Wiley Finance : Inside The Black Box A Simple Guide To Quantitative And High Frequency Trading (2nd Edition) Rishi K. Narang

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Additional Praise for Inside the Black Box
“Rishi presents a thorough overview of quant trading in an easy-to-read
format, free of much of the hype and hysteria that has recently surrounded
computerized trading. The book clearly categorizes the different types of
strategies, explaining in plain English the basic ideas behind how and when
they work. Most importantly, it dispels the popular notion that all quants
are the same, exposing the diversity of the types of skills and thinking that
are involved in quant trading and related disciplines. An excellent read for
anyone who wants to understand what the field is all about.”
—Shakil Ahmed, PhD, Global Head of Market Making, Citi Equities
“To look at the man, you would never know that Rishi could write so clearly and effectively about something as complex as quantitative trading and
investment. But he does and does it brilliantly. And, even if you already own
the first edition, you should buy this one, too. The new material on high
speed trading is worth the price of admission, and you will have a chance,
especially in Chapter 16, to see Rishi at his incisive and high spirited best. If
you don’t laugh out loud, you have no soul.”
—Galen Burghardt, Director of Research, Newedge
“Quant managers will find their meetings with investors to be smoother if
the investors have read this book. And even more so if the manager him or
herself has read and understood it.”
—David DeMers, Portfolio Manager, SAC Capital Advisors, LP
“In this second edition of Inside the Black Box Rishi highlights role of quant
trading in recent financial crises with clear language and without using any
complex equations. In chapter 11 he addresses common quant myths. He
leads us effortlessly through the quant trading processes and makes it very
easy to comprehend, as he himself is a quant trader.”
—Pankaj N. Patel, Global Head of Quantitative Equity Research,
Credit Suisse

Inside the
Black Box

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Inside the
Black Box
A Simple Guide to Quantitative
and High-Frequency Trading
Second Edition

Rishi K Narang

John Wiley & Sons, Inc.

Cover image: © Istock Photo/Maddrat.
Cover design: Paul McCarthy.
Copyright © 2013 by Rishi K Narang. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
First edition published by John Wiley & Sons, Inc. in 2009.
Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data:
Narang, Rishi K, 1974Inside the black box : a simple guide to quantitative
and high-frequency trading/Rishi K. Narang. — Second edition.
pages cm. — (Wiley finance series)
Includes bibliographical references and index.
ISBN 978-1-118-36241-9 (cloth); ISBN 978-1-118-42059-1 (ebk);
ISBN 978-1-118-58797-3 (ebk); ISBN 978-1-118-41699-0 (ebk)
1. Portfolio management—Mathematical models. 2. Investment analysis—
Mathematical models. 3. Stocks—Mathematical models. I. Title.
HG4529.5.N37 2013
332.64’2—dc23
2012047248
Printed in the United States of America.
10 9 8 7 6 5 4 3 2 1

This edition is dedicated to my son, Solomon K Narang,
whose unbridled curiosity I hope will be with him always.

Contents

Preface to the Second Edition

xiii

Acknowledgments

xvii

Part ONE

The Quant Universe
Chapter 1
Why Does Quant Trading Matter?

The Benefit of Deep Thought
The Measurement and Mismeasurement of Risk
Disciplined Implementation
Summary
Notes

Chapter 2
An Introduction to Quantitative Trading

What Is a Quant?
What Is the Typical Structure of a Quantitative Trading System?
Summary
Notes

8
9
10
11
11

14
16
19
20

Part two

Inside the Black Box
Chapter 3
Alpha Models: How Quants Make Money

Types of Alpha Models: Theory-Driven and Data-Driven
Theory-Driven Alpha Models
Data-Driven Alpha Models
Implementing the Strategies

24
26
42
45

Contents

Blending Alpha Models
Summary
Notes

Chapter 4
Risk Models

Limiting the Amount of Risk
Limiting the Types of Risk
Summary
Notes

Chapter 5
Transaction Cost Models

Defining Transaction Costs
Types of Transaction Cost Models
Summary
Note

Chapter 6
Portfolio Construction Models

Rule-Based Portfolio Construction Models
Portfolio Optimizers
Output of Portfolio Construction Models
How Quants Choose a Portfolio Construction Model
Summary
Notes

Chapter 7
Execution

Order Execution Algorithms
Trading Infrastructure
Summary
Notes

Chapter 8
Data

The Importance of Data
Types of Data
Sources of Data
Cleaning Data
Storing Data
Summary
Notes

56
62
64

69
72
76
78

80
85
90
91

94
98
112
113
113
115

117

119
128
130
131

133

133
135
137
139
144
145
146

Contents

Chapter 9
Research

Blueprint for Research: The Scientific Method
Idea Generation
Testing
Summary
Note

147

147
149
151
170
171

Part three

A Practical Guide for Investors in Quantitative Strategies
Chapter 10
Risks Inherent to Quant Strategies

Model Risk
Regime Change Risk
Exogenous Shock Risk
Contagion, or Common Investor, Risk
How Quants Monitor Risk
Summary
Notes

Chapter 11
Criticisms of Quant Trading

Trading Is an Art, Not a Science
Quants Cause More Market Volatility by Underestimating Risk
Quants Cannot Handle Unusual Events or Rapid
Changes in Market Conditions
Quants Are All the Same
Only a Few Large Quants Can Thrive in the Long Run
Quants Are Guilty of Data Mining
Summary
Notes

Chapter 12
Evaluating Quants and Quant Strategies

Gathering Information
Evaluating a Quantitative Trading Strategy
Evaluating the Acumen of Quantitative Traders
The Edge
Evaluating Integrity
How Quants Fit into a Portfolio
Summary
Note

175

176
180
184
186
193
195
195

197

197
199
204
206
207
210
213
213

215

216
218
221
223
227
229
231
233

xii

Contents

Part four

High-Speed and High-Frequency Trading
Chapter 13
An Introduction to High-Speed and High-Frequency Trading*
Notes

Chapter 14
High-Speed Trading

Why Speed Matters
Sources of Latency
Summary
Notes

Chapter 15
High-Frequency Trading

Contractual Market Making
Noncontractual Market Making
Arbitrage
Fast Alpha
HFT Risk Management and Portfolio Construction
Summary
Note

Chapter 16
Controversy Regarding High-Frequency Trading

Does HFT Create Unfair Competition?
Does HFT Lead to Front-Running or Market Manipulation?
Does HFT Lead to Greater Volatility or Structural Instability?
Does HFT Lack Social Value?
Regulatory Considerations
Summary
Notes

237

241

243

244
252
262
263

265

265
269
271
273
274
277
277

279

280
283
289
296
297
299
300

Chapter 17
Looking to the Future of Quant Trading

303

About the Author

307

Index

309

Preface to the Second Edition

History is a relentless master. It has no present, only the past
rushing into the future. To try to hold fast is to be swept aside.
—John F. Kennedy

ithin the investment management business, a wildly misunderstood
niche is booming, surely but in relative obscurity. This niche is populated by some of the brightest people ever to work in the field, and they are
working to tackle some of the most interesting and challenging problems in
modern finance. This niche is known by several names: quantitative trading,
systematic trading, or black box trading. As in almost every field, technology is revolutionizing the way things are being done, and very rarely, also
what is being done. And, as is true of revolutions generally (in particular,
scientific ones), not everyone understands or likes what’s happening.
I mentioned above that this is a technological revolution, which may
have struck you as being strange, considering we’re talking about quant
trading here. But the reality is that the difference between quant traders and
discretionary ones is precisely a technological one. Make no mistake: Being
good at investing almost always involves some math, whether it’s a fundamental analyst building a model of a company’s revenues, costs, and resulting profits or losses, or computing a price‐to‐earnings ratio. Graham and
Dodd’s Security Analysis has a whole chapter regarding financial statement
analysis, and that bible of fundamental value investing has more formulae
in it than this book.
Just as in any other application where doing things in a disciplined,
repeatable, consistent way is useful—whether it’s in building cars or flying
airplanes—investing can be systematized. It should be systematized. And
quant traders have gone some distance down the road of systematizing it.
Car building is still car building, whether it’s human hands turning ratchets
or machines doing it. Flying a plane is not viewed differently when a human
pilot does the work than when an autopilot does the work. In other words,
the same work is being done, it’s just being done in a different way. This is a
technological difference, at its heart.

xiii

xiv

Preface to the Second Edition

If I say, “I’d like to own cheap stocks,” I could, theoretically, hand‐
compute every company’s price‐to‐earnings ratio, manually search for the
cheapest ones, and manually go to the marketplace to buy them. Or I could
write a computer program that scans a database that has all of those price‐
to‐earnings ratios loaded into it, finds all the ones that I defined up‐front as
being cheap, and then goes out and buys those stocks at the market using
trading algorithms. The how part of the work is quite different in one case
from the other. But the stocks I own at the end of it are identical, and for
identical reasons.
So, if what we’re talking about here is a completely rational evolution
in how we’re doing a specific kind of work, and if we’re not being unreasonably technophobic, then why is it that reporters, politicians, the general public, and even many industry professionals really dislike quant trading? There
are two reasons. One is that, in some cases, the dislike comes from people
whose jobs are being replaced by technology. For example, it is very obvious
that many of the most active opponents of high‐frequency trading are primarily fighting not out of some altruistic commitment to the purest embodiment of a capitalist marketplace (though that would be so terrifically ironic
that I’d love if it were true), but because their livelihood is threatened by a
superior way of doing things. This is understandable, and fair enough. But
it’s not good for the marketplace if those voices win out, because ultimately
they are advocating stagnancy. There’s a reason that the word Luddite has
a negative connotation.
A second reason, far more common in my experience, is that people
don’t understand quant trading, and what we don’t understand, we tend
to fear and dislike. This book is aimed at improving the understanding of
quant trading of various types of participants in the investment management industry. Quants are themselves often guilty of exacerbating the problem by being unnecessarily cagey about even the broadest descriptions of
their activities. This only breeds mistrust in the general community, and it
turns out not to be necessary in the least.
This book takes you on a tour through the black box, inside and out.
It sheds light on the work that quants do, lifting the veil of mystery that
surrounds quantitative trading, and allowing those interested in doing so to
evaluate quants and their strategies.
The first thing that should be made clear is that people, not machines,
are responsible for most of the interesting aspects of quantitative trading.
Quantitative trading can be defined as the systematic implementation of
trading strategies that human beings create through rigorous research. In
this context, systematic is defined as a disciplined, methodical, and automated approach. Despite this talk of automation and systematization, people conduct the research and decide what the strategies will be, people select

Preface to the Second Edition

the universe of securities for the system to trade, and people choose what
data to procure and how to clean those data for use in a systematic context,
among a great many other things. These people, the ones behind quant trading strategies, are commonly referred to as quants or quant traders.
Quants employ the scientific method in their research. Though this research is aided by technology and involves mathematics and formulae, the
research process is thoroughly dependent on human decision making. In
fact, human decisions pervade nearly every aspect of the design, implementation, and monitoring of quant trading strategies. As I’ve indicated already,
quant strategies and traditional discretionary investment strategies, which
rely on human decision makers to manage portfolios day to day, are rather
similar in what they do.
The differences between a quant strategy and a discretionary strategy
can be seen in how the strategy is created and in how it is implemented. By
carefully researching their strategies, quants are able to assess their ideas
in the same way that scientists test theories. Furthermore, by utilizing a
computerized, systematic implementation, quants eliminate the arbitrariness that pervades so many discretionary trading strategies. In essence,
decisions driven by emotion, indiscipline, passion, greed, and fear—what
many consider the key pratfalls of playing the market—are eliminated
from the quant’s investment process. They are replaced by an analytical
and systematic approach that borrows from the lessons learned in so many
other fields: If something needs to be done repeatedly and with a great deal
of discipline, computers will virtually always outshine humans. We simply
aren’t cut out for repetition in the way that computers are, and there’s
nothing wrong with that. Computers, after all, aren’t cut out for creativity
the way we are; without humans telling computers what to do, computers wouldn’t do much of anything. The differences in how a strategy is
designed and implemented play a large part in the consistent, favorable
risk/reward profile a well‐run quant strategy enjoys relative to most discretionary strategies.
To clarify the scope of this book, it is important to note that I focus on
alpha‐oriented strategies and largely ignore quantitative index traders or
other implementations of beta strategies. Alpha strategies attempt to generate returns by skillfully timing the selection and/or sizing of various portfolio holdings; beta strategies mimic or slightly improve on the performance
of an index, such as the S&P 500. Though quantitative index fund management is a large industry, it requires little explanation. Neither do I spend
much time on the field of financial engineering, which typically plays a role
in creating or managing new financial products such as collateralized debt
obligations (CDOs). Nor do I address quantitative analysis, which typically
supports discretionary investment decisions. Both of these are interesting

xvi

Preface to the Second Edition

subjects, but they are so different from quant trading as to be deserving of
their own, separate discussions carried out by experts in those fields.
This book is divided into four parts. Part One (Chapters 1 and 2) provides a general but useful background on quantitative trading. Part Two
(Chapters 3 through 9) details the contents of the black box. Part Three
(Chapters 10 through 12) is an introduction to high‐frequency trading, the
infrastructure that supports such high‐speed trading, and some truths and
myths regarding this controversial activity. Part Four (Chapters 13 through
16) provides an analysis of quant trading and techniques that may be useful in assessing quant traders and their strategies. Finally, Chapter 17 looks
at the present and future of quant trading and its place in the investment
world.
It is my aspiration to explain quant trading in an intuitive manner. I
describe what quants do and how they do it by drawing on the economic
rationale for their strategies and the theoretical basis for their techniques.
Equations are avoided, and the use of jargon is limited and explained, when
required at all. My aim is to demonstrate that what many call a black box
is in fact transparent, intuitively sensible, and readily understandable. I also
explore the lessons that can be learned from quant trading about investing
in general and how to evaluate quant trading strategies and their practitioners. As a result, Inside the Black Box may be useful for a variety of participants in and commentators on the capital markets. For portfolio managers,
analysts, and traders, whether quantitative or discretionary, this book will
help contextualize what quants do, how they do it, and why. For investors,
the financial media, regulators, or anyone with a reasonable knowledge of
capital markets in general, this book will engender a deeper understanding
of this niche.
Rishi K Narang

Acknowledgments

am indebted to Manoj Narang, my brother, for his help with Part IV of
this book, and to Mani Mahjouri for all of his suggestions and help. Mike
Beller’s and Dmitry Sarkisov’s help with the micro‐bursting information
was both enlightening and very much appreciated. My colleagues at T2AM,
Myong Han, Yimin Guo, Huang Pan, and Julie Wilson, read through various portions of this text and offered many valuable suggestions. This book
would not be readable without the untiring editing of Arzhang Kamarei,
who edited the first edition.
I must acknowledge the help of the rest of my partners at T2AM: Eric
Cressman, John Cutsinger, and Elizabeth Castro.
For their help getting some metrics on the quant trading universe, I’d
like to thank Chris Kennedy and Ryan Duncan of Newedge, Sang Lee of the
Aite Group, and the Barclay Group. Underlying data, where necessary, were
downloaded from Yahoo! Finance or Bloomberg, unless otherwise noted.
Since ItBB came out in 2009, I have been grateful for the support
shown to me and the book by Newedge (especially Keith Johnson, Leslie
Richman, Brian Walls, Galen Burghardt, and Isabelle Lixi), Bank of America
Merrill Lynch (especially Michael Lynch, Lisa Conde, Tim Cox, and Omer
Corluhan), Morgan Stanley (especially Michael Meade), and the CME
Group (especially Kelly Brown).
For the second edition, I thank Philip Palmedo, Brent Boyer, Aaron
Brown, and Werner Krebs for their constructive criticisms, which resulted
in various improvements. Thanks also to Pankaj Patel, Dave DeMers, John
Burnell, John Fidler, and Camille Hayek for their help with various bits of
new content.

xvii

Part

One
The Quant Universe

Chapter

Why Does Quant
Trading Matter?
Look into their minds, at what wise men do and don’t.
—Marcus Aurelius, Meditations

ohn is a quant trader running a midsized hedge fund. He completed an
undergraduate degree in mathematics and computer science at a top
school in the early 1990s. John immediately started working on Wall Street
trading desks, eager to capitalize on his quantitative background. After
seven years on the Street in various quant‐oriented roles, John decided to
start his own hedge fund. With partners handling business and operations,
John was able to create a quant strategy that recently was trading over
$1.5 billion per day in equity volume. More relevant to his investors, the
strategy made money on 60 percent of days and 85 percent of months—a
rather impressive accomplishment.
Despite trading billions of dollars of stock every day, there is no shouting at John’s hedge fund, no orders being given over the phone, and no
drama in the air; in fact, the only sign that there is any trading going on
at all is the large flat‐screen television in John’s office that shows the strategy’s performance throughout the day and its trading volume. John can’t
give you a fantastically interesting story about why his strategy is long this
stock or short that one. While he is monitoring his universe of thousands
of stocks for events that might require intervention, for the most part he
lets the automated trading strategy do the hard work. What John monitors quite carefully, however, is the health of his strategy and the market
environment’s impact on it. He is aggressive about conducting research
on an ongoing basis to adjust his models for changes in the market that
would impact him.

The Quant Universe

Across from John sits Mark, a recently hired partner of the fund who
is researching high‐frequency trading. Unlike the firm’s first strategy, which
only makes money on 6 out of 10 days, the high‐frequency efforts Mark
and John are working on target a much more ambitious task: looking for
smaller opportunities that can make money every day. Mark’s first attempt
at high‐frequency strategies already makes money nearly 95 percent of the
time. In fact, their target for this high‐frequency business is even loftier:
They want to replicate the success of those firms whose trading strategies
make money every hour, maybe even every minute, of every day. Such high‐
frequency strategies can’t accommodate large investments, because the opportunities they find are small, fleeting. The technology required to support such an endeavor is also incredibly expensive, not just to build, but to
maintain. Nonetheless, they are highly attractive for whatever capital they
can accommodate. Within their high‐frequency trading business, John and
Mark expect their strategy to generate returns of about 200 percent a year,
possibly much more.
There are many relatively small quant trading boutiques that go about
their business quietly, as John and Mark’s firm does, but that have demonstrated top‐notch results over reasonably long periods. For example, Quantitative Investment Management of Charlottesville, Virginia, averaged over
20 percent per year for the 2002–2008 period—a track record that many
discretionary managers would envy.1
On the opposite end of the spectrum from these small quant shops
are the giants of quant investing, with which many investors are already
quite familiar. Of the many impressive and successful quantitative firms
in this category, the one widely regarded as the best is Renaissance Technologies. Renaissance, the most famous of all quant funds, is famed for its
35 percent average yearly returns (after exceptionally high fees), with extremely low risk, since 1990. In 2008, a year in which many hedge funds
struggled mightily, Renaissance’s flagship Medallion Fund gained approximately 80 percent.2 I am personally familiar with the fund’s track record,
and it’s actually gotten better as time has passed—despite the increased
competition and potential for models to stop working.
Not all quants are successful, however. It seems that once every decade
or so, quant traders cause—or at least are perceived to cause—markets to
move dramatically because of their failures. The most famous case by far
is, of course, Long Term Capital Management (LTCM), which nearly (but
for the intervention of Federal Reserve banking officials and a consortium
of Wall Street banks) brought the financial world to its knees. Although the
world markets survived, LTCM itself was not as lucky. The firm, which averaged 30 percent returns after fees for four years, lost nearly 100 percent of
its capital in the debacle of August–October 1998 and left many investors

Why Does Quant Trading Matter?

both skeptical and afraid of quant traders. Never mind that it is debatable
whether this was a quant trading failure or a failure of human judgment
in risk management, nor that it’s questionable whether LTCM was even a
quant trading firm at all. It was staffed by PhDs and Nobel Prize–winning
economists, and that was enough to cast it as a quant trading outfit, and to
make all quants guilty by association.
Not only have quants been widely panned because of LTCM, but they
have also been blamed (probably unfairly) for the crash of 1987 and (quite
fairly) for the eponymous quant liquidation of 2007, the latter having severely impacted many quant shops. Even some of the largest names in quant
trading suffered through the quant liquidation of August 2007. For instance,
Goldman Sachs’ largely quantitative Global Alpha Fund was down an estimated 40 percent in 2007 after posting a 6 percent loss in 2006.3 In less
than a week during August 2007, many quant traders lost between 10 and
40 percent in a few days, though some of them rebounded strongly for the
remainder of the month.
In a recent best‐selling nonfiction book, a former Wall Street Journal
reporter even attempted to blame quant trading for the massive financial
crisis that came to a head in 2008. There were gaps in his logic large enough
to drive an 18‐wheeler through, but the popular perception of quants has
never been positive. And this is all before high‐frequency trading (HFT)
came into the public consciousness in 2010, after the Flash Crash on May
10 of that year. Ever since then, various corners of the investment and trading world have tried very hard to assert that quants (this time, in the form
of HFTs) are responsible for increased market volatility, instability in the
capital markets, market manipulation, front‐running, and many other evils.
We will look into HFT and the claims leveled against it in greater detail in
Chapter 16, but any quick search of the Internet will confirm that quant
trading and HFT have left the near‐total obscurity they enjoyed for decades
and entered the mainstream’s thoughts on a regular basis.
Leaving aside the spectacular successes and failures of quant trading, and
all of the ills for which quant trading is blamed by some, there is no doubt
that quants cast an enormous shadow on the capital markets virtually every
trading day. Across U.S. equity markets, a significant, and rapidly growing,
proportion of all trading is done through algorithmic execution, one footprint
of quant strategies. (Algorithmic execution is the use of computer software
to manage and work an investor’s buy and sell orders in electronic markets.)
Although this automated execution technology is not the exclusive domain
of quant strategies—any trade that needs to be done, whether by an index
fund or a discretionary macro trader, can be worked using execution algorithms—certainly a substantial portion of all algorithmic trades are done by
quants. Furthermore, quants were both the inventors and primary innovators

The Quant Universe

of algorithmic trading engines. A mere five such quant traders account for
about 1 billion shares of volume per day, in aggregate, in the United States
alone. It is worth noting that not one of these is well known to the broader
investing public, even now, after all the press surrounding high-frequency
trading. The TABB Group, a research and advisory firm focused exclusively
on the capital markets, estimates that, in 2008, approximately 58 percent
of all buy‐side orders were algorithmically traded. TABB also estimates that
this figure has grown some 37 percent per year, compounded, since 2005.
More directly, the Aite Group published a study in early 2009 indicating that
more than 60 percent of all U.S. equity transactions are attributable to short‐
term quant traders.4 These statistics hold true in non‐U.S. markets as well.
Black‐box trading accounted for 45 percent of the volume on the European
Xetra electronic order‐matching system in the first quarter of 2008, which is
36 percent more than it represented a year earlier.5
The large presence of quants is not limited to equities. In futures and
foreign exchange markets, the domain of commodity trading advisors
(CTAs), quants pervade the marketplace. Newedge Alternative Investment
Solutions and Barclay Hedge used a combined database to estimate that
almost 90 percent of the assets under management among all CTAs are
managed by systematic trading firms as of August 2012. Although a great
many of the largest and most established CTAs (and hedge funds generally)
do not report their assets under management or performance statistics to
any database, a substantial portion of these firms are actually quants also,
and it is likely that the real figure is still over 75 percent. As of August 2012,
Newedge estimates that the amount of quantitative futures money under
management was $282.3 billion.
It is clear that the magnitude of quant trading among hedge funds is
substantial. Hedge funds are private investment pools that are accessible
only to sophisticated, wealthy individual or institutional clients. They can
pursue virtually any investment mandate one can dream up, and they are
allowed to keep a portion of the profits they generate for their clients. But
this is only one of several arenas in which quant trading is widespread. Proprietary trading desks at the various banks, boutique proprietary trading
firms, and various multistrategy hedge fund managers who utilize quantitative trading for a portion of their overall business each contribute to a much
larger estimate of the size of the quant trading universe.
With such size and extremes of success and failure, it is not surprising
that quants take their share of headlines in the financial press. And though
most press coverage of quants seems to be markedly negative, this is not
always the case. In fact, not only have many quant funds been praised for
their steady returns (a hallmark of their disciplined implementation process), but some experts have even argued that the existence of successful

Why Does Quant Trading Matter?

quant strategies improves the marketplace for all investors, regardless of
their style. For instance, Reto Francioni (chief executive of Deutsche Boerse
AG, which runs the Frankfurt Stock Exchange) said in a speech that algorithmic trading “benefits all market participants through positive effects on
liquidity.” Francioni went on to reference a recent academic study showing “a positive causal relationship between algo trading and liquidity.”6 Indeed, this is almost guaranteed to be true. Quant traders, using execution
algorithms (hence, algo trading), typically slice their orders into many small
pieces to improve both the cost and efficiency of the execution process. As
mentioned before, although originally developed by quant funds, these algorithms have been adopted by the broader investment community. By placing
many small orders, other investors who might have different views or needs
can also get their own executions improved.
Quants typically make markets more efficient for other participants by
providing liquidity when other traders’ needs cause a temporary imbalance
in the supply and demand for a security. These imbalances are known as
inefficiencies, after the economic concept of efficient markets. True inefficiencies (such as an index’s price being different from the weighted basket
of the constituents of the same index) represent rare, fleeting opportunities
for riskless profit. But riskless profit, or arbitrage, is not the only—or even
primary—way in which quants improve efficiency. The main inefficiencies
quants eliminate (and, thereby, profit from) are not absolute and unassailable, but rather are probabilistic and require risk taking.
A classic example of this is a strategy called statistical arbitrage, and
a classic statistical arbitrage example is a pairs trade. Imagine two stocks
with similar market capitalizations from the same industry and with similar
business models and financial status. For whatever reason, Company A is
included in a major market index, an index that many large index funds
are tracking. Meanwhile, Company B is not included in any major index.
It is likely that Company A’s stock will subsequently outperform shares of
Company B simply due to a greater demand for the shares of Company A
from index funds, which are compelled to buy this new constituent in order to track the index. This outperformance will in turn cause a higher P/E
multiple on Company A than on Company B, which is a subtle kind of inefficiency. After all, nothing in the fundamentals has changed—only the nature of supply and demand for the common shares. Statistical arbitrageurs
may step in to sell shares of Company A to those who wish to buy, and buy
shares of Company B from those looking to sell, thereby preventing the divergence between these two fundamentally similar companies from getting
out of hand and improving efficiency in market pricing. Let us not be naïve:
They improve efficiency not out of altruism, but because these strategies are
set up to profit if indeed a convergence occurs between Companies A and B.

The Quant Universe

This is not to say that quants are the only players who attempt to profit
by removing market inefficiencies. Indeed, it is likely that any alpha‐oriented
trader is seeking similar sorts of dislocations as sources of profit. And, of
course, there are times, such as August 2007, when quants actually cause the
markets to be temporarily less efficient. Nonetheless, especially in smaller,
less liquid, and more neglected stocks, statistical arbitrage players are often
major providers of market liquidity and help establish efficient price discovery for all market participants.
So, what can we learn from a quant’s approach to markets? The three
answers that follow represent important lessons that quants can teach
us—lessons that can be applied by any investment manager.

The Benefit of Deep Thought
According to James Simons, the founder of the legendary Renaissance Technologies, one of the greatest advantages quants bring to the investment
process is their systematic approach to problem solving. As Dr. Simons puts
it, “The advantage scientists bring into the game is less their mathematical
or computational skills than their ability to think scientifically.”7
The first reason it is useful to study quants is that they are forced
to think deeply about many aspects of their strategy that are taken for
granted by nonquant investors. Why does this happen? Computers are
obviously powerful tools, but without absolutely precise instruction, they
can achieve nothing. So, to make a computer implement a black‐box trading strategy requires an enormous amount of effort on the part of the
developer. You can’t tell a computer to “find cheap stocks.” You have to
specify what find means, what cheap means, and what stocks are. For example, finding might involve searching a database with information about
stocks and then ranking the stocks within a market sector (based on some
classification of stocks into sectors). Cheap might mean P/E ratios, though
one must specify both the metric of cheapness and what level will be considered cheap. As such, the quant can build his system so that cheapness
is indicated by a 10 P/E or by those P/Es that rank in the bottom decile of
those in their sector. And stocks, the universe of the model, might be all
U.S. stocks, all global stocks, all large cap stocks in Europe, or whatever
other group the quant wants to trade.
All this defining leads to a lot of deep thought about exactly what one’s
strategy is, how to implement it, and so on. In the preceding example, the
quant doesn’t have to choose to rank stocks within their sectors. Instead,
stocks can be compared to their industry peers, to the market overall, or to
any other reasonable group. But the point is that the quant is encouraged to

Why Does Quant Trading Matter?

be intentional about these decisions by virtue of the fact that the computer
will not fill in any of these blanks on its own.
The benefit of this should be self‐evident. Deep thought about a strategy is usually a good thing. Even better, this kind of detailed and rigorous
working out of how to divide and conquer the problem of conceptualizing,
defining, and implementing an investment strategy is useful to quants and
discretionary traders alike. These benefits largely accrue from thoroughness, which is generally held to be a key ingredient to investment or trading
success. By contrast, many (though certainly not all) discretionary traders,
because they are not forced to be so precise in the specification of their
strategy and its implementation, seem to take a great many decisions in an
ad hoc manner. I have been in countless meetings with discretionary traders
who, when I asked them how they decided on the sizes of their positions,
responded with variations on the theme of “Whatever seemed reasonable.”
This is by no means a damnation of discretionary investment styles. I merely
point out that precision and deep thought about many details, in addition to
the bigger‐picture aspects of a strategy, can be a good thing, and this lesson
can be learned from quants.

The Measurement and Mismeasurement of Risk
As mentioned earlier in this chapter, the history of LTCM is a lesson in the
dangers of mismeasuring risk. Quants are naturally predisposed toward conducting all sorts of measurements, including of risk exposure. This activity
itself has potential benefits and downsides. On the plus side, there is a certain
intentionality of risk taking that a well‐conceived quant strategy encourages. Rather than accepting accidental risks, the disciplined quant attempts to
isolate exactly what his edge is and focus his risk taking on those areas that
isolate this edge. To root out these risks, the quant must first have an idea
of what these risks are and how to measure them. For example, most quant
equity traders, recognizing that they do not have sufficient capabilities in forecasting the direction of the market itself, measure their exposure to the market (using their net dollar or beta exposure, commonly) and actively seek to
limit this exposure to a trivially small level by balancing their long portfolios
against their short portfolios. On the other hand, there are very valid concerns
about false precision, measurement error, and incorrect sets of assumptions
that can plague attempts to measure risk and manage it quantitatively.
All the blowups we have mentioned, and most of those we haven’t, stem
in one way or another from this overreliance on flawed risk measurement
techniques. In the case of LTCM, for example, historical data showed that
certain scenarios were likely, others unlikely, and still others had simply never

The Quant Universe

occurred. At that time, most market participants did not expect that a country
of Russia’s importance, with a substantial supply of nuclear weapons and materials, would go bankrupt. Nothing like this had ever happened before. Nevertheless, Russia indeed defaulted on its debt in the summer of 1998, sending
the world’s markets into a frenzy and rendering useless any measurement of
risk. The naïve overreliance on quantitative measures of risk, in this case, led
to the near‐collapse of the financial markets in the autumn of 1998. But for
a rescue orchestrated by the U.S. government and agreed on by most of the
powerhouse banks on Wall Street, we would have seen a very different path
unfold for the capital markets and all aspects of financial life.
Indeed, the credit debacle that began to overwhelm markets in 2007
and 2008, too, was likely avoidable. Banks relied on credit risk models
that simply were unable to capture the risks correctly. In many cases, they
seem to have done so knowingly, because it enabled them to pursue outsized short‐term profits (and, of course, bonuses for themselves). It should
be said that most of these mismeasurements could have been avoided, or
at least the resulting problems mitigated, by the application of better judgment on the part of the practitioners who relied on them. Just as one cannot
justifiably blame weather‐forecasting models for the way that New Orleans
was impacted by Hurricane Katrina in 2005, it would not make sense to
blame quantitative risk models for the failures of those who created and use
them. Traders can benefit from engaging in the exercise of understanding
and measuring risk, so long as they are not seduced into taking ill‐advised
actions as a result.

Disciplined Implementation
Perhaps the most obvious lesson we can learn from quants comes from the
discipline inherent to their approach. Upon designing and rigorously testing a strategy that makes economic sense and seems to work, a properly
run quant shop simply tends to let the models run without unnecessary,
arbitrary interference. In many areas of life, from sports to science, the human ability to extrapolate, infer, assume, create, and learn from the past is
beneficial in the planning stages of an activity. But execution of the resulting
plan is also critical, and it is here that humans frequently are found to be
lacking. A significant driver of failure is a lack of discipline.
Many successful traders subscribe to the old trading adage: Cut losers and
ride winners. However, discretionary investors often find it very difficult to realize losses, whereas they are quick to realize gains. This is a well‐documented
behavioral bias known as the disposition effect.8 Computers, however, are not
subject to this bias. As a result, a trader who subscribes to the aforementioned

Why Does Quant Trading Matter?

adage can easily program his trading system to behave in accordance with
it every time. This is not because the systematic trader is somehow a better
person than the discretionary trader, but rather because the systematic trader
is able to make this rational decision at a time when there is no pressure,
thereby obviating the need to exercise discipline at a time when most people
would find it extraordinarily challenging. Discretionary investors can learn
something about discipline from those who make it their business.

Summary
Quant traders are a diverse and large portion of the global investment universe. They are found in both large and small trading shops and traffic in
multiple asset classes and geographical markets. As is obvious from the
magnitude of success and failure that is possible in quant trading, this niche
can also teach a great deal to any curious investor. Most traders would be
well served to work with the same kind of thoroughness and rigor that is
required to properly specify and implement a quant trading strategy. Just
as useful is the quant’s proclivity to measure risk and exposure to various
market dynamics, though this activity must be undergone with great care
to avoid its flaws. Finally, the discipline and consistency of implementation
that exemplifies quant trading is something from which all decision makers
can learn a great deal.

Notes
1. M. Corey Goldman, “Hot Models Rev Up Returns,” HFMWeek.com, April 17,
2007; Jenny Strasburg and Katherine Burton, “Goldman Sachs, AQR Hedge
Funds Fell 6% in November (Update3),” Bloomberg.com, December 7, 2007.
2. Gregory Zuckerman, Jenny Strasburg, and Peter Lattman, “Renaissance Waives
Fees on Fund That Gave Up 12%,” Wall Street Journal Online, January 5, 2009.
3. Lisa Kassenaar and Christine Harper, “Goldman Sachs Paydays Suffer on Lost
Leverage with Fed Scrutiny,” Bloomberg.com, October 21, 2008.
4. Sang Lee, “New World Order: The High Frequency Trading Community and Its
Impact on Market Structure,” The Aite Group, February 2009.
5. Peter Starck, “Black Box Trading Has Huge Potential—D. Boerse,” Reuters.com,
June 13, 2008.
6. Terry Hendershott, Charles M. Jones, and Albert J. Menkveld, “Does Algorithmic Trading Improve Liquidity?” WFA Paper, April 26, 2008.
7. www.turtletrader.com/trader‐simons.html.
8. Hersh Shefrin and Meir Statman, “The Disposition to Sell Winners Too Early
and Ride Losers Too Long: Theory and Evidence,” Journal of Finance 40, no. 3
(July 1985).

Chapter

An Introduction to
Quantitative Trading
You see, wire telegraph is a kind of a very, very long cat. You pull
his tail in New York and his head is meowing in Los Angeles. Do
you understand this? And radio operates exactly the same way:
You send signals here, they receive them there. The only difference
is that there is no cat.
—Attributed to Albert Einstein, when asked to explain the radio

he term black box conjures up images of a Rube Goldberg device in which
some simple input is rigorously tortured to arrive at a mysterious and distant output. Webster’s Third New International Dictionary defines a Rube
Goldberg device as “accomplishing by extremely complex roundabout means
what actually or seemingly could be done simply.” Many observers in both
the press and industry use markedly similar terms to describe quants. One
Washington Post article, “For Wall Street’s Math Brains, Miscalculations;
Complex Formulas Used by ‘Quant’ Funds Didn’t Add Up in Market Downturn,” contains the following definition: “A quant fund is a hedge fund that
relies on complex and sophisticated mathematical algorithms to search for
anomalies and non‐obvious patterns in the markets.”1 In the New York Post’s
“Not So Smart Now,” we learn that “Quant funds run computer programs
that buy and sell hundreds and sometimes thousands of stocks simultaneously
based on complex mathematical ratios. . . .”2 Perhaps most revealing, this view
is held even by some of the world’s best‐respected investors. David Swensen,
the renowned chief investment officer of the $17 billion Yale University endowment fund and author of Pioneering Portfolio Management, said in an
interview with Fortune/CNN Money, “We also don’t invest in quantitative–
black box models because we simply don’t know what they’re doing.”3

The Quant Universe

The term black box itself has somewhat mysterious origins. From what
I can tell, its first known use was in 1915 in a sci‐fi serial called The Black
Box, starring Herbert Rawlinson. The program was about a criminologist
named Sanford Quest who invented devices (which themselves were placed
inside a black box) to help him solve crimes. Universal Studios, which produced the serial, offered cash prizes to those who could guess the contents
of the black box.4
This connotation of opaqueness still persists today whenever the term
black box is used. Most commonly in the sciences and in finance, a black
box refers to any system that is fed inputs and produces outputs, but whose
inner workings are either unknown or unknowable. Appropriately, two favorite descriptors for quant strategies are complex and secretive. However,
by the end of this book I think it will be reasonably obvious to readers that,
for the most part, quantitative trading strategies are in fact clear boxes that
are far easier to understand in most respects than the caprice inherent to
most human decision making.
For example, an esoteric‐sounding strategy called statistical arbitrage is
in fact simple and easily understood. Statistical arbitrage (stat arb) is based
on the theory that similar instruments (imagine two stocks, such as Exxon
Mobil and Chevron) should behave similarly. If their relative prices diverge
over the short run, they are likely to converge again. So long as the stocks
are still similar, the divergence is more likely due to a short‐term imbalance
between the amount of buying and selling of these instruments, rather than
any meaningful fundamental change that would warrant a divergence in
prices. This is a clear and straightforward premise, and it drives billions
of dollars’ worth of trading volumes daily. It also happens to be a strategy
that discretionary traders use, though it is usually called pairs trading. But
whereas the discretionary trader is frequently unable to provide a curious
investor with a consistent and coherent framework for determining when
two instruments are similar or what constitutes a divergence, these are questions that the quant has likely researched and can address in great detail.

What Is a Quant?
A quant systematically applies an alpha‐seeking investment strategy that
is specified based on exhaustive research. What makes a quant a quant, in
other words, almost always lies in how an investment strategy is conceived
and implemented. It is rarely the case that quants are different from discretionary traders in what their strategies are actually doing, as illustrated
by the earlier example of pairs trading and statistical arbitrage. There is almost never any attempt to eliminate human contributions to the investment

An Introduction to Quantitative Trading

process; after all, we are talking about quants, not robots. As previously
mentioned, although quants apply mathematics and/or computer science
to a wide variety of strategies, whether a fund designed to track the S&P
500 (i.e., an index fund) or to structure exotic products (e.g., asset‐backed
securities, credit default swaps, or principal protection guarantee notes), this
book will remain focused on quants who pursue alpha, or returns that are
independent of the direction of any market in the long run.
Besides conceiving and researching the core investment strategy, humans also design and build the software and systems used to automate the
implementation of their ideas. But once the system “goes live,” human judgment is generally limited in the day‐to‐day management of a portfolio. Still,
the importance of human discretion in such a setup should not be understated. Good judgment is actually what separates the best quants from the
mediocre. The kinds of issues listed in the stat arb example are just a small
subset of the kinds of decisions that quants almost always have to make,
and these fundamental decisions, above all else, drive the strategy’s behavior
from that time forward. As such, good and bad judgments are multiplied
over and over through time as the computer faithfully implements exactly
what it was told to do. This is no different from many other fields. Imagine a
guided missile system. If the engineers make bad judgments in the way they
design these systems, there can be disastrous results, which are multiplied as
more missiles are fired using the faulty guidance systems.
To understand the systematic nature of quants better, it can be helpful to
examine the frontiers of the systematic approach—in other words, the situations in which quants have to abandon a systematic approach for a discretionary one. When a quant intervenes with the execution of her strategy, it is most
commonly to mitigate problems caused by information that drives market
behavior but that cannot be processed by the model. For example, the 2008
merger between Merrill Lynch and Bank of America, which caused Merrill’s
price to skyrocket, might have led a naïve quant strategy to draw the conclusion that Merrill had suddenly become drastically overpriced relative to other
banks and was therefore an attractive candidate to be sold short. But this
conclusion would have been flawed because there was information that justified the spike in Merrill’s price and would not seem to a reasonable person to
lead to a short sale. As such, a human can step in and simply remove Merrill
from the universe that the computer models see, thereby eliminating the risk
that, in this case anyway, the model will make decisions based on bad information. In a sense, this is merely an application of the principle of “garbage
in, garbage out.” If a portfolio manager at a quant trading shop is concerned
that the model is making trading decisions based on inaccurate, incomplete,
or irrelevant information, she may decide to reduce risk by eliminating trading in the instruments affected by this information.

The Quant Universe

Note that in this example, the news of the merger would already have
been announced before the quant decides to override the system. Some
shops are more aggressive, preemptively pulling names off the list of tradable securities at the first sign of credible rumors. By contrast, other quants
do not remove names under any circumstances. Many quants reserve the
right to reduce the overall size of the portfolio (and therefore leverage) if, in
their discretion, the markets appear too risky. For example, after the attacks
of September 11, 2001, many quants reduced their leverage in the wake of
a massive event that would have unknowable repercussions on capital markets. Once things seemed to be operating more normally in the markets, the
quants increased their leverage back to normal levels.
Though the operating definition of quants at the beginning of this section is useful, there is a full spectrum between fully discretionary strategies
and fully systematic (or fully automated) strategies. The key determination
that puts quants on one side of this spectrum and everyone else on the other
is whether daily decisions about the selection and sizing of portfolio positions are made systematically (allowing for the exceptions of “emergency”
overrides such as those just described) or by discretion. If both the questions of what positions to own and how much of each to own are usually
answered systematically, that’s a quant. If either one is answered by a human
as standard operating procedure, that’s not a quant.
It is interesting to note that, alongside the growth in quantitative trading, there are also a growing number of quasi‐quant traders. For instance,
some of these traders utilize automated systems to screen for potential investment opportunities, thereby winnowing a large number of potential
choices down to a much smaller, more manageable list. From there, human discretion kicks in again, doing some amount of “fundamental” work
to determine which names selected by the systematic screening process are
actually worth owning and which are not. Less commonly, some traders
leave the sourcing and selection of trades entirely up to humans, instead
using computers to optimize and implement portfolios and to manage risk.
Still less commonly, a few traders allow the computer to pick all the trades,
while the human trader decides how to allocate among these trades. These
quasi‐quants make use of a subset of the tools in a proper quant’s toolbox,
so we will cover their use of these techniques implicitly.

What Is the Typical Structure of a Quantitative
Trading System?
The best way to understand both quants and their black boxes is to examine
the components of a quant trading system; this is the structure we will use

An Introduction to Quantitative Trading

for the remainder of the book. Exhibit 2.1 shows a schematic of a typical
quantitative trading system. This diagram portrays the components of a live,
“production” trading strategy (e.g., the components that decide which securities to buy and sell, how much, and when) but does not include everything
necessary to create the strategy in the first place (e.g., research tools for
designing a trading system).
The trading system has three modules—an alpha model, a risk model,
and a transaction cost model—which feed into a portfolio construction
model, which in turn interacts with the execution model. The alpha model
is designed to predict the future of the instruments the quant wants to consider trading for the purpose of generating returns. For example, in a trend‐
following strategy in the futures markets, the alpha model is designed to
forecast the direction of whatever futures markets the quant has decided to
include in his strategy.
Risk models, by contrast, are designed to help limit the amount of exposure the quant has to those factors that are unlikely to generate returns but
could drive losses. For example, the trend follower could choose to limit his
directional exposure to a given asset class, such as commodities, because of
concerns that too many forecasts he follows could line up in the same direction, leading to excess risk; the risk model would contain the levels for these
commodity exposure limits.
The transaction cost model, which is shown in the box to the right of
the risk model in Exhibit 2.1, is used to help determine the cost of whatever
trades are needed to migrate from the current portfolio to whatever new
portfolio is desirable to the portfolio construction model. Almost any trading transaction costs money, whether the trader expects to profit greatly or
a little from the trade. Staying with the example of the trend follower, if a

Alpha Model

Risk Model

Transaction Cost Model

Portfolio Construction Model

Execution Model

Exhibit 2.1

Basic Structure of a Quant Trading Strategy

The Quant Universe

trend is expected to be small and last only a short while, the transaction cost
model might indicate that the cost of entering and exiting the trade is greater
than the expected profits from the trend.
The alpha, risk, and transaction cost models then feed into a portfolio
construction model, which balances the trade‐offs presented by the pursuit
of profits, the limiting of risk, and the costs associated with trading, thereby
determining the best portfolio to hold. Having made this determination,
the system can compare the current portfolio to the new target portfolio,
with the differences between the current portfolio and the target portfolio
representing the trades that need to be executed. Exhibit 2.2 illustrates an
example of this process.
The current portfolio reflects the positions the quant trader currently
owns. After running the portfolio construction model, the quant trader generates the new target portfolio weights, shown in the New Target Portfolio
column. The difference between the two indicates the trades that now need
to be executed, which is the job of the execution algorithm. The execution
algorithm takes the required trades and, using various other inputs such as the
urgency with which the trades need to be executed and the dynamics of the
liquidity in the markets, executes trades in an efficient and low‐cost manner.
The structure shown in Exhibit 2.1 is by no means universal. For example, many quant strategies are run without a transaction cost model, a portfolio construction model, or an execution model. Others combine various
components of these models. One can build whatever risk requirements and
constraints are considered necessary into the alpha model itself. Another
variation is to create more recursive connections among the pieces. Some
traders capture data about their actual executions and utilize these data
to improve their transaction cost models. However, the diagram is useful
because, for the most part, it captures the various discrete functions within
a quant trading system, regardless of whether they are organized precisely
in this manner.
Exhibit 2.2

Moving from an Existing Portfolio to a New Target Portfolio
Current Portfolio

New Target Portfolio

Trades to Execute

S&P 500 Index

Short 30%

Short 25%

Buy to Cover 5%

EUROSTOXX
Index

Long 20%

Long 25%

Buy 5%

U.S. 10‐Year
Treasury Notes

Long 40%

Long 25%

Sell 15%

German 10‐Year
Bunds

Short 10%

Short 25%

Sell Short 15%

An Introduction to Quantitative Trading

Alpha Model

Risk Model

Transaction Cost Model

Data
Portfolio Construction Model
Research
Execution Model

exhibit 2.3

The Black Box Revealed

Exhibit 2.1 captures only part of the work of the quant trader because it
considers only the live production trading system and ignores two key pieces
required to build it and run it: data and research. Black boxes are inert and
useless without data—accurate data, moreover. Quant traders build input/
output models that take inputs (data), process this information, and then
produce trading decisions. For example, a trader utilizing a trend‐following
strategy usually requires price data to determine what the trend is. Without
data, he would have nothing to do, because he’d never be able to identify
the trends he intends to follow. As such, data are the lifeblood of quants and
determine much about their strategies. Given data, quants can perform research, which usually involves some form of testing or simulation. Through
research, the quant can ascertain whether and how a quant strategy works.
We also note that each of the other modules in our schematic, when built
correctly, usually requires a great deal of research. We can therefore redraw
our diagram to include these other critical pieces, as shown in Exhibit 2.3.

Summary
Quants are perhaps not so mysterious as is generally supposed. They tend
to start with ideas that any reasonable observer of the markets might also
have, but rather than using anecdotal, experiential evidence—or worse, simply assuming that their ideas are true—quants use market data to feed a
research process to determine whether their ideas in fact hold true over time.
Once quants have arrived at a satisfactory strategy, they build their strategy

The Quant Universe

into a quant system. These systems take the emotion out of investing and
instead impose a disciplined implementation of the idea that was tested. But
this should not be read as minimizing the importance of human beings in
the quant trading process. Quants come up with ideas, test strategies, and
decide which ones to use, what kinds of instruments to trade, at what speed,
and so on. Humans also tend to control a “panic button,” which allows
them to reduce risk if they determine that markets are behaving in some way
that is outside the scope of their models’ capabilities.
Quant strategies are widely ignored by investors as being opaque and
incomprehensible. Even those who do focus on this niche tend to spend
most of their time understanding the core of the strategy, its alpha model.
But we contend that there are many other parts of the quant trading process
that deserve to be understood and evaluated. Transaction cost models help
determine the correct turnover rate for a strategy, and risk models help keep
the strategy from betting on the wrong exposures. Portfolio construction
models balance the conflicting desires to generate returns, expend the right
amount on transaction costs, manage risk, and deliver a target portfolio to
execution models, which implement the portfolio model’s decisions. All this
activity is fed by data and driven by research. From afar, we have begun to
shed light on the black box.
Next, in Part Two, we will dissect each of these modules, making our
way methodically through the inside of the black box. At the end of each of
these chapters, as a reminder of the structure of a quant system and of our
progress, we will indicate the topic just completed by removing the shading
from it.

Notes
1. Frank Ahrens, “For Wall Street’s Math Brains, Miscalculations,” WashingtonPost
.com, August 21, 2007, A01.
2. Roddy Boyd, “Not So Smart Now,” NewYorkPost.com, August 19, 2007.
3. Marcia Vickers, “The Swensen Plan,” Money.CNN.com, February 24, 2009.
4. Michael R. Pitts, Famous Movie Detectives III (Lanham, Maryland: Scarecrow
Press, Inc. 2004), 265.

Part

Two
Inside the Black Box

Chapter

Alpha Models: How Quants
Make Money
Prediction is very difficult, especially about the future.
—Niels Bohr

aving surveyed it from the outside, we begin our journey through the
black box by understanding the heart of the actual trading systems that
quants use. This first piece of a quant trading system is its alpha model,
which is the part of the model that is looking to make money and is where
much of the research process is focused. Alpha, the spelled‐out version of the
Greek letter α, generally is used as a way to quantify the skill of an investor
or the return she delivers independently of the moves in the broader market.
By conventional definition, alpha is the portion of the investor’s return not
due to the market benchmark, or, in other words, the value added (or lost)
solely because of the manager. The portion of the return that can be attributed to market factors is then referred to as beta. For instance, if a manager
is up 12 percent and her respective benchmark is up 10 percent, a quick
back‐of‐the‐envelope analysis would show that her alpha, or value added,
is +2 percent (this assumes that the beta of her portfolio was exactly 1). The
flaw with this approach to computing alpha is that it could be a result of
luck, or it could be because of skill. Obviously, any trader will be interested
in making skill the dominant driver of the difference between her returns
and the benchmark’s. Alpha models are merely a systematic approach to
adding skill to the investment process in order to make profits. For example,
a trend‐following trader’s ability to systematically identify trends that will
persist into the future represents one type of skill that can generate profits.
Our definition of alpha—which I stress is not conventional—is skill in
timing the selection and/or sizing of portfolio holdings. A pursuit of alpha

Inside the Black Box

holds as a core premise that no instrument is inherently good or bad, and
therefore no instrument is worth always owning or perpetually shorting.
The trend follower determines when to buy and sell various instruments, as
does the value trader. Each of these is a type of alpha. In the first case, alpha is generated from the skill in identifying trends, which allows the trend
follower to know when it is good to be long or short a given instrument.
Similarly, a value trader does not say that a given stock is cheap now and
therefore is worth owning in perpetuity. In fact, if a stock is always cheap, it
is almost certainly not worth owning, because its valuation never improves
for the investor. Instead, the idea behind value investing is to buy a stock
when it is undervalued and to sell it when it is fairly valued or overvalued.
Again, this represents an effort to time the stock.
The software that a quant builds and uses to conduct this timing systematically is known as an alpha model, though there are many synonyms
for this term: forecast, factor, alpha, model, strategy, estimator, or predictor.
All successful alpha models are designed to have some edge, which allows
them to anticipate the future with enough accuracy that, after allowing for
being wrong at least sometimes and for the cost of trading, they can still
make money. In a sense, of the various parts of a quant strategy, the alpha
model is the optimist, focused on making money by predicting the future.
To make money, generally some risk, or exposure, must be accepted.
By utilizing a strategy, we directly run the risk of losing money when the
environment for that strategy is adverse. For example, Warren Buffett has
beaten the market over the long term, and this differential is a measure of
his alpha. But there have been times when he struggled to add value, as he
did during the dot‐com bubble of the late 1990s. His strategy was out of
favor, and his underperformance during this period reflected this fact. In the
case of alpha models, the same holds true: Whatever exposures they take on
are rewarding if they are in favor, and are costly if they are out of favor. This
chapter addresses the kinds of alpha models that exist and the ways that
quants actually use the forecasts their models make.

Types of Alpha Models: Theory-Driven and
Data-Driven
An important and not widely understood fact is that only a small number
of trading strategies exist for someone seeking alpha. But these basic
strategies can be implemented in many ways, making it possible to create an
incredible diversity of strategies from a limited set of core ideas. The first key
to understanding quant trading strategies is to understand the perspectives
quants take on science.

Alpha Models: How Quants Make Money

Because most quants are trained first in the sciences and only later in
finance, quants’ scientific backgrounds frequently determine the approach
they take to trading over their entire careers. The two major branches of science are theoretical and empirical. Theoretical scientists try to make sense of
the world around them by hypothesizing why it is the way it is. This is the
kind of science with which people are most familiar and interact most. For
example, viable, controllable, long‐distance airplanes exist largely because
engineers apply theories of aerodynamics. Empirical scientists believe that
enough observations of the world can allow them to predict future patterns
of behavior, even if there is no hypothesis to rationalize the behavior in an
intuitive way. In other words, knowledge comes from experience. The Human Genome Project is one of many important examples of the applications
of empirical science, mapping human traits to the sequences of chemical
base pairs that make up human DNA.
The distinction between theoretical and empirical science is germane to
quantitative trading in that there are also two kinds of quant traders. The
first, and by far the more common, are theory driven. They start with observations of the markets, think of a generalized theory that could explain
the observed behavior, and then rigorously test it with market data to see if
the theory is shown to be either untrue or supported by the outcome of the
test. In quant trading, most of these theories would make sense to you or me
and would seem sensible when explained to friends at cocktail parties. For
example, “cheap stocks outperform expensive stocks” is a theory that many
people hold. This explains the existence of countless value funds. Once precisely defined, this theory can be tested.
The second kind of scientist, by far in the minority, believes that correctly
performed empirical observation and analysis of the data can obviate the need
for theory. Such a scientist’s theory, in short, is that there are recognizable patterns in the data that can be detected with careful application of the right techniques. Again, the example of the Human Genome Project is instructive. The
scientists in the Human Genome Project did not believe that it was necessary
to theorize what genes were responsible for particular human traits. Rather,
scientists merely theorized that the relationships between genes and traits can
be mapped using statistical techniques, and they proceeded to do exactly that.
Empirical scientists are sometimes derisively (and sometimes just as a matter
of fact) labeled data miners. They don’t especially care if they can name their
theories and instead attempt to use data analysis techniques to uncover behaviors in the market that aren’t intuitively obvious.
It is worthwhile to note that theory‐driven scientists (and quants) are
also reliant on observations (data) to derive theories in the first place. Just
like the empiricists, they, too, believe that something one can observe in the
data will be repeatable in the future. Empiricists, however, are less sensitive

Inside the Black Box

to whether their human minds can synthesize a story to explain the data
even if, in the process, they risk finding relationships or patterns in the data
that are entirely spurious.

Theory-Driven Alpha Models
Most quants you will come across are theory driven. They start with some
economically feasible explanation of why the markets behave in a certain
way and test these theories to see whether they can be used to predict the future with any success. Many quants think that their theories are somewhat
unique to them, which is part of the reason so many of them are so secretive. But this turns out, almost always, to be a delusion. Meanwhile, many
outside the quant trading world believe that the kinds of strategies quants
use are complex and based on complicated mathematical formulae. This
generally also turns out to be false.
In fact—and in defiance of both the presumed need for secrecy and the
claims that what quants do cannot be understood by those without doctorate degrees—most of what theory‐driven quants do can be relatively easily
fit into one of six classes of phenomena: trend, reversion, technical sentiment, value/yield, growth, and quality. It is worth noting that the kinds of
strategies that quants utilize are actually exactly the same as those that can
be utilized by discretionary traders seeking alpha. These six categories can
be further understood by examining the data that they use: price‐related
data and fundamental data. As we will see throughout this book, understanding the inputs to a strategy is extremely important to understanding
the strategy itself. The first two categories of strategies, trend and mean
reversion, are based on price‐related data. Technical sentiment strategies are
less commonly found, but can be thought of as a third class of price‐based
strategies. The remaining three strategies, value/yield, growth/sentiment,
and quality, are based on fundamental and/or fundamental sentiment data.
Many successful quants utilize more than one type of alpha model in
conjunction, but to gain a proper understanding of these strategies, we will
first break them down individually and discuss the combination of them
afterward. Exhibit 3.1 provides a summary and outline for understanding
the types of alpha models that quants use.

Strategies Utilizing Price-Related Data
First we will focus on alpha models that utilize price‐related data, which
are mostly about the prices of various instruments or other information
that generally comes from an exchange (such as trading volume). Quants

Alpha Models: How Quants Make Money

RETURN
CATEGORY

WHAT
QUANTS
DO

INPUT

PHENOMENON Trend

Exhibit 3.1

Alpha

Fundamental

Price

Reversion

Technical
Sentiment

Yield

Growth

Quality

A Taxonomy of Theory‐Driven Alpha Models

who seek to forecast prices and to profit from such forecasts are likely to be
exploiting one of two kinds of phenomena. The first is that an established
trend will continue, and the second is that the trend will reverse. In other
words, the price can either keep going in the direction it was going already,
or it can go in the opposite direction. We call the first idea trend following or
momentum, and we call the second idea counter‐trend or mean reversion. A
third idea will be explored as well, which we refer to as technical sentiment.
This is a far less common type of alpha, but which deserves some discussion.
Trend Following Trend following is based on the theory that markets sometimes move for long enough in a given direction that one can identify this
trend and ride it. The economic rationale for the existence of trends is based
on the idea of consensus building among market participants. Imagine that
there is uncertainty about the medium‐term outlook for the U.S. economy.
The labor picture looks fine, but inflation is running rampant, and trade
deficits are blooming. On the other hand, consumers are still spending, and
housing is strong. This conflicting information is a regular state of affairs
for economies and markets, so that some of the information available appears favorable and some unfavorable. In our example, let’s further imagine
that the bears have it right—that in fact inflation will get out of control and
cause problems for the economy. The earliest adopters of this idea place
their trades in accordance with it by, for example, selling bonds short. As
more and more data come out to support their thesis and as a growing mass
of market participants adopts the same thesis, the price of U.S. bonds may
take a considerable amount of time to move to its new equilibrium, and this
slow migration from one equilibrium to the next is the core opportunity that
the trend follower looks to capture.

