
2. Autocorrelations are estimated for a moving window of 30 to 1,000 observations.
3. The obtained autocorrelations are then mapped into a distribution; outliers are
identified, and their origin is examined. The distributional properties can be
analyzed further to answer the following questions:
■■

■■

Have the properties of the distribution changed during the past month, quarter, or year?
Are these changes due to the version of the code or to the addition or removal
of programs on the production box?

The testing should be repeated at different sampling frequencies to ensure that no
systemic deviations occur.

Implementation of HFT Systems

284

Unit Testing
Unit testing verifies that each individual software component of the system works
properly. A unit is a testable part of an application; the definition of a unit can range
from the code for the lowest function or method to the functionality of a mediumlevel component—for example, a latency measurement component of the posttrade
analysis engine. Testing code in small blocks from the ground up ensures that any
errors are caught early in the integration process, avoiding expensive system disruptions at later stages.

Integration Testing
Integration testing follows unit testing. As its name implies, integration testing is a
test of the interoperability of code components; the test is administered to increasingly larger aggregates of code as the system is being built up from modular pieces
to its completed state. Testing modular interoperability once again ensures any that
code defects are caught and fixed early.

System Testing
System testing is a postintegration test of the system as a whole. The system testing
incorporates several testing processes described as follows.
Graphical user interface (GUI) software testing ensures that the human interface
of the system enables the user (e.g., the person responsible for monitoring trading

285
Implementation of HFT Systems

activity) to perform her tasks. GUI testing typically ensures that all the buttons and
displays that appear on screen are connected with the proper functionality according
to the specifications developed during the design phase of the development process.
Usability and performance testing is similar in nature to GUI testing but is not
limited to GUIs and may include such concerns as the speed of a particular functionality. For example, how long does the system take to process a “system shutdown”
request? Is the timing acceptable from a risk management perspective?
Stress testing is a critical component of the testing of high-frequency trading systems. A stress-testing process attempts to document and, subsequently, quantify the
impact of extreme hypothetical scenarios on the system’s performance. For example, how does the system react if the price of a particular security drops 10 percent
within a very short time? What if an act of God occurs that shuts down the exchange,
leaving the system holding its positions? What other worst-case scenarios are there,
and how will they affect the performance of the system and the subsequent P&L?
Security testing is another indispensable component of the testing process that
is often overlooked by organizations. Security testing is designed to identify possible security breaches and to either provide a software solution for overcoming
the breaches or create a breach-detection mechanism and a contingency plan in the
event a breach occurs. HFT systems can be vulnerable to security threats coming
from the Internet, where unscrupulous users may attempt to hijack account numbers, passwords, and other confidential information in an attempt to steal trading
capital. However, intraorganizational threats should not be underestimated; employees with malicious intent or disgruntled workers having improper access to the trading system can wreak considerable and costly havoc. All such possibilities must be
tested and taken into account.
Scalability testing refers to testing the capacity of the system. How many securities can the system profitably process at the same time without incurring significant
performance impact? The answer to this question may appear trivial, but the matter
is anything but trivial in reality. Every incremental security measure added to the
system requires an allocation of computer power and Internet bandwidth. A large
number of securities processed simultaneously on the same machine may considerably slow down system performance, distorting quotes, trading signals, and the P&L
as a result. A determination of the maximum permissible number of securities will
be based on the characteristics of each trading platform, including available computing power.
Reliability testing determines the probable rate of failure of the system. Reliability
testing seeks to answer the following questions: What are the conditions under
which the system fails? How often can we expect these conditions to occur? The
failure conditions may include unexpected system crashes, shutdowns due to insufficient memory space, and anything else that leads the system to stop operating. The failure rate for any well-designed high-frequency trading system should not
exceed 0.01 percent (i.e., the system should be guaranteed to remain operational
99.99 percent of time).
Recovery testing refers to verification that in an adverse event, whether an act of
God or a system crash, the documented recovery process ensures that the system’s

integrity is restored and it is operational within a prespecified time. The recovery
testing also ensures that data integrity is maintained through unexpected terminations of the system. Recovery testing should include the following scenarios: When
the application is running and the computer system is suddenly restarted, the application should have valid data upon restart. Similarly, the application should continue
operating normally if the network cable should be unexpectedly unplugged and then
plugged back in.

Use-Case Testing
The term use-case testing refers to the process of testing the system according to the
system performance guidelines defined during the design stage of the system development. In use-case testing, a dedicated tester follows the steps of using the system
and documents any discrepancies between the observed behavior and the behavior that is supposed to occur. Use-case testing ensures that the system is operating
within its parameters.
Use-case testing is typically performed by professional software testers, not the
programmers who coded the system. The deployment of testers is important for
several reasons:
■■

Implementation of HFT Systems

286

■■

Testers are trained to document discrepancies between a given scenario and actual
performance of the system module.
Testers are not emotionally involved in code development and are impartial to
found errors.
Testers’ labor is considerably less expensive than that of programmers, resulting
in savings for the organization.

Discrepancies or “bugs” reported by testers usually span three levels: critical,
moderate, and inconsequential. Critical bugs significantly impair intended system
performance and need to be addressed with the highest priority. Moderate bugs are
considerable issues and need to be addressed following the bugs in the critical functionality. Inconsequential bugs are more of a cosmetic variety and may not need to
be addressed until a downtime occurs within the ranks of coders.
■■ Summary
Implementation of high-frequency systems is a time-consuming process, in which
mistakes can be very costly. Outsourcing noncritical components of the system may
be a prudent strategy. Testing, however, is the paramount activity that has to be conducted according to best practices established for software development.

■■ End-of-Chapter Questions
1. What are the stages in development of high-frequency trading systems? What are
the stages in HFT implementation?
2. What is a back-test? What are the peculiarities of back-testing?
3. Suppose the back-testing system is placing a limit buy order at 125.13 when the
market price is 125.14. At what market price level can the researcher assume
that the limit order was executed?
4. Suppose a system produces a Sharpe ratio of 12 in the back-test. How much
paper-trading testing does this system need to ascertain its performance?
5. What methodologies can be deployed in data testing?
6. What is use-case testing? Why is it valuable?

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Implementation of HFT Systems

About the Author

Aldridge is an investment consultant, portfolio manager, a recognized expert on the subjects of quantitative investing and high-frequency trading, and a
seasoned educator. Aldridge is currently Industry Professor at New York University,
Department of Finance and Risk Engineering, Polytechnic Institute, as well as Managing Partner and Quantitative Portfolio Manager at ABLE Alpha Trading, LTD, an
investment consulting firm and a proprietary trading vehicle specializing in quantitative and high-frequency trading strategies. At ABLE Alpha, Aldridge designs, implements, and deploys proprietary trading strategies. As part of her duties, Aldridge
also advises broker-dealers, large hedge funds, government entities and trading venues (including exchanges and dark pools) on high-frequency research and optimal
high-frequency strategy design, implementation of trading systems, risk management and regulation of both high- and low-frequency operations. Aldridge is also a
founder of AbleMarkets.com, an online resource making the latest high-frequency
research for institutional investors and broker-dealers. Finally, Aldridge runs an HFT
training program for institutional market participants; the first-of-it-kind program
was developed and is continuously updated by Aldridge and has been well-received
by hundreds of industry professionals. The upcoming schedule of training sessions
worldwide is available at HFTtraining.com.
Prior to ABLE Alpha, Aldridge worked for various institutions on Wall Street
and in Toronto, including Goldman Sachs and CIBC. Over the years, Aldridge has
been called to contribute to numerous government regulatory panels, including the
U.K. Government Foresight Committee for Future of Computer Trading and the
U.S. Commodity Futures Trading Commission’s Subcommittee on High-Frequency
Trading.
Aldridge holds an MBA from INSEAD, an MS in financial engineering from
Columbia University, and a BE in electric engineering from the Cooper Union
in New York, and is presently in the process of completing her PhD at New York
University. Aldridge is a frequent speaker at top industry events and a contributor to
academic, practitioner and mainstream media publications, including the Journal of
rene