Inside the Black Box

It bears mentioning that there is an alternate explanation of why trends
happen; it is affectionately known as the greater fools theory. The idea here
is that, because people believe in trends, they tend to start buying anything
that’s been going up and selling anything that’s been going down, which
itself perpetuates the trend. The key is always to sell your position to someone more foolish, and thereby to avoid being the last fool. Either theoretical
explanation, coupled with the evidence in markets, seems a valid enough
reason to believe in trends.
Trend followers typically look for a “significant” move in a given direction in an instrument. They bet that, once a significant move has occurred, it
will persist because this significant move is a likely sign of a growing consensus (or a parade of fools). They prefer this significance because a great risk
of trend‐following strategies is whipsawing action in markets, which describes a somewhat rapid up‐and‐down pattern in prices. If, in other words,
you buy the S&P because it was up over the past three months (and, symmetrically, sell short the S&P every time it was down over the three months
prior), you need the trend to keep going in the same direction after the
three‐month observation period. If the S&P reverses direction roughly every
three months, a strategy such as this would lose money on more or less every
trade over that period. There are many ways of defining what kind of move
is significant, and the most common terms used to describe this act of definition are filtering and conditioning. This turns out to be an important source
of differentiation among the various players who pursue trend‐following
strategies and will be explored further in “Implementing the Strategies.”
Perhaps the most obvious and well‐known example of a strategy that depends on trends is in the world of futures trading, also known as managed
futures or commodities trading advisors (CTAs). Exhibit 3.2 illustrates the
downward trend in equities that began in the fourth quarter of 2007. One way
to define a trend for trading purposes, known as a moving average crossover
indicator, is to compare the average price of the index over a shorter time period (e.g., 60 days) to that of a longer time period (e.g., 200 days). When the
shorter‐term average price is below the longer‐term average price, the index
is said to be in a negative trend, and when the shorter‐term average price is
above the longer‐term average, the index is in a positive trend. As such, a trend
follower using this kind of strategy might have gotten short the S&P Index
around the end of 2007, as indicated by the point at which the two moving
averages cross over each other, and remained short for most or all of 2008.
Some of the largest quantitative asset managers engage in trend following in futures markets, which also happens to be the oldest of all quant
trading strategies, as far as I can tell. Ed Seykota built the first computerized
version of the mechanical trend‐following strategy that Richard Donchian
created some years earlier, utilizing punch cards on an IBM mainframe in

Alpha Models: How Quants Make Money

S&P 500 Index,
October 3, 2007 to December 9, 2008
1,800
1,600

Crossover point of moving averages

1,400
1,200
1,000

S&P 500
200d MA

800

60d MA

Exhibit 3.2

11/5/2008

11/26/2008

10/15/2008

9/3/2008

9/24/2008

8/13/2008

7/2/2008

7/23/2008

6/11/2008

5/21/2008

4/30/2008

4/9/2008

3/19/2008

2/27/2008

2/6/2008

1/16/2008

12/26/2007

12/5/2007

11/14/2007

10/24/2007

10/3/2007

600

S&P 500 Trend

1970, a year after he graduated from MIT. He was a strong believer in doing
ongoing research, and over the course of his first 12 years, he turned $5,000
into $15,000,000. He went on to a highly successful three‐decade‐long
career, over which he annualized some 60 percent returns.1
Larry Hite represents another interesting example of an early practitioner of trend following. Previously, Hite was a rock promoter in New
York who, after experiencing three separate nightclub shootings on a single night, decided a change of career was in order. In 1972, he coauthored
a paper that suggested how game theory could be used to trade the futures
markets using quantitative systems.2 After turning his attention to trend
following, he created Mint Investments in 1981 with two partners; it became the first hedge fund to manage $1 billion and the first fund to partner with the Man Group, which effectively put Man into the hedge fund
business. Mint annualized north of 30 percent per year, net of fees, for its
investors over the 13 years it existed under Hite’s stewardship. Notably,
Mint made some 60 percent in 1987, in no small part by being on the right
side of the crash that October.3
Lest it seem like this is an overly rosy picture of trend following, it
should be stated clearly: These strategies come with a great deal of risk
alongside their lofty returns. The typical successful trend follower earns less
than one point of return for every point of downside risk delivered. In other
words, to earn 50 percent per year, the investor must be prepared to suffer

Inside the Black Box

a loss greater than 50 percent at some point. In short, the returns of this
strategy are streaky and highly variable.
This is not only true of trend following. Indeed, each of the major classes of alpha described in this chapter is subject to relatively long periods of
poor returns. This is because the behaviors they seek to profit from in the
markets are not ever‐present but rather are unstable and episodic. The idea
is to make enough money in the good times and manage the downside well
enough in the bad times to make the whole exercise worthwhile.
Perhaps quant trading’s most important trend follower in terms of
lasting impact was a firm called Axcom, which later became Renaissance
Technologies. Elwyn Berlekamp, a PhD in engineering from MIT, in 1986
began to consult for Axcom regarding strategy development. Axcom had
been struggling during those years, and Berlekamp bought a controlling
interest. In 1989, after doing considerable research, Axcom resumed trading with a new and improved strategy. For its first year, the firm was up 55
percent after charging 5 percent management fees and 20 percent incentive fees. At the end of 1990, Berlekamp sold his interest to Jim Simons
for a sixfold profit, which might still have been one of the worst trades in
history. Renaissance, as the firm was called by then, is now the most successful quant trading firm and probably the most impressive trading firm
of any kind. It has evolved a great deal from the trend‐following strategies
it used in the mid‐1980s and even from the more sophisticated futures
strategies it employed in the early 1990s. It stopped accepting new money
with less than $300 million under management in 1992 and went on to
compound this money to approximately $10 billion some 20 years later,
despite eye‐popping 5 percent management fees and 44 percent incentive
fees. They have annualized approximately 35 percent per year net of these
fees, from 1989 onward, and perhaps most astonishingly, have gotten better over the years, despite the increased competition in the space and their
own significantly larger capital base.4
It is worth pointing out that quants are not the only ones who have a
fondness for trend‐following strategies. It has always been and will likely
remain one of the more important ways in which traders of all stripes go
about their business. One can find trend following in the roots of the infamous Dutch tulip mania in the seventeenth century, or in the dot‐com
bubble of the late twentieth century, neither of which is likely to have been
caused by quants. And, of course, many discretionary traders have a strong
preference to buy what’s been hot and sell what’s been cold.
Mean Reversion When prices move, as we have already said, they move in
either the same direction they’ve been going or in the opposite. We have
just described trend following, which bets on the former. Now we turn our

Alpha Models: How Quants Make Money

attention to mean reversion strategies, which bet on prices moving in the
opposite direction to that which had been the prevailing trend.
The theory behind mean reversion strategies is that there exists a center
of gravity around which prices fluctuate, and it is possible to identify both
this center of gravity and what fluctuation is sufficient to warrant making a
trade. As in the case of trend following, there are several valid rationales for
existence of mean reversion. First, there are sometimes short‐term imbalances
among buyers and sellers due simply to liquidity requirements that lead to an
instrument being over‐bought or over‐sold. To return to the example mentioned earlier, imagine that a stock has been added to a well‐followed index,
such as the S&P 500. This forces any fund that is attempting to track the index
to run out and buy the stock, and, in the short term, there might not be enough
sellers at the old price to accommodate them. Therefore, the price moves up
somewhat abruptly, which increases the probability that the price will reverse
again at some point, once the excess demand from index buyers has subsided.
Another rationale to explain the existence of mean‐reverting behavior is that
market participants are not all aware of each other’s views and actions, and as
they each place orders that drive a price toward its new equilibrium level, the
price can overshoot due to excess supply or demand at any given time.
Regardless of the cause of the short‐term imbalance between supply and
demand, mean reversion traders are frequently being paid to provide liquidity because they are bucking current trends. This is sometimes explicitly true
in terms of their execution techniques (which we discuss in more detail in
Chapters 7 and 14). But regardless of execution tactics, mean reversion traders
are indeed betting against momentum, and bear the risk of adverse selection.
Interestingly, trend and mean reversion strategies are not necessarily at
odds with each other. Longer‐term trends can occur, even as smaller oscillations around these trends occur in the shorter term. In fact, some quants use
both of these strategies in conjunction. Mean reversion traders must identify
the current mean or equilibrium and then must determine what amount of
divergence from that equilibrium is sufficient to warrant a trade. As in the
case of trend following, there are many ways of defining the mean and the
reversal. It is worth noting that when discretionary traders implement mean
reversion strategies, they are typically known as contrarians.
Perhaps the best‐known strategy based on the mean reversion concept
is known as statistical arbitrage (stat arb, for short), which bets on the convergence of the prices of similar stocks whose prices have diverged. While
Ed Thorp, founder of Princeton/Newport Partners was probably one of the
earliest quantitative equity traders, the trading desk of Nunzio Tartaglia at
Morgan Stanley was a pioneer of stat arb and would prove to have lasting
impact on the world of finance. Tartaglia’s team included scientists such as
Gerry Bamberger and David Shaw, and together they developed and evolved

Inside the Black Box

a strategy that was based on the relative prices of similar stocks. Stat arb
ushered in an important change in worldview, one that focused on whether
Company A was over‐ or undervalued relative to Company B rather than
whether Company A was simply cheap or expensive in itself. This important
evolution would lead to the creation of many strategies based on forecasts of
relative attractiveness, which is a topic we will address in greater detail shortly.
Exhibit 3.3 shows a simplified example of the mean‐reverting behavior
evident between similar instruments, in this case Merrill Lynch (MER) and
Charles Schwab (SCHW). As you can see, the spread between these two
companies oscillates rather consistently in a reasonably narrow range for
long periods. This effect allows a trader to wait for significant divergences
and then bet on a reversion back to the equilibrium level.
Trend and mean reversion strategies represent a large portion of all
quant trading. After all, price data are plentiful and always changing, presenting the quant with many opportunities to trade. It may be interesting to
note that trend and mean reversion, though they are theoretically opposite
ideas, both seem to work. How is this possible? Largely, it’s possible because
of different timeframes. It is obviously correct that both strategies can’t possibly be made to be exactly opposite while both making money at the same
time. However, there is no reason to create both strategies to be exactly the
same. Trends tend to occur over longer time horizons, whereas reversions
tend to happen over shorter‐term time horizons. Exhibit 3.4 shows this effect in action. You can see that there are indeed longer‐term trends and

SCHW versus MER
Daily Spread versus Trailing Five-Day Spread, 2004–2006
SCHW Outperformance
versus MER

15
10
5
—
(5)

Date

Exhibit 3.3

Mean Reversion between SCHW and MER

11/9/2006

9/9/2006

7/9/2006

5/9/2006

3/9/2006

1/9/2006

11/9/2005

9/9/2005

7/9/2005

5/9/2005

3/9/2005

1/9/2005

11/9/2004

9/9/2004

7/9/2004

5/9/2004

1/9/2004

(15)

3/9/2004

(10)

Alpha Models: How Quants Make Money

Trend in the S&P 500 Index

S&P 500 Index Level

1,800

S&P 500 Index

1,600

200-Day Moving Average

1,400
1,200
1,000
800

1/
20
08
1/
20
08

12
/3

1/
20
07

12
/3

1/
20
07

1/
20
06

12
/3

1/
20
05

12
/3

1/
20
04

12
/3

1/
20
03

12
/3

1/
20
02

12
/3

1/
20
01

1/
20
00

12
/3

600

Date
Mean Reversion in the S&P 500 Index

S&P 500 versus 10-Day
Moving Average

100
50
—
(50)
(100)

S&P 500 versus 10-Day Moving Average

(150)

12
/3

1/
20
06

12
/3

1/
20
05

12
/3

1/
20
04

12
/3

1/
20
03

12
/3

1/
20
02

12
/3

1/
20
01

12
/3

1/
20
00

12
/3

1/
19
99

(200)

Date

Exhibit 3.4

Trend and Reversion Coexisting

shorter‐term mean reversions that take place. In fact, you can also see that
the strategies are likely to work well in different regimes. From 2000 to
2002 and again in 2008, a trend strategy likely exhibits better performance, since the markets were trending very strongly during these periods.
From 2003 to 2007, mean‐reverting behavior was more prevalent. Yet both
strategies are likely to have made money for the period as a whole. This can
also be examined on other time horizons, and in some cases, mean reversion
strategies can work as the longer‐term indicator, while momentum can be
used as a faster indicator.

Inside the Black Box

Technical Sentiment. An interesting third class of price‐related strategies tracks investor sentiment—expressed through price, volume, and volatility behaviors—as an indicator of future returns. A word of caution before
delving into these strategies is warranted. Unlike in the cases of momentum
and mean reversion (or the fundamental strategies to be outlined later in
this chapter), there is no clear economic rationale that gives birth to a strategy. In other words, there are widely varying views on the value and use of
sentiment information in forecasting. To some practitioners, a high degree
of positive sentiment in some instrument would indicate that the instrument is already overbought and therefore ready to decline. To others, high
positive sentiment would indicate that the instrument has support to move
higher. For still others, sentiment is only used as a conditioning variable (this
concept will be discussed in more detail in “Conditioning Variables”), for
example by utilizing a trend‐following strategy only if the volumes that were
associated with the price movements were significant, whereas a low‐volume trend might be ignored. It is this last use of sentiment data that is most
common. There are, however, several examples of technical sentiment strategies that can be thought of as standalone ways to forecast future direction.
First is to look at the options markets to determine sentiment on the
underlying. There are two separate “straightforward” ideas to explore here.
One is to look at the volume of puts and calls, and to use this as an indicator of sentiment. If puts have higher volumes relative to calls than they
normally do, it might be an indicator that investors are worried about a
downturn. If puts have lower volumes versus calls than normal, it might be
a bullish sentiment indicator. A second example of options‐based sentiment
in equities utilizes the implied volatilities of puts versus calls. It is natural
to see some level of difference in the implied volatilities of puts versus calls.
This is partially in recognition of the habit of stocks to move down quickly
and up slowly, which would indicate that downside volatility is higher than
upside volatility, which in turn causes the seller of a put option to demand a
higher price (and therefore implied volatility) than would be demanded by
the seller of a call option that is equally far out of the money (or in the case
that they are both at the money). If one analyzes the historical ratio of put
volatility and call volatility, there will likely be some natural ratio (greater
than one, due to the phenomenon just described about upside and downside volatility), and divergences from this natural level might be treated as
indicative of sentiment. A related idea would be to use implied volatility
or a proxy (e.g., credit default swaps, or CDS for short) as an indicator of
investor sentiment.
A second example of a technical sentiment strategy analyzes trading
volume, open interest, or other related type of inputs as an indicator of
future prices. At the shortest timeframes, some higher‐frequency traders
evaluate the shape of the limit order book to determine near‐term sentiment.

Alpha Models: How Quants Make Money

The shape of the order book includes factors such as the size of bids or offers away from the mid‐market relative to the size at the best bid/offer, or
the aggregate size of bids versus offers. For slightly longer‐term strategies,
analyses of volume can include looking at the trading volume, the turnover
(trading versus float), open interest, or other similar measures of trading activity. As I mentioned at the outset of this section, what to do with this kind
of information remains up for debate. It can be used as a contrarian indicator (i.e., high-volume or high-turnover stocks are expected to underperform,
while low volume or low turnover stocks are expected to outperform) or as
a positive indicator. Most of the research I have reviewed, however, focuses
on the contrarian approach.

Strategies Utilizing Fundamental Data
Most strategies utilizing fundamental data in their alpha models can be
easily classified into one of three groups: value/yield, growth, or quality.
Though these ideas are frequently associated with the analysis of equities,
it turns out that one can apply the exact same logic to any kind of instrument. A bond, a currency, a commodity, an option, or a piece of real estate
can be bought or sold because it offers attractive value, growth, or quality
characteristics. While fundamentals have long been part of the discretionary
trader’s repertoire, quantitative fundamental strategies are relatively young.
In quantitative equity trading and in some forms of quantitative futures
or macro trading, much is owed to Eugene Fama and Kenneth French (known
better collectively as Fama‐French). In the early 1990s, they produced a series
of papers that got quants thinking about the kinds of factors that quants frequently use in strategies utilizing fundamental data. In particular, “The Cross
Section of Expected Stock Returns” coalesced more than a decade of prior
work in the area of using quantitative fundamental factors to predict stock
prices and advanced the field dramatically.5 Fama and French found, simply,
that stocks’ betas to the market are not sufficient to explain the differences
in the returns of various stocks. Rather, combining betas with historical data
about the book‐to‐price ratio and the market capitalization of the stocks was
a better determinant of future returns. It is somewhat ironic that an entire
domain of quantitative alpha trading owes so much to Eugene Fama, because
Fama’s most famous work advanced the idea that markets are efficient.
Value/Yield Value strategies are well known and are usually associated with
equity trading, though such strategies can be used in other markets as well.
There are many metrics that people use to describe value in various asset classes, but most of them end up being ratios of some fundamental factor versus
the price of the instrument, such as the price‐to‐earnings (P/E) ratio. Quants
tend to invert such ratios, keeping prices in the denominator. An inverted P/E

Inside the Black Box

ratio, or an E/P ratio, is also known as earnings yield. Note that investors have
long done this with dividends, hence the dividend yield, another commonly
used measure of value. The basic concept of value strategies is that the higher
the yield, the cheaper the instrument. The benefit of the conversion of ratios to
yields is that it allows for much easier and more consistent analysis.
Let’s take earnings as an example: Earnings can (and frequently do)
range from large negative numbers to large positive numbers and everywhere in between. If we take two stocks that are both priced at $20, but
one has $1 of earnings while the other has $2 of earnings, it’s easy to see
that the first has a 20 P/E and the second has a 10 P/E, so the second looks
cheaper on this metric. But imagine instead that the first has –$1 in earnings, whereas the second has –$2 in earnings. Now, these stocks have P/Es
of –20 and –10. Having a –20 P/E seems worse than having a –10 P/E, but
it’s clearly better to only have $1 of negative earnings than $2. Thus, using
a P/E ratio is misleading in the case of negative earnings. In the case that
a company happens to have produced exactly $0 in earnings, the P/E ratio
is simply undefined, since we would be dividing by $0. Because ratios with
price in the numerator and some fundamental figure in the denominator
exhibit this sort of misbehavior, quants tend to use the inverted yield forms
of these same ratios. This idea is demonstrated in Exhibit 3.5, which shows
that the E/P ratio is well behaved for any level of earnings per share for a
hypothetical stock with a price greater than $1 (in the example, we used

100

20%

10%

—

Earnings per Share

Exhibit 3.5

P/E versus E/P (Earnings Yield)

0.5

0.2

–0.2

–30%
–0.5

(150)
–1

–20%

–2

(100)

–3

–10%

–4

(50)

–5

P/E Ratio

30%

P/E Ratio
E/P Ratio

E/P Ratio

150

Alpha Models: How Quants Make Money

$20 per share as the stock price). By contrast, the P/E ratio is rather poorly
behaved and does not lend itself well to analysis and is not even properly
defined when earnings per share are zero.
There is a bigger theme implied by the example of the treatment of earnings data by quants. Many fundamental quantities are computed or quoted
in ways that are not readily used in developing a systematic alpha. These
quantities predated the use of computers to trade, and as a result, can have
arbitrary definitions and distributions. Quants must transform such data
into more usable, well‐behaved variables that can lend themselves more
readily to systematic trading applications.
Most often, value is thought of as a strategy that is defined by buying
cheap. But this strikes me as being too shallow a definition. In reality, the idea
behind value investing is that markets tend to overestimate the risk in risky instruments and possibly to underestimate the risk in less risky ones. Therefore,
it can pay off to own the more risky asset and/or sell the less risky asset. The
argument for this theory is that sometimes instruments have a higher yield
than is justified by their fundamentals simply because the market is requiring
a high yield for that kind of instrument at the moment. An investor who can
purchase this instrument while it has a high yield can profit from the movement over time to a more efficient, fair price. As it happens, instruments don’t
usually become cheap solely because their prices don’t move while their fundamentals improve drastically. Rather, prices are more often the determinant
of value than changing fundamentals, and in the case of a cheap instrument,
this implies that the instrument’s price must have fallen substantially. So in
some sense, the value investor is being paid to take on the risk of standing in
the way of momentum. Ray Ball, a professor of accounting at the University
of Chicago’s Booth School of Business, wrote a paper, “Anomalies in Relationships Between Securities’ Yields and Yield‐Surrogates,” which echoes the
idea that higher‐yielding stocks—those with higher earnings yields—are likely
those for which investors expect to receive higher returns and greater risks.6
When done on a relative basis, that is, buying the undervalued security and selling the overvalued one against it, this strategy is also known
as a carry trade. One receives a higher yield from the long position and
finances this with the short position, on which a lower yield must be paid.
The spread between the yield received and the yield paid is the carry. For
instance, one could sell short $1,000,000 of U.S. bonds and use the proceeds
to buy $1,000,000 of higher‐yielding Mexican bonds. Graham and Dodd,
in their landmark book Security Analysis, propose that value trading offers
investors a margin of safety. In many respects, this margin of safety can be
seen clearly in the concept of carry. If nothing else happens, a carry trade offers an investor a baseline rate of return, which acts as the margin of safety
Graham and Dodd were talking about.

Inside the Black Box

Carry trading is an enormously popular kind of strategy for quants
(and discretionary traders) in currencies, where the currency of a country
with higher short‐term yields is purchased against a short position in the
currency of a country with relatively low short‐term yields. For example,
if the European Central Bank’s target interest rate is set at 4.25 percent,
whereas the U.S. Federal Reserve has set the Fed Funds rate at 2 percent, a
carry trade would be to buy euros against the U.S. dollar. This is a classic
value trade because the net yield is 2.25 percent (4.25 percent gained on the
euro position, less 2 percent paid in U.S. interest), and this provides a margin
of safety. If the trade doesn’t work, the first 2.25 percent of the loss on it is
eliminated by the positive carry. Similar strategies are employed in trading
bonds. In fact, this was one of Long‐Term Capital Management’s central
trading ideas, until the firm imploded in 1998.
Note that, in currencies and in bonds, the connection between higher
yields and higher risk is more widely understood than in equities. In other
words, if some instrument has a higher yield than its peers, there may well
be a good reason that investors demand this higher yield. The reason is usually that this instrument is more risky than its peers. This can naturally be
seen in the juxtaposition of yields on government bonds, AAA‐rated corporate bonds, and various lower‐rated corporate bonds. As riskiness increases,
so too do yields to compensate lenders.
Another important example of value trading is in equities, where many
kinds of traders seek to define metrics of “cheapness,” such as earnings before
interest, taxes, depreciation, and amortization (EBITDA) versus enterprise
value (EV) or book value to price. Book value per share versus price (book
yield or book‐to‐price) is also a fairly common factor, as it has been among
quants since Fama and French popularized it in their papers. Most quant
equity traders who use value strategies are seeking relative value rather than
simply making an assessment of whether a given stock is cheap or expensive.
This strategy is commonly known as quant long/short (QLS). QLS traders
tend to rank stocks according to their attractiveness based on various factors,
such as value, and then buy the higher‐ranked stocks while selling short the
lower‐ranked ones. For example, assume that we ranked the major integrated
oil companies by the following hypothetical book‐to‐price ratios:
Company

Book‐to‐Price Ratio (Hypothetical)

Marathon Oil (MRO)

95.2%

ConocoPhillips (COP)

91.7%

Chevron Corp. (CVX)

65.4%

Exxon Mobil Corp. (XOM)

33.9%

Alpha Models: How Quants Make Money

According to this metric, the higher‐ranked stocks might be candidates for
long positions, whereas the lower‐ranked might be candidates for short positions. The presumption is that a stock with a higher book‐to‐price ratio might
outperform stocks with lower book‐to‐price ratios over the coming quarters.
Value can be used to time any kind of instrument for which valuations
can be validly measured. This is easier in instruments such as individual
equities, equity indices, currencies, and bonds. In the case of most commodities, value is usually thought of more to a “cheap/expensive” analysis,
via concepts of the expected supplies of a commodity versus the expected
demand for that commodity, rather than being focused on yield. There are
classes of strategies in the futures markets (not specifically commodity futures, but most often in that group) that focus on yield explicitly as well.
Roll yield is the spread between the price of a futures contract with some
expiry date in the future, versus that of the spot (or that of the contract with
a shorter‐dated expiry). In backwardated markets, spot prices are higher
than futures contracts as they extend out into the calendar. Because there is
a convergence of futures contracts up to the spot price, futures in this situation are considered to have positive roll yield. In contango markets, spot
prices are lower than futures, and so the yield is considered negative.
Growth/Sentiment Growth strategies seek to make predictions based on the
asset in question’s expected or historically observed level of economic growth.
Some examples of such ideas could be gross domestic product (GDP) growth
or earnings growth. That a given stock is a growth asset implies nothing about
its valuation or yield. The theory here is that, all else being equal, it is better to
buy assets that are experiencing rapid economic growth and/or to sell assets
that are experiencing slow or negative growth. Some growth metrics, such as
the price/earnings‐to‐growth (PEG) ratio (PE ratio vs. EPS growth rate), are
basically a forward‐looking concept of value; that is, they compare growth
expectations to value expectations to see whether a given instrument is fairly
pricing in the positive or negative growth that the trader believes the asset will
likely experience. If you expect an asset to grow rapidly but the market has
already priced the asset to account for that growth, there is no growth trade
to be made. In fact, if the market has priced in a great deal more growth than
you expect, it might even be reasonable to short the instrument. But certainly
many forms of growth trading are simply focused on buying rapidly growing
assets regardless of price and selling assets with stagnant or negative growth,
even if they are very cheap (or offer high yields) already.
The justification for growth investing is that growth is typically experienced in a trending manner, and the strongest growers are typically becoming
more dominant relative to their competitors. In the case of a company, you
could see the case being made that a strong grower is quite likely to be

Inside the Black Box

in the process of winning market share from its weaker‐growing competitors. Growth investors try to be early in the process of identifying growth
and, hence, early in capturing the implied increase in the future stature of
a company. We can see examples of both macroeconomic growth strategies
and microeconomic growth strategies in the quant trading world. At the
macro level, some foreign exchange trading concepts are predicated on the
idea that it is good to be long currencies of countries that are experiencing
relatively strong growth, because it is likely that these will have higher relative interest rates in the future than weaker‐growth or recession economies,
which makes this a sort of forward‐looking carry trade.
In the quant equity world, the QLS community frequently also utilizes
signals relating to growth to help diversify their alpha models. Note that an
important variant of growth trading utilized by a wide variety of quants and
discretionary equity traders focuses on analysts’ earnings estimate revisions
(or other aspects of analyst sentiment, including price targets and recommendation levels). Sell‐side analysts working at various brokerage houses
publish their estimates and release occasional reports about the companies
they cover. The thesis is identical to any other growth strategy, but the idea
is to try to get an early glimpse of a company’s growth by using the analysts’
expectations rather than simply waiting for the company itself to report its
official earnings results. Because this strategy depends on the views of market analysts or economists, it is called a sentiment‐based strategy. The quant
community does not universally agree that sentiment‐based strategies, such
as the estimate revision idea just mentioned, are nothing more than variants of growth strategies, but it is my experience that these two are highly
enough correlated in practice to warrant their being treated as close cousins.
After all, too often Wall Street analysts’ future estimates of growth look a lot
like extrapolations of recent historical growth.
Quality The final kind of theory‐driven fundamental alpha is what I call
quality. A quality investor believes that, all else being equal, it is better to
own instruments that are of high quality and better to sell or be short instruments of poor quality. The justification for this strategy is that capital
safety is important, and neither growth nor value strategies really capture
this concept. A strategy focused on owning higher‐quality instruments may
help protect an investor, particularly in a stressful market environment. Not
coincidentally, these are frequently termed flight‐to‐quality environments.
This kind of strategy is easily found in quant equity trading but not as commonly in macroeconomic types of quant trading, probably because, historically, countries were not thought of as being particularly risky. Given the
unfolding crisis in Europe, we may begin to see quality models deployed in
more macroeconomics‐oriented strategies.

Alpha Models: How Quants Make Money

I generally find that quality signals fall into one of five categories. First
is leverage, which would indicate that, based on some measurement of leverage, one should short higher-levered companies and go long less-levered
companies, all else equal. An example from the QLS world might look at the
debt‐to‐equity ratios of stocks to help determine which ones to buy and sell,
the idea being that less‐leveraged companies are considered higher quality
than more‐leveraged companies, all else equal.
A second kind of quality signal is diversity of revenue sources, which
would find those companies or countries with more diverse sources of potential growth to be of higher quality than those with fewer sources. So, all
else equal, a company that makes money doing a wide variety of things for
a variety of customers should be more stable than a company that makes exactly one kind of widget for some narrow purpose. A special case of this relates to the volatility of revenues (or, in the case of companies, profits). Here,
taking the example of corporate earnings and stock prices, investors would
prefer, all else equal, to own companies whose earnings are more stable (less
volatile) relative to companies whose earnings are less stable (more volatile).
A third type of quality signal is management quality, which would
tend to buy companies or countries that are led by better teams and sell
those with worse teams. A great article in Vanity Fair relates to this very
kind of signal. Entitled “Microsoft’s Lost Decade,” several key management
missteps (according to the article’s author) are highlighted as leading to
Microsoft’s fall from being the largest market capitalization company in the
world to being a “barren wasteland.” As you might expect, given the types
of information involved, this is one of the more difficult types of signals to
quantify. However, there are measures found, for example, in companies’
financial statements, including changes in discretionary accruals (the idea
being, the greater the increase in discretionary accruals, the more likely there
are problems with the management’s stewardship of the company).
A fourth type of quality strategy is fraud risk, which would buy companies or countries where the risk of fraud is low, and sell those where the risk
is greater. An example of this kind of strategy from the QLS world is an earnings quality signal, which attempts to measure how close are a company’s
true economic earnings (as measured by, say, the free cash flow) to the reported earnings‐per‐share numbers. Such strategies especially gained prominence in the wake of the accounting scandals of 2001 and 2002 (Enron and
WorldCom, for example), which highlighted that sometimes publicly traded
companies are run by folks who are trying harder to manage their financial
statements than manage their companies.
A final type of strategy relates to the sentiment investors have regarding
the quality of the issuer of an instrument (again, this can be a company or
a country). Generally, quality‐related sentiment strategies are focused on a

Inside the Black Box

forward‐looking assessment of the four quality categories above. In other
words, one has a prospective view of changes in leverage, revenue diversity,
management quality, or fraud risk. However, this type of strategy is not
particularly common, as the signals would appear very sporadically, and
because there are relatively few sources of sentiment regarding quality, it is
also quite difficult to backtest and achieve any kind of statistical significance.
In recent years, the growth of the CDS markets has provided a much more
regularly available source of quality‐sentiment information. Some investors
would also use implied volatility to serve this purpose, but implied volatilities go up because the market itself goes down, because growth expectations
are lowered, because a company disappoints expectations on their earnings
announcement, or for any number of other reasons unrelated to the quality
of the company itself.
Quality’s performance over time fluctuates greatly and is highly dependent on the market environment. In 2008, quality was a particularly successful factor in predicting the relative prices of banking stocks. In particular,
some quality factors helped traders detect, avoid, and/or sell short those
banks with the most leverage or the most exposure to mortgage‐related
businesses, thereby allowing these traders to avoid or even profit from the
2008 credit crisis. The aforementioned accounting scandals in the early
2000s also would have been profitable for quality signals. However, for all
that these strategies profit when things are very dire, they tend to do poorly
when the markets are performing well, and terribly when the equity markets
go into a state of euphoria.
We now have a summary of the ways that theory‐driven, alpha‐focused
traders (including quants) can make money. To recap, price information can
be used for trend or mean reversion strategies, whereas fundamental information can be used for yield (better known as value), growth, or quality
strategies. This is a useful framework for understanding quant strategies but
also for understanding all alpha‐seeking trading strategies. The framework
proposed herein provides a menu of sorts, from which a particular quant
may “order,” creating his strategy. It is also a useful framework for quants
themselves and can help them rationalize and group the signals they use into
families. Quants sometimes fool themselves into thinking that there are a
broader array of core alpha concepts than actually exist.

Data-Driven Alpha Models
We now turn our attention to data‐driven strategies, which were not included in the taxonomy shown in Exhibit 3.1. These strategies are far less widely
practiced for a variety of reasons, one of which is that they are significantly

Alpha Models: How Quants Make Money

more difficult to understand and the mathematics are far more complicated.
Data mining, when done well, is based on the premise that the data tell you
what is likely to happen next, based on some patterns that are recognizable
using certain analytical techniques. When used as alpha models, the inputs
are usually sourced from exchanges (mostly prices), and these strategies
typically seek to identify patterns that have some explanatory power about
the future.
There are two advantages to these approaches. First, compared with
theory‐driven strategies, data mining is considerably more technically challenging and far less widely practiced. This means that there are fewer competitors, which is helpful. Because theory‐driven strategies are usually easy
to understand and the math involved in building the relevant models is usually not very advanced, the barriers to entry are naturally lower. Neither
condition exists in the case of data‐driven strategies, which discourages
entry into this space. Second, data‐driven strategies are able to discern behaviors whether they have been already named under the banner of some
theory or not, which allows them to discover that something happens without having to understand why. By contrast, theory‐driven strategies capture
the kinds of behavior that humans have identified and named already, which
may limit them to the six categories described earlier in this section.
For example, many high‐frequency traders favor an entirely empirical,
data‐mining approach when designing their short‐term trading strategies for
equity, futures, and foreign exchange markets. These data‐mining strategies
may be more successful in high frequency because, if designed well, they are
able to discern how the market behaves without having to worry about the
economic theory or rationalization behind this behavior. Since there is not
much good literature at this time about the theoretical underpinnings of human and computerized trading behaviors at very short‐term time horizons
(i.e., minutes or less), an empirical approach may actually be able to outperform a theoretical approach at this timescale. Furthermore, at this timescale
there is so much more data to work with that the empirical researcher has a
better chance of finding statistically significant results in his testing.
However, data‐mining strategies also have many shortcomings. The
researcher must decide what data to feed the model. If he allows the
model to use data that have little or no connection to what he is trying to
forecast—for example, the historical phases of the moon for every day over
the past 50 years as the input to a forecast of the price of the stock market—
he may find results that are seemingly significant but are in reality entirely
spurious. Furthermore, if the researcher chooses the set of all data generally
thought to be useful in predicting markets, the amount of searching the algorithms must conduct is so enormous as to be entirely impractical. To run a
relatively thorough searching algorithm over, say, two years of intraday tick

Inside the Black Box

data, with a handful of inputs, might take a single computer processor about
three months of continuous processing before it finds the combinations of
data that have predictive power. If this was not difficult enough, whatever
strategies are found in this manner require the past to look at least reasonably like the future, although the future doesn’t tend to cooperate with this
plan very often or for very long. To deal with this problem, the data‐mining
strategy requires nearly constant adjustment to keep up with the changes
going on in markets, an activity that has many risks in itself.
A second problem is that generating alphas using solely data‐mining
algorithms is a somewhat dubious exercise. The inputs are noisy, containing
a great number of false signals that act like traps for data miners. In general,
strategies that use data‐mining techniques to forecast markets do not work,
though there are a few exceptions.
In spite of (or, perhaps, because of) the aforementioned challenges facing data‐driven quant strategies, there are traders who implement them, and
it is worthwhile to understand some of what goes into these types of models.
Let’s first frame the problem broadly. Data‐driven strategies look at the current market conditions, search for similar conditions in the historical data,
and determine the probability that a type of outcome will occur afterwards.
The model will choose to make a trade when the historical probabilities are
in favor of doing so, and otherwise will not.
It also bears mentioning that, as much as data‐driven quant strategies
are often mathematically more difficult to understand, even here there is
an analog within the discretionary trading world. Technical analysts, also
known as “chartists” because of their use of price and/or volume graphs
to detect market patterns, are also looking for repeated patterns in market
behavior that lead to predictable outcomes.
So, if data mining quants are primarily looking at current market conditions, searching the history for similar conditions, determining the probabilities of various outcomes in the aftermath of that setup, and making
trades in accordance with the probabilities, they must, at a minimum, address several questions.
What defines the “current market condition”? Remember, with a quant
trading strategy, there is no leeway to be vague. Telling one’s computer to
“find me situations in the past that look like the situation right now” isn’t
enough. One must specify precisely what “current” means and what “condition” means. In the case of “current,” and not to get too philosophical about
the concept of time, but the present can refer to an instantaneous moment,
or the last few minutes, or the last 10 years. There is no standard, and the
quant must determine her preference in this regard. So, even in this most
empirical, data‐driven quant strategy, discretion is a key aspect of the creation of a strategy. In the case of “condition,” do we mean merely some aspect

Alpha Models: How Quants Make Money

of price behavior, or do volumes and/or fundamental characteristics matter
also? This is not merely an academic question: It is easy to see that, whether
one treats the price behavior of two small‐capitalization technology companies the same way as one treats the behavior of one of those companies versus that of a mega‐cap diversified financial firm is a matter of fundamental
beliefs about how the market works.
What is the search algorithm used to find “similar” patterns? Hand in
hand with this question is another: What does “similar” mean? And, also
related: By what method does the algorithm determine the probability of the
outcome? These are the least easily conceptualized and the most technical
questions on the list. I can only say that choosing statistical techniques that
are appropriate to the dataset is very obviously critical, and that the quant
must be careful. One of the most common follies in quant trading is to apply
a statistical tool to the wrong problem. There is a great deal of art and judgment that pertains to this decision, making it difficult to generalize a good
answer to this question.
How far into the past will the search be conducted? A decidedly more
straightforward question, conceptually, is how far into the past to look for
similar patterns. The trade-off is simple, and it pervades quant research (and
discretionary investment management). On the one hand, more recent data
matters a lot, because it is the most relevant to the immediate present and
near future. While it’s debatable whether human behavior ever really changes, it’s clear that technology, and therefore the way humans interact with
one another, does evolve, and not only this, but it evolves faster as more
time passes. Market structures, too, evolve. How relevant would data from
the Buttonwood Tree era of the NYSE be to the current world of almost
exclusively electronic exchanges? On the other hand, with data‐mining techniques applied to such noisy datasets as capital markets present, statistical
significance is always of paramount importance. The greater the amount
of data, the greater one’s confidence is in the statistical conclusions drawn
from the data, for most types of statistical tests. So, while the more recent
past is more relevant, the more data, the merrier. The quant (and the investor examining the quant) must determine the appropriate balance between
these conflicting traits of statistical analysis applied to systems with dynamic
conditions.

Implementing the Strategies
There are not many ways for alpha‐focused traders to make money, whether
they are quants or not. But the limited selection of sources of alpha does
not imply that all quants choose one of a handful of phenomena and then

Inside the Black Box

have a peer group to which they are substantively identical. There is in fact
considerable diversity among alpha traders, far more so than may be evident
at first glance.
This diversity stems from the way quants implement their strategies,
and it is to this subject that we now turn our attention. There are many characteristics of an implementation approach that bear discussion, including
the forecast target, time horizon, bet structure, investment universe, model
specification, and run frequency.

Forecast Target
The first key component of implementation is to understand exactly what
the model is trying to forecast. Models can forecast the direction, magnitude, and/or duration of a move and furthermore can include an assignment of confidence or probability for their forecasts. Many models
forecast direction only, most notably the majority of trend‐following strategies in futures markets. They seek to predict whether an asset price will
rise or fall, and nothing more. Still others have specific forecasts of the size
of a move, either in the form of an expected return or a price target. Some
models, though they are far less common, also seek to identify how long
a move might take.
The signal strength is an important (but not ubiquitous) aspect of quant
models. Signal strength is defined by an expected return and/or by confidence. The larger the expected return (i.e., the further the price target is
from the current price), the greater the strength of the signal, holding confidence levels constant. Similarly, the more confidence in a signal, the greater
the signal strength, holding expected returns constant. In general, though
certainly not always, a higher level of signal strength results in a bigger bet
being taken on a position. This is only rational. Imagine that you believe
two stocks, Exxon Mobil (XOM) and Chevron (CVX), both will go up, but
you have either a higher degree of confidence or a larger expected return in
the forecast for XOM. It stands to reason that you will generally be willing
to take a bigger bet on XOM than on CVX because XOM offers a more
certain and/or larger potential return. The same holds for quant models,
which generally give greater credence to a forecast made with a relatively
high degree of confidence or large expected return. This concept can also
influence the approach a strategy will take to executing the trades resulting
from signals with varying strengths, which we will address in Chapter 7.
However, the use of signal strength also bears some caution. Very large signals are unusual, and therefore there may be less statistical confidence that
the relationship between the forecast and the outcome have the same relationship as is the case with smaller signals.

Alpha Models: How Quants Make Money

Time Horizon
The next key component to understanding implementation of the alpha
model is time horizon. Some quant models try to forecast literally microseconds into the future; others attempt to predict behavior a year or more
ahead. Most quant strategies have forecast horizons that fall in the range of
a few days to several months. Notably, a strategy applied to the very short
term can look quite different from the way it would if the exact same idea
was applied to the very long term, as illustrated by Exhibit 3.6. As you can
see, a “medium‐term” version of the moving‐average‐based trend‐following
strategy would have been short the S&P 500 index during the entirety of
April and May 2008 because of the downtrend in the markets that began
in October 2007. By contrast, as shown in the lower graph in Exhibit 3.6, a
shorter‐term version of the same strategy would have been long on the S&P
for all but three days in mid‐April and for the last days of May. This exhibit
illustrates that the same strategy, applied over different time horizons, can
produce markedly different—even opposite—positions.
In general, there is more variability between the returns of a one‐
minute strategy and a one‐hour strategy than between a three‐month and
a six‐month strategy, even though the interval between the latter pair is
significantly longer than that between the first pair. Generalized, we find
that differentiation is greater at shorter timescales than at longer ones. This
general rule especially holds true in more risky environments. This happens because the shorter‐term strategies are making very large numbers of
trades compared with the longer‐term versions of the same strategies. Even
a small difference in the time horizon of a strategy, when it is being run at
a short timescale, can be amplified across tens of thousands of trades per
day and in the millions per year. By contrast, three‐ and six‐month versions
of the same strategy are simply making a lot fewer trades, so the difference
in time horizon does not get amplified. So, for example, a 150‐day moving
average versus a 300‐day moving average trend‐following strategy would
produce the exact same constant short position in the S&P 500 during April
and May 2008 as the trend‐following strategy that uses 60‐ and 100‐day
moving averages. By contrast, taking merely 10 days off of the longer moving average from the shorter‐term system so that it now uses 5‐ and 10‐day
moving averages causes the system to be short the S&P for several extra
days in mid‐April and to add another short trade in mid‐May that the 5‐/20‐
day version would not have done. Instead of being short the S&P for eight
trading days out of the total of 43 during these two months, the 5‐/10‐day
version would be short for 15 out of the 43 days.
The choice of time horizon is made from a spectrum with a literally
infinite number of choices; that is, forecasts can be made for two weeks

Inside the Black Box

S&P 500 Index,
April–May 2008
1,450
1,400
1,350
1,300
S&P 500 Index

1,250

200-Day Moving Average
60-Day Moving Average

1,200
1,450

1,400

1,350

1,300
S&P 500 Index
1,250

20-Day Moving Average
5-Day Moving Average

Exhibit 3.6

5/27/2008

5/20/2008

5/13/2008

5/6/2008

4/29/2008

4/22/2008

4/15/2008

4/8/2008

4/1/2008

1,200

Same Strategy on Different Time Horizons

into the future, or for two weeks and 30 seconds, or for two weeks and
31 seconds, and so on. Yet adding 30 or 31 seconds to a forecast of two
weeks might not cause a great deal of differentiation. Along this line of
thinking, a classification may be helpful in understanding the distinctions
among quant trading strategies by time horizon. High‐frequency strategies are the fastest, making forecasts that go no further than the end of

Alpha Models: How Quants Make Money

the current trading day. Short‐term strategies, the second category, tend to
hold positions from one day to two weeks. Medium‐term strategies make
forecasts anywhere from a few weeks to a few months ahead. Finally, long‐
term strategies hold positions for several months or longer. The lines of
demarcation between these groups are arbitrary, but in my experience, this
shorthand can be helpful in thinking about how various quant strategies
might compare with one another.

Bet Structure
The next key component of an alpha model is bet structure, which, in turn,
is based on how the alpha model generates its forecast. Models can be made
to forecast either an instrument in itself or an instrument relative to others.
For example, a model could forecast that gold is cheap and its price is likely
to rise or that gold is cheap relative to silver, and that gold is therefore likely
to outperform silver. When looking at relative forecasts, one can forecast
the behavior of smaller clusters (e.g., pairs) or larger clusters (e.g., sectors).
Smaller clusters have the advantage of being easier to understand and analyze. In particular, pairs are primarily attractive because, in theory, one can
carefully select instruments that are directly comparable.
However, pairs have several comparative disadvantages. Very few assets
can actually be compared so precisely and directly with one other instrument, rendering a major benefit of pairs trading impracticable. Two Internet
companies might each depend significantly on revenues from their respective search engines, but they may differ along other lines. One could have
more of a content‐driven business while the other uses advertising to supplement the search engine revenues. Meanwhile, one could find other companies with strong advertising or content businesses, each of which shares
some characteristics and sector‐effects with the first pair. Here the trader is
presented with a dilemma: Which pairs are actually the best to use? Or to
put it another way, how should the trader’s pairs best be structured?
Another approach is to make relative bets within larger clusters or
groups. Researchers group securities together primarily in an effort to isolate
and eliminate common effects among the group. A large part of the point of
grouping stocks within their market sector, for example, is to eliminate the
impact of a general movement of the sector and thereby focus on the relative
movement of stocks within the sector. It turns out to be extremely difficult
to isolate group effects with a group size of merely two. On the other hand,
larger clusters allow for a cleaner distinction between group behavior and
idiosyncratic behavior, which is beneficial for many quant strategies. As a result, most quants who trade in groups tend to use larger groups than simply
pairs when they make relative bets.

Inside the Black Box

Researchers also must choose how they create these clusters, either using statistical techniques or using heuristics (e.g., fundamentally defined industry groups). There are many statistical techniques aimed at discerning
when things are similar to each other or when they belong together as a
group. However, statistical models can be fooled by the data, leading to bad
groupings. For example, there may be periods during which the prices of
Internet stocks behave like the price of corn. This may cause the statistical
model to group them together, but Internet stocks and corn are ultimately
more different than they are similar, and most fundamental grouping approaches would never put them together. Furthermore, any time that the
market regime changes, the relationships among instruments frequently also
change, which can lead the system to mistakenly group things together, even
though they no longer will behave like each other.
Alternatively, groups can be defined heuristically. Asset classes, sectors,
and industries are common examples of heuristically defined groups. They
have the advantage of making sense and being defensible theoretically, but
they are also imprecise (for instance, to what industry does a conglomerate such as General Electric belong?) and possibly too rigid. Rigidity in
particular can be a problem because over time, similarities among instruments change. Sometimes stocks and bonds move in opposite directions,
and sometimes they move in the same direction. Because the correlation
between these two asset classes moves in phases, it can be very tricky to
analyze the relationship theoretically and make a static, unchanging declaration that they belong in the same group or in different groups. As a result,
most grouping techniques (and by extension, most strategies that are based
on relative forecasts), whether statistically driven or heuristic, suffer from
changes in market regime that cause drastic changes in the relationships
among instruments.
In evaluating alpha‐oriented strategies, this distinction among bet structures, most notably between directional (single security) bets versus relative
(multisecurity) bets, is rather important. The behavior of a given type of
alpha model is very different if it is implemented on an instrument by itself
than it would be if implemented on a group of instruments relative to each
other. It is critical to balance the risks and benefits of the various approaches
to grouping. In general, relative alpha strategies tend to exhibit smoother
returns during normal times than intrinsic alpha strategies, but they can also
experience unique problems related to incorrect groupings during stressful periods. Some quants attempt to mitigate the problems associated with
any particular grouping technique by utilizing several grouping techniques
in concert. For example, one could first group stocks by their sectors but
then refine these groupings using a more dynamic statistical approach that
reflects recent correlations among the stocks.

Alpha Models: How Quants Make Money

Also, it is worth clarifying one piece of particularly unhelpful, but
widely used, hedge fund industry jargon: relative value. This term refers to
strategies that utilize a relative bet structure, but the value part of the term
is actually not useful. Certainly strategies that make forecasts based on a
notion of the relative valuation of instruments are quite common. However, most strategies called relative value have little to do with value investing. Relative mean reversion strategies, relative momentum strategies, and
other kinds of relative fundamental strategies are all commonly referred to
as relative value.

Investment Universe
A given strategy can be implemented in a variety of instruments, and the
quant must choose which ones to include or exclude. The first significant choice a quant makes about the investment universe is geography. A
short‐term relative mean reversion strategy traded on stocks in the United
States might not behave similarly to the same strategy applied to stocks in
Hong Kong. The researcher must decide where to apply the strategy. The
second significant choice a quant makes about the investment universe relates to its asset class. A growth strategy applied to foreign exchange markets might behave differently than one applied to equity indices. The quant
must decide what asset classes to trade with each strategy. A third significant choice a quant must make about the investment universe relates to the
instrument class. Equity indices, as accessed through the futures markets,
behave differently than single stocks, even though both belong to the equity asset class. Also, the liquidity characteristics and nature of the other
participants in a given market differ from one instrument class to another,
and these are some of the considerations quants must make regarding what
kinds of instruments to trade. There are also tax implications to consider.
Finally, in some cases, quants may include or exclude specific groups of instruments for a variety of reasons.
The choice of an investment universe is dependent on several strong
preferences that quants tend to have. First, the quant generally prefers liquidity in the underlying instruments so that estimations of transaction
costs are reliable. Second, quants generally require large quantities of high‐
quality data. In general, such data can be found in highly liquid and developed markets. Third, quants tend to prefer instruments that behave in a
manner conducive to being predicted by systematic models. Returning to
the example of biotechnology stocks, some quants exclude them because
they are subject to sudden, violent price changes based on events such as
government approval or rejection of their latest drug. Although physicians
with a biotech specialization may have some intuitions on this subject, it’s

Inside the Black Box

simply not something that most quants can model. As a result of these preferences, the most typical asset classes and instruments in which one can find
quants participating are common stocks, futures (especially on bonds and
equity indices), and foreign exchange markets. Some strategies might trade
the fixed‐income asset class using instruments other than futures (e.g., swaps
or cash bonds), though these are significantly less common today than they
were in the middle or late 1990s. Geographically, the bulk of quant trading occurs in the United States, developed Europe, and Japan, with lesser
amounts done in other parts of North America and developed Asia. Quants
are almost completely absent from illiquid instruments, or those traded over
the counter (OTC), such as corporate or convertible bonds, and are less (but
increasingly) common in emerging markets.
This last fact may change going forward as OTC markets become better regulated and electronic. But that also implies that the liquidity of these
markets will improve. As such, this notion of liquidity is perhaps the simplest way to summarize in one dimension the salient characteristics of the
trading universe for a strategy. After all, more liquid instruments also tend
to offer more high‐quality data and to be more conducive to being forecast,
on average.

Model Definition
An idea for a trading strategy, its core concept, is insufficient for use as
a trading strategy: The quant must specifically define every aspect of the
strategy before it is usable. Furthermore, any differences in the way a quant
chooses to specify or define an idea for her strategy might lead it to behave
quite differently from the way other choices would have. For example, there
could be multiple ways to define a trend. Some simply compute the total
return of an instrument over some historical period, and if that number is
positive, a positive trend is identified (a negative return would constitute a
negative trend). Other trend traders use moving average approaches, such
as the ones illustrated in Exhibits 3.1, 3.3, and 3.4, to look for prices to
rise above or below recent average prices and so determine the presence of
a trend. Still other trend strategies seek to identify the breakout of the very
early stages of a trend, found using specific price patterns they believe are
present in this critical phase, but they do not attempt to determine whether
a long‐term trend is actually in place or not.
These are but a few of the more common ways a trend can be defined.
Just so, each kind of alpha strategy can be defined in various ways, and it
is a significant part of the quant’s job to decide precisely how to specify
the strategy mathematically. This is an area for an investor in quant trading to study carefully because it is often a source of differentiation—and

Alpha Models: How Quants Make Money

otentially of comparative advantage—for a quant. In the “Time Horizon”
p
section of this chapter, we saw that even a specification about the time horizon of a strategy for timing the stock market can have a dramatic impact on
whether it is long or short at a given point in time. Given the importance of
time horizon, it is easy to understand the impact of using an entirely different definition of the strategy on its behavior. However, it may be challenging
to get a quant to share with an outsider details on exactly how his model is
specified. For the nonquant, then, model specification may remain a more
opaque aspect of the black box, but exploring this idea as much as possible
with a quant trader could, in fact, highlight the reasons for differences in
performance that are observed versus the quant’s peer group.
One especially important type of specification is in the form of setting
parameters for a model. Returning to our trend example, the number of
days in each moving average (e.g., a 5‐/10‐day moving average crossover
strategy versus a 5‐/20‐day moving average crossover strategy) is a parameter. The specification of parameters is also an area in which some quants
utilize machine learning or data‐mining techniques. In the section “Data‐
Driven Alpha Models,” we mentioned the idea of fitting models to the data
and setting parameter values. This is a problem to which machine learning
techniques, which I described earlier as being neither easily nor commonly
applied to the problem of finding alpha, are better suited and more widely
used. In essence, machine learning techniques are applied to determine the
optimal set of specifications for a quant model. Machine learning algorithms
are designed to provide an intelligent and scientifically valid way of testing
many potential sets of specifications without overfitting.
A subset of the problem of determining parameters relates to how often the models themselves are adjusted for more recent data. This process
is known as refitting because some of the same work that goes on in the
original research process is repeated in live trading in an attempt to refresh
the model and make it as adaptive as possible to current market conditions.
Because this can be a computationally intensive process, sometimes involving millions or even billions of calculations, many quants refit their models
infrequently or not at all. Refitting also leads to a greater risk of overfitting,
a very treacherous problem indeed, since spurious and fleeting relationships
may be mistaken for valid, lasting ones.

Conditioning Variables
Many strategists (those whose job is to create trading strategies) employ
conditioning variables to their strategies. These make the strategies more
complex, but they also may increase the efficacy of the forecasts generated. There are two basic types of conditioning variables. One kind is a

Inside the Black Box

modifying conditioner, which takes a given signal and changes whether
or how it is used, generally based on characteristics of the signal itself or
its results. For example, a strategist may find that utilizing a simple trend
indicator, for example, is not a sufficiently interesting strategy to pursue.
After all, there are many false starts to worry about with a trend‐following strategy, and many experienced practitioners will admit that, without
the “money management” or “risk management” rules they employ, their
strategies would be basically uninvestable. These rules, and others to be
discussed, can properly be thought of as conditioning variables for the
trend‐following strategy.
For example, a stop‐loss is a common conditioning variable to pair with
a trend‐following strategy. The idea would be to follow the trend, unless
that trend has been reversing and causing losses to the position sufficient
to trigger a stop‐loss. There are numerous kinds of stops: stop‐losses,
profit‐targets (or profit‐stops), and time stops. Stop‐losses have already been
described, and are generally employed when strategies have many “false”
signals, but where the “good” signals can yield significant profits. Just so,
most directional trend‐following strategies make money on a minority of
their trades (often less than 40 percent of them!), but the gain on their
winners is substantially larger than the losses on their losers (because of
stop‐loss techniques).
Profit‐targets are utilized when the strategist believes that the position
gets riskier as it generates profits. This is a reasonable enough concept: Markets rarely go in the same direction indefinitely, so it may make sense to take
profits if they’ve been going the same way long enough for the strategy to
generate significant profits. Finally, time‐stops are utilized to avoid the problem of holding positions on the basis of signals that may have been triggered
far enough in the past as to be considered stale. It’s a way of enforcing a
refreshing of the bets being taken in the portfolio, among other things.
A second type of conditioning variable is a secondary conditioner, which
requires the agreement (or some other set of conditions) across multiple
types of signals to trigger a tradable forecast. For example, a large portion
of fundamental equity analysts are “GARP” devotees, meaning they believe
in owning “Growth at a Reasonable Price.” If a company is identified as
being both growing and inexpensive, it is a candidate to buy. Cheapness on
its own would not justify a purchase, just as growth on its own would not.
In price‐driven strategies, sometimes trend at various timescales, or trend
and mean reversion, are combined. For example, a mean reversion strategy
could be conditioned to buy instruments that have experienced price declines, but only when that causes the resulting position to be in the direction
of the longer‐term trend (i.e., this strategy would buy dips in up‐trending
markets, or short sell run‐ups in down‐trending markets).

Alpha Models: How Quants Make Money

Utilizing conditioning variables is how most rule‐based pattern recognition
strategies are designed. Like data‐driven strategies, they are looking for repeated
patterns in market behavior (basically, more complex patterns than “buy winners/sell losers” or “buy dips/sell run‐ups”), but theory‐driven pattern‐recognition models will begin with predefined rules. Data‐driven traders rely on their
algorithms to determine what a “pattern” is in the first place (though, again,
within the bounds specified, as discussed in “Data‐Driven Alpha Models”).

Run Frequency
A final component of building a given alpha model is determining the run
frequency, or the frequency with which the model is actually run to seek
new trading ideas. Some quants run their models relatively infrequently—for
example, once per month. At the other extreme, some run their models more
or less continuously, in real time. Quants must manage an interesting tradeoff here. Specifically, increasing the frequency of model runs usually leads
to a greater number of transactions, which means more commissions paid
to brokers and higher transaction costs. Also, more frequent model runs
lead to a greater probability that the model is moving the portfolio around
based on noisy data that don’t actually contain much meaning. This, in turn,
would mean that the increased transaction costs would cause little or no
incremental improvement in the alpha generated by the strategy and would
thereby reduce its overall profitability.
On the other hand, less frequent model runs lead to a smaller number of
larger‐sized trades. These are expensive in a different way, namely in terms
of the impact these trades can have on the marketplace. If models are run
too infrequently, then at those times when they are run they could recommend making very significant changes to the currently held portfolio. This
would mean transacting larger blocks of trades, which would likely cost
more in terms of moving the market. Less frequent model runs are also
prone to problems associated with the moment of observation of markets.
If a strategy is run once a month, it could miss opportunities to trade at
more favorable prices that occur during the month while the model is dormant. Alternatively, the model may attempt in vain to trade at attractive,
but quickly fleeting, prices that occur if there has been some aberration just
around the time of the model being run.
Whether more frequent or less frequent model runs are better depends
on many other aspects of the strategy, most especially the time horizon of
the forecast and the kinds of inputs. In the end, most quants run their models no less than once a week, and many run continuously throughout the
day. The slower‐moving the strategy, obviously, the more leeway there is,
whereas shorter‐term strategies tend toward continuous, real‐time runs.

Inside the Black Box

An Explosion of Diversity
We have described a few of the kinds of important decisions that quants
must make in building a given alpha model. To succeed in quant trading,
each of these decisions requires good judgment on the part of the quant. In
short, successful quants are characterized in part by an incredible attention
to detail and tirelessness in seeking the right questions to ask and the best
solutions to address them. Nevertheless, for those who do not build quant
trading systems but who are interested in understanding them, the kinds of
issues discussed in this section are straightforward to understand and provide a useful way to distinguish one quant from another.
A final, important implication of these details of implementation is that
they lead to an explosion in the variety of quant trading strategies that actually exist. You can easily see that the number of permutations of a strategy
focused on the concept of value, for example, is enormous when accounting
for differences in the type, time horizon, bet structure, investable universe,
model definition, conditioning variables, and frequency of model run. Just
taking the first four types of implementation details listed here and using
the simplifying categories we described in this section, there are two types
of forecasts (direction and magnitude), four types of time horizon (high
frequency, short term, medium term, and long term), two types of bet structures (intrinsic and relative), and four asset classes (stocks, bonds, currencies, and commodities). Therefore one could build 64 different value models
(2 × 4 × 2 × 4 = 64 permutations), and this excludes the question of how
many ways one can define the idea of value, how one could condition the
use of value on other variables, and how often one can look for value. This
diversity might seem daunting at first glance, but the framework established
here can help anyone interested in understanding what’s inside a black box.
Exhibit 3.7 revisits the taxonomy of alpha models, expanding it to include
the implementation approaches discussed here.

Blending Alpha Models
Each of the decisions a quant makes in defining a trading strategy is an important driver of its behavior. But there is another extremely important set
of choices the quant must make in constructing a trading strategy. Specifically, the quant is not limited to choosing just one approach to a given alpha
model. Instead, he is equally free to choose to employ multiple types of
alpha models. The method used to combine these alpha models is an arena
rich with possibilities. The most sophisticated and successful quants tend to
utilize several kinds of alpha strategies, including trend and reversion, and

Alpha Models: How Quants Make Money

RETURN
CATEGORY

WHAT
QUANTS
DO

Alpha

INPUT

PHENOMENON

SPECIFICATION

Price

Trend

Reversion

Forecast
Target

Time
Horizon

HOW
THEY DO IT
IMPLEMENTATION

High
Frequency

Fundamental

Technical
Sentiment

Model
Definition

Yield

Conditioning
Variables

Bet
Structure

Growth

Quality

Run
Frequency

Instruments

Directional

Liquid

Relative

Illiquid

Short Term
Medium
Term
Long Term

Exhibit 3.7

Taxonomy of Theory‐Driven Alpha Models

various kinds of fundamental approaches across a variety of time horizons,
trade structures, instruments, and geographies. Such quants benefit from
alpha diversification in exactly the same way that diversification is helpful in
so many other aspects of financial life.
Blending or mixing alpha signals has many analogues in discretionary
trading (and decision making) in general. Imagine a mutual fund portfolio
manager who has two analysts covering XOM. One analyst, focused on
fundamental value in the classic Graham and Dodd sense, expects XOM to
rise by 50 percent over the next year. The other analyst, taking a momentum
approach, thinks XOM is likely to be flat over the next year. What is the net
expectation the portfolio manager should have of the price of XOM, given

Inside the Black Box

the two analysts’ predictions? This is the core problem that is addressed by
blending alpha models, each of which can be likened to an analyst.
The three most common quant approaches to blending forecasts are
via linear models, nonlinear models, and machine learning models. A significant fourth school of thought believes that alpha models should not
be combined at all. Instead, several portfolios are constructed, each based
on the output from a given alpha model. These factor portfolios are then
combined using any of the portfolio construction techniques discussed in
Chapter 7.
Each of these four approaches to signal mixing has its disciples, and as
with most everything else we’ve discussed, the best way to blend alphas depends on the model. In general, as in the case of an alpha model, the purpose
of a method of mixing alpha models is to find the combination of them that
best predicts the future. All other things being equal, it is very likely that any
reasonably intelligent combination of alphas will do a better job together
than any one of them could do individually over time. Consider Exhibit 3.8.
Here we can see that Forecasts A and B each occasionally predict future
events correctly. This is illustrated in that there is some overlap between
Forecast A and the actual outcome and between Forecast B and the actual
outcome. But each forecast has only a small amount of success in predicting
the future. However, together, Forecasts A and B are about twice as likely to
be correct about the future outcomes as either is separately.
Linear models are by far the most common way in which quants combine alpha factors to construct a composite forecast. A linear model is a reasonable facsimile for one of the more common ways that humans normally
think about cause‐and‐effect relationships. In linear models, the inclusion of
one factor is independent of the inclusion of other factors, and each factor
is expected to be additive, independently of the other factors that might be

Forecasting
Model A

Exhibit 3.8

Actual
Outcome

A Visualization of Multiple Forecasts

Forecasting
Model B

Alpha Models: How Quants Make Money

included or excluded. For example, for a high school student trying to get
into a good university, she can think of her grades, standardized test scores,
extracurricular activities, recommendations, and essays as being these independent factors in the linear model that predicts her odds of gaining admission. Regardless of the other factors, grades are always important, as is each
other factor. As such, a linear model is relevant. If, on the other hand, it was
the case that, with high enough test scores, her essays wouldn’t matter, a
linear model is no longer the correct way to predict her chances of getting in.
The first step in using a linear model in this way is to assign a weight
to each alpha factor. To return to our example, if we were trying to predict university admissions, this step would require us to define the relative
importance of grades versus, say, test scores. This is typically done using a
technique known as multiple regression, which is aimed at finding the combination of alpha factors that explains the maximum amount of the historical behavior of the instruments being traded. The presumption is that, if a
model reasonably explains the past, it has a reasonable chance of explaining
the future well enough to make a profit. These weights are then applied to
the outputs of their respective alpha factors, which are usually a forecast or
score of some kind. The weighted sum of these multiple forecasts gives us a
combined forecast. Or, to be more specific, by summing the products of the
weights of each factor and the outputs of each factor, we arrive at a composite forecast or score. This composite can then be used to help determine
the target portfolio.
Imagine a trading system with two alpha factors. One of the alpha factors focuses on E/P ratios (and is therefore a yield model), and the other
focuses on price trends (and is therefore a trend model). The yield factor
forecasts a return of +20 percent over the next 12 months for XOM, whereas the trend factor forecasts a return of –10 percent for XOM over the
next 12 months. Based on a historical regression, the models are weighted
70 percent toward the yield factor and 30 percent toward the trend factor.
Taking their scores and weights together, the total 12‐month return forecast
of our two‐factor model is computed as follows:
70% weight × 20% return forecast for the yield factor comes to +14%.
30% weight × -10% return forecast for the trend factor comes to -3%.
The sum of these two products comes to +11 percent, which is the total
expected 12‐month return for XOM using the example above.
A special case of linear models is the equal‐weighted model. Though not
highly quantitative, equal‐weighting methods abound among quant traders.
The general idea behind equal weighting is that the trader has no confidence

Inside the Black Box

in his ability to define more accurate weights and therefore decides to give
all the alpha factors equal importance. A variant of this approach gives each
factor an “equal risk” weighting, which incorporates the concept that giving
a dollar to a highly risky strategy is not the same as giving a dollar to a less
risky strategy. In Chapter 6, we cover both these approaches in more detail
as they apply to portfolio construction. Still another approach would be to
give each factor its own weight discretionarily.
There are many forms of nonlinear models that can be used to combine
alpha factors with each other. In contrast to linear models, nonlinear models
are based on the premise that the relationship between the variables used to
make forecasts either is not independent (i.e., each variable is not expected
to add value independently of the others) or else the relationship changes
over time. As such, the two main types of nonlinear models are conditional
models and rotation models. Conditional models base the weight of one
alpha factor on the reading of another factor.
Using the same two factors as earlier, a conditional model might indicate that E/P yields should drive forecasts, but only when the price trends
are in agreement with the E/P yields. In other words, the highest‐yielding
stocks would be candidates to be bought only if the price trends of these
stocks were also positive. The lowest‐yielding stocks would be candidates to
be sold short, but only if the price trends of these stocks were also negative.
When the agreement condition is met, the yield factor entirely drives the
forecast. But if the price trend doesn’t confirm the E/P yield signal, the yield
signal is ignored entirely.
Revisiting the linear factor combination demonstrated earlier, our conditional model would generate no signal for XOM because the price trend
forecast a negative return, whereas the yield factor forecast a positive return.
If, instead, XOM had a positive return forecast from the trend factor, the
combined nonlinear model would have a targeted return of +20 percent
over the next 12 months for that stock because this is the return expected by
the value factor, which now has been “activated” by its agreement with the
trend factor. Note that mixing models in this way is similar to utilizing more
conditioning variables in the specification of an alpha model (discussed in
“Conditioning Variables”), though it is not required that the conditional
linear model be an “all or none” type of approach. It is possible to utilize
a conditioning variable that simply increases or decreases the weight of a
given factor based on the values of other factors at that point in time. An
example of a conditional model is shown in Exhibit 3.9.
Another type of conditional model for assigning weights to various
forecasts is to consider variables external to those forecasts as the drivers
of weights. For example, some practitioners believe that stat arb strategies
perform better when market volatility is at elevated levels, and when stocks’

Alpha Models: How Quants Make Money

Exhibit 3.9

A Simple Conditional (Nonlinear) Model for Blending Alphas

Value and Momentum Disagree
Value and Momentum Agree

Value

Momentum

Signal

Long

Short

None

Value

Momentum

Signal

Long

correlations to each other are at relatively low levels. Thus, a firm trading both
mean reversion stat arb and directional trend strategies might overweight the
stat arb component when volatility is high and correlations are low. When the
opposite is true in both cases, perhaps they overweight the trend strategies.
And at other times, perhaps they equally weight both strategies.
The second nonlinear way to blend alphas uses a rotation approach.
Rather than following trends in markets themselves, this type of model follows trends in the performance of the alpha models. These are similar to
linear models except that the weights of factors fluctuate over time based
on updated calculations of the various signals’ weights. As time passes, the
more recent data are used to determine weighting schemes in the hope that
the model’s weights are more relevant to current market conditions. This
method usually results in giving higher weights to the factors that have performed better recently. As such, this is a form of trend following in the timing of alpha factors.
Machine learning models are also sometimes used by quants to determine the optimal weights of various alpha factors. As in the case of determining optimal parameters, machine learning techniques applied to the
mixing of alpha factors are both more common and more successful than
machine learning approaches used to forecast markets themselves. These
techniques algorithmically determine the mix of alpha factors that best explains the past, with the presumption that a good mix in the past is likely to
be a good mix in the future. As in the case of rotational models, many machine learning approaches to mixing alpha factors periodically update the
optimal weights based on the ever‐changing and ever‐growing set of data
available. Unlike the example of using machine learning for the generation
of actual alpha signals, applying machine learning to determine the weights
of various alpha forecasts is more common and significantly more successful. Nevertheless, machine learning remains less widely used than the other
techniques for blending alphas described here, and only a relatively small
proportion of the universe of quant traders employs these methods.
We have briefly summarized common approaches to mixing signals, or
combining alpha forecasts. This is a part of the quant trading process that
has received precious little attention in the academic literature and trade

Inside the Black Box

press, but personally I find it one of the most fascinating questions about
quant trading—or any trading. It is exactly the same problem any decision
maker faces when looking at a variety of sources of information and opinions: What is the best way to synthesize all available and relevant information into a sensible decision?
It is worth noting that signal mixing shares some similarities with portfolio construction. Both are questions of sizing and combining, after all. However, they are mostly distinct and separate processes. Signal‐mixing models
size multiple alpha signals to arrive at one composite forecast per instrument,
which is then used in portfolio construction. Portfolio construction models
take multiple kinds of signals as inputs, including alpha signals, risk models,
and transaction cost models (which we cover in the next two chapters), and
attempt to size individual positions correctly, given these inputs.