288

Trading, Futures Magazine, Reuters HedgeWorld, Advanced Trading, FXWeek, FINalternatives,
Dealing with Technology, and Huffington Post.
Aldridge often appears on major television networks, including BBC, CNBC,
FOX Business, CBC, BNN, German ZDF, and has been invited to discuss current
economic issues on National Public Radio (NPR) and Bloomberg radio. In addition,
Aldridge has been quoted by the New York Times, the Wall Street Journal, Associated
Press, Financial Times, Thomson/Reuters, Bloomberg LP, Forbes,The Daily Show with
Jon Stuart, and other major business news outlets.
Aldridge strongly believes into giving back to the community, and she presently
serves as treasurer at Carnegie Hill Neighbors, a not-for-profit organization charged
with continuous improvement of the jewel-like area in New York City.

289
About the Author

About the Web site

T
290

his book is accompanied by a web site, www.hftradingbook.com. The web site
supplements the materials in the book with teaching materials like PowerPoint
presentations, in-class project ideas, and related materials. The web site requires a
valid e-mail address to register. Once registered, subscribers also receive updates on
the latest activity in the HFT space.
To receive these free benefits, visit the book’s web site at www.hftradingbook
.com. When prompted for a password, please enter “high-frequency.”

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index

Administrative and legal costs, 125
Algorithms, 33–35
common elements of, 33
critical line–optimizing, 238–239
execution, 245–247
genetic, 241–242
order-routing, 247–258
maximize execution speed, 249–250
maximize trading size, 250–253
minimize execution costs, 248
minimize footprint, 250
obtain best price, 248
time-weighted average price (TWAP), 253–254
volume-weighted average price (VWAP), 254–257
sample market-making, 34
Algorithmic trading, 10–11
Alpha, 103–104
Alternative investments, 126
Arbitrage strategies, 16
Automated market-making strategies, 17
Average gain/loss, 102–103
Back-test, 278
Basis trading, 142–143
Bayesian approach, 241
Benchmarking. See Performance attribution
Beta, 103–104
Bid-ask spread, 59, 78
tightness of, 173
Bollinger bands, 8
Broker commissions, 76–77
Burke ratio, 107, 109
Calmar ratio, 107, 109
Cancel orders on system disconnect, 216
Capacity evaluation, 112–114
Capital asset pricing model (CAPM), 137
Central processing unit (CPU), 22–23
Cointegration, 143–144
Commodity Futures Trading Commission (CFTC), 210, 212
Commodity markets, event arbitration in, 162
Comparative ratios, 106–110
Complex orders, 44–45
Conditional Sharpe ratio, 107
Connectivity, cost of, 123
Convergence and divergence, market, 46

Core engine, 274–276
Correlation, 103
Counterparty risk, 226
Credit risk, 226
Cuban, Mark, 193
Custody and clearing, cost of, 125
Dark pools, 39, 46–47, 221–222
Data, costs of, 122–125
administrative and legal, 125
connectivity, 123
custody and clearing, 125
electronic execution, 124–125
hardware, 122–123
software, 123–124
staffing, 125
Data set testing, 283–284
“Direct access” to markets, 6
DirectEdge exchange, 211
Directional traders, 131
Directional trading around events, 147–163
event arbitrage, application of, 155–162
commodity markets, 162
emerging economies, 161–162
equity markets, 157–160
fixed-income markets, 160–161
foreign exchange markets, 156–157
futures markets, 161
real estate investment trusts (REITs), 162
events, 148–150
forecasting methodologies, 150–153
strategies, developing, 148
tradable news, 153–155
corporate, 153–154
industry, 154
macroeconomic, 154–155
Discrete pairwise (DPW) optimization, 239–241
Drawdown, 100–101
Electronic trading, 10, 34
cost of, 124–125
Emerging economies, event arbitration in, 161–162
Equities, 133–140
arbitraging different classes of same issuer,
135–136
fragmentation in, 46–50
large-to-small information spillovers, 139–140