Summary
In his excellent book The Signal and the Noise, Nate Silver presents a somewhat different—though complementary and related—type of distinction between approaches to forecasting.7 Rather than being a distinction based on
the type of science one performs, as laid out in this chapter, it is a distinction
based on the branch of statistics to which one subscribes.
One major branch of statistics, now popularly known as Bayesian statistics (after Thomas Bayes), placed a strong emphasis on the role of a “prior” in forecasting. A prior in this case refers to a belief held by the forecaster.
For example, imagine that you have heard your spouse (with whom your
relationship is generally good) make what seems like an insulting statement
in reference to you. But what is the probability that this statement was, in
fact, an insult? Bayes would advise that you begin your analysis of this statement by considering what the chances are that your spouse would insult
you, before you heard this particular comment. Those odds are probably
low, in particular if the relationship is fine to begin with. Let’s say that this
probability is 10 percent. Next, we would be advised to account for the
probability that the statement we heard was not insulting, given that your
partner is unlikely to insult you. If the statement sounded really negative
(for example, “my husband is an idiot”), this, too, might be unlikely. Let’s
place these odds also at 10 percent. Finally, one should account for the possibility that you heard your partner make this statement because she is, in
fact, insulting you. If she thought you weren’t within earshot, perhaps the
odds are higher. If she sees you directly in front of her, the odds are naturally
expected to be lower. For this example, let’s assume that your partner thinks

Alpha Models: How Quants Make Money

you are not home. This makes the odds that this statement was uttered by
your partner as an insult, say, 65 percent.
Accounting for all of this information, Bayes’ Theorem would tell you
that the odds you were in fact insulted, given your priors, are just under
42 percent.8 This is a pleasingly intuitive result: Your dear spouse is not expected to insult you. However, her statement was quite negative, and it was
made in a context that increases one’s suspicion of it being meant badly. The
resulting odds are lower than they would have been without the prior that
your partner is unlikely to insult you to begin with, but much higher than if
you hadn’t heard this statement under dubious circumstances.
Readers may note the philosophical kinship between a prior and a theory. This is more than a coincidence: The two concepts are closely related.
The basic idea behind Bayesian forecasting methods is to allow new information to change a prior. The more that this new information is surprising
(i.e., in conflict with the prior), the more we move away from our prior.
Another major branch of statistics is known as frequentist statistics.
Frequentist statistics calls for the data to inform us about probabilities and
confidence intervals around those probabilities. For example, if the data indicate that a stock that has an Earnings‐to‐Price ratio of 0.03 or lower (i.e.,
a P/E ratio of 33.33 or higher, or which is negative) has historically declined
by 10 percent, with a confidence interval of six percent over the 12 months
after this ratio was observed, then you have what you need for your forecast
of any specific stock.
Again, there is a philosophical link between this idea and the data‐driven
approach described in this chapter. Furthermore, there is even a similarity
in the ways in which these distinctions can be shown to be imperfect. Many
theory‐driven scientists are big believers in looking at the data, and in allowing the data to drive decisions such as parameter values in a model. Just so,
many self‐described Bayesians can be found using frequentist techniques. In
fact, in his fascinating review of Silver’s book, Larry Wasserman of Carnegie Mellon University makes the point that Silver himself relies heavily on
frequentist approaches to ascertaining the efficacy of a model—so much so
that Wasserman calls Silver a frequentist.9
Having made so many decisions about what approach to forecasting
one should utilize, what sort of alpha should be pursued, how to specify
and implement it, and how to combine this alpha with others, the quant is
left with an output. The output is typically either a return forecast (expected
return = X percent) or a directional forecast (expected direction = up, down,
or flat). Sometimes quants add elements of time (expected return over the
next Y days) and/or probability (Z percent likelihood of expected return)
to help utilize the output effectively in trading decisions. See Exhibit 3.10

Inside the Black Box

Alpha Model

Risk Model

Transaction Cost Model

Data
Portfolio Construction Model
Research
Execution Model

Exhibit 3.10

Schematic of the Black Box

for a recap of the structure of a quant trading system. As we continue our
progress through the black box, we will highlight the components discussed.
I am consistently amazed by the juxtaposition of the simplicity and relatively small number of concepts used to manage money quantitatively and
the incredible diversity of quant trading strategies as applied in the real
world. The decisions quants make in the areas discussed in this chapter are
major sources of the significant differences in the returns of traders who
may be pursuing the same sources of alpha. Those evaluating quant traders (or quants who are evaluating trading strategies of their own) can use
the framework provided in this chapter to help determine the nature of the
strategies being traded. We now turn our attention to risk modeling, another
key component of a quant trading strategy.

Notes
1. www.turtletrader.com/trader‐seykota.html.
2. Larry Hite and Steven Feldman, “Game Theory Applications,” Commodity
Journal (May–June 1972).
3. Ginger Szala, “Making a Mint: How a Scientist, Statistician and Businessman
Mixed,” Futures, March 1, 1989.
4. Gregory Zuckerman, “Renaissance Man: James Simons Does the Math on
Fund,” Wall Street Journal, July 1, 2005.
5. Eugene Fama and Kenneth French, “The Cross Section of Expected Stock
Returns,” Journal of Finance 47 (June 1992): 427.

Alpha Models: How Quants Make Money

6. Ray Ball, “Anomalies in Relationships Between Securities’ Yields and
Yield‐Surrogates,” Journal of Financial Economics 6, nos. 2–3 (1978): 103–126.
7. Nate Silver, The Signal and the Noise: Why Most Predictions Fail but Some
Don’t (New York: Penguin Press, 2012).
8. This was calculated using Bayes’ Theorem.
9. https://normaldeviate.wordpress.com/2012/12/04/nate‐silver‐is‐a‐frequentist‐
review‐of‐the‐signal‐and‐the‐noise/.

Chapter

Risk Models
The market can remain irrational longer than you can remain
solvent.
—John Maynard Keynes

isk management should not be thought of solely as the avoidance of risk
or reduction of loss. It is about the intentional selection and sizing of
exposures to improve the quality and consistency of returns. In Chapter 3,
we defined alpha as a type of exposure from which a quant trader expects
to profit. But we also noted that, from time to time, there can be a downside
to accepting this exposure. This is not what we classify as risk per se. By
pursuing a specific kind of alpha, we are explicitly saying that we want to be
invested in the ups and downs of that exposure because we believe we will
profit from it in the long run. Though it would be great fun to accept only
the upside of a given alpha strategy and reject the losses that can be associated with it, sadly, that is not possible. However, there are other exposures
that are frequently linked to the pursuit of some kind of alpha. These other
exposures are not expected to make us any money, but they frequently accompany the return‐driving exposure. These exposures are risks.
Risk exposures generally will not produce profits over the long haul,
but they can impact the returns of a strategy day to day. More important
still, the quant is not attempting to forecast these exposures, usually because
he cannot do so successfully. But the fact remains that one of the great
strengths of quant trading is to be able to measure various exposures and to
be intentional about the selection of such exposures. This chapter deals with
how quants define, measure, and control risks.
Imagine a relative alpha strategy that focuses on the value (yield) of various stocks, buying higher‐yielding stocks and selling short lower‐yielding
stocks. This strategy clearly can lose money if “cheap” (higher‐yield) stocks

Inside the Black Box

underperform “expensive” (lower‐yield) stocks, according to whatever definition the quant chooses for “cheapness” (or yield). That risk is inherent to
the pursuit of a value strategy, even if the quant has reason to believe that
value strategies should make money in the long term. However, a value
strategy without further specification can end up taking significant sector
bets in addition to the intentional bet on value. After all, it’s easy to see that
stocks within a sector tend to move together. So if one technology stock
has gotten very cheap, there’s a reasonable chance that many other technology stocks have also gotten cheap. This means that an unconstrained
value‐hunting strategy is likely to end up with a net long position in the
technology sector (in this example). But there is no evidence that there exists
a long‐term benefit of overweighting one industry or sector versus another.
More important, assume that the strategy has neither the intention nor
the capability to forecast the performance of various sectors. Therefore, sector exposure would be considered a form of risk in our framework, because
sector performance is not being intentionally forecast, but having net exposure to various sectors can alter the strategy’s results day to day. So the key
to understanding risk exposures as they relate to quant trading strategies
is that risk exposures are those that are not intentionally sought out by the
nature of whatever forecast the quant is making in the alpha model.
If alpha models are like optimists, risk models are like pessimists. Risk
models exist largely to control the size of desirable exposures or to deal with
undesirable types of exposures. Their job is to raise hell about things that
can cause losses or uncertainty, particularly those bets that are unintentionally made or are incidental byproducts of the alpha model. Risk models both
highlight and attempt to remove undesirable exposures from a portfolio.
There are, however, only a few things you can do with a given type
of exposure, aside from simply accepting it outright. Mostly you can limit
its size or eliminate it altogether. The function of risk management in the
investment process is to determine which of these courses of action is most
prudent for each kind of exposure and to provide that input to the portfolio construction model. In general, risk models reduce the amount of
money a quant can make, but this is a trade-off many quants are willing to
accept. Managing risk has the day‐to‐day benefit of reducing the volatility of a strategy’s returns. But it also has the far more important benefit
of reducing the likelihood of large losses. In many ways, the failures of
investment managers, in general (quant or not), are usually precipitated
by failures to manage risk. This can be seen with Long‐Term Capital Management (LTCM) in 1998, with Amaranth in 2006, with U.S. quant equity
traders in August 2007, and with a great many investors in the fall (no pun
intended) of 2008.

Risk Models

Limiting the Amount of Risk
Size limiting is an important form of risk management. It is easy to imagine having a tremendously good trading idea, seemingly a sure thing, but
without some sense of risk management, there can be a temptation to put
all one’s capital into this single trade. This is almost always a bad idea.
Why? Because, empirically, a sure thing rarely exists, so the correct way to
size a trade in general is certainly not to put all your chips on it. Otherwise
it is likely that in the process of going all in, at some point the trader will
go bankrupt. In other words, it is prudent to take just as much exposure
to a trade as is warranted by the considerations of the opportunity (alpha)
and the downside (risk). Quantitative risk models that are focused on limiting the size of bets are common, and many are quite simple. The following
sections explain how they work.
There are several kinds of quantitative risk models that limit size, and
they vary in three primary ways:
1. The manner in which size is limited.
2. How risk is measured.
3. What is having its size limited.

Limiting by Constraint or Penalty
Approaches to the size limits come in two main forms: hard constraints
and penalties. Hard constraints are set to draw a line in terms of risk. For
instance, imagine a position limit that dictates that no position will be larger
than 3 percent of the portfolio, no matter how strong the signal. However,
this hard limit may be somewhat arbitrary (e.g., imagine a 3.00 percent position size limit; why is a 3.01 percent position so much worse?), so quants
sometimes build penalty functions that allow a position to increase beyond
the limit level, but only if the alpha model expects a significantly larger
return (i.e., a much larger expected return than was required to allow the
position merely to reach the limit size in the first place). The penalty functions work so that the further past the limit level we go, the more difficult
it becomes to increase the position size additionally. So, using our example,
it would be far easier to see a 3.01 percent position than to see a 6 percent
position, because the latter is further from the limit than the former.
In this way, the model attempts to address the idea that an opportunity
can sometimes be so good as to warrant an exception to the rule. In a sense,
penalty functions for size limits can be thought of as making rules to govern
exceptions.

Inside the Black Box

The levels of limits and/or penalties can be determined in the same
ways as most other things in the quant world, namely either from theory
or from the data (the latter via data‐mining approaches). Theory‐driven
approaches mostly look like an arbitrary level that is set, tested, and, if
needed, adjusted until it produces an acceptable outcome. So, to return
to the earlier example of a 3 percent limit on position sizes, the quant
researcher could have started with a risk limit of 5 percent because his
experience seemed to dictate that this was a reasonable level to choose.
But through testing and simulating the historical results of this strategy, he
could have come to realize that a far more appropriate level is 3 percent,
which better balances the ability to make sizeable bets when attractive opportunities appear against the necessity of recognizing that any given trade
could easily go wrong. Data‐driven approaches are more varied and can
include machine learning techniques to test many combinations of limits
or simply testing various limit levels and letting the historical data empirically determine the final outcome. Either way, these levels and the severity
of any penalty functions are parameters of the risk model that the quant
must set, based on either research or heuristics.

Measuring the Amount of Risk
There are two generally accepted ways of measuring the amount of risk
in the marketplace. The first is longitudinal and measures risk by computing the standard deviation of the returns of various instruments over time,
which is a way of getting at the concept of uncertainty. In finance circles, this
concept is usually referred to as volatility. The more volatility, the more risk
is said to be present in the markets.1
The second way to measure risk is to measure the level of similarity in
the behavior of the various instruments within a given investment universe.
This is frequently calculated by taking the cross‐sectional standard deviation
of all the relevant instruments for a given period. The larger the standard
deviation, the more varied the underlying instruments are behaving. This
means that the market is less risky because the portfolio can be made of a
larger number of diversified bets. This can be seen easily at the extreme: If all
the instruments in a portfolio are perfectly correlated, then as one bet goes,
so go all the other bets. This concept is known among quants as dispersion.
Dispersion can also be measured by the correlation or covariance among
the instruments in a given universe. Here, too, the more similarly the instruments are behaving, the more risky the market is said to be.
There are many other, less commonly utilized, approaches to measuring risk as well. These include the use of measures such as credit spreads or
credit default swaps (CDSs), or the use of implied volatilities.

Risk Models

Where Limits Can Be Applied
Size‐limiting models such as these can be used to govern many kinds of
exposures. One can limit the size of single positions and/or groups of positions, such as sectors or asset classes. Alternatively, one can limit the size of
exposure to various types of risks. For example, in equity trading, one can
limit the exposure of a model to market bets (such as a +/–5 percent net
exposure limit) or to market capitalization bets. In general, risks that are
subjected to limits or penalties are those that are not being forecast explicitly by the alpha model. If an alpha model attempts to forecast individual
stocks but makes no attempt to forecast the stock market as a whole, it may
be prudent to constrain the size of the bet that the portfolio can ultimately
take on the stock market.
Still another component of a risk model may be to govern the amount
of overall portfolio leverage. Leverage can be controlled in a variety of ways.
For example, one can manage money under the premise that when opportunities abound, more leverage is desirable, whereas when fewer opportunities
are present, less leverage is desirable. Alternatively, many quants attempt to
offer their investors or bosses a relatively constant level of risk. Using volatility and dispersion as proxies for risk, quants can measure the amount of
risk in markets and vary their leverage accordingly to produce a more stable
level of risk. The most common tool used for this purpose is known as a
value at risk (VaR) model, but there are others that are similar philosophically. These models typically consider the dollar amount of exposures in a
portfolio and, based on current levels of volatility, forecast how much the
portfolio can be expected to gain or lose within a given confidence interval.
For instance, most VaR models calculate what a daily single standard deviation move in portfolio returns will be, based on current volatility levels.
The way that these models control risk in the face of rising volatility is to
reduce leverage. Therefore, in general, the higher the reading of risk in a VaR
model, the lower the level prescribed for leverage.
In Chapter 10, we discuss some of the significant problems with these
kinds of risk models. For now I will simply point out that the core purpose
of such risk models seems to me to be flawed. Other kinds of investments,
such as stocks, bonds, mutual funds, private equity, or fine wine, do not attempt to offer fixed levels of volatility. Why should quants want to manage
risk in this manner, or be asked to do so? Furthermore, if a quant is good at
forecasting volatility or dispersion, there are far more interesting and productive ways to utilize these forecasts (for example, in the options markets)
than there are in a risk model that governs leverage. These kinds of models
often cause traders to take too little risk in more normal times and too much
risk in very turbulent times. Nevertheless, they are wildly popular.

Inside the Black Box

A more theoretically sound approach, though substantially harder to
implement practically, seeks to increase leverage when the strategy has better odds of winning and to decrease risk when the strategy has worse odds.
The trick, of course, is to know when the odds are on one’s side. Some
quants solve this problem by allowing the level of leverage to vary with
the overall strength and certainty of the predictions from the alpha model,
which seems to be a reasonable approach.2

Limiting the Types of Risk
Though limiting the amount of an exposure is important, some approaches
to risk modeling focus on eliminating whole types of exposure entirely. Imagine that an investor’s analysis indicates that Chevron Corporation (CVX)
is likely to outperform Exxon Mobil Corporation (XOM). But the trade the
investor makes is simply to go long CVX while ignoring XOM. If the market drops precipitously afterward, or if the oil sector performs very poorly,
the investor will most likely lose money on the trade, despite the correctness
of his thesis. This is because the investor is exposed to market directional
risk and to oil sector risk, even though he didn’t have any particular foresight as to where the market or the oil sector was going. The investor could
have substantially eliminated the unintentional or accidental market direction risk if he had expressed his analysis by buying CVX and shorting an
equivalent amount of XOM. This way, whether the market rises, falls, or
does nothing, he is indifferent. He is only affected by being right or wrong
that CVX would outperform XOM.
As a general rule, it is always better to eliminate any unintentional exposures, since there should be no expectation of being compensated sufficiently for accepting them. Quantitative risk models designed to eliminate
undesired exposures come in two familiar flavors: theoretical and empirical.
Each is discussed in detail in the subsequent sections.
It is also worth noting that alpha models can (and often do) incorporate risk management concepts. Let’s assume that a quant is building a
relative alpha strategy. A significant amount of work is required to match
what “relative” means to the exposures he intends to take or hedge. Revisiting an earlier example, if the quant is building a relative alpha strategy to
forecast equity returns, he might not believe he has a valid way to forecast
the returns of the sectors to which these equities belong. In this case, the
quant may design his bet structures so that he is making forecasts of stocks’
returns relative to their sectors’ returns, which means that he never has a
bet on the direction of the sector itself, only on which stocks will outperform and which stocks will underperform the sector. This, in turn, helps

Risk Models

him eliminate sector bets, which is clearly a risk management exercise as
much as it is alpha generation. As such, it is theoretically possible (and not
infrequently seen in practice) to incorporate all the needed components of
his risk model fully into his alpha model by specifying the alpha model such
that it only forecasts exactly the exposures from which it expects to make
money and structures its bets to avoid exposure to nonforecasted factors.
Although not all quant strategies do this, it is worth remembering to look
inside the alpha model for elements of risk management, especially for those
evaluating a quant strategy.

Theory-Driven Risk Models
Theory‐driven risk modeling typically focuses on named or systematic risk
factors. Just as in the case of theory‐driven alpha models, systematic risks
that are derived from theory are those for which the quant can make a reasonable, economic argument. Theory‐driven risk modeling uses a set of predefined systematic risks, which enables the quant to measure and calibrate a
given portfolio’s exposures.
It is important to note that the use of the term systematic in defining
risk is completely different from the use of the term systematic in describing quant strategies. Systematic risks are those that cannot be diversified
away. In the world of single stocks, the market itself is a systematic risk
because no amount of diversification among various single stocks eliminates
an investor’s exposure to the performance of the market itself. If the market is up a lot, it is extremely likely that a portfolio that is long stocks is
also going to be up. If the market is down a lot, it is extremely likely that a
portfolio that is long stocks will be down. Sector risk is another example of
systematic risk, as is market capitalization risk (i.e., small caps versus large
caps). A practical example of such a problem, and one that has been well
documented by the hedge fund replication crowd, is that an unconstrained
market‐neutral value model will very likely be making a bet on small caps
outperforming large caps.3
The world of fixed income, similarly, contains a host of systematic risks.
For example, whether one owns corporate bonds or government bonds,
owners of these bonds are all subject to interest rate risk; that is, the risk
that rates will go up, regardless of the level of diversification of the actual portfolio of bonds. Similar examples can be found in any asset class
and frequently also across asset classes. Any economically valid grouping
of instruments, in other words, can be said to share one or more common
systematic risk factors. An investor who traffics in any of those instruments,
then, should be aware of this risk factor and should be either making intentional bets on it or eliminating his exposure.

Inside the Black Box

Empirical Risk Models
Empirical risk models are based on the same premise as theory‐driven models, namely that systematic risks should be measured and mitigated. However, the empirical approach uses historical data to determine what these
risks are and how exposed a given portfolio is to them. Using statistical
techniques such as principal component analysis (PCA), a quant is able to
use historical data to discern systematic risks that don’t have names but that
may well correspond to named risk factors.4 For example, a PCA run on
bond market data using Treasury bonds across various maturities usually
shows that the first (most important) risk factor statistically corresponds
to the level of interest rates, or what a theory‐driven risk model might call
interest rate risk. PCA and other statistical models are commonly used in equity markets as well, and these models typically find that the market itself is
the first, most important driver of returns for a given stock, usually followed
by its sector. These statistical risk models are most commonly found among
statistical arbitrage traders, who are betting on exactly that component of
an individual stock’s returns that is not explained by systematic risks. It is
important to note that such statistical methods may discover entirely new
systematic risk factors, which a reasonable observer might be inclined to
acknowledge exist but for which names have not been assigned. On the
other hand, statistical risk models are subject to being fooled by the data
into finding a risk factor that will not persist for any useful amount of time
into the future. It is also possible for a statistical risk model to find spurious
exposures, which are just coincidences and not indicative of any real risk in
the marketplace. This is a delicate problem for the researcher.

How Quants Choose a Risk Model
Quants are attracted to theory‐driven risk models because the risk factors
they encapsulate make sense. It is hard to make the argument that market
risk does not exist as a strong systematic risk factor in equities. Note that this
is much the same reasoning that supports theoretical approaches to alpha
modeling: Any reasonable person can understand the theory and see that it
is likely to be true. This in turn can give the quant faith in the models when
it isn’t performing very well. Warren Buffett, for example, didn’t change
his stripes just because he dramatically underperformed the stock market
during the Internet bubble. He was able to keep the faith in no small part
because his approach to markets has very strong theoretical underpinnings.
Quants that choose empirical risk models typically seek the benefits of
adaptiveness. Theoretical risk models are relatively rigid, meaning that the risk
factors are not altered often (otherwise the theory would not have been very
strong in the first place). Yet the factors that drive markets do change over

Risk Models

time. For a while in early 2003, daily reports about the prospect, and later the
progress, of the U.S. invasion of Iraq drove stock, bond, currency, and commodity markets almost singlehandedly. More recently, in early 2008, commodity prices were a significant factor. At other times, expectations of how much
the Federal Reserve might cut or raise rates are the key drivers of market behavior. As markets evolve, the data that the markets produce reflect this evolution, and these data drive empirical risk models. For these reasons, an empirical
model may be more adaptive to ever‐changing market conditions by detecting through new data whatever factors are implicitly driving markets. There
are two stages to this adaptation. During the early phases of a market regime
change (for example, when equity investors rapidly change their behavior from
risk seeking to risk aversion), the quant is using now irrelevant historical data
to determine relationships and measure risk factors. Thus, during this phase,
the empirical risk model will be modeling market risks incorrectly. Later, if the
new behavior persists, the empirical risk model eventually will catch up to the
newly prevailing theme driving markets, and all will be well again.
Besides exhibiting a weakness during a regime change, a basic understanding of statistics reveals another problem with empirical risk models. To
achieve statistical significance and reduce the potential for measurement error
in computing relationships among various instruments, empirical risk models
require a rather large amount of data. But this leads to a trade-off that could
squelch most of the adaptiveness benefits of empirical risk models. The more
data that are used—that is, the further back into history we must look—the
less adaptive a model can be, because each new data point is but one of a very
large number. If we use two years’ worth of rolling daily data, or approximately 520 trading days, each new day adds a new data point and causes the oldest
one to fall out of the sample. So for every day that passes, only two days’ data
have changed out of 520. It will therefore take a long time to turn the ship and
have the empirical model find the new drivers of risk from the data. However,
if the quant attempts to improve adaptiveness by shortening the historical
window used, the power of the statistics diminishes significantly so that there
cannot be sufficient confidence in the measurements to act on them.
Still, there may be benefits to empirical risk models. If the theoretical
risk models are any good at being right, an empirical model should capture
these effects without having to know the names of the factors beforehand.
If market risk is indeed a big driver of stock prices, an empirical model
should pick this up from the data. If the data don’t bear it out, what good
is the theory? Furthermore, the competing objectives of statistical significance and adaptiveness can be dealt with in part by using intraday data. For
example, if a quant uses one‐minute intraday snapshots of price activities
instead of simply a single closing price for each day, he is able to extract
almost 400 data points for each day in his sample, which allows him to use

Inside the Black Box

far fewer days to achieve the same statistical significance as another quant
using a single data point for each day (the closing price).
Ultimately, because of the comfort level with the concepts involved in theory‐driven risk modeling, most quants tend to use theory‐driven risk models
rather than empirical risk models. It is worth noting that these two kinds of risk
models are not mutually exclusive. Quants may perfectly reasonably use a combination of both, if they deem it appropriate. A small minority of managers also
attempt to use their judgment and discretion to monitor market behavior and,
should it become clear to them—for example, from the way that the financial
media and their peers in the business are behaving—that there is a “new” risk
factor that is driving markets, they build a made‐to‐order risk factor to measure
this temporary phenomenon. When they see that the new driver has faded in
importance, they can remove it from the risk model, again using their judgment.
It is worth mentioning that quants have the option, as is the case with
most of the modules of the black box, to build their own risk model or to
purchase one that is off the shelf. Most premade risk models are not of the
empirical variety because empirical solutions require a specifically set universe of instruments, and the analytical techniques are usually relatively easy
to implement with simple price data. Also, the vast majority of premade risk
models are useful only for equity trading strategies. Several purveyors of risk
models—such as BARRA, Northfield, Axioma, and Quantal—have made a
healthy business of licensing their software to quant traders. The advantage
of buying risk models is that they are ready to be deployed immediately,
without extensive R&D by the quant trader, and usually at least reasonably
well thought through. However, they are also by nature somewhat generic.
There are advantages to building risk models as well, primarily because they
can be customized to the specific needs of the particular quant trader.

Summary
Risk management is frequently misunderstood to be an exercise designed to
reduce risk. It is really about the selection and sizing of exposures, to maximize
returns for a given level of risk. After all, reducing risk almost always comes at
the cost of reducing return. So, risk management activities must focus on eliminating or reducing exposure to unnecessary risks but also on taking risks that
are expected to offer attractive payoffs. This is true whether one uses a systematic investment process or a discretionary one. The main difference between
the two is that quants typically use software to manage risk, whereas discretionary traders, if they use software in the risk management process at all,
primarily attempt merely to measure risk in some way, without any systematic
process for adjusting their positions in accordance with predefined guidelines.

Risk Models

Whether a quant uses a theoretical or empirical risk model or some
hybrid thereof, the goal is the same: The quant wants to identify what systematic exposures are being taken, measure the amount of each exposure in
a portfolio, and then make some determination about whether these risks
are acceptable. What is good about these kinds of analyses, along with many
of the other quantitative risk‐modeling approaches, is that they require the
quant to be intentional about risk taking, rather than slapping together
some positions that seem like good trades and more or less ignoring the incidental exposures these trades may share. For example, if oil prices become a
dominant theme in investors’ sentiment about the markets, positions across
a variety of sectors and asset classes can be driven by oil. This can lead to
a significant downside if a previously profitable trend in the price of oil reverses. A risk model may allow the quant to see this kind of exposure and
make a choice about whether to do something about it. This is an important
point. Quantitative approaches to risk management, by virtue of seeking to
measure and make explicit what exposures are driving a portfolio, put the
power into the hands of the portfolio manager to make rational, deliberate
decisions. Of course, whether this intentionality is helpful or hurtful depends on the judgment of the portfolio manager, even among quants. But at
least quantitative risk management techniques offer the opportunity to see
what risks are present in a portfolio and to what extent.
In the next chapter, we examine transaction cost models, which are the
final providers of input to help determine the most desirable target portfolio for a quant. Before doing so, let’s look at Exhibit 4.1 to examine our
progress through this journey inside the black box.

Alpha Model

Risk Model

Transaction Cost Model

Data
Portfolio Construction Model
Research
Execution Model

Exhibit 4.1

Schematic of the Black Box

Inside the Black Box

Notes
1. Uncertainty has broadly been adopted as being synonymous with risk. There
is usually not much justification for its use, other than expediency for the purposes of relatively easy computations to answer the question “How much risk
is there?”.
2. This concept was formalized in the Kelly criterion, in a paper by John L. Kelly,
Jr., in the Bell System Technical Journal in 1956. The Kelly criterion provides
a systematic way of sizing the risk taken on each of a series of bets based on
the bettor’s edge, which maximizes the expected gains by the end of the series
of bets. The edge is defined as a combination of the payoff for winning and
the odds of winning. This concept has been widely applied in gambling and
somewhat in investing. The noted quant Edward Thorp is credited with first
applying the Kelly criterion to trading strategies. However, some critics of the
Kelly betting strategy point out that a critical assumption of this criterion is that
each bet is expected to be independent of the next, which is true in many forms
of gambling, for example. However, in investing, bets can be serially correlated,
which is to say that returns to investment strategies tend to be streaky. As such,
in general many investors who believe in the concept of the Kelly criterion use
a derivative version of the strategy, such as “half Kelly,” to bet less than Kelly
suggests. Useful background on Kelly and the criterion can be found on William
Poundstone’s website or in his book about Kelly, called Fortune’s Formula.
3. This phenomenon exists, if for no other reason, because the value investor tends
to buy stocks that have fallen in price, which tend therefore to have experienced a shrinkage in their market capitalization. A market‐neutral value investor would also tend to sell expensive stocks, which are likely to have rallied and
therefore will have experienced market capitalization appreciation as well.
4. Principal components analysis (PCA) is a statistical technique used to reduce
the complexity of a set of instruments down to a manageable set of risk factors,
each of which is called a vector. Each vector represents a statistically derived
systematic risk among the instruments and is derived by analyzing the historical
relationships among all the instruments in the set.

Chapter

Transaction Cost Models
Without frugality, none can be rich, and with it, very few
would be poor.
—Samuel Johnson

o far we have examined alpha models and risk models, both critical elements of the black box. The alpha model plays the role of the starry‐eyed
optimist, and the risk model plays the role of the nervous worrier. In this
metaphor, transaction cost models would be the frugal accountant.
The idea behind transaction cost models is that it costs money to trade,
which means that one should not trade unless there is a very good reason
to do so. This is not an overly draconian view of trading costs. Many highly
successful quants estimate that their transaction costs eat away between 20
and 50 percent of their returns.
In the world of quant trading, there are only two reasons to make
a trade: first, if it improves the odds or magnitude of making money (as
indicated by the alpha model), or second, if it reduces the odds or magnitude of losing money (as indicated by the risk model). These reasons,
however, are subject to a caveat: A tiny, incremental improvement in the
reward or risk prospects of a portfolio might not be sufficient to overcome the cost of trading. In other words, the benefits of the trade need to
clear the hurdle of the cost of transacting. Neither the market nor your
broker care what the benefits of a trade are. Rather, making a given trade
utilizes services that cost the same regardless of the purpose or value the
trade holds for the trader. A transaction cost model is a way of quantifying the cost of making a trade of a given size so that this information can
be used in conjunction with the alpha and risk models to determine the
best portfolio to hold.

Inside the Black Box

Note that transaction cost models are not designed to minimize the
cost of trading, only to inform the portfolio construction engine of the
costs of making any given trade. The part of the black box that minimizes
costs is the execution algorithm, which we discuss at length in Chapter 7.
It is less glamorous to describe costs than it is to minimize them, but the
former remains critically important. If a trader underestimates the cost of
transacting, this can lead to the system making too many trades that have
insufficient benefit, which in turn leads to a problem of bleeding losses as
a result of the constant acceptance of trading costs. If the trader overestimates the cost of transacting, this can lead to too little trading, which
usually results in holding positions too long. Either way, the trader ends
up with suboptimal performance, which highlights the importance of correctly estimating transaction costs. But there is also a trade‐off between using more complex models that more accurately describe transaction costs
and using less complex models that are faster and less computationally
burdensome.

Defining Transaction Costs
It is useful to understand what the costs of trading actually are, since we are
describing ways to model them. Transaction costs have three major components: commissions and fees, slippage, and market impact.

Commissions and Fees
Commissions and fees, the first kind of transaction costs, are paid to brokerages, exchanges, and regulators for the services they provide, namely,
access to other market participants, improved security of transacting, and
operational infrastructure. For many quants, brokerage commission costs
are rather small on a per‐trade basis. Quant traders typically do not utilize
many of the services and personnel of the bank but instead use only the
bank’s infrastructure to go directly to the market. The incremental cost of
a trade to a bank is therefore very small, and even very low commissions
can be profitable. Given the volume of trading that quants do, they can be
extremely profitable clients for the brokerages, despite the diminutive commissions they pay. Some quants utilize significantly less of the bank’s infrastructure and therefore pay even lower commission rates than others who
use more and pay higher rates.
Commissions are not the only costs charged by brokerages and exchanges. Brokers charge fees (which are usually a component of the commissions) for services known as clearing and settlement. Clearing involves

Transaction Cost Models

regulatory reporting and monitoring, tax handling, and handling failure,
all of which are activities that must take place in advance of settlement.
Settlement is the delivery of securities in exchange for payment in full,
which is the final step in the life of a trading transaction and fulfills the
obligations of both parties involved in the transaction. These services take
effort and therefore cost money. And, given that many quants are doing
tens of thousands of trades each day, there can be a significant amount of
work involved.
Exchanges and electronic matching networks provide a different kind
of service from conventional brokers, namely access to pools of liquidity.
Exchanges must attract traders to their floors for trading, and this trading
volume then attracts other traders who are seeking liquidity. Exchanges,
too, have some operational effort to make by virtue of their roles, and they
also guarantee that both counterparties in a given trade uphold their contractual responsibilities. As such, exchanges also charge small fees for each
transaction to cover their costs and risks (and, of course, to profit as a business). More recently, dark pools, which are effectively matching engines to
pair buyers and sellers of the same instrument at the same time within a
given bank’s customer base, have come into prominence, and now account
for a large percentage of all U.S. equity trading volumes (32 percent in 2012,
according to the Tabb Group).1

Slippage
Commissions and fees certainly are not negligible. But neither are they the
dominant part of transaction costs for most quants. They are also basically
fixed, which makes them easy to model. If the all‐in commissions and fees
add up to, say, $0.001 per share, the quant must simply know that the trade
in question is worth more in terms of alpha generation or risk reduction
than this $0.001 per‐share hurdle. On the other hand, slippage and market
impact are considerably trickier to measure, model, and manage.
Slippage is the change in the price between the time a trader (or quant
system) decides to transact and the time when the order is actually at the
exchange for execution. The market is constantly moving, but a trading
decision is made as of a specific point in time. As time passes between
the decision being made and the trade being executed, the instrument being forecast is likely to be moving away from the price at which it was
quoted when the forecast was made. In fact, the more accurate the forecast, the more likely it is that the price of the instrument is actually going
toward the expected price as more time passes. But the instrument makes
this move without the trader benefiting, because he has not yet gotten
his trade to market. Imagine a trader decides to sell 100 shares of CVX

Inside the Black Box

while the price is at $100.00 per share. When the trader finally gets the
order through his broker and to the exchange, the price has gone down to
$99.90 per share, for a decline of $0.10 per share. This $0.10 per share is
a cost of the transaction because the trader intended to sell at $100.00, but
in fact the price had already moved down to $99.90. In the event that the
price actually moves up from $100.00 to $100.10, the trader gets to sell
at a higher price, which means that slippage can sometimes be a source of
positive return.
Strategies that tend to suffer most from slippage are those that pursue
trend‐following strategies, because they are seeking to buy and sell instruments that are already moving in the desired direction. Strategies that tend
to suffer least from slippage, and for which slippage can sometimes be a positive, are those that are mean reverting in orientation, because these strategies are usually trying to buy and sell instruments that are moving against
them when the order is placed. A quant trader’s latency or speed to market
has a large effect on the level of slippage his strategy will experience over
time. This is because slippage is a function of the amount of time that passes
between the order being decided and the order reaching the market for execution. The more latency in a trader’s system or communications with the
marketplace, the more time passes before her order gets to the market and
the further the price of an instrument is likely to have moved away from the
price when the decision was made. Worse still, the more accurate a forecast,
particularly in the near term, the more damaging slippage will be.
In addition to time, slippage is also a function of the volatility of the
instrument being forecast. If we are forecasting 90‐day Treasury bills, which
tend to move very slowly throughout the day and which can go some weeks
without much movement at all, it is likely that slippage is not a major factor.
On the other hand, if we are forecasting a high‐volatility Internet stock, slippage can be a major issue. Google, Inc. (GOOG) has had an average daily
range of 2.6 percent of its opening price, which is about 16 times larger than
its average move from one day to the next. Clearly, slippage makes a huge
difference if you’re trading GOOG.

Market Impact
Market impact, the third and final major component of transaction costs,
is perhaps the most important for quants. The basic problem described by
market impact is that, when a trader goes to buy an instrument, the price
of the instrument tends to go up, partly as a result of the trader’s order. If
the trader sells, the price goes down as he attempts to complete his trade.
At small order sizes, this price movement usually bounces between the current best bid and offer. However, for larger orders, the price move can be

Transaction Cost Models

substantial, ranging in the extremes, even to several percentage points. Market impact, then, is a measurement of how much a given order moves the
market by its demand for liquidity. Market impact is normally defined as the
difference between the price at the time a market order enters the exchange
and the price at which the trade is actually executed.
The basic idea behind market impact is simple enough and is based
on the ubiquitous principle of supply and demand. When a trader goes to
market to execute a trade for some size, someone has to be willing to take
the other side, or supply the size he is looking to trade. The bigger the size
of the demand by a trader, the more expensive the trade will be because the
trader must access more of the supply. As simple as the idea of market impact is, quantifying it is actually not so straightforward. One doesn’t know
how much a particular trade impacts the market until the trade has already
been completed, which may be too late to be useful. Also, there are many
other factors that can drive a given observation of market impact and that
can complicate its measurement. For example, the number of other trades
that are being made in the same direction at the same time or whether news
in the stock is causing impact to behave differently from normal are both
issues that would affect measurements of market impact and are nontrivial
to quantify. These other factors are also usually impossible to predict, much
less control. Therefore, market impact as used in transaction cost modeling
usually does not account for these factors but rather focuses on the size of
the order relative to the liquidity present at the time. Liquidity can be defined in a number of ways, whether by the size available at the bid or offer
or by measurements of the depth of book, which relate to those bids or offers that have been placed away from the best bid/offer prices.
In addition, there could be some interaction between slippage and market impact that makes it tricky to segregate these two concepts in a model.
A stock might be trending upward while a trader is trying to sell it, for
example. In this case, both slippage and impact could look like negative
numbers. In other words, the trader might deduce that he was actually paid,
not charged, to sell the stock. For instance, assume that a trader decides to
enter a market order to sell a stock he owns, and at that moment, the stock’s
price happens to be $100.00. But by the time his order hits the market, the
stock, continuing its trend upward, is now trading at $100.05. Slippage is
actually negative $0.05 because his order entered the marketplace at a more
favorable price than the one at which he decided to sell. But now assume
that the price continues to drift upward as his order makes its way to the
front of the line of sale orders, simply because the marketplace’s demand to
buy the shares might simply overwhelm the orders, including his, to sell it.
The trader ultimately sells his stock at $100.20, generating negative market
impact of $0.15 on top of the negative slippage of $0.05. Clearly, entering

Inside the Black Box

sell orders does not usually make stocks go up, but in this case, it might not
be possible to differentiate impact from slippage or either concept from the
move the stock was making independently of the trader’s order. Did his sell
order slow the rise of the stock somewhat, and if so, by how much? These
are the kinds of complications that traders must account for in building
transaction cost models.
Some kinds of trades further complicate the measurement of transaction costs. We have discussed trades that demand liquidity from the marketplace, and these behave as one might expect intuitively: If a trader demands
liquidity, there is a cost charged by those providing it. Looking at this from
the opposite perspective, someone gets paid to supply liquidity. Historically,
the party that supplied liquidity was a market maker or specialist whose
job it was to make sure that traders can execute an order when they want
to. More recently, volumes across many electronically tradable instruments
have increased sufficiently to allow for well‐functioning marketplaces without the presence of a market maker in the middle.
Electronic communication networks (ECNs) are examples of platforms
for customers to trade directly with one another. The challenge for ECNs
is to attract enough customer order flow to show abundant liquidity on
their exchanges. ECNs also must provide robust technology so that their
exchanges can continue to function without disruption. To attract providers
of liquidity, most ECNs in equity markets have established methods to pay
traders who provide liquidity and take payment from traders who demand
liquidity. It might cost something like three‐tenths of a penny per share for
a trader who buys shares at the offer or sells shares at the bid, whereas
those providing the bids and offers that are getting hit are earning closer to
two‐tenths of a penny. The ECN keeps the difference, around one‐tenth of
a penny per share, as its source of revenue. Some kinds of trading strategies
(usually mean reversion strategies) actually call for a mostly passive execution approach in which this act of providing liquidity is modeled as a source
of profit due to the rebate programs that ECNs put in place to attract liquidity providers. It is worth noting that some ECNs and exchanges, especially
outside of the equities markets, offer no rebates and do not charge customers to take liquidity. There are also inverse exchanges, which pay takers of
liquidity and charge providers of liquidity.
Dark pools also allow customers to interact with one another. Dark
pools are created by brokers or independent firms to allow their customers
to trade directly with each other in an anonymous way. They arose in part
because of concerns about the market impact associated with large orders.
On a dark pool, there is no information provided about the limit order
book, which contains all the liquidity being provided by market makers
and other participants. Customers are simply posting their orders to the

Transaction Cost Models

pool and if someone happens to want to do the opposite side of those orders, the orders get filled. As a result of this anonymous process of matching orders, the market is less likely to move as much as it would in a more
public venue, where automated market making practitioners require compensation to take the other side of large orders. One fact that makes dark
pool transactions somewhat unusual is that they are over‐the‐counter, off‐
exchange transactions in instruments that are exchange traded. Dark pools
could not exist without the public markets, because the securities traded on
dark pools are listed on public exchanges. Furthermore, the public markets
provide the only transparent sense of price discovery, without which dark
pool participants would have a significantly harder time determining what
prices to bid and offer. Partly because of these issues, coupled with the fact
that dark pools are available only to selected customers, controversy surrounds dark pools.

Types of Transaction Cost Models
There are four basic types of transaction cost models—flat, linear, piecewise‐linear, and quadratic—all of which are trying to answer the basic
question of how much it will cost to transact a given trade. Some of these
costs are fixed and known—for example, commissions and fees. Models
of transaction costs use these fixed charges as a baseline, below which the
expense of trading cannot go. Other costs, such as slippage and impact,
are variable and cannot be known precisely until they have been incurred.
Slippage is affected by a number of factors, such as the volatility of the
instrument in question (i.e., the higher the volatility, the greater the expectation of slippage) or its prevailing trend (i.e., the stronger the trend, the
more slippage is likely to cost if one attempts to transact in the direction
of the trend). Impact also has many drivers, including the size of the order
being executed, the amount of liquidity that happens to be available to
absorb the order, and imbalances between supply and demand for the instrument at the moment. Traders use transaction cost models in an attempt
to develop reasonable expectations for the cost of an order of various sizes
for each name they trade.
It is worth mentioning that each instrument has its own unique characteristics based on the investor base that tends to transact in it and the
amount of liquidity and volatility present in the instrument over time.
GOOG doesn’t trade exactly like Amazon (AMZN), and CVX doesn’t
trade exactly like XOM. As a result, in an effort to improve their estimates of transaction costs, many quants build separate models for transaction costs for each instrument in their portfolios and allow each of

Inside the Black Box

these models to evolve over time based on the trading data the quant collects from his execution systems. In other words, many transaction cost
models are highly empirical, allowing the actual, observable, recorded
transaction data from a quant’s own strategy to drive and evolve the
model over time.
The total cost of transactions for an instrument, holding all else constant (such as liquidity, trend, or volatility), can be visualized as a graph with
the size of the order (in terms of dollars, shares, contracts, or the like) on
the x‐axis and the cost of trading on the y‐axis. It is generally accepted by
the quant community that the shape of this curve is quadratic, which means
that the cost gets higher ever more quickly as the size of the trade gets larger
(due to market impact). Certainly many quants do model transaction costs
as a quadratic function of the size of the trade (more on this later). However,
modeling transaction costs this way can be more complicated and computationally intensive, whereas the other choices of modeling transaction costs
are simpler and less intensive.
With advances in computer hardware and processors, the extra computational burdens are now rather easily managed, but that does not alter the
fact that a proper quadratic cost function is inherently more complicated.
These functions, from the simplest to the most complex, are described in the
following sections.

Flat Transaction Cost Models
The first kind of transaction cost model is a flat model, which means that
the cost of trading is the same, regardless of the size of the order. This
is extremely straightforward computationally, but it is rarely correct and
is not widely used. A graph of a flat transaction cost model is shown in
Exhibit 5.1.
As you can see, this graph models the cost of a trade as being fixed,
regardless of the size of the trade, which is an assumption that seems obviously incorrect in most circumstances. The main circumstance in which such
a model is reasonable is if the size being traded is nearly always about the
same and liquidity remains sufficiently constant. In this case, one can simply
figure out the total cost of such a trade and assume that it will always cost
the same. This assumption is wrong, but being wrong has no consequence
because the size of the trade is always the same. Note that where the solid
line crosses the dashed line, the model is close to a correct estimate of transaction costs. So, if this point of intersection corresponds to the size of trading normally done, and if the range of that trade size is within the region
where the flat line is close to the curved line, a flat t‐cost model may not be
problematic.

Transaction Cost Models

Flat Transaction Cost

Cost of Trade

True Transaction Cost

Size of Trade

Exhibit 5.1

Flat Transaction Cost Function

Linear Transaction Cost Models
The second kind of transaction cost model is linear, which means that the
cost of a transaction gets larger with a constant slope as the size of the transaction grows larger, as shown in Exhibit 5.2. This is a better fit relative to
the true transaction cost, but it is still mostly useful as a shortcut to building
a proper model.
As you can see, the linear transaction cost model must trade off overestimating costs at smaller trade sizes with underestimating costs at larger
trade sizes. Here, again, the model is correct where the solid line crosses the
dashed line and is close to correct in the immediate vicinity of that intersection. As with the flat t‐cost model, if the trades being done are always within
that region, a linear t‐cost model is reasonable. In any case, across the curve,
it appears to be a better estimator of the real transaction cost than is given
by the flat transaction cost model.

Piecewise-Linear Transaction Cost Models
Piecewise‐linear transaction cost models are used to help with precision
while using reasonably simple formulas to do so. The idea of a piecewise‐
linear transaction cost model is that, in certain ranges, a linear estimate is
about right, but at some point, the curvature of the quadratic estimator
causes a significant enough rise in the slope of the real transaction cost line

Inside the Black Box

Linear Transaction Cost

Cost of Trade

True Transaction Cost

Size of Trade

Exhibit 5.2

Linear Transaction Cost Function

that it is worthwhile to use a new line from that point on. This concept is
illustrated in Exhibit 5.3.
As you can see, the accuracy of this type of model is significantly better
than what can be achieved with flat or linear models across a much wider
range of trading sizes; as a result, this model is rather popular among quants
as a happy medium between simplicity and accuracy.

Piecewise Linear Transaction Cost

Cost of Trade

True Transaction Cost

Size of Trade

Exhibit 5.3

Piecewise‐Linear Transaction Cost Function

Transaction Cost Models

Quadratic Transaction Cost Models
Finally, quants can build quadratic models of transaction costs. These are
computationally the most intensive because the function involved is not
nearly as simple as what is used for a linear model, or even for a piecewise‐linear model. It has multiple terms and exponents, and generally is
a pain to build. A plot of a quadratic transaction cost model is shown in
Exhibit 5.4.
This is clearly the most accurate estimate we have seen of transaction costs. And yet it is not perfect, and it is significantly more difficult
to build and utilize than a linear or piecewise linear model. You might be
wondering how it is that we have estimated a quadratic function using a
quadratic function and still ended up with a less than perfect estimate of
the true transaction cost. The reason is that the solid line reflects what is
expected, whereas the dotted line reflects what is actually observed after the
fact. This is a significant difference because the solid line must be specified
before trading, whereas the dotted line is what is observed empirically after
trading. Because the actual transaction cost is an empirically observable
fact and any estimation of transaction costs is a prediction, the prediction
is unlikely to be perfect. Causes of differences between estimated and realized transaction costs might include changes in liquidity or volatility in the
instrument over time or changes in the types of traders (e.g., market makers, hedge funds, mutual funds, or retail investors) who are transacting in

Quadratic Transaction Cost

Cost of Trade

True Transaction Cost

Size of Trade

Exhibit 5.4

Quadratic Transaction Cost Function

Inside the Black Box

the same stock over time. Of course, the quant is trying as hard as possible
to make good forecasts, but given that it is known that the forecast is very
unlikely to be perfect and that speed and simplicity are both also desirable,
the trade‐off between accuracy and simplicity is one that requires the judgment of the quant.
Regardless of the type of model used, the quant must describe the cost
of trading each instrument in her universe. After all, a less liquid small cap
stock is likely to be more expensive to trade than a more liquid mega cap
stock, and that must be a factor in deciding how much of each to trade.
Furthermore, the quant should refresh empirical estimations of transaction costs both to keep the model current with the prevailing market conditions as well as to indicate when more research is required to improve
the model itself.

Summary
The role of transaction cost models is simply to advise the portfolio construction model how much it might cost to transact. Its job is not to minimize the cost of trading, just as the job of the alpha model is not to generate returns but rather to make forecasts and to provide these forecasts
to the portfolio construction model. Cost minimization happens in two
phases. First, the portfolio construction model, using the input provided
by the transaction cost model, accounts for cost in generating a target
portfolio. Second, the target portfolio is passed along to the execution
algorithms, which explicitly attempt to transact the desired portfolio as
cheaply as possible.
There are several kinds of transaction models, ranging from extremely
simple to rather complex. The simpler models are useful for traders who either do trades of roughly the same size in a given instrument all the time or
who trade in such small sizes that they can simply assume a modest cost and
be close to correct most of the time. The more complex models are useful for
quants who have the potential to trade significant, or significantly variable,
quantities of a given instrument in a short period. Any of the four models
described here can be valid in the right set of circumstances. The question
to consider is whether the model chosen fits the application and facts of the
situation.
We turn our attention next to portfolio construction models, which
utilize the inputs provided by the alpha, risk, and transaction cost models
described over the past three chapters, and come up with a target portfolio
designed to maximize returns relative to risk. But first we check our progress
on the map of the black box in Exhibit 5.5.

Transaction Cost Models

Alpha Model

Risk Model

Transaction Cost Model

Data
Portfolio Construction Model
Research
Execution Model

Exhibit 5.5

Schematic of the Black Box

Note
1. Matthew Philips, “Where Has all the Stock Trading Gone?” May 10, 2012, www
.businessweek.com/articles/2012‐05‐10/where‐has‐all‐the‐stock‐trading‐gone.

Chapter

Portfolio Construction Models
No sensible decision can be made any longer without taking into
account not only the world as it is, but the world as it will be.
—Isaac Asimov

he goal of a portfolio construction model is to determine what portfolio
the quant wants to own. The model acts like an arbitrator, hearing the
arguments of the optimist (alpha model), the pessimist (risk model), and the
cost‐conscious accountant (transaction cost model), and then making a decision about how to proceed. The decision to allocate this or that amount to
the various holdings in a portfolio is mostly based on a balancing of considerations of expected return, risk, and transaction costs. Too much emphasis
on the opportunity can lead to ruin by ignoring risk. Too much emphasis
on the risk can lead to underperformance by ignoring the opportunity. Too
much emphasis on transaction costs can lead to paralysis because this will
tend to cause the trader to hold positions indefinitely instead of taking on
the cost of refreshing the portfolio.
Quantitative portfolio construction models come in two major forms.
The first family is rule based. Rule‐based portfolio construction models are
based on heuristics defined by the quant trader and can be exceedingly simple or rather complex. The heuristics that are used are generally rules that
are derived from human experience, such as by trial and error.
The second family of quantitative portfolio construction models is optimized. Optimizers utilize algorithms—step‐by‐step sets of rules designed
to get the user from a starting point to a desired ending point—to seek
the best way to reach a goal that the quant defines. This goal is known as
an objective function, and the canonical example of an objective function
for an optimizer is to seek the portfolio that generates the highest possible

Inside the Black Box

return for a unit of risk. By their nature, optimizers can be more difficult to
understand in great detail, but they are straightforward conceptually.
As in the case of blending alpha models, discussed in Chapter 3, portfolio construction models are a fascinating area to study. Furthermore, portfolio construction turns out to be a critical component of the investment
process. If a trader has a variety of investment ideas of varying quality but
allocates the most money to the worst ideas and the least money to the best
ideas, it is not hard to imagine this trader delivering poor results over time.
At a minimum, his results would be greatly improved if he could improve his
approach to portfolio construction. And yet, actual solutions to the problem
of how to allocate assets across the various positions in a portfolio are not
exceedingly common. This subject receives rather a lot less time and space
in the academic journals and in practitioners’ minds than ways to make a
new alpha model, for example. This chapter will give you the ability to understand how most quant practitioners tackle this problem.

Rule-Based Portfolio Construction Models
There are four common types of rule‐based portfolio construction models:
equal position weighting, equal risk weighting, alpha‐driven weighting, and
decision‐tree weighting. The first two are the simplest and have at their core
a philosophy of equal weighting; they differ only in what specifically is being equally weighted. Alpha‐driven portfolio construction models mainly
rely on the alpha model for guidance on the correct position sizing and
portfolio construction. Decision‐tree approaches, which look at a defined
set of rules in a particular order to determine position sizing, can be rather
simple or amazingly complex. I describe these approaches from simplest to
most complex.

Equal Position Weighting
Equal position‐weighted models are surprisingly common. These models are
used by those who implicitly (or explicitly) believe that if a position looks
good enough to own, no other information is needed (or even helpful) in determining its size. There is a further implicit assumption that the instruments
are homogeneous enough that they do not need to be distinguished on the
basis of their riskiness or otherwise. The notion of the strength of a signal,
which, as already discussed, is related to the size of a forecast for a given instrument, is ignored except insofar as the signal is strong enough to be worthy of a position at all. At first glance, this might seem like an oversimplification of the problem. However, some serious quants have arrived at this

Portfolio Construction Models

solution. The basic premise behind an equal-weighting model is that any
attempt to differentiate one position from another has two potentially adverse consequences, which ultimately outweigh any potential benefit from
an unequal weighting. In other words, they choose an equal‐weighting model because of the many disadvantages they see in unequal weighting.
The first potential problem with unequal weighting is that it assumes
implicitly that there is sufficient statistical strength and power to predict not
only the direction of a position in the future but also the magnitude and/
or probability of its move relative to the other forecasts in the portfolio.
Quants utilizing equal‐weighting schemes believe, instead, that the alpha
model is only to be trusted enough to forecast direction, and as long as there
is sufficient confidence in a forecast of direction that is sufficiently large to
justify trading the instrument at all, it is worth trading at the same size as
any other position.
The second potential problem with unequal weighting of a portfolio
is that it generally leads to a willingness to take a few large bets on the
“best” forecasts and many smaller bets on the less dramatic forecasts. This
weighting disparity, however, may lead to the strategy’s taking excess risk of
some idiosyncratic event in a seemingly attractive position. This can be the
case regardless of the type of alpha used to make a forecast. For instance,
in momentum‐oriented strategies, many of the strongest signals are those
for which the underlying instrument has already moved the most (i.e., has
showed the strongest trending behavior). In other words, it might be too
late, and the trader risks getting his strongest signals at the peak of the trend,
just as it reverses. Similarly, for mean reversion–oriented strategies, many of
the largest signals are also for those instruments that have already moved
the most and are now expected to snap back aggressively. But frequently,
large moves happen because there is real information in the marketplace
that leads to a prolonged or extended trend. This phenomenon is known to
statisticians as adverse selection bias. Mean reversion bets in these situations
are characterized as “picking up nickels in front of a steamroller,” which is a
colorful way of saying that betting on a reversal against a very strong trend
leads to being run over if the trend continues, which it often does.
This last benefit can be seen in other scenarios as well. While practitioners do what they can to clean the data they utilize in trading (which we discuss further in Chapter 8), there are occasions in which bad data points end
up filtering into a trading strategy. Equal weighting positions, in particular
if there are many of them, ensure that the risk of loss associated with the
large forecasts that could result from significantly wrong data does not get
out of hand. For example, if a stock price is off by a factor of 100 (e.g., it
is quoted in pence instead of pounds, as happens occasionally in U.K. equities), it is likely that an alpha model might be fooled into wanting to take

Inside the Black Box

an enormous position in this ticker. An equal-weighting scheme can reduce
the size of that position such that it does not end up a catastrophic event.
Indeed, since alphas are generally tested against real datasets, most of
their statistical significance and strength generally come from the meat of a
distribution, not from the tails. If we observe a real tail event (not just some
accident of a bad data point) that drives a large alpha forecast, this is perhaps a better trade, but it almost certainly involves dramatically higher risk
than a more normative level of alpha. Here, too, an equal position weighting
scheme can control the risk associated with such tail observations.
Analogous arguments can be made for almost all alpha strategies, making it easy to construct good arguments against unequal‐weighting positions. Therefore, the basic argument in favor of an equal‐weighted approach
is one of mitigating risk by diversifying bets across the largest useful number
of positions. It is worth mentioning that equal weights are sometimes subject
to constraints of liquidity, in that a position is weighted as close to equally as
its liquidity will allow. Such liquidity considerations can be applied to each
of the other rule‐based allocation methodologies discussed in this chapter.

Equal Risk Weighting
Equal risk weighting adjusts position sizes inversely to their volatilities (or
whatever other measure of risk, such as drawdown, is preferred). More volatile positions are given smaller allocations, and less volatile positions are
given larger allocations. In this way, each position is equalized in the portfolio, not by the size of the allocation but rather by the amount of risk that the
allocation contributes to the portfolio. An example is shown in Exhibit 6.1,
which shows an example of a two‐stock portfolio. As you can see, the more
volatile stock (GOOG) gets a smaller allocation in the portfolio than the less
volatile stock (XOM).
The rationale is straightforward. A small‐cap stock with a significant
amount of price volatility might not deserve quite the same allocation as a
mega cap stock with substantially less volatility. Putting an equal number
of dollars into these two positions might in fact be taking a much larger
and inadvertent real bet on the small cap stock. This is because the small
cap stock is much more volatile, and therefore every dollar allocated to that
Exhibit 6.1

A Simple Equal Risk–Weighted Portfolio
Equal Weight

Volatility

Volatility‐Adjusted Weight

GOOG

50%

2.5%

39%

XOM

50%

2.0%

61%

Portfolio Construction Models

stock would move the portfolio more than the same dollars allocated to
the larger cap (and, likely, less volatile) position. As such, some quants who
believe that equal weighting is the most appropriate method will utilize an
equal risk–weighting approach in an effort to improve the true diversification achieved.
However, the equal risk–weighting approach also has its shortcomings.
Whatever unit of risk is equalized, it is almost always a backward‐looking
measurement, such as volatility. Instruments with higher volatilities would
have smaller allocations, whereas lower‐volatility instruments would have
larger allocations. But what if the less volatile instruments suddenly became
the more volatile? This is not merely a hypothetical question. For many
years, bank stocks were very stable. Then, in 2008, they suddenly became
highly volatile, more so even than many technology stocks. Any backward‐
looking analysis of the volatility of stocks that didn’t emphasize the last
debacle among financial stocks (10 years earlier, in 1998) would likely have
been misled by the steady behavior of these stocks for the decade prior to
2008, and therefore an equal‐risk model is likely to have held much larger
positions in banks than were warranted once volatility spiked in 2008.

Alpha-Driven Weighting
A third approach to rule‐based portfolio construction determines position
sizes based primarily on the alpha model. The idea here is that the alpha
model dictates how attractive a position is likely to be, and this signal is
the best way to size the position correctly. Still, most quants who utilize this
approach would not allow the size of the largest position to be unlimited.
As such, they would use the risk model to provide a maximum size limit for
a single position. Given the limit, the strength of the signal determines how
close to the maximum the position can actually be. This is much like grading on a curve, where the best score receives the largest position size, and
the scores below the best receive smaller sizes. The types of constraints used
with this approach to portfolio construction can also include limits on the
size of the total bet on a group (e.g., sector or asset class).
For example, one could constrain individual positions to be less than
3 percent of the portfolio and each sector to be less than 20 percent. There
still needs to be a function that relates the magnitude of the forecast to
the size of the position, but these functions can be straightforward, and in
general, the bigger the forecast, the larger the position. Alpha weighting is
favored by some quants because it emphasizes making money, which is after all the goal of the whole exercise. However, some quant strategies, such
as futures trend following, that utilize this method can suffer sharp drawdowns relatively frequently. This is because these models usually have the

Inside the Black Box

largest signals when a price trend is already well established. As the trend
proceeds, the size of the position grows, but this will often leave the trader
with his largest position just when the trend reverses. Caution is therefore
advisable when utilizing an alpha‐driven portfolio construction algorithm,
because such an approach causes a heavy reliance on the alpha model being
right—not only about its forecast of the direction of an instrument but also
about the size of the move the instrument will make.

Summary of Rule-Based Portfolio Construction Models
Regardless of which type of rule‐based portfolio construction model is used,
the alpha model, risk model, and t‐cost model can be incorporated in portfolio building. In an equal‐weighted model, for example, constraints on the
equal weighting can exist because certain instruments are too expensive to
transact in, according to the transaction cost model. These considerations
can be accounted for within the alpha model itself, for example by adding
a conditioning variable that sets the expected return (or score, or whatever
other form of forecast) to “0” if the expected return is less than the expected
transaction cost threshold. Thus, any signal that comes out of the alpha
model can now be equally weighted. Obviously, the exact nature of the interaction between the other components of the black box and the portfolio
construction model depends entirely on the type of portfolio construction
model. For example, an equal-weighting approach may make use of a risk
model in an entirely different way from an alpha‐weighting approach.
To summarize, rule‐based portfolio construction models can be extremely simple (as in the case of an equal‐weighted portfolio) or rather complex (in the case of an alpha‐weighting with many types of constraints).
The challenge common to all of them is to make the rules that drive them
rational and well‐reasoned.

Portfolio Optimizers
Portfolio optimization is one of the most important topics in quantitative
finance. This is one of the first areas in quant finance to receive the attention
of serious academic work; in fact, the case could easily be made that the
father of quantitative analysis is Harry Markowitz, who published a landmark paper entitled “Portfolio Selection.”1 He invented a technique known
as mean variance optimization, which is still ubiquitous today, though much
sophistication has been built around its core. In 1990, he shared a Nobel
Prize with William Sharpe for both their contributions to the understanding
of the quantitative analysis of portfolio construction.

Portfolio Construction Models

Portfolio optimizers are based on the principles of modern portfolio
theory (MPT), which are canonical in the asset management industry. The
core tenet of MPT is that investors are inherently risk averse, meaning that
if two assets offer the same return but different levels of risk, investors will
prefer the less risky asset. A corollary is that investors will take on extra risk
only if they expect to receive extra return as compensation. This introduced
the concept of risk‐adjusted return. Mean variance optimization is a formal
way of building portfolios based on MPT. Mean and variance are two of
the inputs to the optimizer, and the output is a set of portfolios that have
the highest return at each level of risk. The mean in question is the average
expected return of each asset being evaluated. Variance is a proxy for the
expected risk of each asset and is computed as the standard deviation of
the returns of the various assets one is considering owning. A third input to
the optimizer is the expected correlation matrix of these same assets. Using
these inputs, the optimizer delivers a set of portfolios that offer the highest
possible return for various levels of risk, known as the efficient frontier.
Quant trading strategies that utilize risk and transaction cost models,
in addition to alpha models, also need to account for the information contained in (and any constraints associated with) those models. For example, the portfolio optimizer might be required to solve for the optimal (i.e.,
maximum risk‐adjusted return) portfolio, which accounts for the expected
returns of each potential holding, the variability of those holdings, the correlation of those holdings to one another, and which minimizes exposure to
various prespecified risk factors as specified in the risk model. Several additional inputs are utilized by quants in real trading applications, including (a)
the size of the portfolio in currency terms; (b) the desired risk level (usually
measured in terms of volatility or expected drawdown); and (c) any other
constraints, such as a hard‐to‐borrow list provided by a prime broker in equity trading, which reduces the size of the universe with which the optimizer
can work. These inputs are not required by the optimizer, and the first two
are also mostly arbitrary, but they help yield a portfolio that is practical and
useful to the quant trader.
The reason this technique is known as optimization is that it seeks to
find the maximum (optimal) value of a function that has been specified by
the researcher. This function is known as the objective function, where objective is used in the sense of goal. The optimizer seeks this goal by an algorithm that conducts a directed search among the various combinations of
instruments available to it. As it examines the return and risk characteristics
of a given combination, it compares this with previously examined combinations and detects what seems to cause the portfolio’s behavior to improve
or degrade. By this method, the optimizer is able to rapidly locate a series
of optimal portfolios, which are those for which returns cannot be bested

100

Inside the Black Box

by those of any other portfolio at a given level of risk. What is allowed or
disallowed is determined by the alpha model, risk model, and transaction
cost model. The objective function that many quants use is the same as
the original: maximizing the return of a portfolio relative to the volatility
of the portfolio’s returns. However, an infinite array of objective functions
can be used. For example, one could specify an objective function that will
cause the optimizer to maximize portfolio return relative to peak‐to‐valley
drawdown instead of return volatility. The use of return versus risk is itself
entirely optional, and one could very easily optimize an objective function
focused entirely on the total expected return of a portfolio.
We can graphically illustrate the technique of optimization as shown in
Exhibit 6.2. Here, we see that on the X (horizontal) and Z (depth) axes of
the graph are every possible combination of ownerships of two imaginary
instruments, ABC and DEF. The Y‐axis (vertical) shows the expected Sharpe
ratio of each possible portfolio containing ABC and DEF. The Sharpe ratio
was chosen simply for illustrative purposes, as a typical objective function
for an optimizer. Imagine further that we have a positive return expectation (forecast) on ABC, and an equal but negative forecast for DEF. The
optimizer searches for which portfolio produces the maximum value for
the objective function, which in this case is to be 100 percent long ABC and
0.30

0.20

Sharpe Ratio

0.10

—

(0.10)

–100%
–60%

(0.20)

–20%
(0.30)
–100% –80%

20%
–60% –40%
–20%

% of Portfolio
60% Allocated to DEF
0%

% of Portfolio
Allocated to ABC

Exhibit 6.2

20%

40%

60%

80%

100%
100%

Visual Representation of the Search Space for an Optimization

Portfolio Construction Models

101

100 percent short DEF. The optimizer obviously does not look at a graph
to pick the point, but this visual can be helpful in illustrating what an optimizer is attempting to achieve.

Inputs to Optimization
The inputs required for an optimizer, as already mentioned, are expected
returns, expected volatility, and a correlation matrix of the various instruments to be considered for the portfolio. It is worth understanding where
practitioners get the estimates and expectations used in optimization, since
they are critical to the model itself. We consider each of the aforementioned
inputs in order.
Expected Return In more traditional finance, such as private wealth management, expected returns are usually set to equal very long‐term historical
returns because usually the goal is to create a strategic asset allocation that
won’t need to be dynamically readjusted. By contrast, quants tend to use
their alpha models to drive expected return. As we mentioned in our discussion of alpha models, the output of the alpha model typically includes an
expected return and/or an expected direction, or some other output that
indicates the attractiveness of each potential portfolio holding (e.g., a score).
Forecasts of direction can be used as forecasts of return simply by making
all positive forecasts equal and all negative forecasts equal (often subject to
minimum threshold parameters, so that at least the return forecasts have to
be of some significant size before making a bet). In this kind of optimization,
it is not important to have a precise forecast of return, but rather a forecast
of the attractiveness of each potential position in terms of the expected return. So directional forecasts are indifferent between the expected return of
each position, and the only relevant feature of the forecast is its sign.
Expected Volatility Many practitioners, whether in traditional finance or in
quant trading, tend to use historical measures for the second input to the
optimizer, namely volatility. Some, however, develop and use their own forecasts of volatility. The most common approaches to forecasting volatility
utilize stochastic volatility models. Stochastic, in Greek, means random. In
statistics, a stochastic process is one that is somewhat predictable but that
has some element of unpredictability or randomness built in. In case you’re
wondering what statisticians mean by the word process, they are referring
to some continuous series of changes, which is basically a synonym for a
time series in this context. The basic idea behind the stochastic family of
volatility forecasting methods is that volatility goes through phases in which
it is at high levels, followed by periods in which it is at low levels (i.e., the

102

Inside the Black Box

somewhat predictable phases of the volatility cycle), with occasional jumps
(the somewhat random and unpredictable part). The most widely used such
technique is called Generalized Autoregressive Conditional Heteroskedasticity (GARCH), which was proposed in 1986 in the Journal of Econometrics by the Danish econometrician Tim Bollerslev.2 Other approaches to
stochastic volatility modeling and variants of the original GARCH forecast
abound. All these techniques basically share the notion that volatility goes
through clustered periods of relative calm, followed by periods of swings,
followed by a return to calm, and so forth. This can be seen in Exhibit 6.3
as being a relatively useful way to describe market volatility. From 2000
to 2003, the S&P 500 was rather volatile. This was followed by a period
of calm from mid‐2003 to mid‐2007, and after that by another period of
extreme volatility from mid‐2007 through 2008. Even during the relatively
calm period, short, seemingly periodic bursts in volatility occurred. GARCH
types of models do a reasonable job of forecasting volatility in this sort of
pattern.
Indeed, there exist many other approaches to forecasting volatility, and
they can be understood in much the same way that we evaluated strategies
for forecasting price. They tend to make forecasts based on ideas of trend,
reversion, or some fundamental model of volatility; they can be made over
various time horizons; they can forecast either the volatility of a single instrument or the relative volatility of more than one instrument, and so forth.
S&P 500 Index Rolling 20-Day Volatility, 2000–2008
6%

Daily Volatility (%)

5%
4%
3%
2%
1%

Date

Exhibit 6.3

Historical S&P 500 Volatility

5/31/08

10/31/08

7/31/07

12/31/07

2/28/07

9/30/06

4/30/06

11/30/05

6/30/05

1/31/05

8/31/04

3/31/04

5/31/03

10/31/03

7/31/02

12/31/02

2/28/02

9/30/01

4/30/01

11/30/00

6/30/00

1/31/00

Portfolio Construction Models

103

GARCH forecasts, for example, are a way of understanding how a time
series behaves. The “A” in the acronym GARCH stands for Autoregressive,
which is a statistical term that characterizes a mean reverting process. A
negative value for autoregression implies that the time series exhibits trending behavior (which is also called autocorrelative). In this case, the time
series relates to the volatility of an instrument.
Expected Correlation The third input to the optimizer is the correlation matrix. Correlation is at heart a measure of the similarity of the movements
of two instruments, expressed in a number between –1 and +1. A +1 correlation implies exact similarity, whereas a –1 correlation implies that the
two instruments are exactly opposite, or anti‐correlated. A 0 correlation is
perfect non‐correlation and implies that the two instruments are entirely
dissimilar, but not opposite. An interesting fact about correlation is that it
says nothing about the trend in the instruments over time. For example, imagine two companies in the same industry group, such as airline companies.
If the first company is simply outcompeting the other and winning market
share, the first will likely have a positive trendline, while the second may
well have a negative trendline (assuming the overall market is roughly flat).
Nevertheless, these two companies will likely have a high positive correlation, because their returns are still driven heavily by the overall market, by
their sector, and by their industry, not to mention the more specific market
factors associated with being an airline company (e.g., the price of oil).
There are a number of problems with using standard correlation measures in quant trading, most of which we will address at various points later.
Most relevant for the moment, the measurement of the relationships between two instruments can be very unstable over time. They can even be
unreliable over long time periods. For example, imagine a portfolio with
two investments: one in the S&P 500 and one in the Nikkei 225. Taking the
data on both since January 1984, we can see that these two indices correlate
at a level of 0.37 since inception. The range of correlations observed using
weekly returns over any consecutive 365 calendar days (a rolling year) is
shown in Exhibit 6.4. Please note that we choose to use weekly returns in
this case, rather than daily returns, because of the time‐zone difference between the United States and Japan. In general, there is a one‐day lag between
the movements that occur in Japan, with respect to the moves that occur
in the United States. This can be handled either by using less frequent than
daily returns (as in this example) or by lagging the Japanese returns by a day.
You can see that the level of correlation observed between the S&P
500 and the Nikkei 225 depends quite a lot on exactly when it is measured.
Indeed, this correlation reaches the lowest point in the sample (+0.01) in
October 1989 and by mid‐2008 was at its highest point (+0.66). What’s

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Inside the Black Box

1/1984–8/2008 (Weekly returns)
0.70
0.60

Correlation

0.50
0.40
0.30
0.20
0.10
1/3/2007

1/3/2005

1/3/2003

1/3/2001

1/3/1999

1/3/1997

1/3/1995

1/3/1993

1/3/1991

1/3/1989

1/3/1987

1/3/1985

—

Date

Exhibit 6.4

Rolling Yearly Correlation between S&P 500 and Nikkei 225

worse, the correlation between these indices went from +0.02 to +0.58,
and then back to +0.01 all during the course of about four years, from
November 1985 until October 1989. Even using a rolling five‐year window,
the range is +0.21 to +0.57.
If the strategy specifies appropriate groupings of instruments, as in our
earlier example of industry groups, the stability of the correlations over time
improves. This specification can be made either in the definition of relative
in a relative alpha strategy and/or in the specification of the risk model. So,
for example, if the model groups together companies such as XOM and
CVX, this can be seen as reasonable, because these two companies have
much in common. Both have market capitalizations on the same general
scale, both are oil companies, both are based in the United States and have
global operations, and so on. Meanwhile, a comparison between CVX and
Sun Microsystems (JAVA) might be less defensible based on fundamental
factors, such as the fact that JAVA isn’t an oil company but is a much smaller
capitalization company in the technology sector. Somewhat predictably, this
theoretical difference in the comparability between these two pairs of stocks
(XOM vs. CVX, CVX vs. JAVA) also bears out in the data, as shown in
Exhibit 6.5.
As you can see, CVX and XOM correlate relatively well over the entire
period of more than 20 years. The lowest correlation level observed between
this pair is approximately 0.40, and the highest is 0.89. The correlation
over the entire period is 0.70. Meanwhile, CVX and JAVA correlate poorly,
at a level of only 0.14 over the whole sample, with a minimum two‐year

105

Portfolio Construction Models

1.0

r (JAVA, CVX)
r (XOM, CVX)

0.8
0.6
0.4
0.2
–

3/31/2008

3/31/2007

3/31/2006

3/31/2005

3/31/2004

3/31/2003

3/31/2002

3/31/2001

3/31/2000

3/31/1999

3/31/1998

3/31/1997

3/31/1996

3/31/1995

3/31/1994

3/31/1993

3/31/1992

3/31/1991

3/31/1990

(0.2)
3/31/1989

Correlation Over Prior Two Years

Rolling Two-Year Correlation,
March 1987 to March 2008

Date

Exhibit 6.5

Correlation Over Time between Similar and Dissimilar Instruments

correlation of –0.14 and a maximum of 0.36. Furthermore, the correlation between CVX and XOM changes more smoothly over time than that
between CVX and JAVA. Though both pairs can be said to be somewhat
unstable, it is quite clear that grouping CVX with XOM is less likely to be
problematic than grouping CVX with JAVA. To be clear, the instability of
correlations among financial instruments is more or less a fact of the world.
It is not the fault of optimizers, nor of correlation as a statistic, that this happens to be the case in the finance industry.
The main source of this instability is that the relationships between financial instruments are often governed by a variety of dynamic forces. For
example, if the stock market is experiencing a significant downdraft, it is
probable that the correlation between CVX and JAVA will be temporarily
higher than usual. If, on the other hand, there is uncertainty about oil supply, this may affect CVX but not JAVA, and correlation may be reduced
temporarily. If either company has significant news, this can cause decoupling as well.

Optimization Techniques
There are many types of optimizers. They range from basic copies of
Markowitz’s original specification in 1952 to sophisticated machine learning

106

Inside the Black Box

techniques. This section provides an overview of the most common of these
approaches.
Unconstrained Optimization The most basic form of an optimizer is one that
has no constraints; for example, it can suggest putting 100 percent of a portfolio in a single instrument if it wants. Indeed, it is a quirk of unconstrained
optimizers that they often do exactly that: propose a single‐instrument portfolio, where all the money would be invested in the instrument with the
highest risk‐adjusted return.
Constrained Optimization To address this problem, quants figured out how
to add constraints and penalties in the optimization process, which forces
more “reasonable” solutions. Constraints can include position limits (e.g.,
not more than 3 percent of the portfolio can be allocated to a given position) or limits on various groupings of instruments (e.g., not more than
20 percent of the portfolio can be invested in any sector). An interesting
conundrum for the quant, however, is that, if the unconstrained optimizer
would tend to choose unacceptable solutions, to the extent that constraints
are applied it can become the case that the constraints drive the portfolio
construction more than the optimizer. For example, imagine a portfolio
of 100 instruments, with the optimizer limited to allocating no more
than 1.5 percent to any single position. The average position is naturally
1 percent (1/100 of the portfolio). So, the very best positions (according to
the alpha model) are only 1.5 times the average position, which is relatively
close to equal‐weighted. This is fine, but it somewhat defeats the purpose
of optimizing.
Another class of constraints for optimization involves the integration of
risk models. Here, too, there are several ways to implement a constraint (as
discussed in Chapter 4), including penalties and hard limits. If, for example,
we simply want to eliminate sector risk, a simple way might be to modify
the correlation matrix so that all stocks within a given sector are given high
positive correlations. The optimizer would otherwise solve for the best solution given this modified correlation structure. Alternatively, we could introduce a penalty function that penalizes a small amount of sector risk at a
low level (i.e., the expected return needed to overcome this penalty would
be itself relatively small); but, as the level of sector risk increases to double
the prior level, the expected return needed to justify this increase is substantially larger than double the alpha required at the lower level of sector risk.
In other words, the expected marginal reward must increase substantially
faster than the expected marginal risk, and the larger the increase in risk, the
faster the expected return must increase to make the optimizer accept the
trade‐off and allow the increased risk exposure.

Portfolio Construction Models

107

Transaction costs, too, can be addressed in various ways. One can build
an empirical model of every stock’s market impact function, and use this set
of individual market impact models to feed into the optimizer. Alternatively,
one could simply specify a market impact function that takes inputs such as
volatility, (dollar) volume, and the order size, and have a generalized solution for a market impact model. These are but two of the many ways that
quants can account for expected transaction costs as an input to a portfolio
optimization.
The mathematics and programming that achieve optimization are designed to account for the types of inputs mentioned above, iteratively solving for the trade‐off that maximizes the objective function (for example,
the expected return versus the expected volatility) of a portfolio. The optimizer is trying to solve a lot of problems at once, potentially: maximize
returns per unit of risk, accounting for correlation and volatility, while staying within various hard limits (e.g., maximum position size constraints), and
while accounting for risk factor exposures and transaction costs. While it’s
complicated, compared to many other aspects of a systematic trading strategy, these are generally very well‐understood solutions, and there are many
canned, off‐the‐shelf (including free, open source codebase) packages that
compute these solutions relatively painlessly.
If we think back to Exhibit 6.2, visually, constraining an optimization
involves cutting out regions of the surface that do not satisfy the conditions. For example, imagine that we impose a market exposure constraint,
such that the maximum difference between the bets on ABC and DEF is 20
percent. In this case, most of the surface will be ignored by the optimizer,
and only the parts of the surface that satisfy the maximum exposure constraint are searched. This is illustrated in Exhibit 6.6. As you can see by comparing this exhibit to Exhibit 6.2, the excluded areas of search due to the
constraint on net exposure are the flat, somewhat triangular “wings” along
the plane at a 0 Sharpe Ratio. Note that, since we are limiting the region for
the optimizer to search through, it is possible to add so many constraints
that there is no solution.
It is also worth recognizing that our example is extremely oversimplified. We have a portfolio of only two assets, high correlation, and one simple constraint. In a more realistic scenario, the surface is unlikely to be so
simple‐looking, with a clear trend toward a single peak. In a more complex
case, there may be many peaks scattered around various regions of the overall space. The algorithm used to seek the optimal outcome must be designed
with a specific trade‐off in mind, namely between thoroughness and speed.
A faster, less thorough optimization algorithm might find a local peak in
the curve and stop looking, even though somewhere else in the universe
of possible portfolios, there is an even better portfolio to consider. A more

108

Inside the Black Box

0.30

0.20

Sharpe Ratio

0.10

—

(0.10)

–100%
–60%

(0.20)

–20%
20%

(0.30)
–100% –80%
–60% –40%
–20%

60%
0%

% of Portfolio
Allocated to ABC

20%

40%

60%

80%

% of Portfolio
Allocated to DEF

100%
100%

Exhibit 6.6

Visual Representation of Constraining the Search Space for
an Optimization

thorough search algorithm might find that globally optimal solution, but its
search might take far too long to be practicable.
Black-Litterman Optimization Fischer Black, of Black‐Scholes fame, and Bob
Litterman, of Goldman Sachs, in 1990 produced a new optimization method that was first introduced in an internal memo at Goldman but was later
published in 1992 in the Financial Analysts Journal.3 Their Black‐Litterman optimizer addresses some of the problems associated with errors in the
measurement of inputs to an optimizer. Most important, they proposed a
method of blending an investor’s expectations with a degree of confidence
about those expectations, and these with the historical precedent evident
in the data. For example, imagine that CVX and XOM correlate at 0.7
historically, but going forward, a trader’s alpha model forecasts that XOM
will rally while CVX will fall. In this case, the correlation between CVX
and XOM over the period being forecast may be quite low, perhaps even
negative, despite the evidence from history. Black‐Litterman provided a way
to adjust historically observed correlation levels by utilizing the investor’s
forecasts of return for the various instruments in question. Furthermore, to
the extent that the investor has greater confidence in some forecasts and less

Portfolio Construction Models

109

in others, this fact can be incorporated. If the investor forecasts significant
divergence between instruments that historically have correlated at a high
level but has a low level of confidence in the forecast, something much closer
to the historical level of correlation is used. To the extent that the investor
has greater confidence, the forecast returns play a more important role in
determining the correlation coefficient utilized by the Black‐Litterman optimizer. Some quants prefer this method of optimization because it allows
for a more holistic approach to combining the alpha model with the other
inputs to optimization.
Grinold and Kahn’s Approach: Optimizing Factor Portfolios Another kind of optimizer that bears mentioning is described in Grinold and Kahn’s seminal Active Portfolio Management.4 This kind of portfolio optimization technique is
directly aimed at building a portfolio of signals, whereas most optimizers try
to size positions. The method of optimizing proposed by Grinold and Kahn is
fairly widely used. The idea of this approach is to build factor portfolios, each
of which is usually rule‐based (in fact, very often equal‐weighted or equal
risk–weighted) portfolios based on a single type of alpha forecast. So, for example, one could imagine building a momentum portfolio, a value portfolio,
and a growth portfolio. Each of these portfolios is in turn simulated historically, as though it were making stock picks through the past. For instance, the
value factor’s portfolio would look back at the historical data and simulate
the results it would have achieved by buying undervalued instruments and
shorting overvalued instruments through this historical sample, as though it
were reliving the past. In this way, a time series of the returns of these simulated factor portfolios is generated. These simulated factor portfolio returns
are then treated as the instruments of a portfolio by the optimizer.
One benefit of this approach is that the number of factor portfolios is
typically much more manageable, usually not more than about 20, corresponding to the number of individual factors in the alpha model. What is
therefore being optimized is not a portfolio of thousands of instruments but
rather the mixing of a handful of factor portfolios. This is certainly an easier
hurdle to clear in terms of the amount of data needed. Factor portfolio optimization allows for the inclusion of the risk model, transaction cost model,
portfolio size, and risk target as inputs, in much the same way as described
for other optimizers.
Given the weight of each model, we ultimately need to ascertain the
weight of each position. The way that each position’s weight is computed in
this approach is perhaps easiest to understand by example. Imagine we have
two alpha factors, both of which yield only a directional forecast (i.e., +1 for a
buy signal or –1 for a sell signal). We have 100 stocks in the factor portfolios,
which are equally weighted for simplicity’s sake. This means that each stock

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is 1 percent of each factor portfolio. Let’s assume that the factor optimization
procedure dictated that we should have a 60 percent weight on the first factor
portfolio and a 40 percent weight on the second. The allocation to any stock
in this example is 1 percent (the weight of each name in each factor portfolio)
times the signal given by that factor (i.e., long or short) times the weight of
each factor portfolio. Let’s say that the first alpha factor’s forecast for a given
company is +1, and the second is –1. So the total allocation to the company
is [(1%) * (+1) * (60%)] + [(1%) * (–1) * (40%)] = +0.2%, meaning that we
would be long 0.2 percent of our portfolio in this company.
Resampled Efficiency In Efficient Asset Management, Richard Michaud proposed yet another approach to portfolio construction models.5 Rather than
proposing a new type of optimization, however, Michaud sought to improve
the inputs to optimization. His Resampled Efficiency technique may address
oversensitivity to estimation error. Michaud argues that this is in fact the
single greatest problem with optimizers. Earlier, we gave the example of
the instability of the correlation between the S&P 500 and the Nikkei 225.
This implied that, if we used the past to set expectations for the future—in
other words, to estimate the correlation between these two instruments going forward—we are reasonably likely to have the wrong estimate at any
given time, relative to the actual correlation that will be observed in the
future. A quant will have such estimation errors in the alpha forecasts, in the
volatility forecasts, and in the correlation estimates. It turns out that mean
variance optimizers are extremely sensitive to these kinds of errors in that
even small differences in expectations lead to large changes in the recommended portfolios.
Michaud proposes to resample the data using a technique called Monte
Carlo simulation to reduce the estimation error inherent in the inputs to the
optimizer. A Monte Carlo simulation reorders the actually observed results
many times, thereby creating a large number of time series all based on the
same underlying observations. For example, imagine we are testing a trend‐
following strategy that is based on the closing prices of the S&P 500 from
1982 through 2008. But now we want to get a sense of how robust the strategy might be if the future doesn’t look exactly like the past. So, we can take the
return distribution of the S&P 500, which tells us how often the S&P gains or
loses various amounts, and use it to create a large number of alternate histories for the index. By reshuffling the returns in this way, we have less dependence on the past looking just like the future, because we now have thousands
of “pasts” over which to test our strategy. Interestingly, the average return and
the volatility of returns will remain the same across all these alternate histories
because they are based on the same underlying return distribution. But now
we can see how often our strategy performs well or poorly across all these

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hypothetical scenarios and therefore how likely it is to work well or poorly in
a future that might not resemble the past precisely. This technique is thought
to produce more robust predictions than are possible from simply using only
the actual sequence of returns the instrument exhibited, in that the researcher
is capturing more aspects of the behavior of the instrument. It is this intuition
that is at the heart of Monte Carlo simulations.
A word of warning regarding such resampling techniques, however:
Re‐using a historical distribution is only really useful if you have sufficient
confidence that the sample in the historical distribution is a fair representation of the whole population. For example, if you were to use the S&P’s
daily returns from 1988 through 2006, you might believe you had a very
good data sample: approximately 19 years of daily returns. However, you
would be missing many of the largest negative observations, because both
the 1987 crash and the 2007–2008 bear market would be missing. Specifically, using the 19‐year sample, you’d have only nine days in your sample
during which the S&P declined by more than 4 percent, and only 11 days
where the S&P rose by more than 4 percent. By including those extra three
years of data, you would see an extra 19 days on which the S&P declined
by more than 4 percent (including one day larger than –20%), as well as 16
extra days on which the S&P rose by more than 4 percent (including one
day of almost +12%).
Data-Mining Approaches to Optimization As a final note on the types of optimizers, we turn our attention briefly to data‐mining approaches applied to portfolio construction models. Some quants use machine learning techniques,
such as supervised learning or genetic algorithms, to help with the problem
of optimization. The argument in favor of machine learning techniques in
portfolio construction is that mean variance optimization is a form of data
mining in that it involves searching many possible portfolios and attempting to find the ones that exhibited the best characteristics, as specified by the
objective function of the optimizer. But the field of machine learning aims
to do much the same thing, and it is a field that has received more rigorous
scientific attention in a wide variety of disciplines than portfolio optimization, which is almost exclusively a financial topic. As such, there may be
good arguments for considering machine learning approaches to finding the
optimal portfolio, especially due to the quality of those algorithms relative
to the mean variance optimization technique.

Final Thoughts on Optimization
One interesting byproduct of portfolio optimization is that there are instances in which an instrument that is forecast to have a positive return

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in the future by the alpha model might end up as a short position in the
final portfolio (or vice versa). How can this happen? Imagine we are trading a group of equities in the United States and that one of the constraints
imposed on the optimization by the risk model is that the portfolio must
be neutral to each industry group. In other words, for every dollar of long
positions within, say, the software industry, we must have a corresponding
dollar of short positions within the same industry (to create a zero net position in the software industry). But what if we have positive return expectations for every stock in the software industry? The optimizer would likely
be long those software companies with the highest positive return expectations and short those software companies with the lowest positive return
expectations.
Certainly, among sophisticated quants that use optimizers to build their
portfolios, the most simplistic optimization techniques (particularly unconstrained) are in the minority. Still, though the intuition behind optimization
is sound, the technique itself is perhaps the most properly labeled black
box part of the quant trading system. The output is sometimes confusing
relative to the inputs because of the complexity of the interactions among
an alpha model, a risk model, and a transaction cost model, along with
the constraints of size and desired risk level. Compounding the complexity,
we have to consider the interaction among various kinds of alpha factors
within the alpha model. That said, it is highly likely that the larger positions
in the portfolio are those with the strongest expected returns. The strange
behavior described here—having a position in the opposite direction as the
alpha model’s forecast—is observable mainly with the smaller positions in
the portfolio because it is among these that the expected returns can be overcome by transaction cost or risk management considerations.
This last phenomenon is sometimes known as the substitution effect. If
we have a higher forecasted return for ABC than we do for DEF, it might
be expected that our portfolio should reflect this. However, if ABC is also
expected to be dramatically more expensive to trade, and if ABC and DEF
are reasonably correlated, the optimizer might well choose to invest in DEF
instead of ABC.

Output of Portfolio Construction Models
Regardless of the type of portfolio construction approach used, the output of the quantitative portfolio construction model is a targeted portfolio:
the desirable individual positions and the targeted sizes of each. This target
portfolio is compared to the current portfolio, and the differences are the
trades that need to be done. In the case that a brand‐new portfolio is being

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built from scratch, all the positions recommended by the portfolio construction model will need to be executed. If, instead, the quant is rerunning the
portfolio construction model as he would do periodically in the normal
course of business, he would need to do only the incremental trades that
close the gap between the newly recommended portfolio and the existing
portfolio he holds.

How Quants Choose a Portfolio Construction Model
I have observed that the significant majority of quants using rule‐based
allocation systems seem to take an “intrinsic” alpha approach (i.e., they
forecast individual instruments rather than forecasting instruments relative to each other). Most, but not all, of these are actually futures traders.
Meanwhile, quants utilizing optimizers tend to be focused on a “relative”
alpha approach, most typically found among equity market neutral strategies. There is no obvious reason for the difference in the preferred portfolio
construction approach for relative and intrinsic traders. However, it is likely
that quants that use relative alpha strategies already believe implicitly in the
stability of the relationships among their instruments. After all, in a relative
alpha paradigm, the forecast for a given instrument is as much a function
of that instrument’s behavior as it is about the behavior of the instruments
to which the first is being compared. If these relationships are unstable, the
strategy is doomed to start with, because its first premise is that certain comparisons can be made reliably. If the relationships are stable, however, it is
entirely logical and consistent that the quant can rely on them for portfolio
construction as well.
Meanwhile, if a quant takes an intrinsic alpha approach, he is making
an implicit statement that his portfolio is largely made up of a series of independent bets, so relying on a correlation matrix (one of the key inputs to the
optimizer) might not be very useful. Instead, this kind of quant would focus
efforts more directly on risk limits and alpha forecasts subject to transaction costs. This more direct approach to portfolio construction is usually
best implemented with a rule‐based model. It is interesting to note that the
kind of alpha model a quant builds is likely to impact the choice of portfolio
construction model that makes the most sense to use.

Summary
We have described the two major families of portfolio construction models. Rule‐based models take a heuristic approach, whereas portfolio opti-

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mizers utilize logic rooted in modern portfolio theory. Within each family
are numerous techniques and, along with these, numerous challenges. How
does the practitioner taking a rule‐based approach justify the arbitrariness
of the rules he chooses? How does the practitioner utilizing optimization
address the myriad issues associated with estimating volatility and correlation? In choosing the “correct” portfolio construction technique, the quant
must judge the problems and advantages of each, and determine which is
most suitable, given the type of alpha, risk, and transaction cost models
being used.
All of these techniques share one common thread, however: They are
taking the expected returns (from the alpha model’s forecasts) and transforming those into a portfolio. This transformation can be extremely simple
or very complex, and the choice is determined by the approach that the
quant researcher takes to the problem. However, all of these approaches
are attempting to maximize the goodness of the outcome. What determines
goodness is also entirely up to the researcher. For example, some seek to
maximize the Sharpe ratio, others seek to maximize the ratio of return to
maximum peak‐to‐valley drawdown, and still others might seek to maximize the expected return without consideration given to the level of risk.
In each case, the researcher can choose also whether and what to constrain
as far as risk exposures. Still, the goal is to maximize the goodness of the
outcome, subject to any relevant constraints.
We have completed the penultimate stop on the trip through the inside
of the black box, as seen on our road map (Exhibit 6.7). Next we will see
how quants actually implement the portfolios that they derived using their
portfolio construction models.

Alpha Model

Risk Model

Transaction Cost Model

Data
Portfolio Construction Model
Research
Execution Model

Exhibit 6.7

Schematic of the Black Box

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Notes
1. Harry Markowitz, “Portfolio Selection,” Journal of Finance 7, no. 1 (March
1952): 77–91.
2. Tim Bollerslev, “Generalized Autoregressive Conditional Heteroskedasticity,”
Journal of Econometrics 31 (June 1986): 307–327.
3. Fischer Black and Robert Litterman, “Global Portfolio Optimization,” Financial Analysts Journal (September–October 1982): 28–43.
4. Richard Grinold and Ronald Kahn, Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk (New
York: McGraw‐Hill, 1999).
5. Richard Michaud, Efficient Asset Management: A Practical Guide to Stock
Portfolio Optimization and Asset Allocation (New York: Oxford University
Press, 2001).

Chapter

Execution
Quality is never an accident; it is always the result of high
intention, sincere effort, intelligent direction and skillful execution.
—William A. Foster

o far in our tour through the black box, we have seen how quants determine what portfolio they want to own. Quants build alpha models, risk
models, and transaction cost models. These modules are fed into a portfolio
construction model, which determines a target portfolio. But having a target
portfolio on a piece of paper or computer screen is considerably different
from actually owning that portfolio. The final part of the black box itself
is to implement the portfolio decisions made by the portfolio construction
model, which is accomplished by executing the desired trades.
There are two basic ways to execute a trade: either electronically or
through a human intermediary (e.g., a broker). Most quants elect to utilize
the electronic method, because the number of transactions is frequently so
large that it would be unreasonable and unnecessary to expect people to
succeed at it. Electronic execution is accomplished through direct market
access (DMA), which allows traders to utilize the infrastructure and exchange connectivity of their brokerage firms to trade directly on electronic
markets such as ECNs. For ease, I will refer to any type of liquidity pool—
whether ECN, exchange, or otherwise—as an exchange, unless a specific
point needs to be made about a particular type of market center.
Several points bear clarification. First, DMA is available to any trader,
whether quant or discretionary, and in fact, many discretionary traders also
utilize DMA platforms offered by their brokers to execute trades. Trades
submitted via DMA can still be done manually if so desired, but they are
manually entered into computer software, which then directly communicates with the electronic exchanges.

117

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In the past, traders would call their brokers, who would “work” orders,
which meant the latter trying to pick the best times, sizes, and prices, or
occasionally contacting other counterparties to negotiate a better price on
a larger block trade. Now, particularly on electronic exchanges, execution
algorithms are far more commonly responsible for working orders. Execution algorithms contain the logic used to get an order completed, including
instructions about how to slice up an order into smaller pieces (to minimize
market impact), or how to respond to various kinds of changes in the limit
order book and price behavior.
One can acquire execution algorithms in one of three ways: build them,
use the broker’s, or use a third‐party software vendor’s. This chapter will, in
part, detail the kinds of things execution algorithms are designed to handle.
We will then discuss more recent developments related to the infrastructure
quants utilize to execute trades. A more thorough coverage of infrastructure‐ and execution‐related issues, particular to latency‐sensitive execution
and trading strategies (including high‐frequency trading) will be addressed
in Part Four of this book.
Though most orders executed by quants are algorithmic, traders occasionally utilize a service most brokerages offer, namely, portfolio bidding. I
describe this idea only briefly, since it is not a particularly quantitative way
to execute trades. In a portfolio bid, a blind portfolio that the trader wants
to transact is described by its characteristics in terms such as the valuation
ratios of the longs and shorts, the sector breakdown, market capitalizations,
and the like. Based on these characteristics, brokers quote a fee, usually in
terms of the number of basis points (100 basis points = 1 percent) of the
gross market value of the portfolio being traded. In exchange for this cost,
a guaranteed price is given to do the transaction. The quant using this arrangement, in other words, is buying certainty of the prices of his trades
and in exchange is paying the broker for providing that certainty. Once
an agreement is reached between the broker and the quant, he receives the
transactions from the broker at the pre‐agreed price, and the broker receives
his fee for the service and assumes the risk of trading out of the portfolio
at future market prices, which may be better or worse than the prices they
have guaranteed. Human execution of quant portfolios often looks like a
portfolio bid rather than a series of individual orders being worked.
Generally, the workflow for a quant trader is not materially different
now from what it was in the days that preceded automated execution. Some
traders preferred to more actively work their own orders, and many others
would outsource order working to brokers. Some firms would outsource
their executions to third‐party execution services firms, who would interface with brokers on behalf of the trader. Today, while some firms continue
to employ human traders, more often quant trading firms execute orders

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through algorithms. As before, some of these firms have their own order
working algorithms, while others utilize those offered by their broker or
other service providers. In most cases, they still send their orders to a broker
for execution. As such, the vast majority of volumes on various exchanges
around the developed world are executed by algorithms on behalf of clients.
And, just as before, these volumes are a form of currency for the trading
firms that drive them. They bring valuable commission dollars to brokers,
and in exchange for a trader bringing his business to a particular broker, the
broker may be willing to offer research, data, or capital‐raising assistance,
among other services.1

Order Execution Algorithms
Order execution algorithms determine the way in which systematic execution of a portfolio is actually done. We can examine the kinds of decisions
the algorithms must make in real time in much the same framework in
which we’d think about how discretionary traders implement their orders.
The kinds of considerations are the same in both cases, and as has been
the theme throughout this book, we find that quants differ here from their
discretionary counterparts principally in the mechanics and not so much in
the ideas. The principal goal of execution algorithms, and the function of
most execution desks in general, is to minimize the cost of trading into and
out of positions.
The primary goals of an order execution algorithm are to get the
desired amount of a trade done as completely as possible and as cheaply
as possible. Each of these goals is equally interesting and important. Completeness is important because the best portfolio is selected by the portfolio construction model, and if those trades are not implemented, then a
different portfolio is owned from what was intended. Cheapness is important for all the reasons we described in Chapter 5: In short, if you can save
money every time you make a trade, you will be better off. An obvious corollary is that the more you trade, the more important it is to save money
on each trade. This statement, simple and obvious as it is, has important
implications for how a rational quant trader goes about building an execution capability. For strategies that require infrequent execution, it may be
reasonably viewed as overkill to build a very expensive high‐speed trading
infrastructure. After all, the savings of being high speed versus standard
speed are very small, so they are only worth pursuing if they can be made
up for in frequency.
Cheapness has several facets, including market impact and slippage, as
discussed in Chapter 5. However, one driver of both impact and slippage

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is what is known as a footprint, which refers to a detectable pattern of
behavior by a market participant (think of footprints in the same way a
tracker does, when hunting some animal in a forest). If an order execution
algorithm leaves an obvious footprint, its activities become predictable to
other market participants, and these other participants may well react in
such a way as to increase the market impact and slippage incurred by such
an algorithm.
An important question is how to measure the efficacy of an execution
algorithm. There are a few important concepts worth mentioning here. First
is the notion of the mid‐market, which is the average of the best bid and the
best offer (which is, by definition, the midpoint between those two levels)
on an instrument. This is the most standard way to judge the fair price of a
given transaction. If, for example, one is able to buy at the best bid, which
is obviously below the then‐current mid‐market, that particular transaction
is considered to have been executed at a favorable price (just as a sale at the
then‐current best offer might be).
Second, the notion of the volume‐weighted average price (VWAP, for
short) is the most standard benchmark for judging the quality of an execution algorithm over multiple trades (either within a day or over multiple
days). The idea here is that the VWAP may give a fair sense of how the day’s
volumes were priced. Since this is the weighted average price at which the
day’s trading was transacted, it is a reasonable start at thinking about the
efficacy of an algorithm. The trouble is that some investors may be fooled
by looking at VWAP. If a buyer of stock executes huge volumes during some
day, his volumes will most likely increase the price of that stock, and the
VWAP. As such, his own activities impact the benchmark against which his
execution algorithm is measured, making the interpretation of this benchmark tricky.
The major considerations that go into the making of an order working
algorithm are as follows: whether to be aggressive or passive; what type of
order to utilize; how to determine the ideal order size; and where to send it.
We will briefly address each of these issues.

Aggressive versus Passive
There are two general approaches to execution: aggressive and passive.
Aggressive orders (most often in the form of market orders) are submitted to
the marketplace and are generally unconditional. They can be filled in pieces
or in full at whatever price prevails at the market at the time the order’s turn
to be executed arrives (within reasonable boundaries, and so long as there is
a bid or offer resting in the order book to take the other side of the market
order). In contrast, passive orders (a subset of all limit orders) allow the

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trader to control the worst price at which he is willing to transact, but the
trader must accept that his order might not get executed at all or that only
a part of it might be executed. There is also a significant problem of adverse
selection, which we will describe in further detail in Chapter 14.
The collection of all available bids and offers (all of which are passive orders) for a given security is known as the limit order book, which
can be thought of as a queue of limit orders to buy and sell. In electronic
markets, each order that is placed on the exchange is prioritized. Highest
priority is given to orders at the best prices (the best bids for buy orders
and the best offers for sell orders), whereas lower priority is given to those
who are bidding or offering worse prices. For two traders offering the same
price, traders who show their orders are given higher priority (by most exchanges) than those who hide them (more on this shortly), and for traders
who are still tied, the tiebreaker is, not surprisingly, (most often) which one
came first.
For some markets, rather than time priority, all orders at a given price
are given equal priority, but they are filled according to a pro rata allocation of any active order. For example, imagine there are two bids on some
instrument at $100.00 (which we will assume is the best bid price), one for
100 units and another for 900 units. Now imagine that an active order to
sell 100 units comes into the market. The order would be filled at $100.00,
and the passive orders would be allocated as follows: 10 units allocated to
the 100 unit order, leaving 90 units remaining on the bid at $100.00, and
90 units allocated to the 900 unit order, leaving 810 units remaining at the
bid price. Special considerations apply to these markets, namely a trade‐off
between oversizing and overtrading.
Oversizing refers to one technique that a trader might consider using to
deal with pro rata markets. Since an active trade is allocated to the various
relevant limit orders resting in the order book, proportionately to the size
of a given limit order versus the other orders resting in the book at the same
price, some traders intentionally oversize their limit orders. This will allow
that order to get a larger share of any active order that interacts with the
order book. However, there is also the risk that the order is so large that it
causes the position to be bigger than the passive trader desired.
On the other hand, if the trader sizes his orders smaller, he must deal
with placing and canceling large numbers of orders, which is known as
overtrading. Imagine some trader wishes to passively buy 100 units of some
instrument, and that at the time an active order to sell 100 units comes in,
there is another trader’s 900 unit order already in the limit order book. He
will only receive a 10 unit fill. Depending on the volume of orders that join
his limit order price as he awaits a complete fulfillment of his desired size,
he runs the risk of having a very large amount of selling need to take place

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before his 100 units is finally filled. And, as we will see in more detail in
Chapter 14, this means that he runs a severe risk of experiencing adverse
selection2 (i.e., it is often bad news when the fills actually take place, because
the price is likely to move against you in the short term by the time that
happens). This in turn means that the trader must be quick to cancel orders
and replace them as he competes with larger orders. Without high cancellation rates in this type of market, there would be a vicious cycle of oversizing
that theoretically might never end. But as traders cancel, an oversized order
might need to cancel as well, because it now is vulnerable to being filled at
a larger size than the trader intended.
Regardless, the first kind of decision an execution algorithm must
make is how passive or aggressive to be. Passivity and aggression represent how immediately a trader wants to do a trade. Market orders are
considered aggressive, because the trader is saying to the market that he
just wants his order filled immediately, at whatever the prevailing market
will bear. As such, a market order to buy is likely to pay at least the offer,
whereas a market order to sell is likely to receive, at most, the current best
bid. If the order size is larger than the amount available at the current best
bid or offer (whichever applies), the transaction will take out multiple
bids or offers at increasingly adverse prices. Paying this kind of cost to
transact might be worthwhile if the trader really wants the trade done
immediately.
Limit orders can be placed at differing levels of aggressiveness as well.
For example, a limit order to buy at the current best offer is an aggressive
order because it crosses the spread and removes the best offer from the order
book (this is also known as lifting the offer). By contrast, a limit order to
buy at or below the current best bid is passive because the trader is effectively saying he is fine with the lower probability of being executed, but if
he does execute, he is at least only paying the price he’s specified. In addition
to accepting this uncertainty, the passive order is further subject to a serious
problem known as adverse selection. A trader who is willing to cross the
bid‐offer spread by placing an active order may well have information that
the trade he is conducting is actually worth it paying the bid‐offer spread
to get put on right away. To complicate matters further, as we discussed in
the discussion of transaction cost models, many exchanges actually pay providers of liquidity for placing passive orders while they charge traders for
using liquidity being provided. To phrase it another way, orders that cross
the spread (orders to buy that are executed at the offer, or orders to sell that
are executed at the bid) are using, or “taking,” liquidity in that each share
or contract executed in this manner is taking out a passive order that’s been
placed by another trader, which reduces the liquidity available for other
participants.

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The practice of paying for liquidity provision sweetens the deal for a
passive order, but only if the order is actually executed. Not only does the
passive trader get a better transaction price, but he also receives a commission rebate from the exchange (typically on the order of two‐tenths of a cent
per share). But again, the trade‐off is a reduction in certainty of being filled
and suffering from potential adverse selection. It is worth noting that some
exchanges do the opposite: charge providers of liquidity while paying takers
of liquidity. Thus, the liquidity provision (or taking) rebate (or fee) factors
into the decision of how passive or aggressive to be. This also factors into
answering the question of where to route an order, which is a topic we will
cover further in “Where to Send an Order.”
It is generally true that alpha strategies that are based on a concept of
momentum will be paired with execution strategies that are more aggressive, because the market can tend to run away from the trader if he is not
aggressive. It is also generally the case that mean reversion strategies utilize
more passive execution strategies because they are taking the risk that the
prevailing trend persists, and at least by executing at a better price, this mitigates the downside risk of standing in front of the steamroller.
Another factor driving the use of passive or aggressive execution strategies is the strength of the signal and the model’s confidence level in the signal. A stronger, more certain signal probably will be executed with greater
aggressiveness than a weaker or less certain signal. This idea is easily demonstrated by extreme examples. If you had inside information that a stock
was going to double in the next day because some other company was set
to announce an acquisition of the stock in question at a large premium, and
if trading on inside information was legal (which it, of course, is not), you
should be perfectly happy to pay a lot of money to the marketplace to fill a
large order to buy this stock. It would be illogical to fret over a few pennies
per share when many dollars are the upside. On the other hand, if you have
no view on a stock but were being asked what you’d be willing to pay for it
by someone who wants to sell it, you are likely to offer a low enough price
that there is some margin of safety.
A fairly common middle ground is to put out limit orders somewhere
between the best current bid and offer (this is only feasible if the spread
between the best bid and offer is larger than the minimum tick size). This
way, the trader jumps to the front of the queue for executions, and though
he pays a bit more than he would have to if he simply waited for his order
to get executed passively, the limit order caps the amount by which he is
worse off. At the same time, he has a higher probability of execution than
he would if he simply added his order to the current best bid or offer.
Finally, he is less likely to suffer from adverse selection in this case. In trading parlance, adding an order to the best bid or offer is known as joining

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it; placing an order that constitutes a new best bid or offer is known as
improving.
As data have been collected and researched by quants on the limit order book, there has been an increase in sophistication of order execution
algorithms to adjust passiveness or aggression based on various changes
in the “shape” of the limit order book. This is an example of factoring in a
so‐called micro price or fair value for an instrument. The most conventional
ways to quote the price of an instrument are either to state its last traded
price or its best bid and offer prices. But the last traded price only tells you
what someone else just did, not what you can do now, making it of limited
use for trading purposes. The best bid and offer are clearly useful, but what
if the best bid has 10,000 units quoted, while the best offer has only 1 unit
quoted? This clearly implies that the bid price is more relevant than the offer
price. As such, many algorithms account for such imbalances by computing
a fair price that reflects things like the imbalance between bids and offers in
the limit order book.
To summarize, the first characteristic of an order execution algorithm is
its level of aggressiveness, and this can be thought of as a spectrum. At the
most aggressive end of the spectrum are market orders; at the least aggressive end of the spectrum are limit orders with prices that are far away from
the current market. The level of aggressiveness is usually a function of the
type of strategy being employed and depends on the strength of the signal,
the system’s confidence in that signal, and sometimes also on considerations
from the order book, such as a micro price.

Other Order Types
Given the plethora of exchanges and their rules, it would not be fruitful to
attempt to cover every kind of order possible in this book. This is especially
true because new order types are frequently being created by exchanges, and
other order types are retired. However, it is worth understanding some of
the types common in some of the largest and most active markets. We will
outline several such order types in this section.
Hidden orders are a way to mask one’s limit orders from the market, at
the cost of losing priority versus visible orders at the same price. The goal
here is to hide one’s hand in terms of buy/sell intentions from other market players while still being able to trade. As discussed, any time a trader
puts into the queue a visible order—that is, an order that he has allowed
the rest of the market to see—he gives away a bit of information. If many
units are already being bought, and yet another trader submits another order
to buy, you can imagine a scenario where the price goes up quickly, causing the transaction to cost a significant amount more. In other words, the

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marketplace has a broad‐based sense of market impact, based on the total
imbalance between the buyers and sellers at the moment (this relates back to
what we discussed regarding the micro‐price in the previous section). Placing
a hidden order provides no information to the market, which helps reduce
the market’s perception of imbalances. However, it also reduces the priority
of the trade in the queue, leading to a lower probability of execution.
One algorithmic trading technique that utilizes hidden orders is known
as iceberging, which takes a single large order and chops it into many smaller orders, most of which are posted to the order book as hidden orders. In
this way, the bulk of the order is hidden from other traders, just as only the
tip of an iceberg is visible above sea level. It is worth noting that not all exchanges allow hidden orders.
In addition, several versions of market and limit orders, such as
market‐on‐close orders or stop‐limit orders, exist. Market‐on‐close orders
instruct the broker to release the order as a market order during the closing
auction for that day. Stop limit orders instruct the broker to enter a limit
order at a predetermined price, but to wait until the instrument trades at
that price before entering the order. There are also modifiers to orders,
such as fill or kill, all or none, and good till canceled. A fill‐or‐kill order is a
limit order in which all the shares for the order must be filled immediately
or the order is automatically canceled. An all‐or‐none order is like a fill‐
or‐kill order without the cancellation feature, so if an order is not immediately completed in its full size, it remains untouched. A good‐till‐canceled
order is a limit order that is not automatically canceled at the end of the
day but remains in effect for days or weeks, until explicitly canceled by
the trader.
Depending on the market and asset class, there are many other kinds
of orders. Moreover, order types are regularly introduced and retired based
on customer demands and requests. In the process of executing orders, the
quant must determine the kind of orders that will be used in various circumstances. The more execution‐intensive a strategy is, the more it matters for a
given quant to stay abreast of the latest order types available, and how the
various exchanges’ rules work.
One type of order deserves special discussion. Intermarket sweep orders
(ISOs) exist in U.S. equities because of a flaw in the Regulation National
Market System (NMS). Reg NMS includes a ban on so‐called locked markets. A market is said to be locked when the best bid for a given ticker
is equal to the best offer on that same ticker, but where these two orders
do not interact with each other. Theoretically, you might expect that if a
buyer is willing to buy shares at $100.00, and a seller is willing to sell the
same shares for $100.00, those two traders’ orders would interact, and both
trades would be filled. However, because of technological weaknesses in

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the way that the order book is updated by exchanges after a trade has been
completed, a market can sometimes look “locked” when it is not.3
For example, imagine that a trader enters a limit order to buy 5,000
shares of some stock (we’ll call it WXYZ) at $100.00, which happens
to be the best offered price at that moment. Further, the best bid at the
time is $99.99. There are only 3,000 shares offered at $100.00. What
you would think should happen is that the 5,000 share order interacts
partially with the 3,000 share order, and that the remaining bid of 2,000
shares of WXYZ at $100.00 would go into the limit order book as the
new best bid (because it is a bid to buy WXYZ at a higher price than the
former best bid of $99.99). However, because a piece of software that Reg
NMS requires exchanges to use to communicate with one another regarding the aggregated limit order book is slow, the 3,000 share offer will not
disappear immediately from the consolidated book.4 And, because of the
ban on locked markets, the remaining 2,000 share bid at $100.00 will not
be allowed to be posted to the limit order book until after this delay has
been overcome.
The problem is that any firm with direct data feeds from each exchange
in the consolidated book experiences no such delay in seeing the best offer being taken out of the order book. Furthermore, having noticed that
there was a large buy order, and they can come in and directly post a bid
at $100.00, anticipating that the price of WXYZ is set to rise. Then, once
the Reg NMS feed finally allows the original trader’s 2,000-share bid at
$100.00 to be posted, this order will be lower in priority than the second
trader’s bid, even though the 2,000-share order actually happened first. We
discuss in more detail in Chapter 14 why this is a problem, but for now, let
it suffice to say that it is extremely problematic to be forced to wait to enter
an order artificially. To avoid this problem, very sophisticated traders can be
granted the right to use ISOs to execute their trades.
Broker‐dealers have the right to recognize a given client’s ability to be
compliant with Reg NMS directly, without the trader having to use the publicly available consolidated limit order book. Instead, these traders have direct feeds from each exchange and build the same limit order book faster
than the official one is made. They perform their own compliance checks,
and if their brokers believe this is true, then they are allowed to use the ISO
flag on their orders, which allows them to post the order correctly. In our
earlier example, the trader would have been able to hit the offer of $100.00
on 3,000 shares and immediately be the highest priority, best bid for 2,000
shares at $100.00.
ISOs exist solely because of the ban on locked markets within Reg
NMS, coupled with the slow technology that is used by exchanges to remain
compliant with NMS. This is a topic we will revisit in Chapter 16.

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Large Order versus Small Order
Whether for market orders or for limit orders, the quant has to determine
how much of a total order to send at once. Recall from our discussion of
transaction cost models that a large order costs disproportionately more to
execute than a small order because demand for liquidity starts eating into
more and more expensive supplies of liquidity. As such, a common technique for automated execution involves taking a large transaction for, say,
100,000 shares of a stock, breaking it into 1,000 orders of 100 shares each,
and spreading the orders out over a window of time. Of course, by spreading the order out over time, the trader runs the risk that the price may move
more while the order is being spread out than it would have if it had been
executed right away, even with the extra cost of market impact.
Generally, however, it is agreed that spreading out trades is a useful way
to reduce the cost of transacting, and this is an extremely common feature
in execution algorithms. The exact size of the chunks that are sent to market to be executed depends on the transaction cost model’s estimate of the
transaction cost of variously sized orders for the instrument in question. The
determination of the size of each order is related to the analysis of the correct level of aggressiveness. Again, a highly attractive trade warrants taking
on more of it quickly than a trade that is relatively less appealing.
But if not, this much aggressiveness in the order placement might not be
necessary, and the transaction can be executed in a different manner. For example, a trader might find that taking whatever liquidity is available at the
best offer (on a buy trade, for example) and then waiting for others to step
in and offer the same price a moment later could allow the same volume of
shares to be acquired at whatever the best offer was at the time that the first
piece of the order was executed, rather than a worse average price achieved
by sweeping through multiple levels of the order book.

Where to Send an Order
In some markets, there are several pools of liquidity for the same instruments. For example, BATS and Archipelago are currently two alternative
pools of liquidity for trading U.S. stocks. There is a whole field of work in
the area of smart order routing, which involves determining to which pool
of liquidity it is best to send a given order at the current moment. Typically,
the determination itself is straightforward. If one pool of liquidity has the
units of a security you want for a better price than another pool of liquidity,
you are better off routing the order to the first pool.
We described a problem with Reg NMS in “Other Order Types.” The purpose of NMS was to mitigate the perceived problem of having different “best”
prices for a given stock in different pools of liquidity, and it was enacted in

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2007. One of the consequences of this rule is that the best bid and offer for
a stock across any valid pool of liquidity must be displayed by all pools of
liquidity concurrently. This somewhat mitigates the purpose of smart order
routing in U.S. equities. However, there are many other markets in which
a fragmented structure exists, and in those, the importance of smart order
routing is unchanged. Further, there remain other temporal or longer‐lived
differences between the various liquidity pools in U.S. equities. For example,
the depth of liquidity for a given name may vary tremendously from moment
to moment on various exchanges. There are also differing rebate and fee levels for providing or taking liquidity on various exchanges, so intelligence still
needs to be applied to order routing even in the case of the U.S. equity market.
A more recent development in market structure is the increased role of
so‐called dark pools to execute orders. Exchanges can be categorized as being lit or dark. Lit exchanges show market participants the prices and sizes
of bids and offers available in the limit order book. Dark exchanges provide
no such information. The most relevant feature of a dark pool is that it facilitates the execution of large orders, because orders placed on a dark pool are
not revealed. Instead, if there is a buyer or seller who has placed an offer (for
example) that takes the other side of a large trade, then the order executes at
that price. But no investors other than the two parties that transacted know
that the trade happened. Thinking back to what we described in “Aggressive
versus Passive” about the shape of an order book factoring into a prospective participant’s trading decision, giving no information about your order
to the rest of the marketplace is clearly beneficial. In the U.S. equity market,
it is estimated that more than 30 percent of volumes are now transacted
on dark pools.5 Given the rise to prominence of dark liquidity pools, they
require consideration in the forming of order routing logic.
It is worth noting that the term dark liquidity encapsulates any transactions that do not occur on the lit exchanges. For example, as we will discuss in
more detail in Chapter 15, most retail orders are filled by contracted market
makers, and these orders never actually make it to the exchange. Coupled with
dark pool volumes, dark liquidity has been an increasing portion of the volumes in U.S. equities, which has made for an interesting storyline to watch. In
some senses, there is a battle being waged between exchanges and dark pools,
between exchanges and contractual market makers, and between contractual
market makers and noncontractual market makers.

Trading Infrastructure
We have already mentioned that, to execute and process electronic trades,
connectivity needs to be set up between the trader and the exchange.

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Furthermore, a protocol for messages between these two parties is required.
The hardware and software quants utilize in implementing their trading
strategies are the final pieces of infrastructure. As in most things, quants face
a choice between building or buying infrastructure in all three of these areas.
Due to regulatory and other constraints, most traders utilize the services of
independent brokerage firms that act as the trading agents for their strategies. One of the benefits of using a broker is that the infrastructure requirements are handled by that broker, and this infrastructure can be costly to
replicate.
The most common type of exchange connectivity offered to a trader is,
as already discussed, DMA access. This involves using the broker’s servers
and routing orders through them to the various pools of liquidity being
traded. However, some quants, especially those engaged in high‐frequency strategies, utilize a more recently available form of connectivity called
colocation. Brokers offer easy access to markets through DMA platforms,
but they add a fair amount of latency to the process. Quant strategies that
are sensitive to this latency utilize the colocation option as a way of improving their communication speeds. In a colocation setup, the trader attempts to place his trading servers as physically close to the exchange as
possible. In many cases, this means hosting servers in the same data centers
as those of the exchange. The reason for the desire for proximity is quite
literally to cut down to as short as possible the distance that the order must
travel—at the speed of light—over the communication lines between the
quant’s server and the exchange. A typical and relatively high‐quality DMA
platform tends to cause between 10 and 30 milliseconds of delay between
the time the order is sent from the quant’s server and the time the order
reaches the exchange. By contrast, a well‐designed colocation solution can
have an order travel from the quant’s server to the exchange in a fraction
of a millisecond. For latency‐sensitive execution strategies, this can be a
useful improvement.
In terms of communication, the most important piece of infrastructure
in electronic trading is known as the Financial Information eXchange (FIX)
protocol. The FIX protocol began in 1992 as a communications framework
between Fidelity Investments and Salomon Brothers and has grown to become the method of choice for real‐time electronic communication among
most of the world’s banks, money managers using electronic executions, and
exchanges offering electronic equities or futures trading. The FIX protocol
is a standardized way for various participants in the trading process to communicate information. Considering that the number of order and execution
messages is measured in billions per day, it is obviously critical to have a
standard format for these communications. The FIX protocol is free and
open source, but the software that implements the FIX protocol is known as

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a FIX engine, and not all FIX engines are created equal. Quants must choose
whether to build or buy such engines, and a fair number of quants land in
each camp. In general, quants who are extremely sensitive to latency, such as
high‐frequency traders, will likely build their own customized FIX engines
to ensure optimal speeds.
The final component of trading infrastructure relates to the hardware
and software used. Again, quants can choose to build or to buy various
solutions. For example, it is easy to buy computers built with standard
hardware (such as microchips, data storage, etc.), utilize off‐the‐shelf order management systems (which process and manage trades), or utilize
third‐party execution algorithms. On the other hand, some quant firms
have customized their own microchips to perform specialized trading‐
related functions with greater speed than conventional, commercially
available chips. It is generally found that such hardware customization allows greater speeds than any purely software‐based solution. However, it
is a more rigid process, and unlike software, once hardware is customized,
it is difficult to change.
Beyond this, quants attempt to make their algorithms, databases, and
execution software leaner, to reduce the internal latency of processing market data and sending an order out to the market. Even the most fundamental
choices about computers—for example, the operating system of choice—are
considered. For instance, most quants use either Linux or UNIX operating
systems because they are more easily configurable and more efficient and
therefore provide better computing performance than a PC/Windows configuration. I remember some years ago having a quant firm describe to me
their use of the processors that were used in the Sony Playstation 3, because
it was a categorically faster processor than what was found in even a powerful PC or server. Since then, Graphics Processing Units (GPUs), which drive
the video cards found in our computers, have been pressed into service for
quant trading applications, because they are designed to operate at higher
speeds than CPUs usually can.

Summary
We have detailed a variety of issues related to the execution of orders
for a quant trading strategy. The very first choice the quant must make
is whether to build or buy a trading solution. The technical expertise
and cost of building a world‐class execution infrastructure lead many
quants, especially those utilizing longer‐term trading strategies or those
trading smaller portfolios, to choose the route of buying these services,
either from brokers or execution service providers. Both brokers and

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Alpha Model

Risk Model

Transaction Cost Model

Data
Portfolio Construction Model
Research
Execution Model

Exhibit 7.1

Schematic of the Black Box

execution vendors do, in fact, charge for the service of providing execution algorithms and connectivity. This charge normally is made by increasing commission costs. It can often cost five or more times as much
per share to trade through a third party’s algorithms than to trade using
one’s own. Thus, for traders who have expertise in this area and for those
managing significant sums, it can be worthwhile to build custom execution models and infrastructure.
Execution is where the rubber meets the road for a quant system and
how the quant interacts with the rest of the marketplace. This continues to
be a fruitful area of research, as it has been ever since markets have begun
to become electronic. This chapter concludes our stroll inside the black box,
as we can see from Exhibit 7.1. We turn our attention now to understanding
the data that feed quant trading strategies.

Notes
1. In addition to the commissions earned by brokers from customers’ trading volumes, brokers have other sources of revenue from the activities of their clients.
For example, clearing fees also apply for management of settlement and holding positions for clients as a custodian. Stock loan fees also sometimes create
revenue.
2. Adverse selection in the sense that applies to capital markets is defined as a situation in which there is a tendency for bad outcomes to occur, due to asymmetric
information between a buyer and a seller. This is covered in greater detail in
Chapter 14.

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3. The term locked is itself a misnomer. There is nothing frozen about a locked
market. It is simply a market with a $0.00 bid/offer spread, which should actually be desirable to encourage.
4. This piece of software in general is called a Securities Information Processor
(SIP). The specific SIP used by various U.S. equity exchanges, including Archipelago and INET, is called the UTP Quote Data Feed (UQDF). UTP stands
for Unlisted Trading Privilege, which relates to tickers listed on the Nasdaq
exchange. The analogous software for stocks listed on the NYSE, AMEX, and
some other regional exchanges in the United States is known as the Consolidated Quote System (CQS).
5. Matthew Philips, “Where Has All the Stock Trading Gone?” May 10, 2012,
www.businessweek.com/articles/2012-05-10/where-has-all-the-stock-tradinggone#p1.

Chapter

Data
I’d sell you my kids before I’d sell you my data, and I’m not selling
you my kids.
—Anonymous quantitative futures trader

he old adage is “garbage in, garbage out,” meaning that if you use bad
inputs, you’ll get bad outputs. This relates to quant trading because most
quants utilize some form of input/output model, which is a term that comes
from computer science (and that has been borrowed by econometricians). It
refers to the way in which information processors (such as computers) communicate with the world around them. One of the things we love about input/
output models is that if you provide the same input a million times, the output
should be consistent every time. The process that transforms an input into an
output is typically the part that people call the black box in quant trading, and
we have seen the inside of this box in the preceding chapters. In this chapter, we
examine the inputs of quant trading models, namely, the data they depend on.
Mechanically, data reach the black box through data servers, which are
connected to one or more data sources. On receipt of these data, the black box
processes them for use by the alpha, risk, transaction cost, portfolio construction, and execution models that constitute the internal organs of the quant
trading machine. These data servers usually process data using software some
quants call data feed handlers, which are designed to convert the data to a form
in which they can be stored and utilized by the modules of the quant system.

The Importance of Data
It is difficult to overstate the importance of data, and it can be seen from
many perspectives. First, data, as we know, are the inputs to quant trading

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systems. It turns out that the nature of the inputs to a system dictates what
you can do with the system itself. For example, if you were handed a lot of
lettuce, tomatoes, and cucumbers, it would be very difficult to build, say, a
jet engine. Instead, you might decide that these inputs are most suited for
making a salad. To make a jet engine, you more or less need jet engine parts,
or at least materials that can handle high velocities and acceleration, high
altitude, and a wide range of temperatures. The same is true with quant
systems. To the extent that you are given data that focus on macroeconomic
activity, it is extremely difficult to build a useful model that doesn’t somehow reflect macroeconomic concepts.
Frequently, many details of the model itself are driven by characteristics
of the inputs that are used. Refining our example, imagine that you are given
slow‐moving macroeconomic data, such as quarterly U.S. GDP figures; furthermore, you receive them only a week after they are released to the public.
In this situation, it is unlikely that you can build a very fast trading model
that looks to hold positions for only a few minutes. Furthermore, note that
the U.S. data you get might be useful for predicting bonds or currency relationships, but they might not be sufficient to build a helpful model of equity
markets. U.S. GDP data will also tell you little about what is happening in
Uruguay or Poland in any of their securities markets.
The nature of the data you are using is also an important determinant
of the database technology you would rationally choose for storage and
retrieval, a subject we will discuss in greater detail later in this chapter. Data
sometimes even drive decisions about what types of hardware and software
make the most sense. Again and again, we see that the nature of data—and
even how they are delivered—determines a great deal about what can be
done and how one would actually go about doing it.
Still another perspective on the importance of data can be understood
by examining the consequences of not doing a good job of gathering and
handling data. Returning to the idea that quant trading systems are input/
output models, if you feed the model bad data, it has little hope of producing accurate or even usable results. A stunning example of this concept can
be seen in the failure of the Mars Climate Orbiter (MCO) in 1999. The
$200 million satellite was destroyed by atmospheric friction because one
team of software engineers programmed the software that controlled the
craft’s thrusters to expect metric units of force (Newtons) while another
team programmed the data delivered to the satellite to be in English units
(pound‐force). The software model that controlled the satellite’s thrusters
ran faithfully, but because the data were in the wrong units (causing them
to be off by a factor of almost 4.5 times), the satellite drifted off course, fell
too close to Mars’ surface, and ended up being destroyed. In the aftermath,
National Aeronautic and Space Administration (NASA) management did

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not blame the software error but rather the process used to check and recheck the software and the data being fed to it.1
Problems, however, can be easy to miss. After all, the results frequently
are numbers that can be seen to as many decimal places as you care to see.
But this is false precision. That we have a number that goes out to several
decimal places may not mean that we can rely on this number at all. Because
the kind of trading with which we are concerned is all about timing, timeliness is critical. If you build a fantastic model to forecast the price of a stock
over the next day, but you don’t provide it data until a week later, what good
is the model? This is an extreme example, but it is almost exclusively the
case that the faster you can get accurate information into a good model, the
better off you’ll be, at least if succeeding is part of your plan.
Bad data can also lead to countless hours of squandered research and,
in extreme cases, even to invalid theorization. Data are generally needed
to develop a theory about the markets or anything else in science, just
as physical scientists utilize their observations of the world to generate
their theories. So, if we provide the scientist with incorrect information
without her knowledge, she is likely to develop theories that are incorrect
when applied to the real world. Bad data lead to bad outcomes. If the data
have serious problems, it will be impossible to tell whether a system being
tested, no matter how sophisticated the testing nor how elegant the model,
is good or bad.
Many quant trading firms recognize this point in their behavior. Most
of the best firms collect their own data from primary sources rather than
purchasing it from data vendors. They also expend significant resources in
the effort to speed up their access to data, to clean data, and even to develop better ways of storing data. Some firms have dozens or even hundreds
of employees dedicated exclusively to capturing, cleaning, and storing data
optimally.