303

Equities (continued )
liquidity arbitrage, 138–139
pairs trading, 134–135
risk arbitrage, 137–138
Equity markets, event arbitrage in, 157–160
Evaluation period, length of, 115–116
Event arbitrage, 9. See also Directional trading around events
Excess return on value at risk, 107
Exchange fees, 77
Execution
aggressive vs. passive, 43–44
process, 283
speed of, 282–283
Exponential market resiliency, 265–267

index

304

Field programmable gate array (FPGA), 22–25
Fill-or-kill orders, 45
Financial Industry Regulatory Authority (FINRA), 210
Financial Information eXchange (FIX) protocol, 27–29, 30, 46,
119, 212, 274–275
First-in-first-out (FIFO) execution schedule, 40–42, 113
Fixed income, fragmentation in, 51
Fixed-income markets, event arbitration in, 160–161
Foreign exchange, 140–141, 156–157
event arbitration in, 156–157
triangular arbitrage, 140
uncovered interest parity arbitrage, 141
Forex, fragmentation in, 51
Fournier analysis, 259–262
Front-running, 219–220
Fundamental analysis, 8–9
Futures
arbitrage, 143
fragmentation in, 50–51
Futures Industry Association (FIA), 210
Futures markets, event arbitration in, 161
Gambler’s Ruin Problem, 176–178
Geometric Brownian motion, 264–265
Graphics processing unit (GPU), 22–23
Hardware
cost of, 122–123
history of, 21–25
Hedging, 235–238
delta, 236–237
portfolio, 237–238
High-frequency data, 53–74
bid-ask bounce and, 59–61
buy-and-sell identifiers, lack of, 70–73
defined, 53–54
deviation from normality, 62
irregular spacing, 62, 65–70
properties of, 56
recording, 54–56
volume, 57
High-frequency trading (HFT)
capitalization of, 125–127
defined, 13–15
economics of, 122–125
costs of doing business, 122
costs of data, 122–125
event arbitrage, 9
as evolution of trading methodology, 7–13
financial markets suitable for, 121–122
key processes of, 117–121
leverage of, 126–129
number of traders, 17
participants in, 17–18, 129–130
competitors, 129
government, 130

investors, 129
service and technology providers, 130
risk management of. See Risk management
strategies, performance and capacity of, 97–116
alpha decay, 116
basic performance measures, 98–106
capacity evaluation, 112–114
comparative ratios, 106–110
evaluation period, length of, 115–116
measurement, principles of, 97–98
performance attribution, 110–112
systems, implementation of, 271–287
common pitfalls in, 280–284
model development life cycle, 271–273
key steps in, 273–279
testing trading systems, 283–286
High water mark, 101, 127
Hurst exponent, 221
Iceberg orders, 44–45
Ignition, 200–201
Integration testing, 284
Interactive Brokers, 5, 77
International Organization of Securities Commissions
(IOSCO), 210
Internet communication models, common, 31
Interval price limits (IPLs), 215–216
Investor protection, 219–221
front-running, 219–220
intentional market manipulation, detecting, 219
market crashes, predicting, 220–221
based on abnormal trading patterns, 220
based on asymmetry of liquitidy in limit order books, 220
Jensen’s alpha, 106, 108, 109
Kappa 3, 107
Kill switches, 217–218
Knight Capital Group, 214
Kurtosis, 104–106
Kyle’s lambda, 175–176, 243–244
Latency arbitrage, 196–197
strategies, 16
Latency costs, 78–89
Law of One Price, 132, 141, 196–197
Layering, 32, 200
Lee-Ready rule, 72
Legal entity identifiers (LEIs), 218–219
Limit order books, 39–43
Linear market resiliency, 268–269
Liquidity, 39, 126
Liquidity arbitrage, 138–139
Liquidity risk, 243–244
“Lit” pools, 221–222
Low-latency trading, 34
Lower partial moments (LPMs), 110
Machine learning, 207–208
Market crashes, predicting, 220–221
based on abnormal trading patterns, 220
based on asymmetry of liquidity in limit order books, 220
Market impact (MI)
costs, 81–82
estimation of, 85–88
minimizing, 245–270
advanced models, 262–269
basic models, issues with, 258–262
execution algorithms, 245–247
optimal execution strategies, practical implementation
of, 269
order-routing algorithms, 247–258