Types of Data
There are basically two kinds of data: price data and fundamental data.
Price data are actually not solely related to the prices of instruments; they include other information received or derived from exchanges or transactions.
Other examples of price data are the trading volumes for stocks or the time
and size of each trade. Indeed, the entire order book, which shows a continuous series of all bids and offers for a given instrument throughout the
course of a day as well as the amounts of each, would be considered price‐
related data. Furthermore, we would place anything that can be derived
from the levels of various indices (e.g., percent changes computed from the

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daily values of the S&P 500 index) in the price‐related data category, even if
the computed value is not a traded instrument.
The rather broad variety of fundamental data can make it difficult
to categorize effectively. In a sense, fundamental data relate to anything
besides prices. However, what all types of data have in common is that they
are expected to have some usefulness in helping to determine the price of an
instrument in the future, or at least to describe the instrument in the present.
Also, we can do a bit more to create a reasonable taxonomy of fundamental
data. The most common kinds of fundamental data are financial health,
financial performance, financial worth, and sentiment. For single stocks, for
example, a company’s balance sheet is mostly used to indicate the financial
health of the company. Meanwhile, for macroeconomic securities (e.g.,
government bonds or currencies), budget, trade deficit, or personal savings
data might serve to indicate the financial health of a nation. Portions of the
income and cash‐flow statements (e.g., total net profits or free cash flow)
are used to determine financial performance; other portions are used to
indicate financial health (e.g., ratios of accruals to total revenue or cash
flow to earnings). Similarly, the U.S. GDP figure might be an example of
macroeconomic financial performance data, whereas the trade balances
figure is an example of macroeconomic financial health data. The third
type of fundamental data relates to the worth of a financial instrument.
Some common examples of this kind of data in the equities world are
the book value or the amount of cash on hand. The last common type
of fundamental data is sentiment. How analysts rate a stock, the buying
and selling activity of company insiders, and information related to the
implied volatility of the options on a stock are examples of sentiment data
for stocks; economists’ forecasts for GDP growth for next quarter are an
example of macroeconomic sentiment data.
We don’t want to oversimplify the matter. Clever researchers are constantly looking for new and innovative sources of information that might not
be used by other players. Technology advances in the broader marketplace
have greatly aided this kind of activity. For example, some firms (and now
even some data vendors) quantitatively analyze news stories written in plain
English. Quants can systematically parse these stories, extract quantifiable
information, and build strategies around this type of data. However, this
remains largely an exercise in getting faster and more robust indicators of
sentiment (or other types of fundamentals already described), so we believe
that sources such as this are still fundamental in nature. We know of at least
one company that is attempting to use aggregated global positioning system
(GPS) data to determine the level of various types of economic activity more
quickly and accurately than is possible using government‐reported statistics.
But this too seems to be a potential improvement (even a revolution) in the

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approach to collecting such data; the nature of the fundamental information
being sought is by no means different than it was. This is not to diminish the
ingenuity of those who developed such ideas. We simply point out that our
classification scheme seems to do a reasonable job of explaining the kinds
of data that exist.
An interesting pattern has emerged in our discussion of data. Much
of what we saw in the price category of data tended to focus on shorter
timescales. We spoke about daily values and even continuous intraday values.
Meanwhile, in the fundamental category, we tend to see new information
released on the scale of weeks, months, or quarters. One implication we can
immediately discern from these differing periodicities is that, in general, trading strategies utilizing price‐related information have the option to be much
faster than those utilizing primarily fundamental information. Again, this is
simply because the information we have about the securities is refreshed more
frequently with price‐related information than it usually is with fundamental
data. This statement is not universal, since some fundamental strategies, especially those focused on changes in fundamentals or sentiment, can be very
short‐term‐oriented. However, this statement holds most of the time and is a
handy rule of thumb to bear in mind when looking at a quant strategy.

Sources of Data
One can get data from many sources. Most direct, but also perhaps most
challenging, is to get raw data from the primary sources. In other words, a
quant would get price data for stocks traded on the New York Stock Exchange directly from the NYSE. This has the benefit of allowing the quant
maximum control over the cleaning and storing of data, and it can also
have significant benefits in terms of speed. However, there is also a massive cost to doing things this way. It would require building connectivity to
every primary source, and if we are speaking about trading multiple types
of instruments (e.g., stocks and futures) across multiple geographical markets and exchanges, the number of data sources can explode. With each,
software must be built to translate the primary sources’ unique formats into
something usable by the quant’s trading systems.
Examples of the kinds of primary sources and data types include:
Exchanges. Prices, volumes, timestamps, open interest, short interest,
order book data.
■■ Regulators. Financial statements from individual companies, filings related to large owners of individual stocks as well as insider buying and
selling activities.
■■

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Governments. Macroeconomic data, such as employment, inflation, or
GDP data.
■■ Corporations. Announcements of financial results and other relevant
developments (e.g., changes in dividends).
■■ News agencies. Press releases or news articles.
■■ Proprietary data vendors (or data generators). House‐created data that
might be of interest. For example, brokerage firms frequently issue reports about companies, and some firms track and license investment
funds‐flow data.
■■

Because of the scope of the work involved in accessing data directly
from primary sources, many firms use secondary data vendors to solve some
aspects of the data problem. For example, some data vendors take financial
statement data from regulatory filings around the world and create quantified databases that they then license to quant traders. In this example, the
data vendor is being paid for having solved the problem of building a consistent framework to house and categorize data from many direct sources.
But imagine that the quant firm wants to collect both price and fundamental
data about companies around the world. It is frequently the case that entirely different companies provide each of these types of data. For instance,
for a given stock, there may be one data vendor providing price data and a
completely different one providing fundamental data. These data vendors
may also differ in the way they identify stocks. One might use the ticker; another might use a SEDOL code or some other identifier.2 With two or more
different data sets regarding the same security, the quant will have to find a
way to ensure that all the data ultimately find their way into the same company’s record in the quant’s internal database. The tool used to help with
this is frequently called a security master in that it is the master file mapping
the various ways that data vendors identify stocks to a single, unique identifier method that the quant will use in her trading system.
As you may have guessed, still other firms have cropped up to provide
unified databases across many types of vendors and data types. These we
can call tertiary data vendors, and they are paid to make data easy to access for the quant. They establish connections with many primary and
secondary data vendors, build and maintain security masters, and even
perform some data‐cleaning activities (a subject we will discuss in more
detail presently). As a result, they are immensely popular among many
firms. However, we should make it clear that as much benefit as they offer
in terms of ease, tertiary data vendors do add another layer between the
quant and the original data. This layer can result in loss of speed and possibly in less control over the methods used to clean, store, or access data
on an ongoing basis.

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Cleaning Data
Having established the types and importance of data, we now turn to the
kinds of problems quants face in managing these raw materials and how
they handle such flaws. Despite the efforts of primary, secondary, and sometimes even tertiary data vendors, data are often either missing or incorrect in
some way. If ignored, this problem can lead to disastrous consequences for
the quant. This section addresses some of the common problems found with
errors and some of the better‐known approaches used to deal with these
challenges. It’s worth noting that although some of the following data problems seem egregious or obvious to a human, it can be challenging to notice
such problems in a trading system that is processing millions of data points
hourly (or even within one minute, as in the case of high‐frequency traders).
The first common type of data problem is missing data, as we alluded
to already. Missing data occur when a piece of information existed in reality
but for some reason was not provided by the data supplier. This is obviously
an issue because without data, the system has nothing to go on. Worse still,
by withholding just some portion of the data, systems can make erroneous
computations. Two common approaches are used to solve the problem of
missing data. The first is to build the system so that it “understands” that
data can in fact go missing, in which case the system doesn’t act rashly
when there are no data over some limited time period. For example, many
databases automatically assign a value of zero to a data point that is missing. After all, zero and nothing have a lot in common. However, there is a
very different implication to the model thinking the price is now zero (for
example, if we were long the instrument, we’d be showing a 100 percent loss
on the position) versus thinking that the price is unknown at the moment.
To fix this problem, many quants program their database and trading
systems to recognize the difference between zero and blank. This frequently
means simply using the last known price until a new one is available. The
second approach is to try to interpolate what a reasonable value might be
in place of the missing data. This is useful for historical data rather than
real‐time data, but a variation of the method described here can be used for
real‐time data as well.
Let’s take an example of a semiconductor company’s listed stock.
Imagine that we know the price of a semiconductor stock immediately before and immediately after the missing data point (this is why this technique
is mainly useful to back‐fill missing data points in a database). We could
simply interpolate the price of the stock as being midway between the price
immediately before and immediately after the gap. Imagine further that
we know how the stock index, the tech sector, the semiconductor industry,
and some close competitors performed for the period that is missing. By

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Inside the Black Box

combining information about the periods around the missing point and the
action of related things during the missing period, it is possible to compute
a sensible value for the stock’s missing data point. Though we aren’t guaranteed and in fact aren’t terribly likely to get the number exactly right, at
least we have something reasonable that won’t cause our systems problems.
A second type of data problem is the presence of incorrect values. For
instance, decimal errors are a common problem. To take the example of
U.K. stocks, they are sometimes quoted in pounds and sometimes in pence.
Obviously, if a system is expecting to receive a figure in pounds and it receives a
number that doesn’t advertise itself as being anything other than pounds, problems can abound. Instead of being quoted as, say, £10, it is quoted as 1,000;
that is, 1,000 pence. This can result in the model being told that the price has
spiked dramatically upward, which can cause all sorts of other mayhem (for
example, a naive system without data checks might want to short the stock
aggressively if it suddenly and inexplicably jumped 100‐fold in an instant).
Alternatively, a price might simply be wrong. Exchanges and other sources of
data frequently put out bad prints, which are data points that simply never
happened at all or at least didn’t happen the way the data source indicates.
By far the most common type of tool used to help address this issue
is something we call a spike filter. Spike filters look for abnormally large,
sudden moves in prices and either smooth these out or eliminate them altogether. Further complicating the matter, it should be noted that sometimes
spikes really do happen. In these circumstances, a spike filter may reject a
value that is valid, either ignoring it or replacing it with an erroneous value.
An interesting example of this is shown in Exhibit 8.1. In this case, during
the trading day of July 15, 2008, the U.S. dollar’s exchange rate with the
Mexican peso quickly fell about 3 percent, then regained virtually all that
ground in a matter of seconds.
9.650
9.625
9.600
9.575
9.550
9.525
9.500
9.475
9.450
9.425
9.400
9.375
9.350
9.325
08.00

Exhibit 8.1

09.00

10.00

11.00

12.00

13.00

14.00

15.00

September 2008 Mexican Peso Futures Contract on July 15, 2008

16.00

141

Data

This behavior is not reserved for less commonly traded instruments,
however. The 10‐year German bund, one of the more liquid futures contracts in the world, dropped about 1.4 percent in a few seconds during the
day of March 28, 2008, only to recover immediately (see Exhibit 8.2).
A spike filter might well have called this a bad print, but it really happened. To reduce the impact of this problem, some quants use spike filters
to alert a human supervisor to look into the matter further, and the human
can then decide, based on what she sees as the facts, on what to do about the
strange price. Still another common approach, though useful only if there
is more than one source for a given piece of data, is to cross‐check a data
set given by one provider against one provided by a second source. If they
match, it is more likely to be a correct price. If they do not match, one or
both of them must be wrong. Of course, what to do when two vendors don’t
match each other is a whole other ball of wax. A final common approach to
cleaning data problems is to utilize the same approach as described earlier
in addressing the problem of missing data by looking to the points before
and after the “bad” data point and/or by looking to the behavior of related
instruments to interpolate an approximate value.
Another very common type of data error relates to corporate actions
such as splits and dividends. Imagine a ticker that splits 3:1. Generally,
the price drops by about two‐thirds to offset the threefold increase in the
number of shares.3 Imagine that the data vendor doesn’t record this as a
split, and therefore doesn’t adjust the back‐history to reflect this corporate
action. In this scenario, the quant trader’s system may be misled to believe
that the stock simply dropped 67 percent overnight. This is generally handled by independently tracking corporate actions, together with the human‐
oversight version of a spike filter, described previously.

116.0
115.9
115.8
115.7
115.6
115.5
115.4
115.3
115.2
115.1
115.0
114.9
114.8
114.7
114.6
114.5
114.4
114.3
114.2
114.1
114.0
03.00

04.00

Exhibit 8.2

05.00

06.00

07.00

08.00

09.00

10.00

11.00

12.00

13.00

14.00

15.00

16.00

June 2008 German Bund Futures Contract on March 28, 2008

17.00

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Inside the Black Box

Another frustrating problem is that the data sometimes contain incorrect timestamps. This is generally a problem with intraday or real‐time data,
but it has been known to be an issue with other data as well. This is also
one of the tougher problems to solve. Obviously, the path of a time series
is fairly important, especially since the goal of the quant trader focused on
alpha is to figure out when to be long, short, or out of a given security. As
such, if the time series is shuffled because of an error in the data source,
it can be deeply problematic. A quant researcher could believe her system
works when in reality it doesn’t,4 or she could believe her system doesn’t
work when in reality it does.5 If the quant trading firm stores its own data
in real time, it can track timestamps received versus the internal clocks of
the machines doing the storing and ensure that there are correct timestamps,
which is perhaps the most effective way of addressing this issue. But to do so
requires storing one’s own data reliably in real time and writing software to
check the timestamp of each and every data point against a system clock in
a way that doesn’t slow the system down too much, making this a difficult
problem to address. It should be noted that this approach only works for
those quants who capture and store their own data in real time. For those
that are relying on purchased databases, they can only cross‐check data
from various sources.
Finally, a more subtle type of data challenge bears mentioning here.
This is known as look‐ahead bias and is a subject to which we will devote
attention several times in this book. Look‐ahead bias refers to the problem
of wrongly assuming that you could have known something before it would
have been possible to know it. Another way to phrase this is “getting yesterday’s news the day before yesterday.” We will examine look‐ahead bias in
the chapter on research, but for now, let’s examine a particular form of this
bias that comes from the data. Specifically, it derives from asynchronicity in
the data.
A common example of asynchronicity can be found in the regulatory
filings of financial statements (known as 10‐Qs) made by companies each
quarter in the United States. Companies report their financial statements as
of each quarter end. However, these reports are usually released four to eight
weeks after the end of the quarter. Let’s imagine the first quarter of 2010
has just ended. On May 1, 2010, Acme Concrete Inc. reports that its first‐
quarter earnings were $1 per share as of March 31 and furthermore that the
general analyst community was expecting only $0.50 per share, making the
result a strongly positive surprise. Once the data point is available, most data
vendors will report that Acme’s earnings per share were $1 per share as of
March 31, even though the number wasn’t released until May 1.
Three years later, a quant is testing a strategy that uses earnings data
from this vendor. The data indicate that Acme’s earnings were $1 per share

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for the quarter ending March 31, and her model assumes this to be true,
even though in reality she would never have been able to know this until
the estimate was released a month later, on May 1. In the back‐test, she sees
that her model buys Acme in April because its P/E ratio looks appealing
from April 1 onward, given the $1‐per‐share earnings result, even though
the model would not have known about the $1 earnings figure until May 1
if she had been trading back then. Suddenly the strategy makes a huge profit on the position in early May, when the world, and her model, actually
would have found out about the earnings surprise. This kind of problem
also happens with macroeconomic data (such as the unemployment rate),
which frequently get revised some months after their initial release. Without
careful tracking of the revision history for such data, the quant can be left
with the same issue as demonstrated in the equity example: believing that
she could have had revised data in the past when in fact she would only have
had the less accurate initial data release.
If the quant ignores this data error, she can end up making a Type I error
again: believing that her strategy is profitable and sound, even though it may
in fact only look that way because she’s made a substantial data error. To address look‐ahead bias in the data, quants can record the date at which new
information is actually made available and only make the data available for
testing at the appropriate time. In addition, quants can put an artificial lag
on the data they are concerned about so that the model’s awareness of this
information is delayed sufficiently to overcome the look‐ahead bias issues.
Note that look‐ahead issues with regard to data are specific to research,
which we will discuss further in the next chapter. In live trading, there is no
such thing as look‐ahead bias, and in fact quants would want all relevant
data to be available to their systems as immediately as possible.
Another type of look‐ahead bias stemming from asynchronicity in the
data is a result of the various closing times of markets around the world.
The SPY (the ETF tracking the S&P 500) trades until 4:15 p.m., whereas the
stocks that constitute the S&P 500 index stop trading at 4:00 p.m. European
stock markets close from 11:00 a.m. to 12:00 p.m., New York time. Asian
markets are already closed on a given day by the time New York opens.
In many cases, the considerable impact that U.S. news and trading activity
have on European or Asian markets cannot be felt until the next trading day.
On Friday, October 10, 2008, for example, the Nikkei 225 fell more than
9 percent for the day. But it was already closed by the time New York opened.
European markets closed down between 7 and 10 percent for the same day.
At the time of Europe’s closing, the S&P 500 was down about 6 percent for
the day. Suddenly, however, just after 2:00 p.m. EST on the 10th, with two
hours remaining in U.S. trading but the rest of the world already gone for the
weekend, the S&P 500 rallied, closing down just over 1 percent. Monday the

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13th was a market holiday in Japan. Europe tried to make up ground that
Monday, with the key markets closing up over 11 percent but the U.S. market up “only” about 6 percent by midday in New York. However, by the end
of the trading day, the U.S. market closed up over 11 percent as well, leaving
the European markets behind again. The next day, the Nikkei reopened on
the 14th and ended up 14 percent. On their subsequent day, European markets closed up about 3 percent, whereas the U.S. market was down slightly
by the end of its own trading day. Ignoring this kind of asynchronicity can be
extremely problematic for analyses of closing price data because these closing prices occur at different times on the same day.
These are but a few examples of the many subtle ways in which look‐
ahead bias seeps into the process of research and money management, even
for discretionary traders. A key challenge for the quant is deciding how to
manage this problem in its myriad forms.

Storing Data
Databases are used to store collected data for later use, and they come in
several varieties. The first type of database is known as the flat file. Flat files
are two‐dimensional databases, much like an ordinary spreadsheet. Flat file
databases are loved for their leanness, because there is very little baggage
or overhead to slow them down. It is a simple file structure that can be
searched very easily, usually in a sequential manner (i.e., from the first row
of data onward to the last). However, you can easily imagine that searching
for a data point near the bottom row of a very large flat file with millions of
rows may take rather a long time. To help with this problem, many quants
use indexed flat files, which add an extra step but which can make searching large files easier. The index gives the computer a sort of cheat sheet,
providing an algorithm to search large sets of data more intelligently than
a sequential search.
A second important type of data storage is a relational database.
Relational databases allow for more complex relationships among the
data set. For example, imagine that we want to keep track of stocks not
just on their own but also as part of industry groups, as part of sectors,
as part of broader indices for the countries of their domicile, and as part
of the universe of stocks overall. This is a fairly routine thing to want to
do. With flat files, we would have to construct each of these groups as a
separate table. This is fine if nothing ever changes with the constituents of
each table. But in reality, every time there is a corporate action, a merger,
or any other event that would cause us to want to modify the record for a
single stock in any one of these tables, we have to remember to update all

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of them. Instead, in the world of relational databases, we can simply create a database table that contains attributes of each stock—for example,
the industry, sector, market, and universe it is in. Given this table, we can
simply manage the table of information for the stock itself and for its attributes. From there, the database will take care of the rest based on the
established relationship. Though relational databases allow for powerful
searches, they can also be slow and cumbersome because their searches
can span many tables as well as the meta tables that establish the relationships among the data tables.
An important type of relational database is known as a data cube, a label I have borrowed from Sudhir Chhikara, the former head of quantitative
trading at Stark Investments. Data cubes force consistency into a relational
database by keeping all the values for all the attributes of all instruments
in a single, three‐dimensional table. For a given date, then, all instruments
would be listed in one axis of this table. A second axis would store all the
values for a given attribute (e.g., closing price for that date) across the various instruments. The third axis would store other attributes (e.g., earnings
per share as of that date). This method has the benefit of simplifying the
relationships in a way that is rather useful. In other words, it hardwires
certain relationships; furthermore, by keeping all attributes of each instrument available every day, there is no need to search for the last available
data point for a given attribute and security. For every day, a data cube is
created to store all the relevant data. This approach, too, has its potential
disadvantages. Hardwiring the relationships leads to inflexibility, so if the
nature of the relationships or the method of querying the data changes, it
can be problematic.
Each of these data storage approaches has advantages and disadvantages. It would be easy to make some assumptions and declare one the “best,”
but the reality is that the best technique is dependent on the problem that
needs to be solved. Here, as in so many other parts of the black box, the
quant’s judgment determines success or failure.

Summary
In this chapter, we explained some of the basic concepts of data for use by
quant trading systems. Though data are scarcely the most exciting part of a
quant strategy, they are so integral and critical to everything quants do and
inform so much of how to think about a given quant system that they are
well worth understanding.
Next we will dive into the research process as our final stop in the exploration of the black box (Exhibit 8.3).

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Alpha Model

Risk Model

Transaction Cost Model

Data
Portfolio Construction Model
Research
Execution Model

Exhibit 8.3

Schematic of the Black Box

Notes
1. Greg Clark and Alex Canizares, “Navigation Team Was Unfamiliar with Mars
Climate Orbiter,” Space.com, November 10, 1999.
2. SEDOL stands for Stock Exchange Daily Official List, which is a list of ostensibly unique security identifiers for stocks in the United Kingdom and Ireland. Other common security identifiers in equity markets are the International
Securities Identification Number (ISIN) or Committee on Uniform Security
Identification Procedures (CUSIP) number. CUSIPs are primarily relevant for
U.S. and Canadian stocks. Many data vendors utilize their own proprietary
security identifiers as well.
3. For the sake of simplicity, we are ignoring any split effect, which many people
believe exists; this theory states that stocks tend not to fall as much as expected
based on the size of the split because people like to buy nominally lower‐priced
stocks.
4. In science, this is known as a Type I error, which is to accept a false‐positive
result in testing a hypothesis. This is the error of believing a hypothesis is true
when in fact it is false.
5. In science, this is known as a Type II error, which is to accept a falsely negative
result in the outcome of a test. This is the error of believing a hypothesis is false
when in fact it is true.

Chapter

Research
Everything should be made as simple as possible, but not simpler.
—Albert Einstein

esearch is the heart of quant trading. It is in large part because of well‐designed, rigorous, and tireless research programs that the best quants earn
their laurels. This chapter gives an overview of what research really means
for black‐box traders. It focuses mostly on research targeted at developing
the alpha models of trading strategies. Research is also done with regard
to risk models, transaction cost models, portfolio construction models, execution algorithms, and monitoring tools. Relevant research topics in these
other areas will be mentioned as necessary, but the general principles from
this section hold true throughout the black box.
The purpose of research is to scrutinize a well‐conceived investment
strategy. A strategy is a long‐term course of action designed to achieve an
objective, usually success or victory. In most applied settings, strategies are
chosen from a limitless number of alternatives. One can find interesting
examples in nearly every field: curing cancer, a baseball game, a war, a court
case, or financial planning. In each case, one has many choices of strategy; so
how is one chosen? In the case of quant trading, a strategy is chosen based
on research, which has its roots in the natural sciences.

Blueprint for Research: The Scientific Method
A characteristic shared among well‐behaved quants is their adherence to the
scientific method in conducting research, which is of course the way science
is done in every other field of study. This is critical because it forces rigor
and discipline into the single most judgment‐driven portion of the entire

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Inside the Black Box

quant trading process. Without such rigor, quants could easily be led astray
by wishful thinking and emotion rather than the logic and consistency that
make scientists useful to the world in so many other disciplines.
The scientific method begins with the scientist observing something in
the world that might be explainable. Put differently, the scientist sees a pattern in her observations. For example, in most circumstances, if something is
above the ground and is left unsupported, it falls toward the ground. Second,
the scientist forms a theory to explain the observations. Sticking with the
same theme in our examples, the scientist can theorize that there is something inherent in all things that causes them to move toward each other. This
is better known as the theory of gravity. Third, the scientist must deduce
consequences of the theory. If gravity exists, the orbits of planets should be
predictable using the consequences of the theory of gravity. Fourth comes
the all‐important testing of the theory. But rather than looking to “prove” a
theory, properly done science seeks to find the opposite of the consequences
deduced, which would therefore disprove the theory. In the case of gravity,
Newton’s theory was used to predict the existence of Neptune, based on
motions in the orbit of Uranus that could not be explained by other then‐
known celestial bodies. But this success could at best provide support for
Newton’s theory and could never actually prove it. Karl Popper, the eminent
philosopher of science, labeled this technique falsification. A theory that has
not yet been disproved can be accepted as true for the moment. But we can
never be certain that the next observation we make of the theory will not
falsify it. Newton’s theory of gravity was never “proved” and in fact was
superseded by Einstein’s general relativity theory. The latter also has not
been proven, and alternatives have been proposed to help explain problems
(such as the accelerating expansion of the universe or the unexpectedly high
velocities of stars in the outskirts of galaxies) that neither Newton’s laws nor
Einstein’s relativity address in their current form.
Looking at the markets, it is easy to see the parallels with the way
quants conduct research. First, let’s imagine that a quant researcher observes
that the various markets go through phases in which they tend to rise for
extended periods, followed by phases in which they tend to fall for awhile.
She theorizes that a phenomenon called a trend exists, which, for whatever
reason, causes the future performance of a market to be in the same direction as its recent historical performance. The consequence of this theory
would be that she should be able to achieve a better‐than‐random forecast
of how markets will perform, given only information on how these markets
have performed before. So, she sets out to test the theory, and lo and behold,
she finds that the evidence does not contradict her theory. Using some metric
to define the historical trend (such as the moving average crossover example
we used in Chapter 3), she sees that she can indeed forecast markets better

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than random chance is likely to allow. But she can never be sure. At best,
she can have enough confidence that her tests were sufficiently rigorous to
warrant risking some capital on the validity of this theory.
One important distinction, however, exists between quants and scientists. Scientists conduct research for many purposes, including learning
the truth that drives the natural world. And in the natural sciences, a good
theory—one that is well supported by the evidence and is widely useful in a
variety of practical applications (e.g., Einstein’s relativity)—does not require
modification to continue to be valid. Quant researchers, by contrast, have
no choice but to conduct ongoing research and to take every measure to
ensure that their research output is prolific. This is because, though nature
is relatively stable, the markets are not. Whether from regulatory changes,
the changing whims of the aggregate psychology of investors and traders,
the constant competition for alpha among traders, or whatever other phenomena, the markets are in fact highly dynamic processes. For this reason,
quant traders must constantly conduct research so that they can evolve with
as much rigor and forethought as they used in developing their original
strategies.

Idea Generation
Ideally, quants follow the scientific method in their research. In this regard,
the development of theories (or theoretically sound approaches to data mining) is the first key step in the research process. We find four common sources of ideas to be observations of the markets, academic literature, migration,
and lessons from the activities of discretionary traders.
The main way that quants come up with their own ideas is by watching
the markets. This approach most directly embodies the spirit of the scientific
method. An excellent example comes from the history of the oldest of quant
trading strategies: trend following in futures contracts. Richard Donchian
is the father of trend following. He originally traded stocks, but in 1948,
he created Futures, Inc., the first publicly held commodity fund. In December 1960, he published his philosophy toward trading in his newsletter,
Commodity Trend Timing.1 He observed that there are sweeping moves in
many markets that folks tend to call bull or bear markets; he postulated that
one could build a system that would detect that these trends had begun and
then ride the wave. He translated his philosophy into the following strategy:
If a given market’s price is above the highest closing price over the past two
weeks, buy that market. If its price goes below the lowest closing price over
the past two weeks, sell that market short. In the meantime, hold whatever
position you have in that market. Using this incredibly simple system, from

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1950 to 1970 he built a successful track record and spawned an industry
that now manages hundreds of billions of dollars.
The academic literature in quantitative finance, and finance more generally, is replete with papers on a massive array of topics of interest to quant
researchers. For example, many finance papers have been written on clever
ways in which corporate chief finance officers (CFOs) attempt to fudge their
companies’ earnings and other financial figures to retain the confidence of
shareholders. Quant firms have taken note, and several now have strategies in their arsenal that look for the kinds of behaviors described in the
academic literature for trading opportunities. Many quant firms spend significant time scouring academic journals, working papers, and conference
presentations to glean ideas that can be tested using the scientific method.
Such a quant could find papers on topics such as the management of financial statements and could test ideas learned from these papers. Perhaps the
most classic example of an academic paper that made massive waves in the
quant trading community is Harry Markowitz’s paper, modestly entitled
“Portfolio Selection.” As discussed in Chapter 6, in “Portfolio Selection,”
Dr. Markowitz proposed an algorithm to compute the “optimal” portfolio
using a technique called mean variance optimization. For all the research
that has been done on portfolio construction over the decades since Dr.
Markowitz’s paper was published, his technique and variants of it remain
key tools in the toolbox of quant trading. Aside from the literature in finance,
quants also frequently utilize the literature from other scientific fields—such
as astronomy, physics, or psychology—for ideas that might be applicable to
quant finance problems.
Another common source of new ideas is via the migration of a researcher or portfolio manager from one quant shop to the next. Though many
firms attempt to make this more difficult via noncompete and nondisclosure
agreements, quants can effectively take ideas from one place to another,
and this is to be expected. Any rational quant would want to know what
the competition are doing, particularly those who are successful. At least
part of the attraction of a potential new hire who has worked elsewhere
must be the prospect of learning about the activities, and maybe even some
secrets, of competitors. There are countless examples of this sort of thing.
Goldman Sachs gave birth to AQR’s quantitative approach to global tactical
asset allocation and global equity market‐neutral trading. Richard Dennis
trained a group of new traders called the Turtles, none of whom had any
trading experience, in trend following as a social experiment and to settle
a bet with his friend William Eckhardt. D. E. Shaw was created after its
founder cut his teeth at Morgan Stanley’s statistical arbitrage prop trading desk and has itself spawned several successful alumni, including Two
Sigma and Highbridge’s quantitative equity manager. In a fascinating case,

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Renaissance Technologies, famous for its ability to retain talent partly by
having its researchers sign iron‐clad noncompete agreements, once lost two
of its researchers to Millennium Partners. Renaissance sued Millennium
over the incident, and it turned out that the researchers had somehow managed not to sign the noncompete agreements while at Renaissance. Nonetheless, the traders were ultimately terminated by Millennium, who simply
decided that retaining them was more trouble than it was worth. Sometimes,
investors who have peeked behind the curtains as part of their assessment
of a given quant shop, and then shared what they’ve seen with others, act as
the carriers of ideas from one quant shop to the next.
Finally, quants learn lessons from the behavior of successful discretionary traders. For example, an old adage among successful traders is “Ride
winners and cut losers.” This idea can easily be formalized and tested and
has come to be known as a stop‐loss policy, which involves systematically
realizing losses on positions that are not working out. There are many examples of quants working closely with successful discretionary traders in an
attempt to codify aspects of the latter’s behavior into a trading system. Not
all are necessarily bound for success. Technical trader is the label applied
to a trader who subjectively analyzes graphs of market prices and makes
decisions based on “rules” about the implications of various shapes of such
graphs. These shapes are given names such as a head and shoulders pattern
or an upward triangle pattern. Many quant funds have come and (mostly)
gone that have attempted to re-create such patterns into systematic trading
rules. This could be because the idea itself is not based on valid theory, or
it might be because the human version is ultimately less rule based, as one
might like to believe, condemning a truly systematic implementation to be
unsuccessful. However, even here valuable lessons can be learned: Not all
successful traders have skill, and a helpful way to begin figuring out what
really works and doesn’t is to put an idea through the grinder of a research
process and see if it’s still alive at the end.

Testing
The process of testing is central to research. At first glance, the most common version of this process looks fairly simple. First, build a model and train
it on some subset of the data available (the in‐sample period). Then test it on
another subset of the data to see if it is profitable (the out‐of‐sample period).
However, research is an activity that is fraught with peril. The researcher is
constantly offered opportunities to forgo rigor in favor of wishful thinking.
In this section, we address some of the work and challenges inherent in the
research process.

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In-Sample Testing, a.k.a. Training
In quant trading, models are approximations of the world. They are used to
predict the future using data as inputs. The first part of the testing process
is to train a model by finding optimal parameters over an in‐sample period.
That sounds rather like a mouthful of marbles, so let’s walk through it term
by term.
Let’s imagine that we want to test the idea that cheap stocks outperform
expensive stocks. We even theorize that the metric we will use to define
cheapness is the earnings yield (earnings/price), such that a higher earnings
yield implies a cheaper stock. But what level of yield is sufficiently high to
cause us to think that the stock will outperform? And what level of earnings yield is sufficiently low to imply that a stock is expensive and is likely
to underperform? These levels are parameters. In general the parameters of
a model are quantities that define some aspect of a model and can affect
its performance. These are variables that can be set at whatever level one
chooses, and by varying these levels, the model itself is altered and will provide different results.
Imagine that you hire a consultant to help you buy the ideal “optimal”
house. The consultant lists all the relevant variables that might factor into
your decision, things like the size of the house, its condition at the time of
purchase, and the location and school district. If you do not tell him your
ideal levels for each of these variables, he can deduce them by observing
your reaction to various houses. A big house in a poor neighborhood might
generate a lukewarm reaction, whereas a smaller house in a good neighborhood might generate a higher degree of interest for you. In this way, the
consultant can deduce that you dislike the first neighborhood and prefer the
second, and furthermore that the neighborhood might be more important
to you than the size of the house. If he is able to repeat these “experiments,”
he can continue to fine‐tune the choices he presents to you until he finds the
house that matches your desires optimally. To the extent he succeeds in this
endeavor, he has performed well.
In this way, optimal parameters in a quant model are those that lead
to the best performance based on whatever metrics one chooses to use to
measure goodness. Training a model involves simply finding the optimal parameter set, which is usually accomplished by trying a number of them and
hoping that at least one set comes out looking appealing. What constitutes
appeal is a matter we will discuss in some detail forthwith, but first we consider some other aspects of in‐sample research.
In‐sample research is, in a sense, fun for a quant. In the real world, the
quant’s model is constantly buffeted by new information and unpredictable
events. But the historical data from the in‐sample period are known to the

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model in their entirety, and nothing about them needs to be predicted. The
in‐sample period is like the answer key to a test in grade school. It is the
model’s best chance to work, because it doesn’t have to predict anything.
The model simply has to do a reasonable job of explaining the in‐sample
period after the fact, with the whole picture available for review. This is the
one part of the research process in which there is a high degree of hope.
An important decision lies in the process of in‐sample testing: What
exactly constitutes the sample chosen for fitting the model? A sample is
characterized by two things: its breadth and its length. Imagine that a researcher plans to build a strategy to trade the approximately 5,000 listed
U.S. stocks and that she has at her disposal data starting in 1990 and ending now. As far as the breadth of the in‐sample test, the researcher must
choose how many of the stocks to use and decide how to choose the ones
that are used. Should she use a broad cross‐section of stocks across sectors
and capitalization levels? Should she use a narrower cross‐section, or should
she choose all the stocks? As to length of time, the researcher must consider
what window of data will be available to use for fitting the model. Will it be
the most recent data or the oldest data? Will it be a random set of smaller
time windows or the entire set of data from 1990 onward? The most common preference among quants would be to use all the instruments for some
subset of the time, but this is by no means universal, since there is a trade‐off
here to consider.
By using more data, the quant has a broader array of scenarios and
market events that the model has to fit itself to, which can help make it
more robust. By the time it has to succeed in real conditions, it has already
“seen” and been adapted to the scenarios and environments found in the
large in‐sample period. On the other hand, the more data the model is allowed to see while it is being tuned, the greater the risk of creating a model
that is nothing more than a good explanation of the past. For this reason,
many quants utilize a reasonable cross‐section of the data for the purpose of
in‐sample testing and model fitting.

What Constitutes a “Good” Model?
Quants utilize a wide variety of metrics to determine the “goodness” of
a model. This is true for both the in‐sample part of the process and the
out‐of‐sample part of the process, the latter of which we discuss in the next
section. I include here a number of statistics (and other output) that quants
may use. I illustrate these metrics using a strategy for forecasting the S&P
500. It has a one‐day horizon for its forecast, and it uses an adjustment to
a well‐known idea known as the equity risk premium, which is calculated
by taking the difference between the earnings yield of the S&P 500 and the

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Inside the Black Box

10‐year Treasury note each day. If the S&P’s yield is higher than the bond’s,
this is viewed as a signal to be long stocks. If the S&P’s yield is lower than
the bond’s, this is a signal to be short stocks. I built this strategy back in the
mid‐1990s for tactical asset allocation purposes, but I have never traded it,
for reasons that will be obvious after we assess it using these metrics. It is
shown simply as a way of illustrating the kinds of tests that a strategy is required to pass before being implemented in the real world, with real money.
The results I show for the strategy are based on daily closing prices from
June 1982 through December 2000.

9,000
8,000
7,000
6,000
5,000
4,000
3,000
2,000
1,000
–

31
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Cumulative Profits ($1,000 Invested)

Graph of the Cumulative Profits over Time A graph indicating the cumulative
profits over time is one of the most powerful pieces of output in a testing
process because, as they say, one picture is worth a thousand words. From
a graph of cumulative profits, you can see whether the strategy would have
made money, how smoothly, and with what sort of downside risk, just to
name a few things. As you can see in Exhibit 9.1, the S&P strategy shows
as being profitable over the test period, but its return stream is very lumpy,
characterized by long periods of inactivity (several years, in some cases),
some sharp losses, and some very steep gains. Immediately a researcher can
see that this strategy has some real problems. Is it realistic to want to sit on
the sidelines making almost no trades, and certainly no profits, from late
1989 until early 1995?

Date

Exhibit 9.1

Back‐Tested Cumulative Profits of the S&P 500 Strategy

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Average Rate of Return The average rate of return indicates how well the
strategy actually worked (i.e., how much it might have made) in the past.
If it didn’t work in the testing phase, it’s very unlikely to work in real life.
As we will see later, testing offers many opportunities for the researcher to
believe that making money in trading is a trivially easy exercise. Sadly, this
misperception is mainly due to a wide variety of deadly traps. In our S&P
500 example, the total cumulative profits in the simulation were 746 percent, which comes to an average annual rate of return of 12.1 percent before
any transaction costs or fees.
Variability of Returns over Time The variability of returns over time, which
describes the uncertainty around the average returns, is helpful in deciding whether the strategy is worth owning. In general, the less the variability for a given level of returns, the better a strategy is considered to
be. For example, if a strategy averages 20 percent returns per year, with
an annual standard deviation of 2 percent (i.e., 67 percent of the time,
the annual rate of return should fall within +/–2 percent of the average
20 percent figure, or between 18 and 22 percent), this would be a better
outcome than if the same 20 percent average annual return came with
20 percent annual standard deviation (i.e., 67 percent of the time, returns are within 0 and 40 percent). The idea is that one can have more
confidence in a given return if the uncertainty around it is low, and more
confidence is a good thing.
At my shop, we look at a statistic we dubbed lumpiness, which is the
portion of a strategy’s total return that comes from periods that are significantly above average. This is another way of measuring consistency of
returns. Despite the importance of this metric, it is not always the case that
consistency should be a primary goal. Nevertheless, it is good to know what
to expect as an investor in or practitioner of a strategy, if for no other reason than to discern when the strategy’s behavior is changing. In our S&P
500 strategy, the annualized standard deviation of its daily returns over the
entire test period was 21.2 percent.
Worst Peak-to-Valley Drawdown(s) This metric measures the maximum decline from any cumulative peak in the profit curve. If a strategy makes
10 percent, then declines 15 percent, then makes another 15 percent, the
total compounded return for this period is about +7.5 percent. However, the peak‐to‐valley drawdown is –15 percent. Another way of stating
this is that the investor had to risk 15 percent to make 7.5 percent. The
lower the drawdown of a strategy, the better. Many quants measure not
just one drawdown but several, to get a sense of both the extreme and
more routine downside historical risks of their strategies. It is also typical

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to measure recovery times after drawdowns, which give the researcher a
sense of the model’s behavior after it’s done poorly. Long recovery times
are generally disliked because they imply that the strategy will remain in
negative territory for quite a while if it does go into a large drawdown at
some point. The S&P 500 strategy’s worst peak‐to‐valley drawdown in
the back‐test was –39.7 percent, and it came from being short the S&P
500 in the summer of 1987, before the crash in October actually made
that trade look good.
Drawdown information must be handled with care, however. If
we were to look at the returns of a convertible bond arbitrage strategy
from 1990 through 1997, eight years of data (which is considered a long
track record in the hedge fund business) would show you very limited
drawdowns. But in 1998, these strategies were badly hurt. The problem
was sample bias, which means that the sample we used to determine the
“worst” drawdown was not a fair representation of the whole array of
possible outcomes. Rather, even though it was “long,” it covered a period
that was almost entirely favorable to this strategy, which would lead to
an underappreciation of the potential downside risks. There’s not a great
solution to this problem: Either the sample over which the drawdown
was computed is sufficiently large as to cover a large range of market regimes and both favorable and unfavorable environments (specifically as it
relates to the strategy being tested), or it doesn’t. If the sample cannot be
made larger and more representative of all possibilities (the population,
in stats‐speak), then the quant can only exercise some judgment about
how much worse things could look if the environment did turn ugly. This
is self‐evidently an exercise that depends heavily on the judgment of the
researcher, and even then is at best a ballpark figure.
Furthermore, the worst historical drawdown is merely one potential
path that even this biased sample could have produced. Imagine that the
historical return distribution of a strategy is like a deck of cards. If we turn
the cards over in the order that they are already placed in the deck, we get
the historical time series. If, however, we shuffle the deck and then turn the
cards over in this new order, we get a different time series from the same return distribution. If we do this over and over, thousands of times, we will get
many theoretically possible paths from one actual history. This practice is
known as resampling, and it is done to boost the power of a historical sample. With these thousands of resampled histories, we can compute the worst
drawdown(s) of each one, and have a more robust estimate of the potential
downside risk of a strategy. It is therefore a sensible practice to recognize
again that the deck itself contains only a subset of all the cards that might
one day be dealt to us. It may, we worry, contain too many aces and kings,
and not enough twos and threes.

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Predictive Power A statistic known as the R‐squared (R2) shows how much
of the variability of the thing being predicted can be accounted for by the
thing you’re using to predict it, or, in other words, how much of the variability in the target is explained by the signal. Its value ranges from 0 to 1,
and there are a couple of valid ways to compute it. That said, most statistical packages (including Microsoft Excel) can compute an R2 with minimal
effort on the part of the user. A value of 1 implies that the predictor is
explaining 100 percent of the variability of the thing being predicted. In
case it’s not already clear, when we talk about “the thing being predicted,”
we are of course referring to a stock or a futures contract or some other
financial instrument that we want to trade. In quant finance, we’re literally
trying to predict the future prices/returns/directions of such instruments,
making an R2 of 1 basically impossible, unless methodological errors are
being made. In fact, a superb R2 in our industry is 0.05 (out of sample, to
be discussed later in this chapter). A former employee of mine once said,
“If you see an R2 above 0.15 and it’s not because you made a mistake,
run the other way, because the SEC will arrest you for insider trading if
you use it.” Note that an R2 of 0.15 implies that some predictor describes
15 percent of the future variability of the target of the forecast. As another
quant trader put it, “People have gotten rich off a 0.02 R2.” Exhibit 9.2
shows that the R2 of the S&P 500 strategy was less than 0.01 from 1982
through 2000.

Return of S&P 500 on the Next Day

15%
10%

R2 = 0.0085

5%
0%
–5%
–10%
–15%
–20%
–25%
(15)

(10)

(5)

–

Signal (Negative = Short, Positive = Long)

Exhibit 9.2

R2 of the S&P 500 Strategy

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Inside the Black Box

Quants frequently utilize an additional approach to ascertaining predictive power. This approach involves bucketing the returns of the instruments
included in the test by the deciles (or any other quantile preferred by the
researcher) of the underlying forecasts. In general, a model with reliable
predictive power is one that demonstrates that the worst returns are found
in the bucket for which the worst returns are expected, with each successive
bucket of improving expected returns in fact performing better than the
prior bucket. If the returns of the instruments being forecast are not monotonically improving with the forecast of them, it could be an indication that
the strategy is working purely by accident.
A bar chart showing the quintile study for the S&P 500 strategy is
shown in Exhibit 9.3. As you can see, in this study at least, the strategy
looks reasonable. The leftmost bucket of signals coincides with an average return in the S&P 500 (on the subsequent day) of –2.35 percent,
and indeed, this is the worst average S&P return of any of the buckets.
The second bucket from the left shows that the S&P 500 strategy’s second‐most‐bearish group of forecasts for the S&P averages –0.19 percent.
As we move to increasingly bullish signals, the S&P’s returns continue to
improve in accordance with the bullishness of the forecasts, which is what
one would hope for. The fact that each bucket’s average return is better
than the one previous to it is said to imply a monotonic relationship between our alpha signal (the modified equity risk premium signal described
earlier) and the target of our forecasts (the S&P 500 index’s return over
the next day).

S&P Return on the Next Day

0.14%
0.12%
0.10%
0.08%
0.06%
0.04%
0.02%
0.00%
–0.02%
–0.04%

(2.35)

(0.19)

0.02

0.30

1.90

Strategy Signal (Negative = Short, Positive = Long)

Exhibit 9.3

Quintile Study of S&P 500 Strategy’s Signals versus S&P 500 Returns

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Percentage Winning Trades or Winning Time Periods This percentage is another
measure of consistency. It tells the researcher whether the system tends to
make its profits from a small portion of the trades that happened to do
very well or from a large number of trades, each of which might contribute
only modestly to the bottom line. Similarly, one can easily measure the total
number of winning (positive) periods versus the total number of periods.
(This is most often measured by percentage winning, or profitable, days.)
In both cases, one tends to have more confidence in strategies with greater
consistency. In the S&P strategy, the results of this study are somewhat unusual in that the strategy is not designed to produce a signal every day but
instead only when the model perceives that the opportunity is sufficiently
attractive to warrant trading at all. As such, the model produces a zero signal 65 percent of the time. It produces winning trades about 19 percent of
the time and losing trades about 16 percent of the time. Of the days when it
actually has a nonzero signal, it wins approximately 54 percent of the time.
This, too, is not a terrible outcome for a strategy.
Various Ratios of Return versus Risk A great many statistics have been proposed as useful measures of risk‐adjusted return, which are generally all attempts to measure the “cost” (in terms of risk) of achieving some return. The
canonical example is the Sharpe ratio, named after William Sharpe (mentioned earlier in connection with the Nobel Prize in Economics he shared
with Harry Markowitz in 1990). The Sharpe ratio is computed by taking the
average periodic return above the risk‐free rate and dividing this quantity
by the periodic variability of returns. The higher the Sharpe ratio, the better.
Quants (and many in the investment management business) have shortened
this moniker by dropping the word ratio. A strategy with a 2 Sharpe is a
strategy that delivers two percentage points of return (above the risk‐free
rate) for each point of variability (and this is a rather good Sharpe, if you
can get it).
A close cousin of the Sharpe ratio is the information ratio, which is different from the Sharpe only in that it eliminates the risk‐free rate from the
formula. The information ratio of the S&P 500 timing strategy is a mere
0.57, meaning that the investor receives 0.57 percent in return for every
1 percent in risk taken (again, before transaction costs and before any other
fees or costs of implementing the strategy). The Sterling ratio (average return
divided by the variability of below‐average returns), the Calmar ratio (average return divided by the worst peak‐to‐valley drawdown), and the Omega
ratio (the sum of all positive returns divided by the sum of all negative returns) are also widely used among a number of other risk‐adjusted return
metrics. The S&P 500 strategy from 1982 through 2000 displayed a Sterling
ratio of 0.87, a Calmar ratio of 0.31, and an Omega ratio of 1.26. Of these

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ratios, the most discouraging is the low Calmar ratio, which indicates that
the strategy generated only 0.31 percent in returns for every 1 percentage
point of drawdown it experienced.
Relationship with Other Strategies Many quants utilize several kinds of strategies at once. As such, the quant is effectively managing a portfolio of
strategies, which can be thought of much like any other kind of portfolio
in that diversification is desirable. The quant frequently measures how a
proposed new idea will fit in with other, already utilized, ideas, to ensure
that the new strategy is in fact adding value. After all, a good idea that
doesn’t improve a portfolio is not ultimately useful. Though it is common to compute a correlation coefficient between the new idea and the
existing portfolio of strategies, many quants measure the value‐added of
a new strategy by comparing the results of the existing strategy with and
without the new idea. A significant improvement in the results indicates
that there is a synergistic relationship between the new idea and the existing strategy.
Time Decay In testing a strategy, one interesting question to ask is, how
sensitive is this strategy to getting information in a timely manner, and for
how long is the forecast effect sustained in the marketplace? Many quants
will seek to understand what their strategies’ returns would be if they
must initiate trades on a lagged basis after they receive a trading signal.
In other words, if a strategy initiated a signal to sell Microsoft (MSFT)
on April 28, 2006, the quant can see what the performance of his strategy
would be in MSFT if it was not allowed to sell MSFT for one day, two
days, three days, and so on. In this way, he can determine his strategy’s
sensitivity to the timeliness with which information is received, and he can
also gain some information about how crowded the strategy is (because
more crowding would mean sharper movements to a new equilibrium, i.e.,
faster degradation of profit potential). Imagine that a researcher develops
a strategy to trade stocks in response to changes in recommendations by
Wall Street analysts. Increases in the level of analysts’ consensus recommendations for a company lead to a targeted long position in that company, whereas deterioration in the aggregate recommendation level would
lead to a targeted short position in the company. This strategy is popular
and followed by many quants (and discretionary traders). However, its
effects are very short‐lived and are very sensitive to the timing of the information received.
An example of this phenomenon is shown in Exhibit 9.4, using MSFT
from April through October 2006. As you can see, there were five downgrades on April 28, which caused MSFT to underperform the S&P 500 by

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about 11.4 percent on the day the downgrades were announced. In fact, the
opening price of MSFT on the 28th was already down about 11.1 percent
because the downgrades all took place before the market opened. As such,
the quant trader must be careful not to allow his simulation to assume
that he was able to transact in MSFT early enough to capture any of the
11.1 percent change. Instead, to be conservative, he can test what his, say,
two‐week performance on the trade would have been if he initiated the
trade on various days after the initial ratings change.
If he did this, what he would find is that if he sold MSFT at any time
after the close of April 27 (the night before the recommendation changes
were announced), his trade would have actually been pretty mediocre. He
would have made money selling MSFT at the close on April 28, May 1 (the
next business day), or May 2, but from May 3 through May 12 the trade
would have been unprofitable. This illustrates the importance of stress‐
testing a strategy’s dependence on timely information, which might not always be available.
Interestingly, delaying the signal’s implementation does not always
result in a negative outcome. For example, our S&P strategy tends to be

MSFT versus S&P 500, with Cumulative Analyst Estimate Revisions,
March–October 2006
Index of MSFT versus S&P 500 (Rising Values Indicate
MSFT Outperformance of S&P)

MSFT versus S&P 500

1
0

100

–1
–2

–3
90

–4
–5

–6

Date

Exhibit 9.4

Illustration of Time Decay of Alpha

00
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–7

Cumulative Rating Change

Cumulative Changes in Analyst Recommendation Level

105

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“early” on its trades, that is, it tends to be short too early and long too early,
even though the market subsequently does move in the direction forecast,
on average. As such, delaying its entry by merely one day dramatically improves the total return of the strategy, from 746 percent total (12.1 percent
annualized) to 870 percent total (12.9 percent annualized). This does not
necessarily bode well for the use of such a strategy. In general, it is not comforting to know that you get a signal from your trading strategy that you
not only can go without implementing for a little while (which would be the
better result) but that you actually are better off ignoring for at least a full
day after you get the signal.
Sensitivity to Specific Parameters It was mentioned earlier that parameters
can be varied, and by varying them, differing outcomes are likely. But much
can be learned about the quality of a strategy based on how much the outcomes vary as a result of small changes in the parameters. Let’s use our P/E‐
based strategy from earlier as an example. Imagine that we think that any
P/E ratio that is either above 50 or negative (because of negative earnings)
should be considered expensive. Meanwhile, we presume that any P/E ratio
below 12 is cheap. Assume we test the strategy according to the previously
discussed metrics and find that a low P/E strategy with these parameters
(≥50 implies expensive, ≤12 implies cheap) delivers a 10 percent annual
return and 15 percent annual variability.
Now imagine that we vary the parameters only slightly so that any
stock with a P/E ratio below 11 is cheap and any with a P/E ratio that is
negative or above 49 is expensive. If this version of the strategy, with slightly
differing parameters, results in a significantly different outcome from the
first example, we should mistrust both results and use neither in our model.
This is because the model has proven to be overly sensitive to a small change
in the values of the parameters, which makes little real‐world sense. Should
there be any great difference between a 10 P/E and an 11 P/E, or between a
50 P/E and a 49 P/E? What many researchers look for is smoothness of the
goodness of outcomes with respect to parameter values. Near‐neighboring
sets of parameters should result in fairly similar results, and if they don’t, a
researcher should be a bit suspicious about them, because such results may
indicate overfitting.

Overfitting
The previously described metrics represent a sampling of the kinds that
quants use to determine whether a given model is good. These metrics are
used to judge the quality of a model, both while it is being created and when

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it is being used. Indeed, many hedge fund investors look at the majority of
these metrics as ways of gauging the performance of various traders.
There remains, however, one more extremely important guiding principle in determining the goodness of a quant strategy, and this is an absolute terror of overfitting. Overfitting a model essentially implies that the
researcher is asking too much of the data. The more classical definition is
that a researcher has built a model that closely explains the past, but which
is a poor guide to the future. This can happen in several ways.
First, the researcher must be careful about the complexity of a model.
Complexity in a model can come from a couple of sources. One is the number
of predictive factors. In building a model, a researcher could include thousands
of factors to explain the past fluctuations in asset prices. This model could
more or less explain exactly what has happened in the past. But let us recall
that the goal of quant trading models, like the goal of any alpha‐seeking trader,
is to predict the future, not to explain the past. And while we all expect the
past to provide some guidance as to the future, we also must understand that
the past is, at best, an imperfect guide to the future. This in turn implies that
to perfectly explain the past is not necessarily useful in predicting the future.
Second, a researcher can create a very complex model in terms of the
conditionalities utilized. For example, one might conceive of a strategy that
looks for a specific pattern of price behavior in order to determine a long
or short position. A simple model might call for a long position to be initiated in an instrument if that instrument is up more than some amount over
the past 10 days. A more complex model might call for the long position
to be initiated if the instrument is down over the past one day, up over the
past 10 days, down over the past 20 days, and up over the past 100 days.
Of course, as humans, we’re great at rationalizing things, so we might be
able to come up with some explanation for why such a strategy is definitely
going to work. But it is unequivocally complex, in that there are many “if”
statements embedded in it. As such, it is very fragile.
The desire for relatively simple models for use in forecasting is known
as parsimony. Parsimony is derived from the Latin word parsimonia, meaning sparingness and frugality. Among quants, parsimony implies caution in
arriving at a hypothesis. This concept is absolutely central to the research
process in quant trading. Models that are parsimonious utilize as few assumptions and as much simplicity as possible in attempting to explain the
future. As such, models with large numbers of parameters or factors are generally to be viewed with skepticism, especially given the risks of overfitting.
Parsimony has its roots in a famous principle of a Franciscan friar and logician, William of Occam, known as Occam’s razor. Occam’s razor is roughly
translated from the original Latin as follows: Entities must not be multiplied
beyond necessity. In science, this has been understood to mean that it is better

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to use as few assumptions, and as simple a theory, as possible to explain the
observations. Karl Popper pointed out in 1992 that simpler theories are better
because they are more easily tested, which means that they contain more empirical value. All around, scientists agree that parsimony, the stripping away of
unnecessary assumptions and complexity, is simply better science. Einstein’s
saying, quoted at the beginning of this chapter, adds an important caveat,
which is that oversimplifying an explanation is not helpful either.
Looking again at our example of the consultant hired to help you buy a
house: If he adds a large number of factors to the mix, such as the color of
the guest bathroom tiles or the type of roofing material, given that there is no
reason to believe ex ante that such factors are priorities for you as his client,
his analysis would become muddled and confused. The complex model (in
terms of number of factors) might do a decent job of explaining your past behavior, but it is unlikely to do an excellent job of predicting whether you’ll like
a house you haven’t already seen, because it is unlikely all the factors included
are actually important in ascertaining your preferences in a house. On the
other hand, if the agent uses only two factors—say, the size of the house and
its school district—this model might not do a good job of predicting your preferences because it leaves out too many important variables, like the number
of bedrooms, the number of bathrooms, the condition of the property, the size
of the lot, and so on. Just so, an important part of the quant researcher’s job is
balancing on the tightrope between trying to explain the past too perfectly and
trying to explain it too little. To one side is failure due to overcomplicating the
model and to the other is failure due to oversimplifying it.
A related type of overfitting can be seen in strategies that trade only extremely infrequently. Here, we are concerned with the problem that a small
number of trades, no matter how profitable, is unlikely to provide strong statistical significance. For example, imagine a model that buys the S&P 500 any
time it has a drawdown of at least 40 percent, and buy the S&P back again
when it reaches a new high. We will see a strong backtest for this strategy if we
run one. This strategy would have enormous profits and relatively small drawdowns. But it also would see exactly three trading signals in the past 40 years! It
is hard to get too excited about anything that occurs once every 13 years, and it
is certainly risky to put any serious amount of capital at risk in such a strategy.
Another common source of potential overfitting risk comes from the specification of parameters. As a reminder, in Chapter 3, we discussed the fact that
many models have parameters. For example, in constructing a trend model, a
researcher is making the claim that some characteristic of the change in price
over some period in the past is indicative of a likely future continuation of
that move. There are several parameters one could imagine being relevant to
such a model. For example, what is the historical period over which the price
change is computed (this is known as lookback in quant circles)? If there is a

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Research

minimum size for such a move to be considered significant, what is that minimum size? These questions are not central to the definition of the model, but
different answers to these questions can nonetheless have significant impact
on the returns that the model generates. For example, a trend model lookback
of two days may generate returns that are completely uncorrelated to the returns of the exact same trend model with a lookback of six months.
Quants can fix parameters in a few ways. One is to set them discretionarily, based on a prior conviction about how the markets function. The
results of a backtest will then indicate how much promise the strategy has.
Such an approach has the benefit of not being fitted at all. It either works or
it doesn’t. There are drawbacks to this approach, too, in that it relies heavily
on the judgment of the researcher, and the optimal parameter value might
lie reasonably far away from the one set in his model. That said, a researcher
who has Bayesian tendencies (as discussed in Chapter 3) will likely be inclined to set parameters in this manner.
A second approach to parameter fitting is to have a part of the backtest
show the results of the strategy historically over a variety of parameter values, and to select the parameters that optimize the “goodness” of the result.
This decision can be subjective or it can be done by an algorithm that reflects some rule‐based approach to parameter selection. We now turn to a
discussion of the considerations that apply to the selection of parameter
values. Consider Exhibit 9.5.

Outcome as a Function of Parameter Value
3.0
D

Goodness of Outcome

2.5
C

2.0
1.5
1.0
0.5
–
(0.5)

(1.0)
(1.5)

Parameter Value

Exhibit 9.5

Choosing the Right Parameter Values

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Inside the Black Box

Which of these points would you guess is the best choice for a parameter value? Choice A doesn’t look so good, because the strategy seems to do
poorly when using such a parameter value. Choice C looks enticing because
it is the highest point of a broad plateau. But it is so near a cliff’s edge that
we cannot be sure whether we’re at risk of picking unwisely. Choice D seems
to have the best outcome, but it is also fairly unreliable, since its near neighbors are universally poor. This leaves Choice B as the best. Even though we
haven’t picked the highest point on the plateau, we’ve picked one with a
margin of safety around it on both sides. It bears discussing a bit about why
this margin of safety is so important.
When we see a lonely peak like the one represented by Point D in
Exhibit 9.5, it is likely that our testing has uncovered some spurious coincidence in the fitting period that makes it especially favorable for that single
parameter value. Unfortunately, it is likely that this coincidence will not
persist into the future. By selecting Point D, in other words, we are implicitly
betting that the future will look exactly like the past. You might be familiar
with the standard performance disclaimer: “Past performance is not an indication of future results.” Yet we all tend to judge the success of a trader at
least partly by performance, which is a way of saying that we think the past
might actually be some indication of the future. Similarly, and based on the
premises of scientific research in general, all quant trading (and indeed, all
science) assumes implicitly that the past can have some value in helping us
understand the future. This is why the scientific method starts with observations of the world that can be generalized into a theory. But the appropriate
way to think about the past is as a general guide to the future, not as an
exact copy. We build a model that is itself a generalized description of this
general guide to the future, and when phrased this way, it is clear that we
want our model to err on the side of caution. As such, sensible quants would
refer to Point B as being more “robust” than Point D because Point B has a
better chance of being good, but not solely as a result of some accident of
the sample data used to find it.
One final note on parameter fitting is that parameters can either be fit
once, or they can be fit repeatedly in the future, as new data are generated
in the markets. The considerations described here apply to each instance
of such a fitting of parameters. However, the act of repeatedly fitting parameters itself increases the complexity of a model. And, depending on exactly how such a re‐fitting is implemented, this approach may also rely on
fewer data than are desirable for an exercise so fraught with overfitting peril
already.
This leads us directly to a final, important consideration in the subject
of overfitting, one which we alluded to in Chapter 3. The fact is that capital
markets generate an enormous amount of data. Firms like Renaissance are

Research

167

famous for collecting terabytes of data each day. Merely capturing every
message generated on every U.S. equity exchange requires more than one
terabyte of data storage every day. However, the data are extremely noisy.
Why capital markets are such a noisy process is a subject for philosophers
and economists. But it is an undeniable fact that past data yield extremely
little information about future fluctuations. This is the reason that a great
out‐of‐sample r2 is on the order of 0.04 (out‐of‐sample testing is the subject
of the next section). There is just very little signal buried in all that noise.
Something which, therefore, closely explains such a noisy process must be
viewed with an extreme amount of skepticism.
Quant researchers must evaluate the theories they are testing. This is
done using a wide array of measurements and techniques, but ultimately, a
significant amount of discretion is used. It is unquestionably the case that
what separates a successful researcher from the rest is good judgment about
the kinds of issues raised in this chapter. As a general principle, we may note
that good researchers must possess sufficient confidence and skill to believe
that theories can be developed or improved on. At least as important, researchers must also be skeptical and humble enough to know and be entirely
at peace with the fact that most ideas simply don’t work.