modern vs. past, 1–19
financial landscape of the 1970s, 3, 4
HFT as evolution of trading methodology, 7–13
HFT participants, 17–18
media, modern markets, and HFT, 6–7
number of high-frequency traders, 17
Markov state dependency, 230
Maximum quantity limits, 217
Merrill Lynch, 5
Message acknowledgment loops, 280
Message throttle limits, 216–217
Messaging, 25–33
core architecture, 29–30
network throughput, 32–33
protocols, 26–29
Financial Information eXchange (FIX), 27–29, 30
User Datagram Protocol (UDP), 26, 30
Transmission Control Protocol/Internet Protocol
(TCP/IP), 27–28, 30
speed and security, 30–32
Modified Sharpe ratio, 108
Moving average convergence divergence
(MACD), 8
National Best Bid and Offer (NBBO) rule, 46–47
New York Stock Exchange (NYSE), 38–39
No-cancel range, 216
Omega, 107, 110
Opportunity costs, 81
Options, fragmentation in, 51
Order flow, modeling information in
182–192
autocorrelation of order flow as predictor of market
movement, 182–186
evolution of tick data as predictor of market movement,
190–192
adverse selection components of bid-ask spread,
191–192
effective bid-ask spread, 191
information-based impact, 191
quoted bid-ask spread, 190–191
order aggressiveness as predictor of market movement,
186–188
shape of order book as predictor of market movement,
188–190
Pairs trading, 8, 134–135
Paper trading, 279
Parametric bootstrapping, 234–235
Performance attribution, 110–112
Performance measures, basic, 98–106
alpha and beta, 103–104
average gain/loss, 102–103
correlation, 103
drawdown, 100–101
return, 98–99
skewness and kurtosis, 104–106
volatility, 99–100
win ratio, 101–102
Phishing, 201
Pinging, 201
Post-trade analytics, 277
Power-law market resiliency, 268
Prehedging, 10
Price appreciation and timing risk costs, 81
Price reasonability, 217
Price-time priority execution, 40–42
Production, 279
Protection points, 216
Pump-and-dump, 202–207

305
index

permanent, empirical estimation of, 88–96
basic estimation model, 89–96
data preparation, 88–89
Market makers, 132
Market making, automated, 165–193
data, information in, 179–182
market does not move, 180
market moves and rebounds, 180–181
quotes widen, 182
trade moves markets, 181–182
modeling information in order flow, 182–192
autocorrelation of order flow as predictor of market
movement, 182–186
evolution of tick data as predictor of market movement,
190–192
order aggressiveness as predictor of market movement,
186–188
shape of order book as predictor of market movement,
188–190
key principles, 167
naïve strategies, 168–173
fixed offset, 168–169
order-arrival rate, offset as function of, 169–172
trend-dependent offset, 172
volatility-dependent offset, 169
profitable, 176–178
as a service, 173
bid-ask spread, tightness of, 173
block transactions, price sensitivity to, 174–175
market depth at best bid and best ask, 173–174
market resilience, 176
order book, shape of, 174
order-flow imbalance, price sensitivity to, 175
price change per unit volume, 175
technical support and resistance levels, 176
strategy, simulating, 167–168
Market manipulation, detecting, 219
Market orders, 54
Market risk, 227–242
critical line–optimizing algorithm, 238–239
discrete pairwise (DPW) optimization, 239–241
genetic algorithms, 241–242
hedging, 235–238
delta, 236–237
portfolio, 237–238
nonlinear programming, 238
simultaneous equations, 238
stop losses, 227–228
determining parameters, 227–228
value-at-risk (VaR), 230–235
volatility cutouts, 228–230
determining, 229
ex-ante, 229–230
Market structure, 221–222
“lit” and “dark” pools, 221–222
swap execution facilities, 221
Markets
microstructure of, 37–52
aggressive vs. passive execution, 43–44
complex orders, 44–45
equities, fragmentation in, 46–50
forex, fragmentation in, 51
fixed income, fragmentation in, 51
futures, fragmentation in, 50–51
limit order books, 39–43
market convergence and divergence, 46
options, fragmentation in, 51
swaps, fragmentation in, 51
trading hours, 45
types of markets, 37–39

Quote archival, 276
Quote matching, 199–200
Quote stuffing, 201–202
Real estate investment trusts (REITs), event arbitrage in, 162
Real-time position validation, 217
Rebate capture, 198–199
Rebates, 47–48
Regulation, 209–223
global key initiatives, 209
efficient trade matching, 221
investor protection, 219–221
jurisdiction, 209–213
market structure, 221–222
stability of systems, 213–219
Return, 98–99
Risk arbitrage, 137–138
Risk management, 225–244
measuring HFT risk, 225–244
credit and counterparty, 226
market, 227–242
liquidity, 243–244
regulatory and legal, 226

index

306

Securities and Exchange Commission (SEC), 210, 212
Securities Information Processor (SIP), 58
Sharpe ratio, 106, 108–110, 115, 127–129, 239–240
conditional, 107
modified, 108
Simulation, 277–279
back-test, 278
paper trading, 279
production, 279
Simultaneous equations framework,
Skewness and kurtosis, 104–106
Slippage or latency costs, 78–89
Sniffing, 201
Sniping, 201
Software, cost of, 123–124
Sortino ratio, 107, 110
Spaghetti Principle of Modeling, 16
Spoofing, 202
Spread scalping, 197–198
Staffing, cost of, 125
Statistical arbitrage, 16, 131–145
models, 16
practical applications of, 133–144
cross-asset, 142–144
equities, 133–140
foreign exchange, 140–141
general considerations, 133
indices and ETFs, 141–142
options, 142
Sterling ratio, 107, 109
Stop losses, 227–228
determining parameters, 227–228
Supervision, human, 279
Surveillance measures, near-term, 217–219
kill switches, 217–218
legal entity identifiers (LEIs), 218–219
Swap execution facilities, 221
Swaps, fragmentation in, 51
System testing, 284–286
graphical user interface (GUI) software, 284–285
recovery, 285–286
reliability, 285

scalability, 285
security, 285
stress, 285
usability and performance, 285
Systematic trading, 9–10, 34
Taxes, 77–78
Technical analysis, 8
Technological innovations, 21–35
hardware, history of, 21–25
messaging, 25–33
core architecture, 29–30
network throughput, 32–33
protocols, 26–29
speed and security, 30–32
software, 33
Tick data. See High-frequency data
Tick rule, 71
Time distortion, 280–282
Time-weighted average price (TWAP),
253–254, 258–262
Trade matching, efficient, 221
Trading costs, 75–96
background and definitions, 82–85
execution costs, overview of, 75–76
implicit execution costs, 78–82
bid-ask spreads, 78
market impact costs, 81–82
opportunity costs, 81
price appreciation and timing risk costs, 81
slippage or latency costs, 78–89
market impact, estimation of, 85–88
permanent market impact, empirical estimation of, 88–96
basic estimation model, 89–96
data preparation, 88–89
transparent execution costs, 76–78
broker commissions, 76–77
exchange fees, 77
taxes, 77–78
Trading hours, 45
Trading systems, testing, 283–286
data set testing, 283–284
integration testing, 284
system testing, 284–286
unit testing, 284
use-case testing, 286
Transmission Control Protocol/Internet Protocol (TCP/IP),
27–28, 30
Treynor ratio, 106, 108, 109
Triangular arbitrage, 140
Uncovered interest parity arbitrage, 141
Unit testing, 284
Upside Potential ratio, 107, 110
Use-case testing, 286
User Datagram Protocol (UDP), 26, 30, 276
Value-at-risk (VaR), 110, 230–235
Volatility, 99–100
Volatility cutouts, 228–230
determining, 229
ex-ante, 229–230
Volume-weighted average price (VWAP),
254–257, 258–262
Wash trades, 221
Win ratio, 101–102

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