Out-of-Sample Testing
Out‐of‐sample testing, the second half of the testing process, is designed
to tell the researcher whether her formalized theory actually works in real
life, without the benefit of seeing the cheat sheet provided during in‐sample
testing. The model’s parameters have by now been fixed using a different
set of data (from the in‐sample testing period), and it’s simply a question
of whether the model, with whatever parameters are chosen, really works
in a new, out‐of‐sample data set. Many of the same kinds of statistics as
described in this chapter are utilized to make this judgment.
One additional statistic many quants use is the ratio of the R2 in the
out‐of‐sample test to the R2 in the in‐sample test. This ratio is another way
for the researcher to obtain a sense of the robustness of the model. If the out‐
of‐sample R2 is relatively close to the in‐sample R2 (i.e., if the ratio is about
half or better), that is considered a good thing. If it is significantly smaller,
the researcher must be suspicious about the prospects for his model’s success.
There are many approaches to out‐of‐sample testing. The simplest utilizes all the data that were set aside from the in‐sample test. Some researchers
utilize a rolling out‐of‐sample technique in which the single oldest data point
is discarded and one new data point is added to both the fitting (in‐sample)
and testing (out‐of‐sample) period. This process is repeated through the entire
available sample of data. The rolling out‐of‐sample technique is thought to

168

Inside the Black Box

help refresh the model over time so that it does not depend on a single set
of tests that might have been run some years previously. However, depending on the circumstances, this approach can have the weakness of giving the
model the benefit of constant knowledge of the recent past, which could reduce its robustness. This trade‐off is extremely subtle and can be debated in
any individual instance, rendering impractical any general judgment about its
effectiveness. Still another approach utilizes an ever‐growing window of data
for ongoing out‐of‐sample testing as time passes and more data are collected.
Though the objective of out‐of‐sample testing is clearly valid, it turns
out to be a rather tricky thing to do correctly. Imagine a researcher who
completes the model fitting over the in‐sample data. Then, having a model
that seems robust, the researcher tests it over the out‐of‐sample data. But
the model fails to deliver a good result on this new data set. The researcher,
already having invested a lot of time on the model, decides to examine the
reasons for the model’s failure over the out‐of‐sample period and discovers
that the environment changed between the in‐ and out‐of‐sample periods
in such a way that the model was making losing trades during the latter.
Having learned a useful lesson, the researcher goes back to the model and
alters it to account for this new information. He refits the model in sample,
and then retests it out of sample. And, lo and behold, it works much better.
Before we break out the champagne, however, we should consider what
the researcher has just done. By learning from the out‐of‐sample data and
using that information to train the model anew, he has effectively used up
his out‐of‐sample data and has caused them effectively to become part of
the in‐sample data set. In general, going back and forth between the in‐ and
out‐of‐sample data is a terrible idea. This brings up a still more subtle issue,
but one that is closely related.
Often we know enough about that happens in the capital markets during the out‐of‐sample period that we tend to build models and select parameter sets that we believe are likely to work out of sample anyway. This
sullies the purpose of an out‐of‐sample test because we are, in many respects, looking ahead. For example, we can look back on the Internet bubble of the late 1990s and know that the world and the economy in fact did
not change and that negative earnings should not be wildly rewarded in the
long run. If we build a strategy today, we can know that it is possible for the
Internet bubble to happen but that it eventually bursts. However, we could
not have known this with certainty in 1999.
The world finds new and interesting ways to confound our understanding.
As such, to test our current best thinking against competition that existed
in the past is a form of wishful thinking. This is a subtle and nefarious form
of look‐ahead bias, which is a critical problem in research. As researchers
become more and more familiar with the out‐of‐sample periods they use

Research

169

to test their ideas’ validity, it becomes more likely that they are implicitly
assuming they would have known more about the future than in fact they
would have known had they been asking the same questions historically.
This practice is called burning data by some quants.
To mitigate the data‐burning form of look‐ahead bias, some quant shops
take reasonably drastic measures, separating the strategy research function
from the strategy selection function and withholding a significant portion of
the entire database from the researchers. In this way, the researcher, in theory,
cannot even see what data he has and doesn’t have, making it much more difficult for him to engage in look‐ahead activities. With less draconian restrictions, the researcher might simply not be allowed to know or see what data
are used for the out‐of‐sample period, or the portions of data used for in‐ and
out‐of‐sample testing might be varied randomly or without informing the
researcher. Regardless, as you can easily see, the problem of doing testing is
tricky and requires great forethought if there is to be any hope of success.
Another approach is to determine that out‐of‐sample testing is a bit of a
myth in the first place, especially for any experienced, observant researcher. As
a result, out‐of‐sample testing is forgone in favor of a combination of extra
vigilance regarding the in‐sample results, coupled with a minimum of parameter fitting. In this methodology, the quant uses as few parameters as possible,
sets the values at some reasonable level, and simply tests the strategy and looks
for all those metrics of good performance to have sufficiently high readings.

Assumptions of Testing
Another component in the testing process revolves around the assumptions
one makes about trading a strategy that is being tested historically. We discuss two examples here: transaction costs and (for equity market‐neutral or
long/short strategies) short availability.
We have already discussed transaction costs, of which there are several
components: commissions and fees, slippage, and market impact. Interestingly, during the research process there is no empirical evidence of what a
trading strategy would actually have cost to implement in the past. This is
because the trading strategy wasn’t actually active in the past but is being
researched in the present using historical market data. Therefore, the researcher must make some assumption(s) about how much his order would
really have cost in terms of market impact.
These assumptions can prove critical in determining whether a strategy is good or bad. Let’s again look at an extreme case to understand why.
Imagine that we assume that transactions are entirely costless. This might
make a very high‐frequency trading strategy extremely appealing because, as
long as it accurately predicts any movement in price, no matter how small, it

170

Inside the Black Box

will seem to have been worthwhile to trade. Imagine that a model is correct
55 percent of the time and makes $0.01 per share when it is correct. It loses
45 percent of the time and loses $0.01 per share when it is wrong. So, for
every 100 shares it trades, it could be expected to generate $0.10. But when
it is implemented, it turns out that transactions actually cost $0.01 per share
across all the components of cost, on average. This would imply that the
strategy is actually breakeven on 55 percent of its trades (theoretical profit
of $0.01 per share, less the cost of transacting each share of $0.01) and loses
$0.02 per share on 45 percent of its trades. As a result, rather than making
$0.10 per 100 shares, it is in fact losing $0.90, which is obviously a poor outcome. Stated generally, overestimating transaction costs will cause a quant to
hold positions for longer than is likely optimal, whereas underestimating
transaction costs will cause a quant to turn over his portfolio too quickly and
therefore bleed from the excess costs of transactions. If we have to err in this
regard, it makes more sense to overestimate cost than to underestimate, but
it is always preferable to get the cost estimation approximately right.
The second kind of assumption a quant must make in testing a market‐
neutral or long/short strategy in equities relates to the availability of short
positions. Imagine a U.S. market‐neutral quant trader who, by design, holds
a short portfolio that is roughly equal in size to the long portfolio. Over time,
the short portfolio adds a significant amount of value by finding overpriced
stocks and by making money when the stock market tumbles, thereby reducing the risk inherent in the strategy. However, it turns out that the names the
strategy wants to short, and in particular, the most successful short picks,
are on hard‐to‐borrow lists. Hard‐to‐borrow lists are those stocks that are
generally restricted from shorting by the broker, because the broker cannot
mechanically locate shares to borrow, which is required in the act of shorting. If the shares cannot be located, the trade would be considered a naked
short sale, which is illegal in the United States. Therefore, the trade wouldn’t
have been executed as expected by the back‐test. If the model is ignorant of
hard‐to‐borrow issues (and making a model aware of this issue in the past is
not trivial, since such historical data are hard to come by), the researcher can
easily be fooled into thinking that the short portfolio will be able to deliver
value that is, in reality, nonexistent. This is because when he goes to implement the live portfolio, he finds that he is unable to put on the best short
trades and is forced to replace these with inferior short trades instead.

Summary
We have only scratched the surface of the work that a quant must do in research, and must do well, to succeed over time. Research is a highly sensitive

171

Research

Alpha Model

Risk Model

Transaction Cost Model

Data
Portfolio Construction Model
Research
Execution Model

Exhibit 9.6

Schematic of the Black Box

area within the quant’s process. It is where her judgment is most obviously
and significantly impactful. Researchers must therefore go about their research with great care because this is the formative stage of a strategy’s life.
Mistakes made during research become baked into a strategy for its lifetime,
and then the systematic implementation of this error can become devastating. Moreover, the research effort is not a one‐time affair. Rather, the quant
must continually conduct a vigorous and prolific research program to produce profits consistently over time.
Models are, by definition, generalized representations of the past behavior of the market. More general models are more robust over time, but they
are less likely to be very accurate at any point in time. More highly specified
models have the chance to be more accurate, but they are also more likely
to break down entirely when market conditions change. This trade‐off, between generality and specificity, between robustness and accuracy, is the
key challenge faced by quant researchers. While there is no one‐size‐fits‐all
answer that I’m aware of to address this challenge, I think Einstein’s words
provide the best guiding principle: “Everything should be made as simple as
possible, but not simpler.”
We have now completed our tour through the black box (see
Exhibit 9.6), both its component models and the key elements—data and
research—that drive it. The coming chapters will focus on the evaluation of
quant traders and their strategies.

Note
1. From Richard Donchian’s Foundation website: www.foundationservices.cc/RDD2.

Part

Three
A Practical Guide
for Investors in
Quantitative Strategies

Chapter

Risks Inherent
to Quant Strategies
Torture numbers, and they’ll confess to anything.
—Gregg Easterbrook

e have defined two broad classes of exposures: those that generate returns in the long run (alpha and beta) and are intentionally accepted
and those that do not generate long‐term returns (risks) or are incidental to
the strategy. For the kind of quant traders that are the subject of this book,
beta exposures are generally avoided (because they can be easily obtained by
generic, low‐cost index instruments), and therefore we can focus on alpha
and risk exposures.
As we have already stressed, the kinds of alpha exposures quants seek to
capture are generally exactly the same as those that are sought by discretionary managers. However, with any strategy there is always the possibility that
the exposure from which returns are generated is not being rewarded by the
marketplace at a given point in time. This risk of out‐of‐favor exposure is
shared by both quants and discretionary traders alike.
This chapter will help an investor understand the types of risks that are
either unique to quant trading or at least more applicable to quant trading.
In a sense, we also are providing a framework for investors to design their
own risk models that can be used to help determine how to use quant trading as part of a portfolio of strategies. The latter is a topic we address again
in Chapter 12.

175

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A Practical Guide for Investors in Quantitative Strategies

Model Risk
Model risk is the most basic form of risk any quant system brings to an
investor. Models are approximations of the real world. If the researcher
does a poor job of modeling a particular phenomenon—for example, momentum—the strategy might not be profitable, even in a benign environment for momentum in general. In other words, model risk is the risk that
the strategy does not accurately describe, match, or predict the real‐world
phenomenon it is attempting to exploit. Worse still, model risk need not
be evident right away. Sometimes small errors in specification or software
engineering lead to problems that accumulate very slowly over time, then
suddenly explode on a busy trading day. Additionally, model risk can come
from several sources. The most common are the inapplicability of modeling,
model misspecification, and implementation errors. It bears mentioning that
all types of model risk can occur not only in the alpha model but also from
errors in any of the other parts of the strategy. Back‐testing software, data
feed handlers, alpha models, risk models, transaction cost models, portfolio construction models, and execution algorithms can all have model risk
in them.

Inapplicability of Modeling
Inapplicability of modeling is a fundamental error that comes in two forms.
The first is the mistaken use of quantitative modeling to a given problem.
For example, trying to model the quality of a musician is simply the wrong
idea from the start. One could conceive of some relevant factors that correlate with skill in musicianship, such as the source and duration of training.
But ultimately, the goodness of a musician is not a question that can be answered with mathematics or computer models. It is an inherently subjective
question, and to apply computer models to it is an error.
Models that are inapplicable to the problem they’re being used to solve
are often created due to the use of improper assumptions, coupled with
wrong judgment regarding the use of a given statistical method. The global
market turmoil in 2008, which was fueled in part by the securitized mortgage business, could be an example of the problem of the inapplicability of
quantitative modeling to a problem. Though these securitized mortgages
were not in any way like quant trading strategies, part of their rise to prominence resulted from the quantitative modeling work done by various structured products desks inside a wide variety of banks around the world. They
modeled what would happen in various scenarios, and on the back of the
comfort gained in the output of these models, they issued AAA‐rated bonds
backed by instruments that, each on its own, were toxic. It appears that a

Risks Inherent to Quant Strategies

177

fundamental error was made (or ignored to rationalize massive greed) in the
conceptualization of the problem. In this case, the problem was a failure to
realize that there absolutely could be a dynamic in the economy that could
lead to a large number of mortgage defaults simultaneously. The tools used
to model and value these securities were simply not meant to handle the
realities of the market to which they were applied.
A second type of inapplicability is subtler and, probably because of this
subtlety, more common among quant traders. It is the error of misapplication of an otherwise valid technique to a given problem. One example of
this type of error, which we have already touched on in the section on risk
modeling, is the widespread use of value at risk (VaR). Conventional VaR
uses correlation matrices and historical volatility to determine the amount
of risk in a given portfolio at a point in time. However, there are many assumptions inherent in the use of VaR that are invalid. For example, the use
of both correlation matrices and historical volatility (defined as the standard
deviation of returns) assumes that the underlying distributions that describe
the various elements in a portfolio are normal. But in fact, market data
often exhibit fat tails. In other words, there are significantly more observations of extreme values than one would expect from a normal bell‐curve
distribution. A specific example of this situation can be seen with data on
the S&P 500. Based on the daily historical index data (excluding dividends)
from January 3, 2000, through November 30, 2008, a –4 standard deviation day is one on which the S&P posts a return worse than –5.35 percent.
A 4 standard deviation event should occur once every 33,333 trading days
(approximately every 128 years, assuming 260 trading days per year) if the
S&P’s returns are normally distributed. In fact, the S&P has posted a return
this poor on average once per 13 months, or 119 times more frequently than
you’d be led to believe from a normal distribution.
Furthermore, correlation coefficients (a key ingredient in the computation of VaR measurements) should be used only when a linear relationship
exists between the two things being correlated. Instead, many instruments
are not linearly related to each other. Exhibit 10.1 shows an interesting contrast between two relationships.
As you can see from the charts, the relationship between XOM and
JAVA is not linear. Note that the best day for XOM is actually a fairly
poor day (–5 percent or so) for JAVA. Likewise, the best day for JAVA is
also a nearly 5 percent loss for XOM. A line that best fits this relationship
would look more like the Gateway Arch in St. Louis than a straight line.
By contrast, the relationship between XOM and CVX does appear to be
reasonably linear. A researcher using correlation to examine the relationship
between JAVA and XOM would likely be making a model inapplicability
error because the relationship is nonlinear in the first place.

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A Practical Guide for Investors in Quantitative Strategies

JAVA versus XOM,
March 1987 to December 2008
20%

XOM Daily % Return

10%

–10%

–20%

–30%
–30%

–20%

–10%

10%

20%

30%

40%

JAVA Daily % Return

20%

CVX versus XOM,
March 1987 to December 2008

XOM Daily % Return

10%

–10%

–20%

–30%
–20%

Exhibit 10.1

–10%

0%
10%
CVX Daily % Return

20%

A Demonstration of Nonlinear and Linear Relationships

30%

Risks Inherent to Quant Strategies

179

Model Misspecification
The second kind of model risk is misspecification. Model misspecification
means that the researcher has built a model that badly describes the real
world. Practically speaking, a model that doesn’t fit the real world at all is
unlikely ever to make money and therefore is unlikely to be observable for
very long before being shut down. As such, the more prevalent misspecification errors relate to events that are uncommon. These models work fine
most of the time, but they fail when an extreme event occurs. A recent example of this situation can be seen in the aftermath of August 2007, when
many quants concluded that they had done a bad job of modeling liquidity
risk in large‐capitalization U.S. stocks. This is because they looked at only
the liquidity risk associated with their own holdings in these names. What
they learned, however, was that if many large traders liquidate similar holdings at the same time, the aggregate size of these positions matters more
than the size any individual trader holds.
As a direct result of this event, some quants discovered risk model or
transaction cost model misspecifications and have begun to attempt to correct these flaws. But again, the rarity and unique nature of such events make
them extremely difficult to model.

Implementation Errors
The third and perhaps most common variety of model risk is from errors in
implementation. All quant trading strategies ultimately are pieces of software
residing in hardware and network architectures. Implementation errors, or
errors in programming or architecting systems, can cause serious risk for the
quant trader, and in some cases also for the market at large. For example,
imagine that a quant means to have his execution software buy the bid and
sell the offer price using limit orders. But he programs his execution software with the signs reversed so that it buys at the offer and sells at the bid.
Because of this error, he is now paying the bid/offer spread on every trade—
the exact reverse of his intention. This is an example of a programming error. In August 2012, Knight Trading lost more than $400 million in a mere
30 minutes due to a software bug that caused a dormant piece of software to
come back online, multiplying order sizes and causing Knight to accumulate
massive positions at highly elevated prices. As they sold those positions off,
the nine‐figure losses mounted. The losses, both in capital and in confidence,
have had significant repercussions for Knight. The company nearly went
bankrupt and was forced to sell over 70 percent of the firm to a consortium
of investors at a steep discount in order to remain afloat. Not to pick on
them, but this wasn’t Knight’s first implementation error. In March 2011,

180

A Practical Guide for Investors in Quantitative Strategies

a “process error” at Knight caused the values of some newly created exchange‐traded funds (ETFs) to drop from 80 to 100 percent immediately
upon their inception (the exchanges canceled those trades).
AXA Rosenberg, too, had a coding error in its risk model that resulted
in a $217 million loss to clients, which AXA eventually repaid to its investors, along with a $25 million penalty paid to the SEC to settle the case. In
this case, the error appears to have been introduced in April 2007, but it
was not discovered until June 2009, and even after it was discovered, certain
AXA executives apparently decided to hide the issue from their CEO, not
to disclose it to investors, nor even to fix the issue. AXA finally disclosed
the error to clients about three years later, in April 2010. In addition to
the hefty compensation and penalty AXA paid, their assets under management dropped from $62 billion in March 2010 to $18 billion by the end of
June 2012.
In another case, a successful quant trading firm that will remain anonymous made an architectural error. The firm has separate servers for alpha
models and the execution engine. As we discussed earlier, the portfolio construction model looks to the alpha model for information on what positions
it should execute on both the long and short sides. At some point during one
trading day, there was a need to reboot the servers for the system. But when
the servers were restarted, the execution server came online first, and a few
minutes later, the alpha model was restored to service. The execution model,
seeing that it had no signals whatsoever from the alpha model, rapidly and
automatically began liquidating the portfolio of positions in order to eliminate risk. In the few moments before the alpha server came back online, 80
percent of the firm’s portfolio was sold off and then had to be reacquired.
There was no warning that this error existed until it manifested itself in
this unfortunate manner. The strategy was making perfectly good returns
but suddenly broke down due to a combination of a specific quirky error
and the circumstances of the situation. Fortunately, returns were not very
adversely affected, but this was probably merely lucky. Given the massive
quantities of code that go into a quant trading strategy, such software and
architectural errors are unfortunately the most common, but usually least
painful (the Knight episode in 2012 notwithstanding), types of errors.

Regime Change Risk
Most quant models are based on historical data. Even those using analysts’
forecasts or other sentiment signals turn out to depend heavily on the past
because sentiment usually is biased in the direction of historical trends.
Regardless of the type of model, quants use past relationships and behavior

181

Risks Inherent to Quant Strategies

SCHW and MER,
December 1995 to December 2007

180
160

SCHW

140

MER

120
100
80
60
40
20

Exhibit 10.2

Regime Changes in a Relationship between Two Stocks

00
7

00
6

Date

12
/

29
/2

00
5
12
/

29
/2

00
4
12
/

29
/2

00
3
12
/

29
/2

00
2
12
/

29
/2

00
1
12
/

29
/2

00
0
12
/

29
/2

99
9
12
/

29
/2

99
8
12
/

29
/1

99
7

29
/1

12
/

29
/1

12
/

29
/1

12
/

29
/1
12
/

99
6

–

99
5

Stock Price (Normalized to $10 at 12/29/1995)

to develop theories and build models to help predict the future. If markets
have behaved in a particular way for a while, quants will come to depend on
that behavior persisting. If there is a regime change, the quant will typically
suffer because the relationships and behavior he is counting on are altered,
at least temporarily.
Dependence on the past is certainly one of the more interesting problems to consider in analyzing quant strategies and determining how to use
them. In some strategies, dependence on the persistence of historical behavior is explicit, as in the case of trend following. Note that this isn’t necessarily an indictment of these strategies. Indeed, such strategies have made
money for decades and have exhibited better risk‐adjusted returns than the
stock market by far. However, if an established trend reverses, the trend follower will almost certainly lose money. Ironically, mean reversion–focused
quants may also suffer during a large trend reversal, particularly if they
are engaged in a relative mean reversion strategy. We might expect that if a
reversal of trend occurs, this should be good for the mean‐reversion trader,
since he bets against trends. However, if the reversal is also associated with
the breakdown of established relationships, this can be quite painful because of the relative part of the strategy. Exhibit 10.2 illustrates this point.

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As you can see, there are four distinct phases in the relationship between
Charles Schwab (SCHW) and Merrill Lynch (MER). From early 1996 until
the end of 1997, the stocks were reasonably correlated and showed similar
trends. From early 1998 until early 2001, on the other hand, the stocks
behaved very differently from one another, and SCHW in particular began
to exhibit substantially greater volatility than it had earlier or than it would
again later. The Internet bubble appears to be the cause of this shift, during
which investors began to treat SCHW as an online broker, and its shares
rose and fell with the likes of Ameritrade and E*Trade instead of its more
traditional peer, MER. Upon the bursting of the Internet bubble, SCHW
reverted uncannily to MER’s level and tracked it very closely for some time,
from early 2001 until early 2007. Then, in early 2007, you can see another
sharp change in the relationship, with MER dramatically underperforming
SCHW. This, of course, is due to the banking and credit crisis that traces its
roots to early 2007.
A quant betting on this relationship’s persistence would have suffered
through two reasonably significant periods in the past 10 years in which the
relationship did not hold up at all. Whether these stocks have permanently
decoupled or will revert again at some point in the future is a matter that is
beyond my ability to forecast. But this is precisely what regime change risk
is about: A structural shift in the markets causes historical behavior of an
instrument or the relationships between instruments to change dramatically
and quickly.
Another example of this kind of structural shift can be seen in the relationship between value stocks and growth stocks, as measured by the IVE
and IVW ETFs, which represent S&P 500 Value and S&P 500 Growth,
respectively. The historical spread between these two ETFs is illustrated in
Exhibit 10.3.
This figure shows that the S&P Value index outperformed the
S&P Growth index by some 29 percent from the start of 2004 until
mid‐May 2007. The spread then trended a bit lower until mid‐July and
then rapidly fell as quants unwound their portfolios, which clearly had
been betting on Value to outperform Growth. This unwind, combined with
the macroeconomic environment,1 set off a massive rebound in Growth
relative to Value.
Note that there are two substantial, short‐term reversals of this more
recent trend, one in January 2008 and one in July through September 2008,
both of which are circled in the figure. These moves are incredibly sharp,
actually representing the biggest and fastest moves in this spread in a very
long time (certainly going back further than this analysis). In 16 trading
days, from January 9 through 31 of 2008, the Value index recovered more
than half the underperformance it had experienced in the 160 trading days

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Risks Inherent to Quant Strategies

3.5
Value-Growth Spread (Set to 0 at 12/31/2003)

Value-Growth Spread
3.0
2.5
2.0
1.5
1.0
0.5
–

08
12

07
12

06
12

05
20
1/
/3
12

20
1/
/3
12

(0.5)

Date

Exhibit 10.3

Value/Growth Spread, 2003–2008

prior to that point. In other words, the reversal was five times faster than
the trend that preceded it. This was another rather painful experience for
quants, though not on the order of what was felt in the summer of 2007.
Over the subsequent 115 trading days, the Value/Growth spread reversed
over 22 percent, all the way back to breakeven, until mid‐July 2008. At that
point, another brief but violent six‐trading‐day period saw the spread recover almost 40 percent of the lost ground. In other words, the reversal was
almost eight times faster than the trend that preceded it. From late August
through early September, the spread recovered another 36 percent of its lost
ground, and over the 39‐day period from mid‐July through early September
the recovery was more than 50 percent in total.
What’s worse, such sharp reversals frequently cause many other types
of relationships to falter. For example, the sectors that had been underperforming (such as financial companies or homebuilders) become the new outperformers, while those that had been outperforming (such as technology
companies) tend to become the new laggards. Currencies and bonds also
tend to reverse, as do commodities (especially over the past five years). An
illustration of this last point is shown in Exhibit 10.4.

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2
Value-Growth Spread
Oil

18
16

–0.5

8
6

–1

8
/2

8
16
8/

00
/2
16
5/

00
/2
16

20
6/
/1
11

7
00
/2
16
8/

00
/2
5/

/2
16
2/

6/
/1
11

06
20

00
/2
16

–2

–1.5

Oil ETF

0.5

Value-Growth Spread

1.5

Date

Exhibit 10.4

Value/Growth Spreads versus Oil Prices, Normalized to August 16, 2006

Note that the Oil ETF moves almost like the mirror image of the
Value/Growth spread, experiencing mirroring reversals in early January
and mid‐July 2008 (again, indicated by the circled periods on the graph)
and mirroring trends in between. It is for this reason that regime changes
are especially painful for quants: They tend to occur across many levels
simultaneously.

Exogenous Shock Risk
The third in the family of quant‐specific risks comes from exogenous shocks.
I refer to them as exogenous because they are typically driven by information that is not internal to the market. Terrorist attacks, the beginning of a
new war, and political or regulatory intervention are all examples of exogenous shocks. Because quant models utilize market data to generate their
forecasts, when nonmarket information begins to drive prices, quant strategies typically suffer. This is especially true because such shocks usually also
result in larger‐than‐normal moves. So, in situations of exogenous shock, we
have big moves that aren’t explainable by a reasonable model using market
data but rather by information that is entirely external to the markets (see
Exhibit 10.5).

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Risks Inherent to Quant Strategies

1,600
1,500
1,400
Index Value

1,300
1,200
1,100
1,000
900
800
700

08
1/

07
12

06
/3
12

05
/3
12

04
/3
12

20
12

1/
/3

02
12

01
12

00
20
12

1/
/3
12

600

Date

Exhibit 10.5

S&P 500 Price Index, December 1999 to December 2008

The first circled period in the S&P 500 chart in Exhibit 10.5 represents
the terrorist attacks on New York and Washington, D.C., on September 11,
2001. The market was closed for almost a week, and when it reopened, it
dropped precipitously, only to recover much of that ground rather quickly.
Ignoring the obviously horrible nature of the attack on civilians, the downward move in markets was actually a continuation of the downward trend in
stocks that had begun in March 2000 and therefore benefited trend‐following strategies. However, many mean reversion strategies and relative‐alpha
strategies suffered in September 2001 as nonmarket information dramatically and briefly changed the way markets behaved.
A similarly difficult situation was observable with the start of the Iraq
war in early 2003, which is the second circled period. Suddenly global stock,
bond, currency, and commodity markets began moving in lockstep with
each other, all driven by news reports of the U.S. armed forces’ progress
through Iraq. This, too, resulted in losses for many quants, including trend
followers, since the move resulted in a reversal of the prior trend across
several asset classes simultaneously.
The third circled period follows the bailout of Bear Stearns in mid‐
March 2008. This period was negative for many quant strategies because it
was a sharp trend reversal that was caused by information that could not be

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anticipated by machines. Indeed, even the collapse of Bear might well have
been the result of nonmarket “information,” and as of this writing, the SEC
is supposed to be investigating potential wrongdoing in the rumors that
were spread about Bear just in advance of (and which likely contributed to)
its collapse.
The final circled period represents another rally in the financial sector in
equities, this one set off by the SEC’s change in shorting rules, which made
it much harder to short battered financial stocks. Though one can argue
about whether an SEC intervention or a rumor‐based collapse and government‐brokered buyout of a major financial institution are endogenous or
exogenous to the market, it is unassailably true that the kind of information
these events presented to market participants was both unquantifiable and
unusual. As such, exogenous shock risk is a significant byproduct of quant
investing, one that it is difficult to do anything about (other than with discretionary overrides).

Contagion, or Common Investor, Risk
The newest member of the quant‐specific risk family is contagion, or common investor, risk. By this we mean that we experience risk not because of
the strategy itself but because other investors hold the same strategies. In
many cases, the other investors hold these strategies as part of a portfolio
that contains other investments that tend to blow up periodically. The first
part of this risk factor relates to how crowded the quant strategy in question
is. A second part relates to what else is held by other investors that could
force them to exit the quant strategy in a panic, sometimes called the ATM
effect. In an ATM effect, significant losses in one strategy cause liquidation of a different, totally unrelated strategy. This happens because investors
who have exposures to both, especially if highly levered, reduce their liquid
holdings in the face of financial distress and margin calls, since their illiquid
holdings are usually impossible to sell at such times. In essence, the good,
liquid strategy is exited to raise cash to cover the losses of the bad, illiquid
strategy.
This is a particularly challenging type of risk that is certainly not exclusive to quants. However, the clarity with which this risk expressed itself in
both August 1998 (easily argued not to be a quant event) and August 2007
(clearly a quant event) demands specific attention. In August 1998, it was
not quant trading that suffered but other strategies such as merger arbitrage.
We will discuss both of these events in greater detail later, but for the moment, it bears mentioning that there is one striking similarity between the
two: In both cases, a credit crisis leading to illiquidity in credit instruments

Risks Inherent to Quant Strategies

187

sparked a forced sale of more liquid assets that had nothing to do with the
credit crisis.
In 1998, many relative value equity arbitrage positions, which bet on
convergence of share prices between stocks that are either dually listed or
else are merging, suffered dramatically as an indirect result of the Russian
government’s defaulting on its debt obligations. The famous example used
by Lowenstein in When Genius Failed was Royal Dutch and Shell, a dual‐
listed company. Royal Dutch had been trading at an 8 to 10 percent premium
to Shell, and the bet was that the two stocks should eventually converge,
eliminating the premium. In hopes of this, Long‐Term Capital Management
(LTCM) and many others had long positions in Shell and short positions in
Royal Dutch. After all, there was no rational economic reason that a European listing of a given company should outperform a U.S. listing of the same
company. Yet because LTCM had to vacate this position at a time when there
was little liquidity, the spread widened from 8 to 10 percent to more than
20 percent by the time LTCM was trading out of it. The reason that this position had to be sold is that LTCM also had massive losses on its positions in
Russian debt. The Russian bond holdings were part of a relative yield trade
that paired a long position in high‐yield Russian debt and a short position
in lower‐yielding U.S. debt (which was a hedge against interest rates moving
higher globally and which financed the long Russian position). When Russia
defaulted, no one particularly wanted to buy the billions of dollars of their
debt that LTCM was stuck with. And so, LTCM was forced to liquidate equity positions such as Royal Dutch and Shell to raise cash in a panic.2
It is inaccurate to call the LTCM crisis a quant blowup. To be sure,
some of those who worked at LTCM were quite good at mathematics. But
ultimately, the strategies in which they were engaged, in particular the ones
that caused the most trouble, were not quant trading strategies. They were
engaged in a very broad cross‐border and cross‐asset class yield game in
which they constantly sought to own risky assets and sell safer ones against
them. It was, in most respects, a highly leveraged, one‐way bet on ongoing
stability and improvement in emerging markets and the markets in general.
August 2007 was a far different affair and much closer to home for
most quant funds. Several drivers coincided, leading to disastrous performance among relative‐value‐oriented quant strategies. The causes were the
size and popularity of certain quant strategies, the somewhat poor performance of these strategies for the period leading up to August 2007, the cross‐
ownership of these strategies with far less liquid ones by many players, and
the widespread use of VaR‐like models to target constant volatility.
The first driver of the quant liquidation crisis of 2007 was the size and
popularity of quantitative long/short trading strategies. From 2004 to 2007,
many blue‐chip managers launched quant long/short strategies targeted at

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attracting large pools of investor capital, either large institutions or individual retail investors. The firms launching these products were attracted by
the low turnover and longer‐term investment horizons of long/short strategies, both of which are necessary for the placement of large sums of capital.
Investors were also attracted by the positive returns in quant long/short
products from 2004 through the early part of 2007 and by the blue‐chip
brand‐name managers launching the products. In aggregate, it is likely that
hundreds of billions in cash was invested in quantitative long/short funds
and bank proprietary trading desks, and with leverage, quant long/short
traders likely controlled about $1 trillion in gross positions (the value of
longs and absolute value of shorts added together). The vast majority of
these positions were held in larger‐capitalization U.S. securities because the
large numbers of deeply liquid stocks allowed for sufficient diversification
and size of assets under management to accommodate both the managers’
and investors’ needs. Even though there was actually a great deal of diversity in the underlying models of the various firms launching these products,
enough of them had sufficient overlap to make individual trades get very
crowded.
The second driver of the debacle was that many of these operators had
already begun to suffer subpar returns for a period leading up to the summer
of 2007. Many big‐name funds with a U.S. focus were flat or negative year
to date before August. This is partly because “value” had underperformed
“growth” since at least the end of May 2007, after several years of outperforming growth, as discussed earlier in this chapter. Many multistrategy and
prop‐trading desks also tend to chase recent performance, adding capital to
whatever has been doing well and reducing whatever has been doing poorly.
This tendency, coupled with the weak results of quant long/short trading
strategies for the few months leading up to summer 2007, is likely to have
contributed to especially itchy trigger fingers for risk managers who already
felt the need to reduce risk in their broader portfolios.
A third cause, and in my view a critically important one, was the widespread practice, especially among banks’ proprietary trading desks and multistrategy hedge funds, of either explicitly or implicitly cross‐collateralizing
many strategies against each other. The huge profits enjoyed by hedge funds
and prop‐trading desks before this summer attest to their exposure to credit
spreads that kept narrowing in early 2008. These credit‐based strategies
have historically proven to be far less liquid in a crisis than they appear
during “normal market conditions,” and in July 2007 some credit managers
experienced spectacular and sudden losses. This, in turn, drove them to seek
to raise cash by selling whatever strategies were still liquid. This ATM effect
is the main similarity between the 2007 meltdown and the 1998 situation
described earlier.

Risks Inherent to Quant Strategies

189

The fourth factor leading up to the liquidation was risk targeting (which
we discussed in Chapter 7), whereby risk managers target a specific level of
volatility for their funds or strategies. They hope to achieve this “constant
risk” by adjusting leverage inversely with the amount of risk their portfolios
are taking. The most common tool for measuring the amount of risk in a
portfolio is VaR. As already discussed, VaR measures the risk of individual
instruments (using the variability of their returns over time) and combines
this with how similarly they are trading to each other (a correlation matrix).
With models such as these, risk is computed to be higher when market volatility is higher and/or when correlations among individual instruments are
higher. However, note that these two phenomena can be causally linked in
that markets tend to become more volatile precisely because they are being
driven by a risk factor that also leads to higher‐than‐normal correlation
among individual instruments. In other words, both inputs to a VaR risk
model can rise simultaneously, and these increases can be driven by the same
underlying causes.
The decline in market volatility that characterized the period from 2003
through 2006 led to a dramatic increase in the amount of leverage employed
in a wide variety of strategies heading into 2007 through two channels.
The first was by virtue of the use of risk targeting models for leverage, as
described above. When volatility declined, risk targeting models called for
increased leverage to keep volatility constant. To deliver the same volatility in early 2007 as was being delivered in, say, 2002 or 2003 would have
necessitated increasing leverage by at least one‐and‐a‐half to two times. In
other words, what used to be a four‐times gross leverage strategy had become a six‐ or eight‐times leveraged strategy.
Secondly, when volatility declines, opportunity also declines, and returns
tend to go down. Strategies that had been reliable producers of double‐digit
returns in the late 1990s and early 2000s had begun to deliver low single‐
digit results. Investors and managers both wanted better nominal returns,
and thus leverage went up, even with many shops that did not utilize risk
targeting approaches. However, in summer 2007, particularly in late July,
volatility began to spike dramatically as the credit crisis began in earnest.
This led to a requirement for many players to reduce leverage simultaneously because their VaR models reacted very negatively to the simultaneous
jumps in correlations and volatility.
To review, there were four main drivers of the crisis quants faced in
August 2007: (1) large sums of money invested in value‐based quant strategies with at least some similarity to each other—in other words, the “crowded
trade” effect; (2) poor year‐to‐date performance in quant long/short trading
in the United States; (3) cross‐ownership of illiquid credit‐based strategies
that were experiencing large losses alongside more liquid quant strategies,

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causing the latter to be used as an ATM in a time of crisis; and (4) the decline
of volatility, which led to increased leverage both because of volatility targeting‐based leverage adjustments and the desire to produce higher nominal
returns.
It appears that the crisis started when several large multistrategy hedge
funds and/or proprietary trading desks began to deleverage their portfolios
in response to poor performance in credit‐oriented strategies. In addition,
market volatility was rising, leading to higher VaR levels and therefore lower leverage targets. The deleveraging began with quant long/short trading
in the United States, the most liquid strategy at hand, which also happened
to have been underperforming. Managers sold off their longs and covered
their shorts, causing substantial market impact. The stocks that had been
long positions experienced substantial, fundamentally inexplicable price declines while the stocks that had been short positions experienced similarly
violent price increases. This meant that anyone holding any of those stocks
in the same direction as they had been held by the liquidators saw large,
adverse performance as a result. In many cases, stocks were moving at incredible speed on massively increased volume as quants had to unwind their
holdings.
For example, one crowded short trade was in Pulte Homes (NYSE:
PHM). Exhibit 10.6 illustrates the issue.
This table contains several fascinating pieces of data. Note that PHM
was declining through the early part of the summer on an average volume of 3.5 million shares per day. Then, on July 24, the volume spiked to
7.2 million shares per day, and the stock exhibited an accelerating price decline. Over the next four trading days, however, volumes increased another
50 percent, and there was a huge reversal in the stock, which recovered
about half its 44‐day decline in four days (i.e., the stock was moving about
20 times faster than it had been previously). This also happens to be an
interesting illustration of the quadratic nature of market impact. The first
100 percent increase in volume was absorbed by the marketplace without
a change in the stock’s direction. But the next 50 percent increase seemed
to be on the wrong side of a tipping point in the market’s supply of sellers,
Exhibit 10.6

Pulte Homes, Inc. (NYSE: PHM), May 31 to August 31, 2007

PHM, Summer 2007
May 31–July 23

Price Change (%)

Average Daily Volume

−22.0

3.5 million

July 24–August 3

−12.5

7.2 million

August 6–August 9

+15.6

10.4 million

August 10–August 31

−22.6

5.7 million

Risks Inherent to Quant Strategies

191

and indeed, a trader covering a short position on August 9 was paying as
much as 15 percent in market impact, many hundreds of times the average
cost to liquidate. As soon as the liquidation pressure subsided, which by
all accounts was during the afternoon of August 9, the stock resumed its
downward march, falling almost 23 percent on volumes much closer to the
average prior to the quant liquidation.
Other types of quant traders, such as statistical arbitrageurs, seemed
to provide the necessary liquidity to quant long/short players in late July.
Statistical arbitrageurs usually feast on environments like this, and no doubt
many were happy to provide liquidity as they bet that prices would eventually converge. Many long positions with relatively attractive valuation characteristics were being sold at extremely depressed levels while expensive,
poorer‐quality short positions were reaching ever‐higher prices as a result
of the quant long/short liquidations. These stocks had diverged from their
peers so significantly that they must have appeared to be excellent trading
opportunities to the average stat arb trader, who bets that such stocks will
converge again to a “fair” relative value. But at some point, the stat arb
traders were also experiencing significant losses by taking on the inventory
of other quant funds, inventory that kept flooding the market relentlessly. In
front of this tidal wave, stat arb traders could not continue providing liquidity. As they began to experience losses from having acquired these positions,
they, too, became anxious to go to cash, adding fuel to the fire.
This was likely the tipping point, and suddenly both stat arb traders and
quant long/short traders began to experience significant losses that weren’t
explained at all by fundamentals but purely by a lack of sufficient liquidity.
Thus, by August 7 the situation was starting to get very troubling. A broader
set of strategies, such as statistical arbitrage, was losing money at breakneck
speed and beginning to liquidate alongside the quant long/short traders.
Finally, the dam broke on August 8, with huge losses across many types of
strategies and with these strategies responding by suddenly liquidating in
an effort to preserve capital. Losses began to spread from U.S. strategies to
international strategies, especially those implemented in Japan (which was
at that time the most popular non‐U.S. market for quant long/short and
statistical arbitrage trading).
A wide range of fundamental signals began to lose money as the overlap between the aggregate of all liquidating managers began to overwhelm
virtually any level of differentiation between managers. For the first time
during this crisis, even growth‐based and momentum‐oriented factors began to lose money rapidly. Note that these strategies usually hold opposite
positions from the value‐oriented and mean‐reversion‐oriented strategies.
Thursday, August 9, was pure bedlam in Quant Land. An enormous cross‐
section of strategies, many of which were extremely far removed from the

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A Practical Guide for Investors in Quantitative Strategies

original losers, began to bleed money. Intraday P&L charts started negative
in the morning and literally every minute of the day ticked lower and lower
as a huge variety and number of quant equity funds liquidated positions.
Whereas a few signals had still been working on August 8, in quant equity trading it was hard to find anything except cash that made money on
August 9. It appears that any stock that was attractive for any reason was
being sold down, whereas any stock that was unattractive for any reason
was running up. In short, most quant equity traders had the worst day in
their history, and a great many reduced leverage to extremely low levels,
with many shops going completely to cash.
A bit more should be mentioned about why so many managers reacted in
the same way, namely by deleveraging and liquidating positions. Early August
was a period of exceedingly perverse behavior. Not only were tried‐and‐true
factors not working, they were actually working negatively. And because the
primary discretion employed by a great many quant managers is the decision to unwind positions in the event that the models are behaving badly,
quant managers did exactly that, leading other managers with any overlap
experiencing losses and doing exactly the same thing in response. The losses
incurred, it is important to note, were solely the result of market impact.
One of the clearest proofs of this point is that one large, well‐known
quant firm was suffering like everyone else in early August. On August 9,
in a panic, the firm tried to convene its investment committee to determine
what to do. But several members of the committee were on their summer
holidays, so a meeting was scheduled for Monday, August 13, and in the
meantime the lieutenants managing the portfolio day to day kept the fund
fully invested. As shown earlier in Exhibit 10.6, prices returned to their
previous trends fairly quickly when the liquidations stopped. (PHM, for
example, was down about 12.3 percent by the close of business on Monday,
August 13, merely two trading days later.) As such, by the time the investment committee met, its fund had recovered a huge proportion of its losses,
and the committee elected to hold the course.
Perhaps the greatest irony of the broader situation in August 2007 was
that smaller, more boutique quant traders, engaged in less commonplace
strategies that had minimal overlap with the more conventional and larger‐
scale institutional quants, ended up experiencing losses and liquidating their
portfolios only very late in the game. As alluded to earlier, managers whose
losses began to accumulate only in the middle of the second week of August
ended up needing liquidity at the tail end of an already massive deleveraging. This forced them to pay incredible transaction costs (all from market
impact) to reduce their leverage. Reports of losses at extremely prestigious
funds abounded. The range of losses was wide, from –5 to –45 percent, and
few equity traders emerged unscathed from this event.

Risks Inherent to Quant Strategies

193

What separated August 2007 from prior market crises, even from the
great crash of 1987, was that there was no general market panic during this
period. U.S. stocks were approximately flat for the first 10 days of August,
whereas stocks internationally were down in the small single digits. What
we witnessed in this period was nothing short of a liquidity crisis in the most
liquid stocks in the world, driven by market‐neutral investors whose hundreds of billions of dollars of position selling led not to a market collapse but
to almost no change at all in equity index values. It was a situation where
losses were very heavily attributable to the cost of liquidation and market
impact, rather than simply “being wrong” about the trade to begin with.
This is a fine, mostly academic distinction, but in dissecting the incident, it
bears mentioning. This situation illustrated for the first time that contagion/
common investor risk can appear in liquid quant strategies almost as much
as in illiquid or discretionary strategies. For the first time, crowding became
a risk of quant trading strategies.

How Quants Monitor Risk
Any discussion of quant‐specific risks also merits a discussion of quant‐
specific tools used to target those risks. Chapter 7 described risk models at
some length as models that seek to eliminate or control the size of exposures
in a portfolio. But quants also utilize various pieces of software to monitor
these exposures, their systems, and the kinds of quant‐specific risks we have
discussed in this chapter. There are several types of monitoring tools, most
notably exposure monitoring, profit and loss monitoring, execution monitoring, and systems performance monitoring.
Exposure monitoring tools are straightforward enough. They start with
the current positions held and then group and/or analyze these positions for
whatever exposures the manager is concerned about. For example, in a futures portfolio, if the manager wants to see how much of his portfolio he has
invested in the various asset classes (equities, bonds, currencies, and commodities), this is something he can do with exposure monitoring software. Similarly, one can group instruments by any other set of characteristics that are of
interest, such as their valuation, the level of momentum they have exhibited,
their volatility, and so on. Many equity traders (using either proprietary tools
or off‐the‐shelf software such as BARRA or Northfield) monitor their gross
and net exposure to various sectors and industries, to various buckets of market capitalizations, and to various style factors such as value and growth.
VaR‐based tools also measure exposure in terms of the overall, gross level
of risk being taken in a portfolio, at least according to that measure of risk.
The tools are straightforward, but the art is in how to use them. Experienced

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managers can discern from the exposures in their portfolios whether the model is behaving as it should be. If exposures are out of line based on either limits
or expectations, this can be an early warning that there is a problem with the
model or else problematic market conditions.
Profit and loss monitors are similarly straightforward. They also start
with the current portfolio, but they then look at the prices at which the portfolio’s positions closed the previous day and compare those to the current
market prices for the same instruments. Many managers look at charts of
the intraday performance of their strategies to determine quickly and visually how the day is going. These tools are also important in watching out for
several types of model risk. If the strategy appears to be performing in an
unexpected manner, either making money when it should be losing or vice
versa, the manager can check into the reasons for this anomalous behavior.
Or alternatively, the manager can see patterns in his performance that can
alert him to problems. We alluded to this idea in discussing the performance of various quant strategies during August 2007, when the intraday
performance charts were showing deterioration in the performance with
nearly every passing tick. We know of at least one manager who noticed this
intraday pattern and, as a result, quickly conducted research that enabled
him to reduce his risk much earlier than most, thereby saving him much of
the loss experienced by other traders who only acted later.
Other types of profit and loss monitors look at how money is being
made or lost rather than whether money is being made or lost. For example, quants can analyze the realized and unrealized gains and losses of their
strategies. Many strategies are constructed to cut losing positions quickly
and ride winning positions longer. But if a quant sees that her strategy is
holding losers for longer than usual or selling winners more quickly than
usual, this can be an indicator that something is wrong and needs to be
corrected. This kind of tool also frequently tracks a hit rate, which is the
percentage of the time that the strategy makes money on a given position.
Again, the designer of a strategy usually understands what the hit rate of a
trading strategy should look like, and substantial deviations from the norm
in this metric can be important indicators of problems.
Execution monitoring tools are usually designed to show the quant
trader the progress of his executions. They typically show what orders are
currently being worked and which ones recently were completed, along with
the sizes of the transactions and prices. Fill rates for limit orders are also
tracked to help monitor the execution algorithms’ performance, particularly
for more passive execution strategies. Some managers specifically measure
and monitor slippage and market impact in their order execution monitoring software, which allows them to see whether they are getting the kinds of
results from their execution strategies that they would expect.

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Finally, systems performance monitors are used largely to check for
software and infrastructure errors. Quant traders can monitor any aspect
of their technology, from the performance of CPUs or the speed of various
stages of their automated processes to latency in the communication of messages to and from the exchanges. This kind of monitoring is perhaps the
most important for sniffing out systems errors and some types of model risk.

Summary
Quant trading offers many potential benefits to investors and practitioners.
The discipline, computing power, and scientific rigor brought to bear on the
challenge of making money in a highly competitive marketplace certainly
pay dividends overall. However, quants have their own sets of problems to
deal with. Some of these problems are unique to quants (e.g., model risk),
but most are simply more significant for a quant strategy than for a discretionary one (e.g., common investor or contagion risk, exogenous shock risk,
and regime change risk). Quants utilize various types of tools to monitor
their systems and risk, which can mitigate the downside associated with the
risks of quant trading.
Having discussed the challenges facing a quant trader and how the
quant faces these challenges, we turn our attention to various criticisms of
quant trading that are widely espoused in the marketplace.

Notes
1. The macroeconomic environment around this time, and for some time thereafter, favored companies that are in “growth” industries. During this period,
that meant those positively linked to commodity prices, such as oil companies
or gold‐mining companies, and those in businesses that are less dependent on
economic cycles, such as telecommunications firms.
2. Roger Lowenstein, When Genius Failed (New York: Random House, 2000).

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Criticisms of Quant Trading
Computers are useless. They can only give you answers.
—Pablo Picasso

ecently, and periodically in the past, people have loved to hate quants.
In 1987, a quant strategy known as portfolio insurance was blamed for
the crash that occurred that October. In 1998, people blamed quant models
for the LTCM crisis and the near‐collapse of financial markets. In the summer of 2007, though, it might well be that the tide of public opinion turned
from leery and suspicious to overtly negative. There could be many and
various reasons for this sentiment. Some of the predilection is likely owed
to widespread hatred of math classes in grade school, some of it to fear of
the unknown, and some to occasional and sensational blowups by one or
several black boxes. But, as is the case with many things that are not widely
understood, the arguments against quant trading range from entirely valid
to utterly ridiculous. It is worth noting that almost every type of trading in
capital markets faces valid criticisms. In other words, quant trading, like any
other type of trading, has its pluses and minuses.
This chapter addresses many of the most common criticisms of quant
trading and some of my own. Where relevant, I also present counterpoints
in defense of quants.

Trading Is an Art, Not a Science
The markets are largely driven by humans’ responses to the information
they receive. Not all this information is understandable systematically.
Furthermore, the process by which different people interpret the same

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piece of information is not systematic. If the CEO of a company is fired, is
that good news or bad news? One trader might argue that it shows instability at the highest levels of office and is therefore terrible news. Another
might say that the CEO deserved to have been fired, it was a situation well
handled by the board of directors, and the company is far better off now.
Neither can be proven right ex ante. So, critics of quant trading claim, how
can anyone believe that you can really model the markets? Their critique is
that markets are ultimately driven by humans, and human behavior can’t
be modeled.
This criticism of quant trading is rather backward, reminiscent of the
persecution of scientists such as Galileo and Copernicus for proposing ideas
that challenged human authority. Humans have successfully automated and
systematized many processes that used to be done by hand, from manufacturing automobiles and flying planes to making markets in stocks. Yes, of
course there is still room for humans to make or do various products or
services by hand, but when commerce is the main objective, we typically
see that the efficiency and consistency of automated processes outweigh the
benefit and cachet of doing things manually.
The idea that human behavior cannot be modeled is a bit less easily
dismissed, but it is also unlikely to be true. Consider that quantitative techniques are extraordinarily successful for determining what books you might
like at Amazon.com, in mining data in customer relationship management
software, and in human resources departments seeking to determine which
universities produce the best employees. Obviously, as we have already discussed, there is always the risk of trying to get computers to answer questions that shouldn’t have been asked of them and of building models that
are not good representations of the real world. But in many cases, quant
trading included, it is entirely feasible to demonstrate that something humans do with mixed results can be done just as well by computers: to profit
from trading the markets.
Indeed, when done well, computerized trading strategies have
tended to be exceptional performers over very long periods, as demonstrated by the examples we’ve used so far (Ed Seykota, Renaissance,
Princeton‐Newport Partners, D. E. Shaw, and Two Sigma). In the best
cases, models are merely simulations of the real world, not replications.
So we cannot expect a quant’s models to be perfect, just as we cannot
expect Amazon.com to recommend exactly the right book every time.
However, over time, a well‐designed quant strategy can predict enough
of the behavior of the markets to generate substantial profit for practitioners, as evidenced by the results of some of the quant firms we highlighted in Chapter 2.

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Quants Cause More Market Volatility by
Underestimating Risk
This criticism contains components of truth and of falsehood. Many managers, quants included, are subject to a fundamental type of model risk we
discussed in the last chapter, namely asking the wrong questions and using
the wrong techniques. Techniques such as VaR, for example, make numerous wrong assumptions about the market in an effort to distill the concept of
risk down to a single number, which is a goal that itself seems mostly pointless. Furthermore, as illustrated by the August 2007 quant liquidation crisis,
quants have underestimated the downside risk of being involved in large‐
scale, crowded trading strategies. This, too, stems from a fundamental flaw of
quantitative trading. Computers can be given a problem that is badly framed
or makes too many assumptions, and they can come up with an answer that
is both highly precise and entirely wrong. For example, I can drum up a model
of my wealth that assumes that this book will sell 50 million copies, that I will
receive 50 percent of the proceeds, and that I can then invest the proceeds into
a vehicle that will earn 100 percent per year, compounded, forever. With this
model I can get precise answers to the question of my earnings as far into the
future as I want. However, all of my assumptions are highly suspect, at best.
The computer’s job is not to judge my assumptions, so this kind of error is ultimately attributable to my poor judgment. Similarly, some quants
can be blamed for using quantitative models that are either inappropriate or
badly designed to measure risk. That said, they are scarcely alone in making these errors. Indeed, VaR itself was developed to appease risk managers
and banking regulators who were interested in having a single number to
summarize downside risk, rather than do the difficult and nuanced work of
understanding risk from many perspectives. So, though we accept the criticism that quants can underestimate risk or measure it wrongly, it is worth
understanding that they are not alone. Decision makers in almost every field
commonly manage to underestimate worst‐case scenarios, and when they
do not, it is usually to overestimate risk in the aftermath of a disastrous
event. This is largely because extreme risks are so rare that it is very difficult
to ascertain their probability or the damage they can cause. So, we find that
the statement that quants underestimate risk is likely to be true, but we also
find this to be due more to human nature and the circumstances of rare
events than to something specific in quant trading.
The idea that this underestimation of risk on the part of quants is somehow responsible for an increase in market volatility is, however, plainly ridiculous. First, we have already shown in Chapter 2 that quants tend to
reduce market volatility and inefficiency during normal times. Regardless

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of what happens in abnormal, chaotic times, this fact should not be simply discounted. Second, extreme events have been happening since people
could trade with each other. Preliminarily, we can look at extreme events
in stocks and other asset classes. There were five distinct drawdowns in
the Dow Jones Industrial Average that were worse than 40 percent before
quant trading existed (indeed, before there were computers in general use).
The worst of these occurred during the Great Depression, which brought
with it a drawdown of almost 90 percent in the Dow and which took until
1954 to recover. The last drawdown in stocks before quant trading became
a significant force began in January 1973, reached a nadir of –45 percent
in December 1974, and was not fully recovered until November 1982. The
next severe drawdown in stocks since then was the bear market of March
2000 through October 2002, which was set off by the bursting of the dot‐
com bubble. It is ridiculous to claim that a single one of these events of
extreme volatility or prolonged pain was the responsibility of quant traders.
The same analysis holds for other asset classes. The worst event in recent
history in bonds was Russia’s default in 1998. This impacted some “quant”
firms (though, as mentioned in Chapter 10, I reject wholesale the idea that
LTCM was actually a quant trading firm), but was certainly not caused
by quants. The currency problems in Mexico and Asia in 1995 and 1997,
respectively, were also not the result of quants’ activities. In fact, at the
time a rather famous discretionary macro trader, George Soros, was widely
(though not necessarily correctly) blamed by Asian governments for triggering the latter event.
We can also look at the broader question of how quants are related
to market crises from the opposite perspective. How does a crisis in quant
trading relate to changes in or levels of market volatility? Since we so far
have only one example to work from, we will focus on the events of August
2007. The Dow Jones Industrial Average’s historical volatility did move up
during the two‐week period in which quants were experiencing pain that
summer. However, the Dow’s realized volatility moved from a significantly
below‐average level to a level that is equal to its average volatility since 1900.
From the close of trading on August 3 through August 9, 2007, certainly the
worst part of the quant liquidation crisis, the Dow was actually up an estimated 1.1 percent—scarcely cause for alarm. Implied volatility, as measured
by the VIX index, moved up during this period, from 25.16 to 26.48, but
this is by no means a significant change in its level over a four‐day period.
It would be an impressive stretch of the imagination to attribute any change
in market volatility to quant traders. Indeed, of infinitely greater importance to downside risk in markets and upside swings in volatility levels are
policymakers’ decisions, exogenous shocks (e.g., wars or terrorist attacks),

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basic economic cycles, and run‐of‐the‐mill manias and panics. With that, I
believe that the extraordinary events of 2008 bear discussion.

The Market Turmoil of 2008
While I was writing the first edition of this book in the summer of 2008,
the financial world was suffering through its most challenging environment
since the Great Depression. Stocks endured their second distinct 40‐plus
percent decline in a single decade, and dozens of banks around the world
had either gone bankrupt or been nationalized, including two of the five
largest U.S. investment banks. Real estate prices crashed in many parts of
the world. Several money‐market funds lost all or most of their value. Several of the largest insurance and mortgage companies in the United States
were nationalized or required rescuing. The nation of Iceland was effectively
bankrupted and actually went to Russia to seek a loan. Record‐setting bailout packages and unprecedented, multinational government‐backing measures were enacted in an attempt to stabilize the financial system, which U.S.
Secretary of the Treasury Henry Paulson reportedly told the U.S. Congress
was “days from a complete meltdown.” Most forms of financial activity, in
particular credit, were frozen almost entirely. I raise this example of market
turmoil for two reasons: (1) to evaluate whether quants can be blamed for
it and (2) to discuss how quants have fared. This is not intended to be a
thorough examination of the crisis itself.
It turns out that we can understand a fair amount about what brought us
to that precipice: It was caused by irresponsible banks that lent money without
proper diligence to unqualified consumers who acted with total disregard to
their own financial realities; enabled by ratings agencies that had lost all sense
of independence and objectivity; and regulators who ignored or even exacerbated the problem. Dodgy accounting practices, incredible amounts of leverage,
extreme greed and recklessness among people who should know better, skewed
compensation practices, and lofty egos also played significant roles.
Short sellers and hedge funds were widely blamed for causing the crisis,
and indeed, it does appear possible that irresponsible rumor mongering on
the Internet might have been partially to blame. (Though I have not seen
anyone propose banning the Internet or the kinds of sites that give rumors
such wide audiences.) There is no acceptable excuse for those who spread
such rumors. But let us be clear and explicit: This was an equally irresponsible attempt to divert attention from the real causes and culprits, many of
whom were loudly lobbying for banning short sales and hedge funds.
The facts are unchanged, despite the attempted smokescreen: Many
banks did in fact have toxic balance sheets, uncounted and untold billions

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in losses, and no way to solve the problem. The bailout package passed by
Congress in 2008 approved $700 billion of rescue money, and while that,
coupled with the American Recovery Act and the most benign monetary
policy in American history, was enough to stem the pace of the collapse, it
is clear that the U.S. economy has not come close to a full recovery from
this event four years removed from its occurrence. Furthermore, Europe’s
woes have only recently come into focus, but they are at least equally deep
as those in the United States. Even China appears vulnerable lately. In other
words, this is one hell of a very real mess, not just a rumor‐driven illusion.
Nonetheless, to appease those railing against hedge funds and short sellers,
the U.S. SEC banned all short sales of 799 financial stocks from September
19 to October 8, 2008. During this time, the Financial Select Sector SPDR
(AMEX: XLF), an exchange‐traded fund (ETF) tracking the financial sector,
fell another 23 percent (slightly worse, if we exclude a roughly 1 percent
dividend issued during this period). By contrast, one week after the ban was
lifted and financial companies were again allowed to be sold short, XLF
gained slightly versus its closing price on October 8.
Quants, according to some, are at least partly to blame for the housing
bubble which, when it burst, unleashed all this havoc. How? Nonsensical
arguments have been made1 connecting supposedly quant traders like Ken
Griffin and Boaz Weinstein to the crisis. These arguments have two major
flaws. First, most of those funds that were involved in credit trading are not
traded systematically at all. While both Griffin and Weinstein are good at
math, their investment strategies are fully discretionary. Secondly, even if we
were to call them quants, neither fund’s activities in any way precipitated
anything associated with the real economic crisis that unfolded in 2008.
It is, in fact, pretty close to inconceivable how anyone could think otherwise. The kinds of credit trading and other arbitrage trading that dominate
both Griffin’s Citadel and Weinstein’s Saba hedge funds are busy looking
for trades that take advantage (for example) of mispricings between various
tranches of a company’s capital structure (equity and various types of debt
issuances). The art in these kinds of trades is mostly related to legal and
accounting skills, and there is nothing systematic about them whatsoever.
Citadel has also made a name buying massively distressed assets, as they did
in both the cases of Amaranth and Sowood. Connecting such activities with
quant trading is an obvious mistake. But inferring that they were involved
in the creation of a crisis is like saying the world is round because California
grows good avocados.
Less ridiculous arguments were made about the structured products
boom on Wall Street that was far more instrumental in the crisis of 2008. It
is clear that many parties were to blame for the credit crisis. The stories of
modest income‐earners buying fancy houses with no down payments and

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no proof of financial wherewithal are well known. Regulators and ratings
agencies enabled (and quite possibly ensured) irresponsible lending and borrowing that would power the housing bubble. Here, too, other sources are
better than this book on this topic.2 So where do quants come in?
Structured products did play a role in the crisis, making it attractive
to lenders to provide loans to utterly unqualified borrowers at massively
inflated home values and with little collateral to protect them. This was
accomplished by an abuse of the concept of diversification. The thinking
was that making one bad loan was a bad idea. But making a huge number
of equally bad loans was probably a completely fine idea because, it was
infamously assumed, not all those loans would go bad all at once. In other
words, those who transact in these securities composed of a bunch of loans
were making a convenient, but highly questionable, assumption that there
would be no systemic risk that would cause the loans all to go bad at once.
How the possibility of a drop in home values or a serious recession was
ignored, I’m not sure.
There is a tremendous amount of fairly sophisticated mathematics in the
determination of the pricing of these securities and analyses of their credit
risk.3 The techniques have names like copulas, Lévy models, and saddlepoint
approximations. But as I indicated from the very beginning, quant trading
has little to do with the financial engineering that drives the creation of
structured products, and nothing to do with their promulgation throughout
the investment community. Yes, both quant trading and financial engineering utilize mathematics in the field of finance. However, that is the extent of
the similarity, and it is a microscopic overlap. Quant traders do not originate
securities, show them to ratings agencies, market them to pension funds, and
so on. Financial engineers are not responsible for making forecasts of the
future movements of various financial instruments, nor for executing trades.
Quant traders don’t usually have to think about how to value anything:
The prices of the instruments they trade are generally knowable with a high
degree of certainty, as they are generally extremely liquid and most often
exchange traded.
So quants weren’t a cause of the credit crisis, but how did they fare
through it? In short, better than most. In 2008, many quantitative equity
firms struggled, posting losses in the –10 percent range for the year. But
a great many quants, using statistical arbitrage, short‐term trading, and
even some longer‐term trading strategies, actually made substantial gains.
And in other fields of quant trading, 2008 was a banner year. Quantitative
commodity trading advisors (CTAs) and short‐term traders in various asset classes, in particular, performed rather well through the crisis. But even
if –10 percent was the norm, why should this be considered a particularly
bad outcome, especially compared to the alternatives? Stocks have cut

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investors’ money in half twice in the past decade. Many large, storied
money market funds have gone bust. To my way of thinking, these are
examples of extremely risky investments, not quant hedge funds. And as
just mentioned, it is categorically untrue that quants in general struggled
in 2008.
This is also not the first time that quants have demonstrated good performance in turbulent times. In the last two severe market dislocations, in
the summer of 1998 and in the bear market of 2000 to 2002, quants again
proved to be outperformers. Both periods, in fact, were quite good for a
great many quants, with some having the best results in their histories during these times. Even in the crash of October 1987, most quantitative trend‐
following CTAs posted tremendously strong returns. This isn’t to say that
they are immune from losses or unaffected by market turmoil. The point is
that there seems to be an immense double standard applied to quants compared with more traditional markets and even other hedge funds in terms of
what is considered risky.

Quants Cannot Handle Unusual Events or Rapid
Changes in Market Conditions
This is perhaps the most valid criticism of quant trading. Quants must
rely on historical data to make predictions about the future. As a result
of this dependency, it is likely that quants will suffer any time there is a
significant and sudden change in the way markets behave. It bears repeating and emphasizing that, in order for the event to be of importance to a
quant, the regime change must be both large and without much warning.
Perhaps the most challenging time for quant trading in its known history has been the period from late July 2007 through August 2008. Over
this roughly 13‐month window, quants (particularly those implementing
equity market neutral strategies) faced a liquidity crisis and at least three
separate episodes of substantial pain. You can see this illustrated in part
in Exhibit 11.1.
As you can see from this figure, Value outperformed Growth from
mid‐2004 through early 2007. There was a reversal of this trend beginning
in mid‐May 2007, which accelerated aggressively in late July 2007 and was
a likely cause of the poor performance among quants that contributed to
their liquidation. The trend favoring growth over value from May 2007
to January 2008 is easily seen to be sharper than that which favored value
before May 2007. Many quant strategies had adapted to this new regime
by the middle of the fall of 2007, leading to strong performance in the later
part of that year. But two other periods catch the eye: one in January 2008

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Value-Growth Spread, December 2003 to December 2008
3.5
Value-Growth Spread (Set to 0 at 12/31/2003)

Value-Growth Spread
3.0
2.5
2.0
1.5
1.0
0.5
–

08
12

07
12

06
12

05
12

04
20
1/
/3
12

(0.5)

Date

Exhibit 11.1

Regime Changes, as Indicated by the Value-Growth Spread

and the other in July 2008, both of which are circled in the chart. These two
events were rather violent reversals of the strong trend favoring growth that
began in May 2007. These reversals were among the sharpest in the history
of this spread, and both were substantial periods of downside risk for many
quant traders, particularly those in equities. This is because the prevailing
pattern of behavior, on which the quant bases forecasts of future behavior,
becomes inverted at such times.
It is worth mentioning that, although the significant majority of quant
strategies are negatively impacted by regime changes, a small minority are
able to successfully navigate these periods. Some shorter‐term strategies specifically seek to profit from short reversals of longer‐term trends and the resumption of such longer‐term trends. These counter‐trend traders have been
able to profit in many of the most difficult periods for quants (but certainly
not all of them). Others sit on the sidelines during normal times, waiting for
large dislocations to signal the beginning of a potentially profitable trading
period. This kind of trading is known as breakout trading. Both of these
styles can be found in any asset class or instrument class but are most generally done with futures instruments in the most liquid markets.

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Quants Are All the Same
This argument, too, has been widely held to be true, particularly in the wake
of the disastrous performance of many quants in August 2007. However, it
is a patently false claim, and this I can state with both vehemence and certainty. We will focus again on both theoretical and empirical evidence of this
truth, starting with the former.
This book has outlined many of the kinds of decisions each quant must
make in the process of building a quant strategy. These decisions include the
kinds of instruments and asset classes to trade, the sources of data one will
use and how these should be cleaned, ways to research and develop trading
strategies, the kinds of phenomena being traded, how these phenomena are
specified, ways in which various forecasts are combined, how far into the
future forecasts are being made, how bets are structured, ways in which risk
is defined and managed, how transaction costs are modeled, how portfolios are constructed, and how trades are executed. The number of degrees
of freedom for a quant in building a trading strategy is, in other words,
very large. Though the kinds of phenomena are not very numerous, all the
other considerations are ways the quant can differentiate his approach from
those of others who are ostensibly looking for the same types of anomalies.
Depending on the time horizon of the strategy and number of positions it
takes, the number of trades per year can easily get into the millions. I know
many traders who execute 10,000 to 100,000 trades each trading day. As
you can imagine, small differences in how one arrives at a single trade are
amplified when millions of trades are made in a year.
The empirical evidence is abundant and covers both position data and
return information. At my firm, we have separately managed accounts with
both quant and discretionary equity firms. On an average day, 30 percent of
the quants’ positions are held in opposite directions on the exact same names.
This belies the notion that quants are all the same, especially since only about
75 percent of their positions are even in the same country. In other words, of
the positions held in the same country, about 40 percent are held in opposite
directions by various quant traders. As the number of traders is increased, this
ratio naturally also increases. This has been confirmed by several studies. In
2008, Matthew Rothman, then of Lehman Brothers, produced a study of 25
of the largest quant equity market neutral traders and found that approximately 30 percent of their positions were held in directions opposite those
of someone else in the group, on average, using portfolio data spanning over
a year. Among smaller firms, the differences are even more noticeable. With
a third to half of all potentially overlapping positions held in opposite directions, it is difficult to accept an argument that quants are all the same. If they
were, one quant’s long would not be so likely to be another quant’s short.

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Return data confirm what we see in the position data. I have a sample
of a couple of dozen quant managers’ daily returns (some going back as far
as 1997), and the average correlation of these managers to each other is
0.03. There are only nine pairs of correlations that exceed 0.20, out of 252
pairs in total. And during the heart of the crisis, from September through
November 2008, this correlation was merely 0.05. By contrast, the eight
HFRX hedge fund indices that have daily returns (i.e., ranging from convertibles to risk arb and macro strategies) correlate at an average of 0.21
to each other, and 11 of the 28 pairs correlate at greater than 0.20. Five of
the 28 correlate at greater than 0.40, and the maximum correlation is 0.81,
between the equity hedge and event‐driven styles.
The same basic story is told by monthly return data. Measuring the
correlations of some 53 quant equity market neutral traders with at least
25 months of return history, we find that the average correlation among
them is 0.13. Note that we did not even include quantitative futures trading,
which would reduce the correlation still further. By contrast, 22 Hedge Fund
Research Inc. (HFRI) hedge‐fund‐style indices (excluding the broader HFRI
hedge fund and fund of funds indices and excluding the short‐selling managers) correlate at an average of 0.48 to each other, and these span styles as
diverse as macro and distressed debt. The data are strongly in opposition
to the idea that all quants are the same, confirming what we would expect,
given a basic understanding of how quant trading strategies are actually
developed.

Only a Few Large Quants Can Thrive in the Long Run
I’ve heard this criticism repeated countless times by various observers of the
quant trading world. The argument is reasonable enough at first glance, and
it goes something like this: The largest and best‐funded quants can throw
the most and best resources at every aspect of the black box, from data to
execution algorithms, and can negotiate better terms with their service providers. Based on this premise, it is reasonable to expect that, in the long run,
they will outperform their smaller cousins. Ultimately, smaller quant firms
will fall by the wayside due to either underperformance or investor attrition.
The best shops, furthermore, are so good that they ultimately replace their
investors’ capital with their own, leaving the investor who desires to invest
in quant trading in a quandary: Should she select smaller, inferior shops and
be able to keep money with them until they go out of business? Is it better
to invest in a handful of the biggest quants while that is still possible, and if
they kick out their investors later, so be it? Or is it best to simply avoid this
space altogether, since the two other options are unattractive?

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This criticism and its corollaries are interesting theoretically but ignore
many important facts about quant trading and therefore draw an incorrect
conclusion. First, as evidenced very clearly in August 2007 and throughout
2008, having a large amount of money to manage is not always good, because readjustments to such large portfolios can be extremely costly in times
of stress. In other words, one sacrifices nimbleness while gaining size.
Second, whole classes of very appealing strategies are made impossible
or impractical for the largest quants because the amount of money that can
be effectively managed in those strategies is too small to be worth the effort.
For example, large quants rarely engage in statistical arbitrage in markets
such as Australia or Hong Kong because they cannot put enough money to
work there. High‐frequency trading in any market has very limited capacity and is therefore a very uncommon component of a large quant trader’s
portfolio.
Third, there is reasonable evidence that smaller hedge funds actually
outperform larger funds.3 Some observers believe this is partly because
smaller shops are headed by entrepreneurs who are hungry to succeed
rather than already successful managers who can become complacent or
uninvolved. Regardless, there isn’t a particularly good reason to believe that
the lack of resources any small trader faces, relative to those who are much
larger and trade similar strategies, is any more an impediment for quants
than for discretionary traders. As one small discretionary trader put it, “It’s
not like I’m going to get the first call when a broker has useful information
about a company. I just have to work harder and find things on my own.”
In other words, though there is evidence that smaller managers outperform
larger ones, there is no reason to distinguish smaller quants from smaller
discretionary shops. Both face challenges that larger shops don’t, and both
must find ways to cope with them.
Fourth, smaller managers tend to focus on the kinds of things they
know and understand best, whereas larger managers need to diversify into
areas that are increasingly far from their core expertise in order to grow
to such large size. Most very successful trading strategies have somewhat
limited capacity for capital under management. As such, to build on success,
a larger trader must incorporate other strategies, which might not be at all
similar to the ones in which the original success was achieved. This was
certainly the case with LTCM and Amaranth; it is also the case with more
successful large hedge funds such as D. E. Shaw, Caxton, and Citadel. Some
of these have managed a wide diversity of strategies better than others, but
the evidence in favor of large multistrategy hedge funds is mixed at best.
Fifth and finally, the vast majority of the quality of a quant strategy is
determined by the good judgment and sound research process of the people
in charge. Therefore, it is absolutely the case that one good quant, with

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significant applied science and/or trading experience and sound judgment, is
worth dozens of PhDs who lack these traits.
A related point bears mentioning here: Ever since the Industrial Revolution, there has been a trend toward specialization in all variety of businesses.
In quant trading, this usually means that the bigger firms tend to hire people
with very specific skill sets to fill very specific roles. However, I have seen a
great deal of (admittedly anecdotal) evidence that this may be suboptimal.
Instead of having a mathematician who doesn’t understand software development (or hardware issues, or network optimization) and may not have a
great deal of trading expertise or experience, it may be better to have senior partners whose skill sets span multiple areas relevant to quant trading
(math, computer science, and finance).
There is often a loss of information that accompanies communication
between specialists in one area and specialists in another. It is easy to verify this phenomenon by sitting in any meeting that includes participants
of widely varying backgrounds. The jargon is almost always different, the
approach to communicating can be different, the assumptions are often different, and, perhaps most importantly, the understanding of what problems
can be solved (and what can’t be solved) by people in other fields is simply
not at a high enough level to maximize the efficiency of communication
between specialists of differing fields.
I can distinctly remember my first job in the finance industry as a summer intern in a group that built technology for trading desks. An enormous
amount of energy was expended trying to plug the holes in communication between programmers, statisticians, and traders, and this energy was
often spent in vain. This is not an indictment of that particular group: It
is a well‐known problem endemic to any field that requires expertise from
a multitude of disciplines. On the other hand, a great deal of creativity is
inspired by the application of techniques from one discipline into another.
This is most easily seen in the rise of quant trading itself. Applications of
techniques from computer science, physics, statistics, genetics, game theory,
engineering, and a huge number of other fields have found their way into the
capital markets. Individuals who have expertise in a number of disciplines
obviously have an easier time applying techniques across those disciplines.
I have certainly seen firsthand reasonably compelling evidence that a
portfolio of boutique quant traders can be built that is productive and competes favorably with a portfolio of larger quant managers. There are also a
number of quants who are not among the largest but who certainly have
sufficient resources to tackle many of the same advanced problems that the
largest shops can consider. For example, the smallest firms most often rely
on data vendors, but some small boutiques actually collect and clean their
own data, something that it is widely assumed that only the largest firms can

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do. Both theoretically and empirically, there is little evidence to support the
idea that only the largest quants can survive.
This is not to say that the largest firms are without advantages. Those
pluses outlined at the beginning of this section are certainly valid, for example. But the case in favor of larger quants is far from airtight, and equally
strong arguments can be made for boutiques. The good news is that there
are many hundreds of them from which to choose.
In short, we find that there is no substantial difference in quality between smaller and larger quants. There are some larger quant firms that
invest their resources into better infrastructure. Others may not. There are
some smaller firms that have a great deal of expertise and firepower, despite
their size. Others suffer from the lack of resources. We find that it boils
down to an evaluation of managers bottom up, and that there is no valid
top down evidence that either larger or smaller quants have an advantage
over the other. The evaluation of managers is a topic we will save for the
next chapter.

Quants Are Guilty of Data Mining
Data mining is given a fairly bad name in financial circles. It is used interchangeably with another term that is actually deserving of such negative judgment: overfitting. Data mining is an empirical science, to borrow
again from the framework of the two major kinds of science we discussed
in Chapter 6. Data‐mining techniques are generally understood to use
large sets of data for the purpose of deriving information about what happens without worrying about why it happens. This is the biggest difference
between data mining and theory‐driven science: Theorists are interested
in understanding why something happens in order to believe that they
can correctly forecast what will happen. However, as we already learned,
theorists, too, look to historical data for clues about what kinds of theories might explain what has happened. This is a fine line—fine enough that
it is not entirely clear that there is a valid difference between well‐done
empirical science and well‐done theoretical science. The only discernible
difference is that, in theoretical science, a human is expected to derive an
explanation that seems reasonable to other people, whereas in empirical
science, the method of analyzing data is the primary subject of scrutiny. In
other words, nearly everyone mines data, even if only loosely. This is not
problematic. We would not have heard that cheap stocks outperform expensive ones unless someone had some data to support the idea. If the data
were overwhelmingly opposed to such a statement, no one would espouse
it as a valid approach to investing.

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Data mining is very successfully used in many industries in the broader
economy and society. In the defense industry, data mining is widely used in
terrorism prevention. No doubt you have heard of the U.S. government’s
efforts to scan millions of phone calls and e‐mails for information to help
predict and therefore help stop terrorist attacks. The government does not
have individuals sitting on phones listening into each conversation or at
computer terminals reading e‐mails. Rather, computer algorithms are used
to discern defined patterns that are expected to be fruitful in rooting out
potential terrorist activities.
We have already given several other examples of successful data mining
in this chapter. Amazon.com uses data mining to advise you of what kinds
of books you might like, given what you’ve purchased and viewed. Analytical customer relationship management (CRM) software packages help
businesses maximize profit per contact by mining data on these contacts, to
allow sales personnel to focus on the most lucrative clients and spend less
time on less lucrative prospects. Human resources departments use data‐
mining tools to discern which universities produce the best employees (the
“goodness” of an employee is based on measures of her productivity and
quality). Scientists, too, are heavy users of data‐mining techniques. This is
particularly evident in the field of genomics, where patterns of genetic information lead to linkages between specific genes and human health and behavior. So, it might not be entirely fair to claim that data‐mining techniques
cannot be used on market data, given their wide use and success in so many
social and hard sciences. But, perhaps more importantly, as we showed in
Chapter 3, most quants aren’t interested in data‐mining strategies. They are,
instead, utilizing strategies based on strong underlying economic principles.
Many are very careful about fitting parameters and other aspects of the
quant research process that lend themselves to data mining. In short, data
mining doesn’t deserve as bad a name in finance as it has received, but it’s
largely a moot point since most quants aren’t data mining in the first place.
Overfitting is another story entirely. Overfitting a model implies that
the researcher has attempted to extract too much information from the
data. With a sufficiently complex model, it is possible to explain the past
perfectly. But what is the likelihood that a perfect explanation of the past,
using an overly complex model, will have any relevance to the future? It
turns out that the answer is: not bloody likely. Imagine that we find out that
the S&P 500 dropped an average of 1 percent anytime the Federal Reserve
announced a decision during some period. But we have only a handful of
observations of the Fed making announcements, and all their announcements during the historical period were of the Fed announcing rate hikes.
We could, if we were overfitting, draw a conclusion that Fed announcements
are always bad, and this conclusion would be successful so long as future

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Fed announcements are met with the same reaction as past announcements.
But what happens if the next Fed announcement is of a lowering of interest
rates? It’s very likely the strategy would lose money because it was fitted to
a sample that primarily included rate hikes. Therefore, we should be concerned about overfitting the data.
As an experiment, I set up a new Amazon.com account and idly clicked
on a handful of books of interest to me. The recommendations that came back
were not nearly as good as those that I’m given from my main Amazon.com
account, since my main account is based on a lot of real data, whereas the
new account is based on information from fewer than 20 observations of
my clicking on various titles. The recommendations in my new account are
likely to be overfitted, whereas those in my old account are less likely to be
overfitted.
To estimate a given parameter of a model, one needs rather a lot of data.
Overfitting ignores this basic fact and burdens a limited supply of data too
much, asking it to explain more than is realistic, given the amount of data.
These models are finely tuned to the past, but the moment that the future
is out of step with the past, the model breaks down. In quant finance, the
inevitable outcome of overfitting is losing money. There is no question that,
when it is found, overfitting should be eliminated. But it is a gross and incorrect generalization that all quants overfit their models. Those most likely
to be guilty of overfitting are data‐mining quants. And among data‐mining
strategies, I find that a useful rule of thumb is that shorter timescales tend to
be more amenable to data mining than longer timescales.
First, this might be because there are so many more observations of
trades at short time horizons, and therefore the amount of data available for
analysis is increased. If a strategy holds positions for a year, on average, it
would take hundreds of years to be comfortable with any substantial statistical analysis of the strategy’s returns, because the number of betting periods
is so small. If, by contrast, a strategy trading U.S. stocks holds its positions
for one minute, there are 390 trading periods per day (because there are 390
minutes per trading day) and about 100,000 trading periods per year (because there are 250 to 260 trading days per year and 390 minutes per trading day) per stock. If 1,000 stocks are traded, there are about 100 million
trading periods per year to observe, yielding a great deal more data that can
be mined. Remember, the problem of overfitting arises when the model is
too complicated for the amount of data available. The more data are made
available, the less likely it is that overfitting has occurred for a given level of
model complexity.
Second, at very short timescales it is not clear that theoretical scientists
have yet come up with useful explanations of behavior. A practical guideline
is that, for strategies with holding periods of less than a day, data‐mining

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strategies might be fairly useful. For strategies with holding periods on the
order of a week, a hybrid approach that combines data‐mining techniques
and sound market theory can be useful. Finally, strategies that expect to
hold positions for months or years are not likely to work if they rely on
data‐mining techniques.
Overfitting models is not only possible, it actually happens among some
quant traders. But just as we do not reject analysis because some people are
prone to overanalyzing things, we should not so quickly dismiss quantitative modeling (even data mining) just because it is possible (or even easy) for
some people to do it badly.

Summary
Quant trading is no elixir, and certainly there are quants who are guilty of
each or all of the criticisms discussed in this chapter. Some do bad science,
underestimate risk, and lose money when market conditions change suddenly.
Some implement strategies that are commonplace and crowded, and some
overfit their models to limited amounts of data. But most of these criticisms
are equally applicable to discretionary traders. Done well, quant trading can
produce superior risk‐adjusted returns and substantial diversification benefits.
So, what does it mean to do quant trading well? We will cover this
topic in depth in the next chapter, but let’s recap some salient points from
this chapter: Quants must be concerned with falling prey to the temptation
of false precision, particularly in risk management. A printout with a risk
number on it does not imply that the number is accurate or has been properly derived. Quants must also remain aware of relationships within the
market and must have a detailed understanding of the kinds of bets they are
making and how they are expressing these bets in their portfolios, allowing
them to navigate violent regime changes. Quants must conduct innovative
research in alpha modeling and across the entire spectrum of the black box,
to reduce the risk that there is substantial overlap between their models and
those of their peers. Finally, to the extent that data mining is explicitly utilized, it should be done in a manner that does not express overconfidence in
the amount and predictive power of historical data.

Notes
1. Scott Patterson, The Quants (New York: Crown Business, 2010).
2. For starters, the Wikipedia entry entitled “Causes of the United States housing
bubble” gives some good color both on the regulatory and other sources of the

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problem. Another entry entitled “Collateralized debt obligation” gives a good
introduction to the structured products that allowed for all those bad loans to
be made.
3. An interesting, but technical, primer on this topic, along with a quant’s rebuttal to the idea that even financial engineers deserve any blame is provided by
Damiano Brigo. A presentation can be found at: www1.mate.polimi.it/ingfin
/document/Crisis_Models_Mip_16_giugno_2010_Brigo.pdf. Credit Models and
the Crisis: A Journey into CDOs, Copulas, Correlations and Dynamic Models, by
Damiano Brigo, Andrea Pallavicini, and Roberto Torresetti (Hoboken, NJ: John
Wiley & Sons, 2010), goes into more depth on this topic.
4. A study by Pertrac, the hedge fund industry’s leading database and performance analytics provider, was cited by the Medill Reports’ John Detrixhe on
August 14, 2008. The article can be found at http://news.medill.northwestern
.edu/washington/news.aspx?id=97223.

Chapter

Evaluating Quants and
Quant Strategies
. . . talent means nothing, while experience, acquired in humility
and with hard work, means everything.
— Patrick Süskind

n this chapter we discuss methods of assessing quant strategies and practitioners to separate the good from the mediocre and the mediocre from
the poor. As I have said throughout this book, a great deal of the work that
quants do has very natural analogues in discretionary trading. There are
also significant parallels in the work of a quant trader to the work of a corporate CEO or any other person involved in the allocation of resources. In
this regard, the framework presented in this chapter can be used successfully
to judge the work of such decision makers. Indeed, one person I trained in
this method of assessing quants has adapted it for trading credit markets
and now uses the same method to provide a framework for judging the
merit of various corporate bond offerings and the companies behind them.
The first challenge an evaluator of quants faces is to pierce the walls of
secrecy that quants build around their methods. Though it is fair to say that
quants are often secretive, I have had a rather different experience. The vast
majority of quants I have evaluated—and there have been many hundreds
of them—have been willing to answer most or all of my innumerable questions. The difference is due, at least in part, to the questions we ask at my
firm. It also owes to how we ask these questions and how we handle the information we learn from quants. In the next section, I describe the principles
of my approach to interviewing quants.
Armed with the techniques described in this chapter, the evaluator of a
quant has two goals. The first is to understand the strategy itself, including

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the kinds of risks it is taking and from what sources its returns are generated. This is important because it tells the investor what she owns when she
is investing in a given quant strategy. The second goal in the evaluation of
a quant is to judge how good the practitioners themselves are. In many respects, a quant trading team is much like an engineering team at an automobile manufacturer. It is fine for the team to build one great engine, but over
time, that engine must be improved. As times change, the engine might even
need to be redesigned entirely, or other types of engines might need to be
designed for other vehicles. It is critical to ascertain whether the quant team
is skilled at designing engines, evolving them, and designing new types of
engines over time. All these components of the analysis of a quant ultimately
serve to help the evaluator answer perhaps the most central question in the
evaluation of any kind of trader: Why should I believe that this particular
team, utilizing this particular strategy, is actually likely to make money in
the future? In hedge fund parlance, what is this manager’s edge?
Assuming that the investor finds a team and strategy worthy of investment, he must ascertain the integrity of the people involved. After all, skill is
a good thing only if it is in the hands of good people. Here I briefly address
some thoughts on how to judge the integrity of a trader, although this is not
central to quantitative trading. Finally, I provide a few brief thoughts on
portfolio construction using the frameworks provided in this book.

Gathering Information
How does one actually go about finding out what a particular quant does?
Quants are notorious for their secrecy and paranoia. And this is not without reason. Much of the skill of quant trading comes from experience and
know‐how, not from raw mathematical superiority. There is an excellent
book called The Interrogator, by Raymond Toliver, from which many useful
lessons can be learned on how to get information from a quant.1 The book’s
subject is Hanns Joachim Scharff, a former World War II Luftwaffe interrogator who succeeded at gathering information from downed Allied pilots
without the use of any physical force or psychologically stressful techniques.
Instead, Scharff used three major tools: trust building, domain knowledge,
and an organized system for tracking and retrieving information.
Before detailing Scharff’s techniques, I want to stress that I am no fan
of wars or interrogations, nor does the relationship between investor and
quant manager closely resemble the relationship between interrogator and
prisoner. But there is one similarity, I believe, that allows lessons from the
latter to be useful in the former: In both cases, information that one party is
reluctant to provide is needed by the other.

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217

The first technique Scharff used is also the most obvious: He built trust
with the pilots he was interviewing. In fact, Scharff remained friends with a
great many of them after the war, and they seemed universally to respect and
like him. Turning to the quant, trust comes in part from building relationships, but a big chunk of it relates to the behavior of the interviewer. If an
investor asks a quant for sensitive information and has either a reputation
for talking, or an actual propensity to talk about what other quants do, it is
less likely that the quant will or should trust this investor. After all, whatever
the quant tells him is likely to get spread around the industry. At my firm,
we hold quant managers’ strategies in the strictest confidence. Often a quant
will ask us what some other quant does. Our answer is universally and always that we will not discuss what others do, just as we do not discuss what
the quant who asked us does. However, we’ve heard numerous stories and
witnessed numerous firsthand examples of investors or managers passing
along even reasonably proprietary bits and pieces of a quant’s strategy to the
industry. This is an ugly practice.
The second lesson from The Interrogator is that it is hard to feel particularly justified in being secretive with information if the person asking questions already knows most of the possible answers. For example, Scharff knew
the name of the pet dog at the home base of one pilot and the names of most
of the pilot’s colleagues. His goal in a given interview was to learn just a little
bit more about his prisoners and their activities. They were frequently lulled
into thinking that there was no point in keeping secrets, since their captor
knew so much already. Though this never led to blatant tell‐all behavior, it
certainly allowed the interrogator to amass huge amounts of value from the
interviews, a little at a time. It is possible to learn a similarly voluminous
amount about quant trading without asking any particular quant to teach
it to you in a meeting. This is helped along by the fact that most of what an
investor needs to understand about a quant can be learned without compromising proprietary information. In this book, for example, we have outlined
a great majority of the kinds of approaches quants use. None of this information is especially proprietary to any trader. A quant with any hope of being
successful knows most of the material in this book already. In a sense, this
book provides you with a great portion of the menu available to a quant.
There aren’t many dishes he can choose that aren’t on this menu, which obviates the need for most of the secrecy. The investor can, in this way, learn about
the specific items on the menu that the quant being interviewed has chosen
and why these choices were made. For instance, understanding the kinds of
alpha models the quant is using, whether they are relative or intrinsic, how
fast he trades, and in what instruments and geographies tells the investor a
great deal about what risks are being taken. This information is necessary for
building a diversified portfolio and is largely sufficient for that exercise.

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The third and final lesson of The Interrogator is to be organized in the
management of information when it is gathered. This greatly supports efforts to get new information but is also useful in ongoing evaluations of the
quality of a given practitioner. Scharff’s group developed a sophisticated,
almost relational database system using index cards and a card catalogue
file. (Remember, this was before the computer was invented.) As they got
new information, they would organize it by linking it to other relevant cards
in the file. For example, if they found out the name of another pilot from
a given American base, they would tag that card with references to all the
other information, including other pilots, from that base. This way, as they
were interviewing a given pilot, they had a dossier that contained an impressive and extensive array of details, well organized and easy to access. These
days we have powerful computers and databases to rely on, making such a
job easier.
Keeping information organized furthers the goal of developing deep domain knowledge, but it is also quite useful in ascertaining the “goodness” of
a quant team over time. If every three months you ask a quant, for example,
what types of research projects he is working on and what new pieces he
has added to the model over the past three months, over time you should
see a rational life cycle that repeatedly takes a robust research pipeline and
turns it into implemented improvements to the strategy. If the quant has a
process wherein modules that were not part of the research list from the
past suddenly appear in production, this could be evidence of sloppiness in
the research process. When visiting a quant’s office, it is useful to ask to see
firsthand some of the various tools and software that the quant claimed to
use or to have developed in previous discussions. But, even to know that you
should be asking to see something specific, you already had to have carefully
managed the information about the nature of these tools and software.

Evaluating a Quantitative Trading Strategy
In my years of evaluating and creating quant trading strategies, I have noted
an extraordinarily interesting fact: The work that a quant does is, in most
ways, identical to the work that any portfolio manager, any CEO, or any
other allocator of resources must perform. After all, these resources (e.g.,
time or money) are limited and must be invested in a way that results in
maximum benefit. The process used to invest resources—the investment
process—contains six major components:
1. Research and strategy development
2. Data sourcing, gathering, cleaning, and management

Evaluating Quants and Quant Strategies

3.
4.
5.
6.

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Investment selection and structuring
Portfolio construction
Execution
Risk management and monitoring

You may note that these activities are closely parallel to the modules of
the black box and the activities in and around its construction and management. This is because all these areas must be addressed in order for a quant
trading program to function properly over time. One fact about computers,
which we’ve mentioned already, is that they do not do a good job of thinking about things you might have missed. As quant trading programs have
evolved over time, they have had to address the myriad decisions that any
portfolio manager must address. Too often, in discretionary management
activities, important aspects of this process are left without sufficient analysis, and an ad hoc approach is taken. I’ve interviewed scores of discretionary
stock pickers who can spin tremendous yarns about why they are long this
stock or short another. But when asked how they decide how to size these
positions in their portfolios, the answers are often vacuous, given without
deep thought or analysis.
Those charged with evaluating managers must thoroughly examine each
of these areas. And quants, in general, should be willing to answer questions
about each. A few examples of the kinds of questions I ask a quant follow:
Research and strategy development
How do you come up with new ideas for trading strategies?
■■ How do you test these ideas?
■■ What is your approach to fitting the model, as well as your approach
to in‐sample and out‐of‐sample testing?
■■ What kinds of things are you looking for to determine whether a
strategy works or not?
■■ Data sourcing, gathering, cleaning, and management
■■ What data are you using?
■■ How do you store the data, and why that way?
■■ How do you clean the data?
■■ Investment selection and structuring
■■ Can you describe the theory behind your alphas?
■■ Which types of alpha are you using (e.g., trend, reversion, technical
sentiment, value/yield, growth, or quality)?
■■ Are you making relative bets or directional bets?
■■ If relative, what does relative mean, exactly?
■■ Over what time horizon, and in what investment universe, do you
apply your alpha model?
■■

■■

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How are you mixing your various alpha models?
Portfolio construction
■■ How do you do portfolio construction, which is to say, how do you
size your positions?
■■ Are there limits, and why did you set them that way?
■■ What are the inputs to your portfolio construction model?
■■ What are you trying to achieve with portfolio construction (i.e., what
is your “objective function”)?
■■ Execution
■■ What kind of transaction cost model are you using, and why did you
choose to model transaction costs the way you did?
■■ How are you executing trades—manually or algorithmically?
■■ Tell me about your order execution algorithms: What kinds of things
did you build into them (e.g., hidden vs. visible, or active vs. passive)?
■■ Risk management and monitoring
■■ What does your risk model account for, and why those things?
■■ What are your various risk limits, and why did you set them where
you did?
■■ Under what circumstances would you ever intervene with your model?
■■ What are you monitoring about your strategy on an ongoing basis?
■■

■■

This is but a sampling of the hundreds of questions I ask a quant. If he
claims that the answers to such questions are proprietary, I do not simply
accept that response. Rather, I try to ascertain why he thinks the answers
are proprietary and try to make him understand why I need to know.
Most quants I have met are sympathetic to the goals of an investor trying
to understand whether that trader’s approach and the commensurate exposures that it yields are beneficial to the investor’s portfolio’s exposures
and whether the quant is skilled at his work. In other words, the overall
justifications for all the questions one needs to ask about a systematic
trading strategy are as follows. First, the investor must understand what
the strategy is, in order to ascertain whether it is desirable for his portfolio
to be exposed to the strategy’s risks. Second, the investor must ascertain
whether the manager implementing the strategy is actually doing it well
enough to deserve an allocation of capital, which we address in the next
section. Success in the endeavor of evaluating quants ultimately is driven
by building trust, having domain knowledge, and being organized in the
management of information. As I’ve said, the menu of things that quants
can choose to do is reasonably easy to know. It is largely laid out in this
book, and I am certain I’ve revealed nothing proprietary. A quant generally should not claim that he cannot disclose which items he has chosen
from this menu.

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221

The investor has one more tool available for understanding a quant
strategy, and that is the footprint left behind by the strategy: its return history. Imagine that an investor learns, by asking questions such as those I’ve
listed, that a quant is using a trend‐following strategy on various individual
instruments, with a six‐month average holding period. When long‐term
trends are present, the strategy should do well. When longer‐term trends
reverse, the investor should see the strategy do poorly. In other words, the
strategy’s return pattern should corroborate the fundamental understanding
that the investor has gained by asking many questions.

Evaluating the Acumen of Quantitative Traders
If I have tried to stress anything in this book, it is that the judgment of
a quant trader pervades the strategy she builds. So, an evaluation of the
quant’s skill and experience in the fields relevant to the trading strategy
is obviously important, but it is also easier said than done. This section
outlines a few tools that can be used to determine the skill level of quant
traders.
The people developing and managing quant strategies should be well
trained in the methods they use. At least some members of the team should
have substantial live experience in areas of quant trading relevant to the
strategy they are currently pursuing. Experience helps drive good judgment,
especially in light of the massive array of subtleties and traps inherent in the
process of research and trading. From a dispositional standpoint, quants
should be careful and cautious in their analysis, and they must be humble
about their ability to predict the future. There are considerable hurdles to
doing quant trading well, such as polluted data and constantly improving
competition. A good quant does not underestimate such challenges, nor
does she overestimate her ability to meet them. The reality is, however, that
evaluating whether scientists know what they are talking about at a deep
level is not the easiest task for someone who is not technically proficient. As
such, to make a judgment, one may have to rely on the quant’s qualifications
and experience, reputation, history of success, and analyses of the investment process. Although this is a lot of work, the task is doable for those who
want to undertake it.
One of the handiest tricks I know of to evaluate a quant’s skill is to dig
deeply into the details in a few areas of her process. Why? The difference between success and failure is very commonly found in a large number of highly
detailed decisions. If the mechanism used to make these decisions is flawed,
the manager has little hope of success in the long run. Thus, an analysis of the
investment process, and by extension its six major components, is focused on

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understanding what a quant does and, just as important, why the quant does
it. As we discussed throughout this book, a number of approaches to quant
trading can deliver acceptable risk‐adjusted returns. Momentum and mean
reversion strategies can both work, even though they are opposites. Both intrinsic alphas and relative alphas can work. So it is important to understand
what a trader does, but why she does it tells you about her judgment, her
process, and her potential for future success.
Each decision a quant makes in how she builds a strategy represents
a source of potential differentiation from other traders, but also of potential success or failure. And it makes sense that this should be the case.
Many quants have large numbers of positions, frequently in the thousands,
and most engage in strategies that turn these positions over relatively frequently—from once every few minutes to once every few months. If 5,000
positions are turned over once a week, for example, this represents about
260,000 individual trades per year. Now imagine two equity traders, Trader
A and Trader B. They have remarkably similar strategies, even in the details,
and they each manage $500 million. For each dollar managed, they put on
$2 of long positions and $2 of short positions so that each trader has a portfolio of $2 billion. Each turns over about 20 percent of her portfolio per day,
or $400 million in dollar volume each day. They each average 10 percent returns per year. If Trader A is later able to optimize her executions such that
she makes 0.01 percent more per dollar traded than she used to—either by
being faster or reducing transaction costs or improving the alpha model—
this results in Trader A’s annual return improving to 12 percent per year.
This is 20 percent, or $10 million per year in profits, better than the result
generated by Trader B, which is an enormous difference when compounded
over time. Though some quants certainly do things that are plainly incorrect at a high level, the judgment of the quality of a given quant most often
comes down to her decisions at a fairly detailed level.
Another reason that the details matter so much is that there is really
only a tiny amount of predictability in all the movements of the market.
Quants often depend on being right only slightly more often than they are
wrong and/or on making only slightly more on winning trades than they
lose on losing trades in order to generate profits (though trend-following futures strategies tend to lose as much as 70 percent of the time, with dramatically larger payoffs on the winners than the losses suffered on the losers). As
such, small decisions that affect the probability of winning only slightly or
those that skew the size of winning trades versus losing trades slightly can
dramatically impact the outcome over time.
Finally, if the quant has given deep and well‐grounded thought to the
details of the few areas that you spot‐check, it is more likely that she has
given deep thought to other areas of the quant trading process. This, too,

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improves her probability of success in the future, since we have shown that
rigor is a key component of success in quant trading. Though it is likely obvious enough already, I want to make it clear that the fact that a quant has
a PhD in physics (or anything else) is no indication of quality or skill. Some
of the brightest and most successful quants have no advanced degrees, and
some of the biggest failures in quant trading have won Nobel Prizes.
The flaw in this plan of focusing on the details of a quant strategy is that
such details are unlikely to be revealed to an investor during due diligence.
Though the higher‐level topics discussed in the section entitled “Evaluating a Quantitative Trading Strategy” might be relatively uncontroversial to
discuss, the details are not. As I mentioned earlier, it is frequently the details
that separate the best traders from the mediocre ones, and these details often
boil down to know‐how more than, say, better math skills. So, quants are
and probably should be somewhat more reticent to provide such details.
Even if they were to provide details, the investor would have to be knowledgeable and proficient enough to pass judgment on them. In other words,
to try to divine the quality of a quant’s system from clues about its particulars requires significant experience on the part of the quant investor. After
all, just as I require experience in my traders, I also benefit from experience
in judging them. A great many things that seem plausible enough at first
glance simply don’t work. For example, just because a quant pays a lot of
money to a data vendor for clean data, it doesn’t mean that the quant should
actually rely on the cleanliness of that data. The saving grace for the nonquantitative investor seeking to evaluate a quant is thoroughness and strong
information management in the assessment and due‐diligence process.

The Edge
In assessing a portfolio manager, including a quant, a key issue to focus on
is the idea of an edge. We define an edge as that which puts the odds in favor
of the portfolio manager succeeding. An edge can come from three sources,
listed here in order of commonness:
1. The investment process
2. A lack of competition
3. Something structural
In investing and trading, an edge is not the same thing as a competitive
edge. A trader might have absolutely no competitors, yet still manage to
lose money. I’ve seen it more than once. An investment edge is thus more
intrinsic than comparative. Still, competition does matter: A valid idea with

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a valid implementation might make little or no money if there is too much
competition, whereas a mediocre strategy might make money if there is
none. As such, one must ascertain the sustainability of a given trader’s edge.
The odds might be in the trader’s favor today but against him tomorrow as
the world changes or as competition increases, if the trader does not evolve.
An investment process edge must come from one or more of the six
components of the investment process we just outlined. Too often, when
asking a discretionary stock picker what his edge is, we hear him say, “Stock
picking.” But this is merely an invocation of the activity, not evidence that
this particular trader is any good at it. One must dig further into the reason
that the trader claims to have an edge in any of these activities. For quant
traders, most often an investment edge comes from experience and skill
in conducting research and/or the acquisition or cleaning of data. This is
because the goodness of the models for investment selection and structuring, portfolio construction, execution, and risk management is usually determined by the quality of the research and development process that created
them. If some modules have not been particularly well researched, there is
almost no chance that the trader will have an edge in these areas. An edge
in research can derive from superiority in talent or process, but actual experience in conducting successful research in the financial markets is usually
critical. In other words, one must have better people and/or a better process
to put around these people, but in either case experience is needed.
I have already described a bit about how to assess the people at a quant
shop, but one more point bears mentioning. How a quant deals with adversity is critical to understanding his edge and its sustainability. There are
times when the model simply doesn’t make money. Knowing how and when
to react to these episodes is critical. By analogy, an inexperienced or inferior
pilot might decide to emergency‐land his plane along the way to his destination because of a little unexpected turbulence. This is clearly a bad outcome.
By contrast, take the example of Chelsey Sullenberger, the former fighter
pilot who was at the helm of US Airways Flight 1549 when it had an in‐air
collision with a flock of geese about three minutes after takeoff. The plane
lost power from both its engines. Sullenberger recognized that there would
be no opportunity to land the plane safely along its planned southbound
route and decided to turn north to land the plane in the Hudson River. The
155 passengers and crew were all safely evacuated, and even the airplane
was found more or less intact.
The analogy is not a bad one. An inexperienced quant may abandon a
model after a little unexpected adversity. He may liquidate a portfolio or
reduce its leverage drastically. Then, just on the basis of a small window
of observation in which the model is performing better, he may allow the
portfolio to accumulate positions again. But, as we’ve seen, transacting is

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expensive, and occasionally it leads to repercussions (as in the case of the
August 2007 quant liquidation and the Flash Crash of 2010). Too often
quants react in a suboptimal manner to losses in their funds, and a knee‐jerk
reaction can often ruin whatever edge the strategy itself has. At the other extreme, a quant may not recognize when a generally valid strategy is simply
on a crash course with total failure. One could argue that LTCM’s biggest
mistake was forgetting Keynes’ admonition that the markets can remain
irrational longer than an investor can remain solvent. There is a balance
between sound fiduciary caution and being hyper‐sensitive to every bump
in the proverbial road. A sound approach to managing adversity starts with
good monitoring tools, which allow the quant to pinpoint problems and
work to solve them rather than panicking. It is unlikely that a trader has an
edge because of monitoring, but it is easy to throw away a potential edge
through insufficient or badly conceived monitoring processes.
In terms of research, there are several hallmarks of a high‐quality process. The process should be vigorous and prolific, and there must be an ability
to translate models efficiently from research into production. This is because
most quant models eventually decay into mediocrity, and successful ongoing
research must be implemented in live trading strategies to stay ahead of this
decay. The research process should also deal with issues such as overfitting
and look‐ahead bias, and the evaluator should ascertain exactly how the
quant thinks about and deals with these critical issues. Finally, the process
should at least largely follow the scientific method. In evaluating a quant
trader, it is useful to ask many questions about how and why various elements of their strategy are the way they are. If a manager says he will close
a position if it has moved 10 percent against him, ask him how and why he
decided on 10 percent rather than 5 percent or 50 percent. If the quant says
he is running a trend‐following strategy in certain markets, find out why he
picked a trend‐following strategy, how he defines the strategy, and why he
is using the markets he’s using rather than other or simply more markets.
These kinds of details will give you insight into the care with which a manager has developed the entirety of an investment strategy.
A data edge can come from having proprietary access to some sort
of data. Earlier in the book we gave the example of a company that uses
geolocational data derived from GPS signals on cell phones to aggregate
macroeconomic indicators that have far less lag than the typical kinds of
figures released by governments. If, in fact, these data prove useful, they
might be able to trade using this information, and they might then have a
data edge. But in this era of technology and regulation, it is difficult to find
sustainable data advantages. These advantages eventually are competed or
regulated away. It is also possible to build a data edge through superior
data gathering, cleaning, and storage techniques. These are, in principle,

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more sustainable. Again, an interviewer should ask questions about where a
trader gets his data, what work is done to clean the data, and how and why
the data are stored in a certain way. Some answers will be thoughtful; others
could indicate carelessness.
This kind of data edge is quite similar to a lack‐of‐competition edge. But
lack of competition is not a long‐term plan. It is a truism in economics that,
if higher‐than‐average profit margins can be had in some activity, more and
more players will compete until the margins compress and normalize at levels more typical in the broader marketplace. This is likely to have happened
already in at least two quant trading spaces: quant long/short and statistical
arbitrage. In each of these two cases, a small number of practitioners enjoyed
very little competition for some years. And these years produced excellent
results. But excellent results attract a lot of attention and tend to generate
a diaspora of lieutenants who form their own competitors to the original
practitioner. As competition increases, the margins decrease and eventually,
these strategies can even look “dead.” But rather than dying, they have simply become cyclical. Thus, there are periods when players vacate the space
because it offers too little reward, leaving more of the pie (and therefore
better margins again) for the fewer players who remain. This cycle repeats.
In any event, in evaluating a strategy that is supposed to be without
competition, it is also important to ascertain why there is a lack of competition. Some strategies are inherently more difficult for new entrants; others
simply have not yet attracted the attention of new entrants. An example of
the former, at least historically, can be found in purely quantitative options
trading. This is not widely pursued because there are significant challenges
associated with acquiring and cleaning data, structuring trades, and modeling the liquidity of options contracts. But this by no means implies that it
cannot later become a crowded strategy with many competing firms chasing
an ever‐shrinking pie.
As an example of the second outcome, I remember an experienced team
that formed a hedge fund to trade corporate credit in Asia back in 2002.
They had successfully carried out this strategy as proprietary traders at a
bank for several years previously. They had few, if any, competitors, and
their early years were very strong. Then, as time passed and more entrants to
their niche crowded the field, they had to branch into other areas that were
less appealing. Over time their edge, which was largely related to a lack of
competition, was eroded. Ultimately, the new areas into which competition
forced them to participate caused a massive drawdown in their fund. The
lack of competition was really due to a lack of discovery of their niche, and
these are among the most fleeting kinds of edges.
Structural edges generally relate to something in the market structure
that puts the wind in the sails of a market participant. These are usually

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caused and removed by regulation. I once knew a trader in the pits of the
New York Mercantile Exchange who ran a hedge fund that relied on his
short‐term discretionary trading. Because of his status on the exchange, he
was able to supplement a reasonable investment edge with a structural edge
that allowed him to transact very cheaply and extremely quickly. Over time,
however, his markets went from being pit‐traded to electronic, and his structural edge vanished. In quant trading, the most common sort of structural
edge comes from liquidity provision, or the rebate, on electronic communication networks (ECNs). ECNs actually pay market participants for market‐making activities by providing commission rebates. In certain cases I
have seen the act of transacting become a profitable exercise for the trader,
and this too is a structural edge. It is possible that, over time, payments by
ECNs for order flow will dwindle, and this edge, too, will be eradicated.

Evaluating Integrity
Most quants, and most traders in general, are honest and ethical. Therefore,
it is entirely reasonable to work with them on a “trust, but verify” basis. In
other words, for most of the evaluation process it is reasonable to assume
that the trader went to school where she claims, got whatever degree(s) she
claims, and is generally not a criminal. But before making an investment,
most observers would agree that to the extent possible, it’s worth verifying
a quant’s ethics.
Here we have a few tools at our disposal. First, do background checks,
education verifications, and reference checks. In the case of backgrounds
and education verifications, serious problems in a trader’s personal or professional history should probably serve as a red flag. Of course, this is a
tricky proposition. The investor must determine whether the mistakes or
misdeeds in a quant’s past served to teach her a lesson, or whether they
indicate a likely pattern of behavior that will repeat, even if not in exactly
the same way. That judgment cannot be made universally for all cases. But
I encourage the investor to consider this question only from one specific
angle, which might help drive the answer: The job of the investor is not to
judge the quant as a person but rather as a potential fiduciary, acting on behalf of the investor. Fiduciaries are bound to act in their clients’ best interest
and to be very open and up front about any potential conflicts of interest
or anything else that could impede their fulfilling their duties to investors.
Using the mentality of the fiduciary as a compass is something I have found
helpful in a great many difficult circumstances.
When performing reference checks, I find it useful to request references
from existing investors whenever possible and to ask them not only why

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they like the manager but also what they think her weaknesses are. More
helpful still is to seek out references that the manager did not provide herself. It is relatively easy for any trader to find a few people to say something
nice about her. But it is much better if the trader is known by others, and
those others are likely to provide much more useful input than the references a trader provides for herself. If you cannot locate such references in
your own network, it sometimes helps to ask the references provided by the
manager whether they know anyone else you can contact.
It turns out that getting into details with quants helps demonstrate their
integrity as well. Though even less skilled quants might have answers at hand
for higher‐level questions about their strategies and process, even someone
intent on deceiving rarely thinks through low‐level details sufficiently to
be facile in answering questions about them. This is a common and successful interrogation technique in law enforcement. If you ask a suspected
criminal where he was last night, it’s not surprising to hear him quickly and
convincingly provide an alibi, such as “at my girlfriend’s house.” But if you
follow up by asking what time he arrived, how long he stayed, what movie
he watched, what he ate and drank while he was there, and so on, he will
have to make up answers to these questions he likely has not rehearsed
beforehand.
A quant who is lying to cover up a lack of skill would have to be an
expert at making up answers to questions about details on the fly to keep up
with questions about the details of her strategy. And some people are very
good liars, to be sure. However, these answers also have to be able to stand
up on their own. Answers that reveal a lack of understanding of the subject
matter or answers that are internally inconsistent or are deficient in other
ways should not be ignored. They might not lead you to conclude that the
manager lacks integrity, but they should be sufficient to conclude that she
isn’t very good, which is itself sufficient for the purpose of avoiding hiring
her. What’s more, you can use the same technique of looking for details in
assessing a quant’s background as in assessing her strategy. If a quant says
she completed her PhD at Harvard, you can follow up by asking where she
lived while she was there, what her favorite restaurants were, who her dissertation committee included, what her dissertation’s title was, how many
pages it ended up being, and so on. And again, some of these specifics should
be verifiable with her alma mater.
It is worth mentioning one more point about selecting managers,
whether quant or not: Almost no trader is so special that it is worth investing in her strategy without gaining a reasonably deep understanding of it.
It should not take much to say no, in other words, whereas it should take
an incredible amount of confidence to say yes. Seeing a long and attractive
track record should never be sufficient. In fact, I would put forth that it is

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significantly more important to get good answers to good questions than to
see a long track record. If Bernie Madoff and the other scandals that were
announced on a nearly weekly basis in late 2008 provide any sort of lesson
to investors, it must be that reputation and track record are not enough.
Investors cannot validly claim that they understood how Madoff could
have made such consistently positive returns based on the strategy he is
said to have employed. Madoff never addressed questions, maintaining
that his strategy (which was discretionary, not systematic) was too proprietary. Though insufficient to uncover all potentially fraudulent (or simply
unprofitable) investments, the tools provided in this chapter can certainly
help eliminate a great majority of them. These techniques should be used in
conjunction with an equally rigorous operational due diligence process to
further reduce the possibility of being victimized by fraud, malfeasance, or
other misbehavior on the part of traders.

How Quants Fit into a Portfolio
Assuming that you find a quant that is worth hiring or investing in, you have
to decide how to allocate to this trader. To make this determination, you
have to understand how the strategy fits in with the rest of your portfolio.
This is largely a question of balancing the levels of various types of exposures. This section details some of the more important kinds of exposures
associated with quant investing.

A Portfolio of Alphas
First, it is worth remembering that portfolio construction is about allocating to exposures. A portfolio that contains more kinds of exposures is more
diversified than one that is concentrated among a smaller number of exposures. Investors must seek out the appropriate balance of trend, reversion, value/yield, growth, and quality to achieve optimal diversification. A
quant doing trend following is not likely to be so incredibly different, from
a portfolio construction viewpoint, from a discretionary trader who is seeking to identify trends. To be sure, the tireless vigilance of a computerized
trading strategy might find opportunities that the human trader misses. In
addition, the human trader might avoid some bad trades that are taken
on by the computerized strategy out of naïveté. But, as trend following in
general goes, so it is likely that the human and computerized trader both
go. So, at a primary level, the investor must diversify among various alpha
exposures. In the evaluation process, the investor should be able to ascertain
at least roughly the underlying alpha exposures of the various strategies in a

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portfolio. Using this information, the investor can allocate capital such that
the blended allocations to various types of alpha are in line with the levels
that the investor has determined are desirable.

Bet Structures
The second consideration relevant to portfolio construction is bet structure, as described in Chapter 3. Relative bets can behave very differently
from single‐instrument bets, particularly when these bet structures are used
with different types of alpha models. When a quant strategy makes relative
bets, it is inherently counting on the stability of the relationships among
the instruments that are grouped together. This makes bet structure itself
a source of risk in such strategies, and this risk becomes evident when the
relationship between the instruments changes. In such environments, for
example, relative mean reversion strategies are prone to losses. On the other
hand, single‐instrument mean reversion frequently benefits from large regime changes. This is because this strategy tends to bet against the prevailing
trend while remaining indifferent to the destabilizing effects of a large trend
reversal on the relationships depended on by a relative alpha strategy. This
is but one example of how bet structures can impact results and, as a result,
the investor’s portfolio. In short, it is worthwhile to diversify across various
bet structures as well, even within the same domain of alpha exposure (e.g.,
relative and intrinsic mean reversion).

Time Horizon Diversification
Finally, the investor must balance her exposure across time horizons. In general, it is my experience that longer‐horizon quant strategies—those that
hold positions for more than a week or so—tend to go through longer and
streakier performance cycles. They can outperform or underperform for several quarters on end, and it can take several years to evaluate whether there
is really a problem with the manager. Some longer‐term strategies have also
demonstrated conclusively that they are subject to crowding risk, as seen so
vividly in August 1998 and August 2007. While this might make them a bit
less desirable, one can manage significantly more money in such strategies,
which is sometimes a practical necessity.
Short‐term strategies, by contrast, tend to be very consistent performers,
but they cannot handle much capital. They are also far from invulnerable.
As the years since 2008 have shown, short‐term strategies require trading
volumes to remain acceptably high, volatility to be above very low levels,
and correlation among instruments to be below very high levels. They are
nonetheless desirable, but also not always practical. When one does find a

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good short‐term trader to invest in, it is not clear that the trader will remain
small enough to be effective on short timescales. Many traders are tempted
to grow their assets when assets are on offer, and this demands attention on
the part of the investor.

Summary of Portfolio Considerations
Quants can be valuable components of a portfolio. The investor must realize
that quants are ultimately not so different than their discretionary counterparts and therefore that the list of things that matter to building a portfolio
that includes quants isn’t much different from what it would be without
quants. As with all things related to portfolios, the key is to build a diversified portfolio that considers three important elements:
1. Various types of alpha exposures
2. Various bet structures
3. Various time horizons
It is interesting to note that these considerations closely mirror the
taxonomy of theory‐driven alphas, presented here again as Exhibit 12.1.
Equally interesting, I do not believe that the investment universe (asset class,
instrument class, or geography) nor various other subtleties about the models (e.g., model specification or run frequency) are particularly impactful in
portfolio construction. These variations add a great deal of diversity when
markets are behaving normally, but in stressful times they simply matter a
lot less than distinctions along the lines of the three portfolio considerations
listed here.

Summary
To assess a quant trader and a quant strategy, one must understand the strategy being implemented and the quality and vigor of the process that generates strategies. To do this, the investor has three weapons at her disposal:
building trust, gaining as much knowledge as possible about quant trading,
and keeping information she learns as organized as possible. These tools can
be used to extract and piece together information on a given quant, and on
quant trading generally.
Ultimately, an investor has to determine whether a quant has an edge,
what the sources of this edge are, how sustainable the edge is, and what
could threaten it in the future. Edges come from people and/or processes,
and it is in these areas that the evaluation of a quant must focus. Once

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RETURN
CATEGORY

WHAT
QUANTS
DO

INPUT

PHENOMENON

HOW
THEY DO
IT

Alpha

IMPLEMENTATION

Price

Trend

Reversion

Fundamental

Yield

Growth

Quality

Time
Horizon

Bet
Structure

Instruments

High
Frequency

Intrinsic

Liquid

Relative

Illiquid

Short Term
Medium
Term
Long Term

Exhibit 12.1 Taxonomy of Theory‐Driven Alpha Strategies and
Implementation Approaches

quants have been vetted, they should be thoughtfully included in a portfolio.
It is important to diversify across different approaches to alpha generation,
different time horizons, and bet structures to complement best the other
components of the investor’s portfolio.
I remember once interviewing a senior employee at one of the best
quant shops in the world. I asked him how on earth they had done so well,
which of course was a sort of stupid question. His answer, however, was
both concise and seemingly on target. To quote him, loosely: “There is no secret sauce. We are constantly working to improve every area of our strategy.
Our data is constantly being improved, our execution models are constantly
being improved, our portfolio construction algorithms are constantly being

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233

improved . . . everything can always be better. We hire the right kinds of people, and we give them an environment in which they can relentlessly work to
improve everything we do, little by little.”

Note
1. Raymond F. Toliver, The Interrogator: The Story of Hanns Scharff, Luftwaffe’s
Master Interrogator (AERO Publishers, 1978; Schiffer Publishing, 1997).

Part

Four
High-Speed and
High-Frequency Trading

Chapter

An Introduction to High-Speed
and High-Frequency Trading*
I’m so fast that last night I turned off the switch in my hotel room
and was in bed before the room was dark.
—Muhammad Ali

n early 2009, with markets fresh off of a harrying near‐Depression experience, news reports began to circulate that among the few winners in
financial markets in 2008 was a new breed of trading firms—so secretive as
to make quant trading shops look like glass houses—called high‐frequency
traders (HFTs). It didn’t take long for some in the press, political and regulatory circles, and even in the financial industry to begin telling a highly
biased, basically fictional tale about high‐frequency traders.
Following these stories (which immediately prompted a chorus of cries
of “no fair”) came an unfortunate incident involving a programmer, Sergey
Aleynikov. Aleynikov had left Goldman Sachs to join a then-newly launched
HFT firm called Teza (which itself was formed by former Citadel traders).
He was arrested in early July 2009 and accused of stealing code from Goldman to bring with him to Teza. What was most alarming to the public about
this case had nothing to do with Aleynikov, Goldman, or Teza (intellectual
property theft cases are almost never of interest to the broader public). The
prosecuting attorney—in an effort to add weight to Goldman’s allegations—
said that the software that was allegedly stolen could be used to “manipulate markets in unfair ways.”1 This was eye‐catching for many, because it

* Important conceptual, empirical, and editorial contributions were made by Manoj
Narang throughout Part Four of this book. However, all of the writing was done by
Rishi K Narang, and all opinions contained herein are solely his own.

237

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High-Speed and High-Frequency Trading

linked high‐frequency trading with market manipulation. Aleynikov ended
up being convicted, but had his conviction overturned and vacated by an appeals court after almost three years of appeals and jail time. But the damage
was done, and the stage was set.
On May 6, 2010, U.S. equity markets collapsed and recovered dramatically. There was more than a 1,000 point drop in the Dow Jones,
with about 600 points of the drop occurring in a five‐minute period that
afternoon. This was followed by a fierce rally, which wiped out most of the
600 point loss in only 20 minutes. The high‐speed nature of this meltdown
and recovery came to be known as “the Flash Crash.” The Flash Crash
was widely blamed on HFTs, though often for contradictory reasons.
Some claimed that HFTs caused the crash by virtue of their trades. Others
claimed that HFTs caused the crash because they stopped trading once the
markets became too panicked. We will address these claims in more detail
in Chapter 16, but for now, it suffices to say that the Flash Crash was a
major contributor to negative popular opinion about a topic that almost
no one understands.
According to the Aite Group, HFTs now account for a little more than
half of global equity volumes, about the same percentage of futures volumes,
and about 40 percent of currency volumes. In equities specifically, Aite estimates that HFT’s share of trading is highest in the United States (again, a little
over half), more than 40 percent in Europe, and almost 20 percent in Asia.2
While there are various estimates of the exact amount of trading that comes
from HFTs, no further evidence is needed to demonstrate that this kind of
trading is a critically important topic to understand for any electronic market.
It is also worth understanding how HFT relates to the kinds of quant
strategies we explicated in Part Two. In Chapter 3, we described the types
of strategies that are typically pursued by systematic traders. In Exhibit 3.7,
we pointed out various implementation features related to such strategies,
including time horizon. As we point out there, time horizons can range from
“high frequency” to “long term.” In general, I believe the framework presented in Part Two is quite relevant for HFT strategies, including how they
are designed and implemented. However, there are a significant number of
considerations specific to the shortest-term systematic strategies. In other
words, the issues an HFT must carefully consider overlap greatly, but not
perfectly, with the issues that concern a longer-term trader. Longer-term
strategies often focus, for example, on managing the risk factor exposures
of a portfolio. By contrast, high-frequency strategies tend to be concerned
more about managing the risk of accumulating large positions.
So what is high‐frequency trading? Just as Parts One and Two showed
that quant trading is not some monolithic idea but contains an enormously
diverse constituency, it turns out that HFT is not a well‐defined, homogenous

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239

activity, either. There are multiple kinds of high‐frequency traders. But a
definition that probably contains most of these kinds of traders is as follows:
High‐frequency traders (a) require a high‐speed trading infrastructure,
(b) have investment time horizons less than one day, and (c) generally try
to end the day with no positions whatsoever. The fastest HFTs (sometimes
referred to as ultra‐high‐frequency traders, or UHFTs) will no doubt scoff at
the notion that someone who holds positions for as much as six and a half
hours should be considered high frequency. But there is an important distinction between overnight risk and intraday risk, as most news comes out
when markets are closed. Any further attempt to narrow down the holding
period of an HFT strategy would seem arbitrary: What makes one second
“HFT,” while one minute is not? Furthermore, our definition specifies that
the strategy should require a high‐speed infrastructure.
It is worth knowing, however, that HFTs share the high‐speed trading
infrastructure mentioned above (and described in detail in the next chapter)
with many kinds of algorithmic traders. And high‐speed infrastructure does
not have only one speed. As we will see in the next chapter, the challenges
facing engineers of such infrastructure are substantial, and in few instances
does any industry standard exist to meet those challenges.
Within the algorithmic trading community, people tend to think of the
users of high‐speed infrastructure as falling into four categories: UHFTs,
HFTs, medium-frequency traders (MFTs), and algorithmic execution engines. But all of these approaches tend to share commonalities in terms
of the definition above (though algorithmic execution engines generally
attempt to help acquire longer‐term positions, the algorithm itself is usually not interested in what happens tomorrow). As was famously said by
Supreme Court Justice Potter Stewart in 1964, “I shall not today attempt
further to define the kinds of material I understand to be embraced within
that shorthand description; and perhaps I could never succeed in intelligibly
doing so. But I know it when I see it. . . .” He was talking about hard‐core
pornography, of course, but the exact same sentiment applies (in more ways
than it should) to HFT.
This act of definition is important for a variety of reasons. First, it allows us to have a common footing when discussing the topic. Second, there
are implications to any definition, including this one. This definition of HFT
implies that there are several important characteristics of HFTs. First, since
HFTs tend to end the day with no positions (flat, in industry lingo), their
buying and selling activity tends to exactly offset. However many shares or
contracts were bought of a given instrument had to have been sold as well;
otherwise, there would be a net position at the end of the day. Second, since
there is a desire to be flat at the end of the day, an HFT strategy likely does
not seek to accumulate large positions intraday.

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As we showed in Chapter 7, accumulating large positions incurs large
market impact costs. Unwinding such positions would cause further market impact costs. With an intraday holding period, there is not enough
price movement on a typical day to offset the market impact of buying,
plus the market impact of selling. Furthermore, since HFTs cannot accumulate large positions, and since price movements during the trading day
are of limited magnitude, HFT strategies generally have fairly low profit
margins. They must pay the same kinds of costs as other investors and
traders—commissions, market impact, and regulatory fees, for example—
but they participate in relatively small price moves. There are economic
incentives associated with higher volumes of trading (such as exchange
rebates for providing liquidity or cheaper commission rates from brokers),
but the fact is that margins remain very low, and the aggregate cost of
technology, commissions, and regulatory fees is usually a large multiple of
the net profits after these costs.
Multiple sources have pegged the profitability of an HFT strategy in
U.S. equities (in relatively good times) at approximately $0.001 per share
(one‐tenth of a penny). It is instructive to compare this to SEC regulatory
fees of $22.40 per million dollars sold. This fee translates to about $0.006
per share for a $70 per share stock, though it applies only to sales. Since
HFTs tend to buy as much as they sell, we can divide the fee by two to get
a figure that applies to every HFT transaction, and we arrive at a typical
SEC fee of approximately $0.003 per share, which is about triple the profit
margin for a typical U.S. equity HFT.
It is also worth understanding that an HFT who trades 100,000,000
shares per day is responsible for more than 1 percent of U.S. equity volumes.
His profit, at $0.001 per share, is about $100,000 per day, which comes to
$26 million per year. If we multiply this by the 50 percent estimate of the
share of HFT volumes versus overall market volumes, we get $1.3 billion
in total trading profits for the entire HFT industry for an entire year in the
largest equity market in the world. These are lofty numbers, but they are
actually just the revenue side of the ledger.
The reality is that it also costs millions per year for every firm that tries
to achieve these revenues, and there are a large number of firms that fail.
And since there are a large number of firms competing, even a successful one
that accounts for, say, 5 percent of the U.S. equity market’s volumes (which
would make it an extraordinarily successful outlier) is making something
like $65 million per year in revenues, before accounting for the extensive
technological, compliance. and human resource costs that are required to
compete.
To put this in perspective, Apple, Inc. reported that, for the quarter ending June 30, 2012, they had revenues of over $35 billion. One might argue

An Introduction to High-Speed and High-Frequency Trading

241

that Apple, the largest market capitalization in the world at the moment,
makes an unfair comparison. But even E*Trade Financial Corporation, a
single (not particularly huge) online brokerage firm, reported that their trailing 12‐month revenues as of June 30, 2012, were almost $2 billion. This is
astounding, considering that it is generating these revenues at a time when
trading volumes are at multiyear lows, particularly among the retail customers who form their base. E*Trade is a $2.65 billion market capitalization
company at the time of this writing—scarcely a giant.
There is clearly “real money” to be made in HFT. However, in the grand
scheme of things, HFT revenues are minuscule in comparison to the revenues of many other kinds of companies. An interesting question, and one
to which I have no particularly clever answer, is why so much money and so
many smart people are so focused on this niche, considering the relatively
diminutive size of the pie for which they are competing. But we can point
out that many micro-industries experience an initial phase of immense profitability, which in turn attracts a great many new participants. These new
participants drive up competition, which in turn causes profit margins to
diminish. Eventually, so many participants are competing that margins can
turn negative. This leads to a contraction in the field, with weaker or less
willing parties exiting. We see some evidence that this is the case in HFT,
certainly in U.S. equities. Many HFTs who once hoped to make the kinds
of profits that have been hyperbolized in the press have now realized that
their firms are unable to survive on the meager revenues they can generate.
Armed with a definition of HFT, and the background knowledge of the
economic scope of this activity, we will proceed to explain many aspects of
HFT. In Chapter 14, we will explain high‐speed trading, which is the basic
toolkit for all HFT activity—and a large percentage of all other kinds of
trading as well. In Chapter 15, we will outline HFT strategies and explain
how they relate to the concepts introduced in Chapter 14. In Chapter 16, we
will address some of the controversy surrounding HFT and separate truth
from myth.

Notes
1. David Glovin and Christine Harper, “Goldman Trading‐Code Investment Put at
Risk By Theft,” Blooomberg.com, July 6, 2009.
2. Aite Group estimate, September 2012. Figures for 2012 are estimates.

Chapter

High-Speed Trading
In skating over thin ice our safety is in our speed.
—Ralph Waldo Emerson

s we delve into the subject of high‐frequency trading, we must first clarify
a number of important topics. Foremost among these is the difference
between high‐speed trading and high‐frequency trading. These two concepts
are conflated almost continuously by the press, by regulators, and even by
reasonably savvy investors. And it is understandable, because the first, which
is necessary and inevitable, gives rise very naturally to the second. So high‐
speed trading and high‐frequency trading are cousins, but not synonymous.
High‐speed trading is also known as low-latency trading. It refers to
the need, on the part of various types of traders, to access the markets with
minimal delays, and to be able to act on decisions with minimal delays. In
this chapter, we will address why speed is important for many kinds of traders, far beyond HFTs, and also what the sources of latency are and how they
can be addressed.
Speed has always, throughout the history of any marketplace, been an
important part of separating weaker competitors from stronger ones. There
is a good, self‐evident reason that equity trading firms and brokerage houses
established themselves near the exchanges in New York, and that futures
trading firms located themselves near the exchanges in Chicago. The same
thing can be found in almost every market center in almost every instrument
class around the world. Physical proximity is a good start at being fast,
and so is having fast communications between market centers. In 1815, the
Rothschild bank in London famously used carrier pigeons to find out about
Napoleon having lost the battle of Waterloo. They used this information to
go short French bonds and made an enormous sum of money. The founder
of Reuters, one of the world’s leading news and data vendors, got his start

243

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in 1845 by setting up a carrier pigeon network in London, and within five
years, his service was the lowest latency source of information about what
was happening in Paris’ bourses.1

Why Speed Matters
In modern electronic markets, the best way to understand why speed matters is to see how it matters for various kinds of orders. After all, regardless of the types of alpha, risk, or portfolio construction models, orders are
how strategies get implemented. While there are many kinds of orders—
especially when we account for all of the various kinds of exchanges around
the world—orders can generally be understood as being passive or being
active. Furthermore, some orders (passive ones) can be canceled once they
are placed. As such, we will describe the three broad cases that capture most
of the world’s order types as: placing passive orders, placing aggressive orders, and canceling passive orders.
First, a few definitions: Passive orders are limit orders that cannot be
immediately filled. For example, if the best offer on XYZ is 100 shares at
$100.01, and a trader enters a limit order to buy 100 shares of XYZ at
$100.00 or lower, this is a passive order, because it cannot be immediately
filled. In most markets, passive orders are aggregated into an exchange’s
“limit order book,” which shows all of the passive orders for a given ticker
on the exchange at a single point in time. An illustration of an order book
might look something like Exhibit 14.1.
For this hypothetical market, the limit order book shows a price/time
priority. This means that the highest priority goes to orders at the best price
(highest price for a buy order and lowest price for a sell order). If two orders
have the same price, then the time at which they arrived at market is the tie‐
breaker. Other markets (for example, eurodollar futures) have a price/size

Exhibit 14.1

Mockup of an Order Book for a Fictitious Ticker

Size

Bid

Offer

Size

Bid1

100.00

100.01

2,000

Offer1

Bid2

1,000

100.00

100.02

2,950

Offer2

Bid3

3,100

99.99

100.02

600

Offer3

Bid4

200

99.99

100.03

300

Offer4

Bid5

5,000

99.98

100.04

1,000

Offer5

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High-Speed Trading

Exhibit 14.2

Mockup of an Order Book for a Fictitious Ticker after a Large
Market Order to Buy

Size

Bid

Offer

Size

Bid1

100.00

100.02

1,950

Offer2

Bid2

1,000

100.00

100.02

600

Offer3

Bid3

3,100

99.99

100.03

300

Offer4

100.04

1,000

Offer5

Bid4

200

99.99

Bid5

5,000

99.98

prioritization, which puts larger orders at a higher priority than smaller orders at the same price (the best price would always be the first test).
Aggressive orders are immediately actionable orders. There are two major types of aggressive orders. Market orders are always aggressive, because
they are instructions to buy (or sell) a specific amount, without regard to
price. Thus, if the limit order book looks like Exhibit 14.1, and a market
order is entered to buy 3,000 shares, there would be two separate fills. First,
the market order would use up the 2,000 share offer at $100.01 (Offer1),
and then the market order would use up 1,000 of the shares offered at
$100.02 (Offer2). Immediately after this trade, assuming no other orders
have been filled, the order book would be as shown in Exhibit 14.2.
A second type of aggressive order would be a limit order made at the
best offered price (for a buy order). Building from Exhibit 14.2, a limit order to sell 1,000 shares at $100.00 would use up the first 55 shares bid at
$100.00, and 945 of the next 1,000 shares bid at $100.00. The order book
would now be as shown in Exhibit 14.3, assuming no other orders came in.
In this example, 55 shares (which were from Exch1 in the original example) were filled first, and then the sell order was exhausted by taking
945 of the Exch2’s bid at $100.00, leaving 55 shares at $100.00 as the new
best bid. This limit order to sell was aggressive, because it was immediately
actionable.
Exhibit 14.3

Mockup of an Order Book for a Fictitious Ticker after a Limit Order
to Sell at the Bid

Size

Bid

Offer

Size

Bid2

100.00

100.02

1,950

Offer2

Bid3

3,100

99.99

100.02

600

Offer3

Bid4

200

99.99

100.03

300

Offer4

Bid5

5,000

99.98

100.04

1,000

Offer5

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High-Speed and High-Frequency Trading

Exhibit 14.4

Mockup of an Order Book for a Fictitious Ticker after a Limit Order
to Sell, Which Joins the Best Offer

Size

Bid

Offer

Size

Bid2

Bid3

3,100

Bid4
Bid5

100.00

100.02

1,950

Offer2

99.99

100.02

600

Offer3

200

99.99

100.02

1,000

Offer6

5,000

99.98

100.03

300

Offer4

100.04

1,000

Offer5

A couple of other terms that bear definition are joining and improving.
To join implies that one adds to the size of the best bid (or offer), which is
also known as the first level of the order book, or the inside market. An example of joining is shown in Exhibit 14.4, in which we imagine an additional 1,000 shares are added to the offer side of the book at $100.02 (Offer6).
We can see that this new order has a lower priority than the 600 shares
that were previously offered at $100.02 (Offer3), because it came in later.
This is obviously always true of an order to join: It will always have a lower
time‐priority. Orders to join are also always passive as they are not immediately actionable.
Finally, we illustrate improving in Exhibit 14.5. Here, we see a new
passive limit order to sell (Offer7) which narrows the bid/offer spread by
improving the best offer price from $100.02 to $100.01. Because it has the
best price of any offer, it receives the highest priority, even though it is the
most recent of all of them.
Note that many practitioners tend to confuse passive orders with the notion of providing liquidity, and aggressive orders with the notion of taking
liquidity. It is an understandable mistake, because liquidity is often confused
Exhibit 14.5

Mockup of an Order Book for a Fictitious Ticker after a Limit Order
to Sell, which Improves the Best Offer

Size

Bid

Offer

Size

Bid2

100.00

100.01

2,000

Offer7

Bid3

3,100

99.99

100.02

1,950

Offer2

Bid4

200

99.99

100.02

600

Offer3

Bid5

5,000

99.98

100.02

1,000

Offer6

100.03

300

Offer4

100.04

1,000

Offer5

High-Speed Trading

247

with either volume or the size of the order book. However, as we learned
from both the flash crash and the August 2007 quant liquidation, increased
volumes do not always imply increased liquidity. In fact, in both instances,
imbalances in the volumes of buys versus sells led to incredible illiquidity
for anyone on the wrong side of those moves (for example, owners of SPY
who wanted to sell into the downdraft on May 6, 2010). On the other hand,
aggressive orders to buy units at a time when there are many sellers might
be extremely additive to liquidity, even if they technically remove units from
the order book. It is our view that this confusion stems from an inaccurate
definition of liquidity, and this is itself understandable. Even peer‐reviewed
academic journals have inconsistent definitions of liquidity, so it is clearly a
concept that can be defined many ways.
We define liquidity at any point in time as being the immediate availability of units to be transacted at a fair price. This is a useful definition
because it accounts for all of the important dimensions of the topic—
immediacy, size, and a fair price—without being plagued by the problems
associated with volume or order‐book dominated approaches. It allows us
to understand that an execution strategy to acquire a huge position mostly
passively is still removing liquidity from the market. On the other hand,
an aggressive order, which nominally reduces the number of units in the
order book, is sometimes adding liquidity, if it helps push prices toward a
fairer level.
Fairness of price deserves a brief explanation. Here, we refer to a price
as fair if it (a) is broadly reflective of the fundamentals of the instrument’s
underlying economic exposure, or (b) is sensible with regard to other instruments that are similar to it. For example, imagine some company is massively profitable, growing nicely, and trading around $100 per share. If nothing
changes in its business, and the price immediately drops to $2 per share, it
is highly improbable that the test of fairness was met. In this case, we could
say that this company’s stock became illiquid when the price moved so far
without reason. As to the second test, if the index that the company is a part
of, or if the other companies in its sector are moving in a similar way, then
the price may well be fair (we explain this last concept in more detail when
we describe HFT arbitrage strategies in Chapter 15).
With this background, we can now illustrate the importance of speed
for passive orders to buy, passive orders to sell, and cancellations of passive
orders. There is a single, unifying theme that bears mentioning, and it is
known as adverse selection. This is a concept that has broad applications in
finance (and life). Imagine that we post a job listing for a role that sounds
perfectly standard. However, the compensation we offer is extremely low
relative to other similar job openings that are on the market. It is probable
that we will receive resumes mainly from below‐average candidates. This is

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because few self‐respecting candidates would apply for an underpaying job.
The better candidates, and even most of the average candidates, will apply
for the other job openings. And we, rather than drawing a random distribution of good, bad, and average candidates, will be biasing our candidate
pool toward the bad side.
Just so, in trading adverse selection is a significant problem that specifically relates to speed.

The Need for Speed in Placing Passive Orders
Anytime one places a passive order there is a risk of adverse selection.
Consider what is really happening when you place a passive order: You’re
showing the world that you’re willing to buy, for example, some number of
shares of XYZ at $100.00. A prospective seller knows this (because your
bid is in the order book), but you don’t know what information this seller
might possess. That seller’s information might make you rue buying those
shares. Of course, passive orders give the trader the opportunity to earn the
bid‐offer spread. Furthermore, some exchanges pay rebates for filled passive
orders, and posters of passive orders can earn additional profit by virtue of
these rebates. According to internal research conducted by Tradeworx, it is
estimated that the average return of all passive orders on the most liquid
stocks (above $50 million in dollar volume per day) for the year 2010 was
approximately –0.2 cents per share. This assumes that one can exit the trade
at no cost (at the mid‐market price, which is the simple average of the best
bid and the best offer, without regard to the size of the bid or offer) one
minute after entering it. In other words, buying the bid and selling the offer
is a money‐losing proposition in the absence of liquidity provision rebates.
So where does the need for speed come into play? Let’s start with another imaginary order book for XYZ, as shown in Exhibit 14.6.
Imagine that you place an order to buy 1,000 shares of XYZ at $100.00
(Bid4). Further, let’s imagine that there are a large number of shares bid just
after yours at the same price (Bid5). This is shown in Exhibit 14.7.
Exhibit 14.6
ID

Mockup of an Order Book for a Fictitious Ticker
Size

Bid

Offer

Size

Bid1

3,100

99.99

100.01

2,000

Offer1

Bid2

200

99.99

100.02

2,950

Offer2

Bid3

5,000

99.98

100.02

600

Offer3

100.03

300

Offer4

100.04

1,000

Offer5

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High-Speed Trading

Exhibit 14.7
ID

Mockup of an Order Book for a Fictitious Ticker with Additional Bids
Size

Bid

Offer

Size

Bid4

1,000

100.00

100.01

2,000

Offer1

Bid5

6,000

100.00

100.02

2,950

Offer2

Bid1

3,100

99.99

100.02

600

Offer3

Bid2

200

99.99

100.03

300

Offer4

Bid3

5,000

99.98

100.04

1,000

Offer5

If an aggressive order comes into the market to sell 1,000 shares, you
will be filled, and you are now long 1,000 shares of XYZ at $100.00.
However, the best bid remains $100.00, because there were other orders
behind you indicating a willingness to buy at $100.00. Here, the odds are
not bad that you bought at a good price, at least in the extreme near term.
This is illustrated in Exhibit 14.8.
But now let’s imagine that you place the same 1,000‐share order to buy
XYZ, and instead of being at the top of the queue, your order is the last one
in the book at $100.00, with thousands of shares in front of you. Orders
to sell come into the market, and eventually, yours ends up being filled. But
now, the best bid is lower, at $99.99 (Bid1), and most likely, the best offer
is $100.00 (Offer6). So, yes, you did technically buy at the bid, but the bid
immediately went down and the price you received immediately became the
subsequent best offer. This is shown in Exhibit 14.9.
The impact of queue placement was examined empirically by Tradeworx.
They found that there is approximately a 1.7 cents per share difference in
the profitability of being first versus being last at a given price. This is a
truly staggering figure, considering that all passive orders average roughly
–0.2 cents per share.

Exhibit 14.8 Mockup of an Order Book for a Fictitious Ticker after 1,000 Shares
Have Been Removed from the Bid
ID

Size

Bid

Offer

Size

Bid5

6,000

100.00

100.01

2,000

Offer1

Bid1

3,100

99.99

100.02

2,950

Offer2

Bid2

200

99.99

100.02

600

Offer3

Bid3

5,000

99.98

100.03

300

Offer4

100.04

1,000

Offer5

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High-Speed and High-Frequency Trading

Exhibit 14.9 Mockup of an Order Book for a Fictitious Ticker after All $100.00
Shares Have Been Removed from the Bid
ID

Size

Bid

Offer

Size

Bid1

3,100

99.99

100.00

2,000

Offer6

Bid2

200

99.99

100.01

2,000

Offer1

Bid3

5,000

99.98

100.02

2,950

Offer2

100.02

600

Offer3

100.03

300

Offer4

100.04

1,000

Offer5

Thus, when placing any passive order it is clear that speed is important
to the near‐term profitability of the trade. It has been argued by some that
long‐term investors (who hold positions for years and hope for profits on
the order of dollars per share) should not care about the loss of a penny or
two per share by virtue of being a slow, passive trader. But this is an oversimplification. A pension fund with a multiyear time horizon is making a
mistake if it ignores the cost of trading, especially if the number of shares
transacted is very large. On the other hand, reaching the top tier of speed for
a given market costs a great deal of money, and this does not get factored
into simple calculations of cents per share. So there is clearly a trade‐off, and
the need for speed among passive orders is a function of:
1. Adverse selection metrics (such as those described here)
2. Volume of shares traded
3. The cost of building and maintaining top‐tier speed
Typically, the smaller and longer‐term the investor, the less is the need for
higher speed. However, for many strategies (including quantitative alpha strategies such as those described in this book) and many sophisticated large long‐
term funds, transaction volumes are sufficiently high as to warrant at least some
investment in faster speeds. This explains the boom in the institutional execution technology business that has occurred since approximately 2007.

The Need for Speed in Placing Aggressive Orders
Traders placing aggressive orders are willing to pay the bid‐offer spread
because they have a reason to get the trade done with more certainty. As
we have already shown, there are two kinds of aggressive orders. One is an

251

High-Speed Trading

aggressive limit order, which interacts with an order already resting in the
limit order book. The other is a market order. The need for speed is different
in each situation, and we will detail both.
In the case of an aggressive limit order, speed is important because you
are specifying the price at which you are willing to trade, but others may
beat you to that price. As such, the price can move away from you before
you are able to complete your trade. Let us begin again with the order book
shown in Exhibit 14.6. Imagine that two traders each want to buy 2,000
shares at $100.01 and they both enter limit orders to that effect. The first order to reach the market will interact with the resting $100.01 offer for 2,000
shares. The second offer will not get filled immediately, but will become the
new best bid at $100.01 (Bid4). This is illustrated in Exhibit 14.10.
The new best bid belongs to the second order. The first bid interacted
with the $100.01 offer of 2,000 shares and was filled completely. If the price
continues to climb, and the trader whose order came to market second continues to lag behind other participants, one of three scenarios may apply to
his order: (1) it will be filled at $100.01 but is subject to adverse selection
biases; (2) it will be filled at a higher price if he cancels and replaces with
a higher‐priced bid; or (3) it will end up not being filled at all. In any case,
this is a bad outcome versus simply having been the first one to bid $100.01.
The second case is that of a market order. Here, we do not have to
worry about getting filled, as market orders will basically always be filled.
However, with market orders we have very little control over the price of the
fill. Speed matters here because a slowly transmitted market order suffers
from adverse selection. If our order to buy is slow in reaching the market, it
is less likely that there are other buyers immediately behind us, and we will
most likely end up with a worse fill than had we been faster. (This is similar
to adverse selection in limit orders.)
In addition, market orders also unfortunately have slippage issues. Let’s
imagine our order is to buy 2,000 shares of XYZ, and that the order book
is that of Exhibit 14.6. Here, if another trader’s order (a limit order to buy
2,000 shares at $100.01, or a market order to buy 2,000 shares regardless
Exhibit 14.10

Mockup of an Order Book for a Fictitious Ticker after Two 2,000
Share Bids at $100.01

Size

Bid

Offer

Size

Bid4

2,000

100.01

100.02

2,950

Offer2

Bid1

3,100

99.99

100.02

600

Offer3

Bid2

200

99.99

100.03

300

Offer4

Bid3

5,000

99.98

100.04

1,000

Offer5

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High-Speed and High-Frequency Trading

of price) reaches the queue and gets filled first, our market order incurs
slippage and will be filled at $100.02. This may not be a total disaster in a
slow‐moving market, but as we have seen in any very fast‐moving markets,
getting filled first can have extremely large consequences in the slippage we
pay. What’s more, the greater the accuracy of the forecasts (from the alpha
model) that drove the desire to trade in the first place, the larger our concern
over slippage. After all, a more accurate forecast is more likely to move in
the direction we expect, which means that our best trading ideas are also the
most important to implement well, when utilizing market orders.

The Need for Speed in Canceling Passive Orders
The cancelation of passive orders that have already been placed is also highly sensitive to latency. If I send a passive limit order to sell 2,000 shares of
XYZ at $100.00, this order is simply added to the order book. Let’s imagine
that the current best offer is to sell at $99.98, two cents better than my offer. I might expect that my order will eventually get filled by virtue of some
small fluctuation in XYZ’s price. After all, my order is only approximately
0.02 percent away from the current best offer. However, if the market begins
moving quickly (as it has a tendency to do at the most inopportune times), it
is highly likely that my order will have the same adverse selection problem
as any high‐latency order that gets placed. Thus, though I would want to
lift my order as quickly as possible, by the time I succeed in doing so, XYZ
might well be on its way up to well above my $100.00 offer price. If I’d been
able to cancel this order quickly and replace it with a higher‐priced offer, I
might have saved myself money on this trade. Similarly, if similar or correlated instruments begin to rally (e.g., due to some favorable macroeconomic
news), it is highly probable that my offer will be lifted and the price at which
I sold would be inferior to what I could have sold at if I was (a) aware of the
upward pressure in these other instruments, and (b) fast enough to cancel
my current offer and replace it with a higher‐priced one.
Perhaps on one 2,000 share order, this difference is not something I
care about. But to repeatedly suffer from adverse selection by virtue of a
slow cancellation capability will no doubt cost me dearly over the course of
a year. There is some controversy regarding the rate of cancelations in U.S.
equities (and some other markets), which we will address in Chapter 16.

Sources of Latency
Having established that it is clearly important for any trader responsible for
a reasonably large amount of volume to have access to a low-latency trading

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platform, we now turn our attention to the potential sources of latency that
can be controlled by the trader, and what can be done about each of these
sources of latency.

Transmission to and from Market Centers
The first potential source of delay for an algorithmic execution engine comes
from the time it takes to get data from and orders to market centers. Much
of the work of a good execution engine involves reacting quickly to changes
in the marketplace; having as close to a real‐time access to those changes is
logically the first order of business. Furthermore, getting your orders to the
exchange soon after you’ve decided what to do allows orders to be fresh (as
opposed to stale, which is what practitioners call orders that haven’t been
refreshed very recently).
Information coming from or going to a given venue will arrive fastest
if it is going to a location that is physically near the exchange’s matching
engine itself. The matching engine is the software used by the exchange to
time‐stamp and prioritize all inbound orders, provide the logic that puts
buyers and sellers together, and broadcast the data about all of this activity.
This software is physically housed on servers in various data centers (there
is usually one data center per exchange). These data centers almost always
openly offer space within the same physical location to anyone willing to
pay for it. When a trading firm colocates its server (which contains its trading algorithms) in the same facility as an exchange’s matching engine, the
connection between its server and that matching engine is known as a cross‐
connect. In some cases—either because a facility does not allow colocation
or because it is too expensive to colocate in a large number of data centers—quants can elect to host nearby (with nearby being a totally arbitrary
term here). This is known as proximity hosting.
The difference between being near the exchange and being far away
can be material in terms of making sure that the orders that are driven off
of that data don’t suffer from adverse selection. To put some metrics on
it, imagine that a given market’s data center is in New York. Rather than
colocating your servers alongside the exchange’s matching engine in New
York, you choose to put your servers in San Francisco. A reasonable expectation of the time for information to travel on a relatively fast fiber optic
connection between New York and San Francisco is about 50 milliseconds
each way, or about 100 milliseconds round trip. To make a decision and
place an order, information has to travel from the exchange to your servers
and back to the exchange. Thus the total time needed to place an order is
about 100 milliseconds. (It will take some time to process and handle this
information, but let’s assume that this time is negligible for now. It is in

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any case a constant whether you colocate in New York or use a data center
in San Francisco.)
A lot can happen within these 100 milliseconds. For example, in the
space of 100 milliseconds there are between zero and more than 40 messages (at the 99th percentile) posted to the various order books for EBAY
(just to take a single example).2 The largest number of messages are posted
during the more liquid times of day. This implies that almost any sensible
trading algorithm will concentrate its activities during the times when the
number of messages is highest. If your trading algorithm located in San
Francisco trades during these times, your orders will be very far behind
other orders, given the 100 millisecond delay. For this reason, we care far
more about the message rate and activity at the 99th percentile than we do
about the median level, for example. This is an effect we will describe in
more detail in “Data Bursts.”
It also bears mentioning that data handling software, order generation
software, and everything in between resides on servers. These servers must be
located somewhere. One possibility is to locate them on your own premises.
In addition to the problem with latency described above, an office building
rarely has adequate power, cooling (servers generate an extreme amount of
heat), network speed, and emergency backup capabilities to ensure continuity.
As such, most people locate expensive, mission critical servers in data centers
(also known as colocation facilities). If you’re going to colocate a server, the
least arbitrary and most useful place to do so is at or near the exchange.

Transmission between Market Centers
Another potential source of latency for an algorithmic execution algorithm
comes from the aggregation of data between market centers. Even for a
single instrument class there are often multiple venues on which to transact
these securities. For example, in the case of U.S. equities there are 13 different official exchanges on which investors can trade, and dozens more
(approximately 60 as of the writing of this book) dark pools as well. When
information arrives from multiple venues, it has to be aggregated into one
big set of data. (Although there are services that consolidate the data for
you, these consolidated data feeds contain substantial latency. It is far better
to consolidate the data yourself, if you can do it well.) We will address the
issue of consolidation separately, but in order to consolidate the data, all
of the data have to be in one place physically. The connections between the
various exchanges can be visualized as a mesh. As in the previous section,
the further away a given market’s various data centers are from one another
in the mesh, the more natural latency there is in the system, and the harder
it is to consolidate all of the data into one place physically. All of the points

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made in the previous section apply here: The further away a given market’s
various data centers are from one another, the more natural latency there
will be, and the harder it is to solve this problem.
Let us further look at the problem of consolidating data between market centers. Many strategies look across instrument classes to make trades.
For example, most market makers in U.S. equities (which generally trade in
the vicinity of New York City) are very keen to know, with minimal latency,
what the S&P E‐Mini futures contract (called the “ES” futures contract)
is doing in Chicago. This is because the ES tends to lead both the SPY (an
extremely important ETF that tracks the S&P 500 index) and the independently traded constituents of the S&P 500 index.3
The most important long‐distance problems in the finance world are
getting information back and forth between Chicago and New York, and
between New York and London.4 Data travel at the speed of light, but the
problem is that one must transmit data over some medium. Data can’t be
beamed through the air (in the form of light) in a “straight line” over thousands of miles due to the curvature of the earth and a wide variety of potential physical obstacles along the way (e.g., buildings, airplanes, birds). If this
were somehow possible, it would take just under four milliseconds for data
to reach New York from Chicago (and vice versa). As of the writing of this
book, a typical commercially available solution for low-latency communications between Chicago and New York has a one‐way latency of seven to
eight milliseconds. This is over a fiber optic network, which (a) transmits
data through glass (the material that fiber optics are essentially made from),
and (b) is somewhat circuitous, as there is no telecommunications company
with a direct route between Chicago and New York. Light travels about
1.3 times faster through the air than through glass—this explains some
of the extra latency. The indirect route a conventional fiber optic network
takes between Chicago and New York explains most of the rest, and the
small remainder is attributable to suboptimal hardware.
To solve this problem, a company called Spread Networks undertook
a fascinating endeavor to make a much more direct path between Chicago
and New York. They leased and bought tracts of land along this path, and
found the straightest path possible (cutting through mountains in some
cases). They used the best equipment that money could buy. They reportedly
employed 126 four‐person crews to lay a one‐inch‐wide line. Ultimately they
reduced the distance over which light had to travel by more than 100 miles.5
In order to use their service (which immediately sold out), customers had to
sign multiyear contracts rumored to cost on the order of $10 million. In exchange, the one‐way latency between Chicago and New York was reduced
to about 6.5 milliseconds—1 millisecond faster than the more conventional
telecommunications solution described earlier.

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But this arms race to zero (as the pursuit of minimum latency is less‐
than‐affectionately known) scarcely ended with Spread Networks’ unveiling. Several firms, including Thesys technologies (a subsidiary of Tradeworx)
and McKay Brothers, are planning microwave solutions (which bounce microwave transmissions between towers) in a still‐straighter path between
Chicago and New York. McKay claims to have a one‐way latency of around
4.5 milliseconds, and Thesys expects a latency of 4.25 milliseconds. These
latencies are achievable because microwaves tend to move faster through
the air than photons move through glass (as with fiber optic cables).6
There is some light (no pun intended) at the end of the tunnel, however. The arms race to zero appears to be nearing an end. The potentially
faster microwave solution may not be as reliable as a closely monitored,
dedicated fiber optic line, due to weather and other factors. Furthermore,
the amount of information that can be transmitted via microwave is also
quite small.
The state of the art connection between London and New York for
some years was Global Crossing’s AC‐1 transatlantic cable, with one‐way
transmissions with approximately 65 milliseconds of latency. However, Hibernia Atlantic spent some $300 million laying a transatlantic fiber optic
cable that allows for one‐way latencies of 59.6 milliseconds. This translates
into a latency reduction of approximately five milliseconds.7 The line was
activated in May 2012, and reportedly was sold out far in advance to a
handful of trading customers.

Building Order Books
The data that a given exchange broadcasts to traders is actually in the form
of messages (new orders, cancellations, and trades), not in the form of an
order book. It is the job of the quant to build an order book from these
messages. This turns out to be a very challenging task. In order to have an
accurate order book at a given point in the day, every message from the
beginning of the day onward must be processed. There can be no dropped
messages. Furthermore, this processing has to be very fast; otherwise, latency is introduced. As we all know, there is a trade‐off between speed and
accuracy that is difficult to overcome. And this is no exception. Worse still,
there are a number of algorithmic solutions that solve this problem, and
none are considered industry standard.
A subtler part of this problem (which relates to our next topic) is
time stamping. Each stream of messages from each exchange has its own
timestamp. It is crucial to have the sequence of these messages accurately
recorded as well. So, not only are we processing the messages themselves,
but the timestamps of each message.

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Consolidating Order Books
For markets that are fragmented (as in the case of U.S. equities), we have
multiple streams of messages that need to be aggregated into one consolidated order book. The challenges described above are compounded by the
task of combining these multiple information sources correctly. For example, even if we have an accurate order book for two different exchanges on
which XYZ is traded, and even if we have the messages correctly ordered
for each of these two, there can still be problems. The messages from the second exchange may be presented to us with greater latency than the first, and
this must be accounted for when building the consolidated order book. Otherwise, it will appear that things happened in a sequence that is incorrect.

Data Bursts
One of the most significant (and somewhat unique) challenges facing someone building a high‐speed trading infrastructure is the fact that messages do
not arrive at an even rate throughout the day. This is an extremely sneaky
problem that bears some discussion.
The pioneers of the mathematics of traffic engineering were involved
in engineering telephone networks. They assumed that rates of consumption of bandwidth would be basically stationary within some reasonable
interval, like minutes or seconds. There is a concept in mathematics called
the Poisson‐distribution (after a French statistician who introduced it in the
nineteenth century) that is tailor‐made for this application. This assumption
made sense in engineering phone networks, where average rates could be assumed to be stationary over some intervals. For example, Mother’s Day has
an incredibly high average call rate, but basically you could assume that call
arrival rate was constant and calls arrived independently over the busiest
hour on Mother’s Day.
However, in trading, the very action of one person trading causes another to take action (for example in the placement or cancelation of orders).
This results in a positive feedback loop, and there is absolutely no stationarity in the message rates inside anything that a normal person would consider
a reasonable period. To further elaborate, the average of the message arrival
rate in the one‐second time frame tells you very little about the arrival rate
in the one‐millisecond time frame.
Let’s return to the example of EBAY. Exhibit 14.11 shows the number
of messages at various percentiles, for various slices of time from one second
down to 1 millisecond.
What is most interesting about this table is that it shows directly and
empirically how nonstationary the message rates are. At each percentile,
you would expect to see one‐tenth the number of messages in one row as

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Exhibit 14.11

Breakdown of Messages at Various Intervals and Percentiles for
EBAY on July 20, 2012
50th
Percentile

99th
Percentile

99.9th
Percentile

99.99th
Percentile

99.999th
Percentile

259

546

1,755

4,179

100 milliseconds

863

1,306

10 milliseconds

269

557

1 millisecond

106

1 second

in the preceding row. For example, if there are 259 messages per 1 second
at the 99th percentile, you would expect to see about 26 messages per
100 milliseconds (because there are 10 separate 100 millisecond periods in
each second). Instead, we see that there are 13 messages at the 99th percentile per 100 milliseconds. By contrast, when we get out to the 99.99th
percentile, the situation is dramatically different. There are 1,755 messages
per second in the top 0.01 percent of seconds in the trading day. Thus, you
might expect to see 176 or so messages per 100 milliseconds at the top 0.01
percent of millisecond periods during the same trading day. Instead, we see
863, about five times the expectation.
Comparing 1‐second intervals to 1‐millisecond intervals is even more
interesting. At the 99.99th percentile, you would expect about 2 messages
per 1 millisecond, given the number of messages at the 99.99th percentile
per 1 second (1,755 divided by 1,000—the number of milliseconds in a single second—is 1.755). In reality, we find that the number of messages per
1 millisecond at the 99.99th percentile is 56! Even comparing message rates
per 10 milliseconds to message rates per 1 millisecond yields surprising results
(around double the number of messages are transmitted at the 1 millisecond
level versus what you would expect from looking at the 10 millisecond level.
One could argue that it is silly to worry about the 99.99th percentile.
Events in this realm happen far less than 1 percent of the time. But consider
that there are about 23.4 million milliseconds in a 6 ½ hour trading day.
This means that there are 234,000 observations that occur with 1 percent
probability during the day. So a system that is designed to capture “only”
99 percent of all messages transmitted during the day may miss the busiest
234,000 milliseconds worth of data. This should self‐evidently be a massive
problem for any algorithmic system. There are 2,340 millisecond intervals
that constitute the busiest 0.01 percent of observations in a single trading
day. This is itself a big number. Whereas the tails of the distribution of messages per 10‐seconds are relatively well‐behaved, the tails of the distribution
of messages per millisecond are incredibly badly behaved.

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Why is this a problem? Because if you are trying to engineer a system to
be responsive at a given timescale, you need to be able to handle arrival rates
at around the same timescale. So if you only care about millisecond response
times, then you can be satisfied with understanding and handling the message
rates at the one‐millisecond level. But if you care (as many high‐frequency
traders do) about tenths of a millisecond, you must be able to handle message
arrival rates at the level of tenths of a millisecond. Here the variability is of
course even greater. Compounding the problem is the fact that there is a seasonality of busyness within each day. On a typical day, the period just before
the close is the busiest, and the period just after the open is the second busiest.
Otherwise things are fairly quiet. This means that on a typical day you have
to handle outlier amounts of data simultaneously across all tickers. And during other busy times (e.g., after a Federal Reserve rate announcement or some
other big news), the same data‐burst problem reoccurs.
A quant system that is able to handle these problems must deal with potential problems in any number of areas: the connection between the HFT’s
server and the exchange’s matching engine (known as a cross‐connect), the
network switch, connections between the colocation facilities of the various exchanges, and the data feed handler for each exchange—just to name
a few. Moreover, bursts of data that might have been handled individually
could become overwhelming as one aggregates order books from multiple
exchanges to re-create a real‐time consolidated book.
And if this wasn’t enough of a challenge already, the models used by
HFTs to process the data and come up with trading signals add latency. It
takes time to decide exactly what to do. The preferred approach of implementing trading signals is to split them up across multiple servers. But this
in itself is a further challenge. There are issues with hardware, software,
and network engineering. How do you distribute consolidated data in a
timely manner to various servers, for example, when each server is charged
with computing and running the actual trading strategy? Distributing data
to various servers adds varying amounts of latency. The better one handles
these kinds of issues, the less latency introduced during data bursts. The
worse one handles them, the more latency there is during times of high‐message traffic.

Signal Construction
Once data have been properly handled and distributed, a reaction to that
data needs to be properly constructed and implemented. Broadly speaking, we can define two categories of strategies that can be implemented
within such a system: execution algorithms (covered in Chapter 7) and an
HFT strategy. These strategies can be widely varying in the degree of their

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c omplexity. For example, an HFT strategy attempting to control for risk
factors continuously throughout the day would obviously be more complex
than an alpha model with an intraday time horizon but no risk management. Even alpha models with intraday horizons can vary tremendously
in their complexity. (We detail the kinds of strategies that HFTs employ in
the next chapter.) But even if we take two exactly identical HFT strategies,
there are (in most cases) multiple algorithms that can be used to calculate
the signals. And not all of these algorithms are equally fast.
To give an example, index arbitrage is a widely known HFT strategy.
This strategy involves trading the value of the SPY ETF against the values of the 500 stocks that constitute it. (Note that index arbitrage can be
traded on any index versus its constituents, and we use the SPY simply as an
illustrative and well‐known example.) If you know that the S&P 500 index
consists of 500 stocks and 500 weights, you should be able to compute a
bottom‐up estimate of the value of the S&P index. If, however, you find that
the actual value of the SPY ETF, after accounting for expense ratios and
other similar structural differences between the ETF and a basket of stocks,
is trading at a different value, then theoretically free money is to be had by
virtue of buying whichever side is undervalued and selling short whichever
side is overvalued. As you might imagine, there’s a lot of competition for free
money. This means that you have to make decisions about what is overvalued or undervalued very quickly. As simple as it sounds, comparing the SPY
ETF to the basket of stocks that compose it at very high speeds is not trivial.
There are a number of algorithmic solutions for this, and they don’t all do
the computations equally quickly.
As a sidebar, it is this kind of strategy that you often see in HFT. Very
simple ideas, very simple calculations, but that require astoundingly fast
infrastructure to capture. It is therefore very ironic when we hear the press
talk about “sophisticated, complicated algorithms.” The difficulty is not in
understanding what’s being done, but in doing it very quickly.

Risk Checks
The last step before sending an order to the marketplace (in some markets,
such as U.S. equities) is submitting the order to what’s known as a regulatory risk check. Regulators (under the Market Access Rule) have indicated
that broker‐dealers (who give trading firms access to the marketplace) are
responsible for ensuring that each trade is (a) within the means of the trader,
(b) not in error, and (c) compliant with regulatory requirements. They also
mandate that the risk‐checking software should be in the full and exclusive control of the broker‐dealer whose customer is trying to make a trade.
This rule was adopted in July 2011 as a response to criticism of HFT and

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concerns over the stability of a marketplace without such rules. Elaborating
a bit further on the kinds of things that need to be checked before an order
is sent to market:
Does the trader’s buying power allow for the order(s) in question to be
made?
■■ Does the number of open orders seem to be valid, or does it appear that
the trader has a bug that leads to an excessive number of open orders?
■■ Does this individual trade seem too large to be intentional?
■■

Prior to the adoption of the Market Access Rule, most broker‐dealers
operated in accordance with the rule anyway. But a small number of very‐
high‐volume trading firms operated differently. These firms engaged in what
is called naked access. This meant that customers of the broker‐dealer were
allowed direct access to the market if the broker was ultimately comfortable enough (after performing many checks of its own) with the client’s
risk‐checking technology. Why does this matter? Because a risk check provided by the broker generally resides on a broker’s server. For a trade to go
through a risk check, it must be transmitted by the customer to the broker
before going out to the market.
This added hop (in network engineering terms) adds more latency for
two reasons. First, there is another connection between servers that must
take place (between the customer’s trading server and the broker’s risk‐
checking server). Second, the broker’s risk‐checking software is generally
going to be inferior to that designed by a speed‐sensitive trader. This could
be for any number of reasons, including the presence of superior talent at
the best HFTs or quant trading firms versus the typical brokerage firm,
or simply different goals. The broker generally cares a lot more about issues like scalability than being hyper‐fast. By contrast, speed‐obsessed HFT
engineers (who are willing to tackle all the issues above) want the tick‐to‐
trade total latency to be as little as 10 microseconds (0.1 milliseconds).
They are scarcely going to be satisfied with an added risk‐check latency of
50 microseconds.
Thus, some HFT firms opted to send their trades directly to the exchange
after utilizing their own in‐house risk checks. Not many brokers were willing to accept an arrangement like that because the broker ultimately bears
responsibility if there is a problem with the customer’s risk check. However, some brokers made a business of providing naked access to HFTs, and
these firms definitely enjoyed a speed advantage for several years. With the
Market Access Rule, the SEC banned this practice, and now one must use a
broker‐dealer’s risk check. This drove some of the largest HFTs to build out
their own broker‐dealer units so that they could continue to use their own

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risk checks with additional regulatory overhead. It also drove a new arms
race to create the fastest commercial risk checks. As of today’s writing, there
are roughly three top‐tier solutions; the others lag well behind. Solving the
risk check problem remains an area where some HFTs (and, primarily, their
service providers) focus on reducing latency.

Summary
In this chapter, we have elaborated on the reasons that high speed (or low
latency) trading matters, as well as the sources of latency. Depending on
the type of trade or trading strategy being implemented, there are differing
reasons for the emphasis on speed. And, while this has received a significant
amount of negative attention in the press, it is absolutely no different from
the situation in any other industry. If an advantage can be developed within
the rules of a competitive game, then the most competitive players will seek
to develop that edge. But, as is the case for quant trading in general, there
is clearly a double standard when it comes to HFT and low-latency trading.
People seem to be really angry that HFTs, having solved the incredibly difficult problems enumerated above, have achieved a (completely legal, ethical,
and fair) competitive advantage over other traders.
The irony, as we will discuss further in Chapter 16, is that low‐latency
trading is like any other enterprise in a reasonably free‐enterprise system:
Taking risk does not imply that one will succeed. Countless HFTs have
invested enormous sums of time and money into infrastructure, only to
find that they lack the ability simply to generate acceptable returns. Many
more HFTs either cannot afford the huge investment of resources, or simply lack the expertise, to create their own infrastructure. A typical build
versus buy decision is made, and some firms end up utilizing commercial
vendors for many or all parts of this infrastructure. Some firms advertise
themselves as “HFT‐in‐a‐Box” solutions, which allow a strategist with a
good idea to implement her strategy without having to build all of these
other elements. Unfortunately, few of these vendors deliver what is advertised (just as is true in basically any industry). The result is that when
the opportunities to add value are the most plentiful (when trading activity is at its most frenzied level), relatively few vendors are able to deliver
true low-latency solutions. To quote Mike Beller, CTO of Tradeworx, who
helped me with this chapter: “Be suspicious of anyone who quotes averages, or even averages and standard deviations. Responsible people engineer for the 99th percentile.”
Even firms that have the resources and that have been successful are
subject to substantial risks. While detractors of HFT have pointed to the

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near‐death experience of Knight Capital in 2012 as evidence that HFTs
cause instability in the markets, the reality is extremely different: Knight
made a change to its software that introduced a bug. It was a mistake of its
own doing. And who suffered? Knight. It nearly went out of business and
had to secure emergency funding to stay afloat, at the expense of a large
portion of the value of its business. While it’s sad for Knight and those who
own their stock, it is exactly fair. Knight made a mistake, and Knight paid
the price. No mom and pop investors, no pensioners, no market systems
were harmed. And all of this is in pursuit of what amounts to a $0.001 per
share profit expectation.
This point is perhaps the most important to remember. A tenth of a
penny per share is the expected profit margin of a successful U.S. equity
high‐frequency trader. In exchange for this, these traders take on the risks
associated with the capital and time expenditures of competing in a hypercompetitive space. For traders who are expecting to hold positions for a
year and make 25 percent or more on that trade, HFTs add liquidity. That
they might make $0.001 per share to provide that liquidity is both inconsequential and totally fair. We now turn to the kinds of strategies that HFTs
employ.

Notes
1. Christopher Steiner, “Wall Street’s Speed War,” Forbes, September 27, 2010.
2. All message traffic statistics in this section are courtesy of Tradeworx, Inc. proprietary research, September 2012.
3. In case you were wondering why the ES futures tend to lead SPY ETFs, the reason is primarily that the ES futures are where the largest dollar volumes exist.
This is probably for two reasons. The first is that ES futures have been around
a lot longer than SPY ETFs, so some of this is just incumbency, both because of
habit (once an instrument becomes the instrument of choice for a given exposure, it tends to retain that title with a large amount of inertia on its side), and
because it is a pain in the neck to change one’s infrastructure to trade stocks
(ETFs are listed and traded the same way as stocks, for all intents and purposes)
when one is already trading futures. Second, the futures markets do offer a
couple of structural advantages over ETFs. Profits on many futures contracts
are subject to less onerous taxes than profits on equity or ETF trades. Also, futures contracts offer a fairly substantial amount of leverage, so whether a trader
wants to make a big bet or simply doesn’t want to spend a lot of money to put
on that bet, futures can be an efficient way to implement the trade. However, the
gap has been narrowing somewhat, driven by the migration of retail investors
away from actively managed mutual funds into passive ETFs, and partially by
virtue of the fact that, in many ways, the ETFs are often cheaper (in aggregate)
to transact.

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4. It is worth noting that, while New York is the city we associate with the U.S. stock
market, the realities of the amount of real estate needed for the massive data centers that house stock exchanges are actually mostly located in New Jersey.
5. Melissa Harris, “Some High‐Speed Traders Convinced Microwave Dishes Serve
Up Bigger Returns,” chicagotribune.com, August 19, 2012.
6. Jerry Adler, “Raging Bulls: How Wall Street Got Addicted to Light‐Speed Trading,” wired.com, August 3, 2012.
7. Matthew Philips, “Stock Trading Is About to Get 5.2 Milliseconds Faster,”
bloomberg.com, March 29, 2012.

Chapter

High-Frequency Trading
If you have a mouse in your hand, you are too late!
—Blair Hull, December 2000

e have described the importance of, components of, and challenges
to building a high-speed (low-latency) trading infrastructure. These
components are used, primarily, for either high‐frequency trading (HFT)
applications or for implementing automated execution algorithms. In this
chapter, we will focus on HFT, seeking to understand the kinds of strategies
employed by these traders and how these techniques relate to the infrastructure we have outlined.
There is no widely accepted classification of HFT strategies. However,
we can consider them to fall into one of four broad categories: contractual
market making, noncontractual market making, arbitrage, and fast alpha.
In this chapter, we will describe each of these kinds of strategies, as well as
the risk management and portfolio construction considerations that apply
to them.

Contractual Market Making
A contractual market maker (CMM) is the class of HFT practitioner that
has the closest analog to a traditional feature of the markets. First, we should
understand the concept of market making.
The odds that two customers simultaneously want to do exactly opposite things (e.g., customer A wants to buy 2,000 shares of XYZ at $100.00,
while customer B wants to sell 2,000 shares of XYZ at $100.00) are fairly
small. Of course, it is reasonably likely that there is at least some portion of a
customer’s desired trade that could be filled by another customer. Taking our

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example above, maybe customer A wants to buy 2,000 shares, while customer B wants to sell 5,000 shares. The balance—a desired sale of 3,000
shares—either goes unfilled until a later time (usually at a time adverse to
the seller), or it can be filled by an intermediary who is willing to take the
risk of buying 3,000 shares for the sole reason that customer B wants to sell
them. Market makers are precisely this kind of intermediary: They provide
liquidity to those who have a utility for it.
An analogy from daily life is useful here. Manufacturers rarely sell their
goods directly to retail customers because, practically speaking, they have
operations lifecycles to manage. They cannot afford to change how much
and what they are supplying at the whims of retail customers. Thus, distributors buy goods from manufacturers and warehouse those goods until the
retail market is ready for them. In the same way, market participants don’t
necessarily make investment decisions that coincide perfectly, and market
makers get paid to warehouse the risk in the interim.
There are two types of market makers. In this section, we will describe
CMMs, who are sometimes referred to as order flow internalizers. The first
key to understanding CMMs is to look at the economic and contractual
relationships that CMMs have with the market. The CMM’s obligations
vary by market, instrument, and geography, but we can examine U.S. equity
market making as one example. CMMs engage in legal relationships with
various brokerage firms (whose clients wish to make trades), so that the
brokerage routes its customers’ orders to the market maker to be executed.
In exchange for the broker sending its retail order flow to the CMM, the
CMM often is required to: (a) pay the broker1 and (b) fill 100 percent of the
orders that customers send to it. Generally, this last obligation has two different types of commitments to fill: one in the case of small orders and one
in the case of large orders.
CMMs in U.S. equities generally are required to fill 100 percent of
“small” orders on an automated basis (this is aptly known as autofill). So,
for example, a typical investor in U.S. equities has an account with some online broker. This investor decides to buy, say, 200 shares of XYZ as a market
order. The CMM has agreed with the broker that it will sell 200 shares of
XYZ to this customer at whatever the prevailing market’s best offer is. But
interestingly, neither the customer’s order to buy nor the CMM’s taking the
other side of that trade ever goes into the exchange’s limit order book. The
transaction happens away from the exchanges, but it references the activity
that is taking place on the exchanges (specifically, the best bid or offer).
The CMM, by virtue of having agreed to this contractual relationship
with the broker, gains an advantage that supersedes even the fastest traders.
In effect, it doesn’t even need to post bids and offers because it passively
takes the other side of all customer order flow as it comes in. This happens

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in the reverse sequence to what happens in a normal market situation:
Generally a passive order is resting in the limit order book, and an active
order comes into the market later and takes the liquidity offered by the
passive order. In this case, the active order to buy comes to the CMM, and
the CMM uses the prevailing best offer from the exchanges to fill the active
order. While the CMM’s orders are not actually in the queue, there is always
at least some support behind their positions. After all, the CMM is piggybacking on whatever the prevailing best offer was at the time the CMM
elected to fill the customer order. All that said, so far, it is not at all obvious
that the customer is any worse off by virtue of his broker having established
this contractual relationship. The customer’s order is filled at the prevailing
best price available and does not need to compete with other active orders.
We contended in Chapter 14 that trading passively is not necessarily
a highly profitable activity (especially before the incentives provided by
some exchanges for providing liquidity), because of the problem of adverse
selection. However, when facing off against retail order flow, a passive participant enjoys the most favorable selection possible. Retail order flow generally consists of a large number of small orders, and the aggregate of these
orders on a given name is usually a fairly small net quantity. This means that
there is unlikely to be any significant price impact, which is another important determinant of the level of adverse selection.
For larger orders, CMMs generally have the right to act as an agent
of the customer, trying to get the order filled at market, without taking the
whole order for itself. So, if the customer wants to buy 10,000 shares of
XYZ, the market maker acts on behalf of the customer in attempting to get
the order filled. However, here, a perverse incentive may exist. At the very
least, it is quite an interesting situation. Let’s start with an illustrative order
book for XYZ, immediately before the customer’s 10,000 share buy order
comes in, shown in Exhibit 15.1.
If we imagine the 10,000 share buy order comes in at this moment, the
CMM can go to market, lift all 2,000 shares offered at $100.01 (Offer1)
Exhibit 15.1
ID

Mockup of an Order Book for a Fictitious Ticker
Size

Bid

Offer

Size

Bid1

1,000

100.00

100.01

2,000

Offer1

Bid2

3,100

99.99

100.02

3,000

Offer2

Bid3

2,000

99.99

100.02

1,000

Offer3

Bid4

5,000

99.98

100.03

4,000

Offer4

Bid5

6,000

99.97

100.04

1,000

Offer5

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High-Speed and High-Frequency Trading

and all 4,000 shares at $100.02 (the sum of Offer2 and Offer3). He has
now filled 6,000 shares at an average price of $100.0167. Then he can take,
say, 3,500 shares of the 4,000 offered at $100.03 (Offer4), and fill the last
500 shares himself. Now that the prevailing best offer is $100.03, he will fill
them at $100.03. The order book immediately after this order is filled looks
as shown in Exhibit 15.2.
Those first 9,500 shares offered had no idea that the price was about
to move up by 2–3 cents immediately. So in this case, since the CMM knew
that this customer’s order was about to push the price up, he delayed selling
until the buy order was almost exhausted. Those last 500 shares, however,
are likely to have been profitable to sell. If there was no other buying pressure behind that 10,000 share buy order, the upward move is likely to be
immediately reversed, and the offered side of the book is likely to replenish
with offers that are lower priced than $100.03. This will allow the CMM to
exit his position at a profit, and at the expense of those traders whose orders
were at lower‐priced offers initially.
I mentioned that this is, at the very least, an interesting dynamic. It
may incentivize the CMM to act in a way that is adverse to the customer,
however. If the CMM has the ability to act as an agent of the customer and
to fill the last portion of a trade, the CMM has an incentive to do the worst
possible job of filling the bulk of the customer’s order, because it pushes the
price to a level that almost certainly makes taking the other side of it very attractive. In other words, the CMM could use a horribly ineffective execution
strategy for the first 9,500 shares, specifically designed to get the customer
the worst possible price (especially on the last few hundred shares), so that
the CMM can come in and take those last few hundred shares into his own
inventory at an untenably high price.
Exchanges have begun to fight back against internalization of order
flow. Interestingly, the near‐destruction of Knight Capital in August 2012

Exhibit 15.2 Mockup of an Order Book for a Fictitious Ticker after a Market
rder to Buy 10,000 Shares Is Mostly Filled by a CMM Acting as an Agent of
O
the Customer
ID

Size

Bid

Offer

Bid1

1,000

100.00

100.03

500

Offer4

Bid2

3,100

99.99

100.04

1,000

Offer5

Bid3

2,000

99.99

Bid4

5,000

99.98

Bid5

6,000

99.97

Size

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was an indirect result of the NYSE’s introduction of a new program designed specifically to combat order flow internalization. This program,
called the Retail Liquidity Program (RLP), offers retail orders access to better fill prices than they historically could get. To deal with this change in the
market structure, Knight made some changes to its own software. And due
to a bug in that new release, Knight’s brush with bankruptcy unfolded in
merely a half hour. It is not a coincidence that the roughly 140 stocks that
Knight lost money on were all NYSE tickers. That said, programs such as
the RLP are not intended to put CMMs out of business. Indeed, thus far the
biggest participants in such programs are the CMMs themselves. The idea is
simply to get as much share volume on the lit venues as possible.
As we relate the activities of CMMs to what we showed in Chapter 14
about high-speed trading and the various types of orders, we can see clearly
why CMMs need to be fast. While they do not need to compete with other
participants for better queue placement in order to get into a position (this
comes to them from the brokerage firms directly), they do need to (a) have
a precise, timely estimate of the market in order to fill orders at the correct
price; and (b) be able to exit positions rapidly. They, after all, are taking on
the other side of others’ trades. And while retail orders may not be the worst
kind to take the other side of, there is still a real risk that retail participants
will move heavily in one direction on a given instrument (for example, if
a stock has good news, many customers are likely to want to buy it). This
can result in the market maker taking on a significant amount of size on the
wrong side of the news and short‐term momentum in such an instrument,
which highlights the need for speed in placing orders to reduce the inventory acquired. All that said, a CMM’s need for speed is categorically not at
the same level as it is among the HFTs we will describe in the subsequent
sections of this chapter.

Noncontractual Market Making
Noncontractual market making (NCMM) also involves taking the other
side of active orders. NCMMs provide bids and offers that rest in the order books of various exchanges, particularly lit exchanges (as described in
“Where to Send an Order”). In many markets, they are incentivized to provide liquidity by virtue of liquidity provision rebates. In other markets, active order flow is sufficiently benign that a fast NCMM can still turn a profit
even without any further compensation. In general, an NCMM acquires
positions by placing passive orders, waiting for someone to lift his bid or
offer. Once acquired, the NCMM may exit passively or actively, depending
on liquidity provision rebates and the market’s movements.

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Given their reliance on passive orders, the biggest risk that any market
maker is exposed to is adverse selection. A market maker taking the other
side of one order can hope he is able to take the other side of another order
immediately, and at a profit that at least equals the bid/offer spread. Or, if
the market moves his way, he may be able to exit actively, and make money
on the move. This is the embodiment of “buy low, sell high,” but modified: “buy low, sell ever‐so‐slightly higher, very soon, and repeatedly.” And
indeed, in normal times, in the absence of a very short‐term trend, this is at
least somewhat achievable.
But first, there is the matter of being fast enough to avoid the adverse
selection problems that plague any passive order in the lit markets. As we
showed in Chapter 14, this is no small feat in the first place. When we look
at the kinds of trades that NCMMs in U.S. equities take the other side
of, for example, we find that most of the best order flow is internalized,
either by CMMs or by dark pools. This leaves NCMMs to interact primarily with professional investors in the lit exchanges, against whose orders
it is dangerous to trade. Thus, while speed matters to any market maker,
NCMMs have a particularly acute need to be fast. As an aside, NCMMs do
usually have access to dark exchanges as well, and often will route orders
through these dark pools first, taking advantage of superior liquidity taking
fees, before sending the remainder out to the lit exchanges.
Second, NCMMs must have fast access to information sets that can
help them avoid adverse selection problems. We showed in Chapter 14 that
the ability to cancel passive orders quickly is critical to a passive trader’s
likelihood of success. For example, if some stock index’s futures contract
is rallying sharply, there is a very strong probability that a wide variety of
stocks will also rally sharply in the immediate future. A NCMM who cannot
access information about the futures market in a timely manner will likely
end up failing to cancel his passive offers at the top of the order book, which
will cause him to experience adverse selection in the fills he receives on his
sell‐trades.
A key challenge for NCMMs is how to manage and dispose of the inventory they acquire by virtue of having other market participants lift their
bids and offers. This can be particularly challenging when markets are trending, leaving the NCMM with large positions in the opposite direction of
the trend. As mentioned earlier, NCMMs bear such substantial risks when
holding positions that they sometimes actively exit their trades, even though
this means crossing the bid‐offer spread and possibly also paying a liquidity
taking fee. Another approach to dealing with inventory risk is to take opposing positions in instruments that closely correlate with those in inventory. For
example, if UVW is an imaginary company that is a peer of XYZ, in the same
industry group, with a similar market capitalization (and so on), it is highly

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likely that any large, directional move in XYZ will be mirrored in UVW.
Thus, if the market maker is filled on a passive bid in XYZ (which makes
him long XYZ), his algorithms can consider putting passive offers on UVW,
or actively selling it, to hedge his risk that XYZ experiences a large move.

Arbitrage
The word arbitrage connotes riskless profit. This has obvious appeal, and
it is equally obvious that risk‐free profits are hard to come by. Arbitrage
opportunities exist when instruments that are structurally correlated behave differently. We define structural correlation as a correlation that exists
because it must. Instruments that track the S&P 500 index, for example,
should all correlate roughly perfectly. If the S&P 500 futures contract (ES) is
up 1 percent for today, while the SPY ETF (which tracks the S&P 500 also)
is up only 0.6 percent, a riskless profit opportunity exists, to go short the
futures and go long the ETF. In this way, the trader has virtually guaranteed
himself a 0.4 percent profit. These two instruments are both meant to track
the performance of the same 500 stocks, and when one is outperforming the
other, it is necessarily because there are temporary imbalances in the trading of one versus the other. For example, if a large order to buy the futures
suddenly hits the market, moving the futures contract up suddenly, it might
take a small amount of time for the passive orders (both bids and offers) in
the ETF to cancel and ratchet upward. During that time, a sufficiently fast
arbitrageur can pick off a slow‐to‐cancel passive order and acquire a riskless
profit position.
In order to qualify as a true arbitrage, a trade must capture an inefficiency in the marketplace that causes the price of an instrument (or derived version of the instrument) to be different in different locations (e.g., exchanges)
or formats (e.g., an ETF versus the stocks that constitute that same ETF) at
precisely the same moment. The arbitrageur sells the relatively overpriced
one and buys the relatively underpriced one, so that when they converge, he
reaps the profit.
The most common form of HFT arbitrage is index arbitrage, which is
the broader label for our earlier example of S&P futures versus the SPY ETF.
This is a strategy that compares the value of an instrument that tracks an index either to another instrument that tracks the same index, or to the value
of the constituents of the same index. Take an imaginary futures contract
that tracks an index that contains two instruments at a 50/50 weighting.
The index can be priced either directly in the futures contract or indirectly
by taking the value of each of the constituents and multiplying that value
by the weight (50 percent each, in our example). Because the index trades

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separately from its constituents (often on different exchanges), the prices of
the index traded as a whole versus index that can be created synthetically by
buying its constituents in the correct weighting can and do diverge by small
amounts and for short amounts of time.
Another type of arbitrage is venue arbitrage, which exists only in fragmented markets. A venue arbitrage takes advantage of a fragmented market
structure (which means that there are multiple exchanges that allow trading
on the same instrument), which can sometimes cause a price to be different
on one venue from what it is on another. Here, the instrument isn’t merely
structurally correlated to another instrument; it is actually the exact same
instrument traded in more than one place. For the same reason that index
arbitrage opportunities can come to exist, these venue arbitrage opportunities also can exist. In U.S. equities, Reg NMS was enacted in 2007 in an
attempt to deal with this problem. In certain other markets, venue arbitrage
remains a possibility.
In a sense, when a CMM receives customer orders that include requests
to buy and sell the same instrument at the same time, she has an arbitrage
opportunity, because she can sell the instrument to one party and buy it
from another at the same time, at different (advantageous) prices. The buy
order is filled at the prevailing best offer, and the sell order is filled at the
prevailing best bid (which, by definition, is lower than the offer). To address
this extremely obvious inequity, some brokers have begun to require CMMs
to fill both such customer orders at the best mid‐price when there are matching and opposed orders.
While risk‐free profits are undeniably attractive, the cost of remaining
at the highest tier of the technological capabilities required to be fast enough
to capture such opportunities is substantial. At first glance, it is evident that
speed should matter, for the same reason that $100 bills don’t get left on the
street for very long. If you can cross the bid‐offer spread and realize an arbitrage opportunity, then it makes sense to do so. But occasionally, depending
on the size of the opportunity, passive orders can be used to improve returns.
If the price discrepancy is very large, and if the exchange(s) involved provide
liquidity provision rebates, it may be an added benefit to implement an arbitrage trade using limit orders. But in general, these are active trades. It is
better to capture some riskless profit with 100 percent certainty than to risk
missing the whole opportunity by trying to make it marginally better.
As a practical matter, not all HFT arbitrages are strictly riskless. In more
efficient markets (e.g., U.S. equity indices and single stocks), it is often impossible to do both legs of the arbitrage trade. The opportunity is so fleeting that
only one leg at a time can be implemented. So, for example, a strategy that
compares ETFs to futures might be able to trade the ETFs only, betting on
a lead‐lag relationship between the instruments. But the futures might well

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move again before the trader can lock in a profit. This is still a good trading
strategy, but on a given trade, its odds are not substantially better than even.
In less efficient markets, there remain opportunities for truly riskless profit.

Fast Alpha
The fourth type of HFT strategy we will consider is fast alpha. Fast alpha
strategies are in essence engaged in the same kinds of strategies as discussed
in Chapter 3. They mainly use price‐based signals, such as momentum, mean
reversion, and technical sentiment. If we consider what we described in
Chapter 8, regarding the influence of data types on the kinds of strategies
that can be implemented using such data, it makes sense that this should
be the case. Fundamental information does not change very often. When it
does, it usually takes some time (more than a day in most cases) to be fully
priced‐in. Furthermore, most fundamental information is released during after‐hours or pretrading sessions, when liquidity is poor. However, important
(i.e., surprising) fundamental data do have an impact on prices on a very
short (intraday) timescale. In 24‐hour markets such as currencies, this can be
even more true, though there are natural increases in liquidity during certain
more conventional market hours. In any case, various growth or value types
of strategies can be implemented on an intraday timescale, but this is in the
tiny minority of cases. Mostly, fast alpha strategies act on information that
changes frequently throughout the trading day: prices, volumes, and limit
order book information. Because changes in fundamentals can result in high
volumes, HFTs can be quite active when these changes occur, even if they are
not explicitly trying to trade based on the fundamental information itself.
Contrasting fast alpha strategies with arbitrage strategies is also useful.
Whereas arbitrage strategies are taking advantage of price discrepancies between instruments that are structurally correlated, fast alpha strategies are
sometimes looking to profit from price discrepancies on a statistical basis.
For example, if XYZ and UVW are two companies in the same industry
group that are close peers, with similar market capitalizations and fundamental features, one would expect them to track each other most of the
time. If XYZ diverges from UVW, you can reasonably expect that it should
converge. But what if the divergence stems from some real information that
implies the beginning of a decoupling between XYZ and UVW? Just as we
showed in the example of MER and SCHW in Chapter 10, instruments can
go through periods of being closely correlated, and periods of being completely different. In other words, there is no structural reason that correlation
between the two instruments must remain related. And as a result, we are
dealing with a statistical relationship, which by definition implies some risk.

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This is also true for directional types of forecasts, which look at historical behavior as a guideline for future behavior. There may, for example, be a
good chance that, if some instrument makes consecutive new intraday highs
several seconds in a row, it will decline briefly thereafter. But this is still a
matter of chance. There is no structural relationship between the past performance of the instrument and the future performance of the instrument
that causes this setup to remain a return generating strategy.
Some fast alpha strategies are more passive, for example, intraday versions of statistical arbitrage. They can be considered as close cousins of
NCMMs, in the sense that they are passively placing orders that provide liquidity, but perhaps with a certain selectivity that (hopefully) reduces adverse
selection issues. For such strategies, everything we discussed in Chapter 14
regarding the need for speed in placing and canceling passive orders applies. Intraday momentum strategies can also be implemented passively, by
canceling passive orders that would take the other side of the prevailing
trend and working orders that would get the strategy into a position in the
direction of the trend. Obviously, these orders are less likely to be executed,
because they are attempting to capture small pullbacks in a trend. Furthermore, adverse selection issues apply, particularly when the trend reverses. As
such, the need for speed here stems from a desire to get passive orders to the
top of the book, and from the need to cancel stale passive orders to avoid
adverse selection issues.
More often, intraday trend following is an actively implemented strategy. These strategies have a particularly difficult challenge because market
impact and slippage are both working severely against the strategy’s objectives. If an instrument is trending down on a very short timescale, a fast
trend-following strategy will naturally want to get short that instrument (or
instruments that closely correlate to it). However, any delay in processing
data or getting orders back to the marketplace can be detrimental, because
the market will not wait for a slow trader to figure out what to do. The
trend can move the instrument away from the slow trader, resulting in large
slippage costs. Furthermore, because the trader is desiring to buy (or sell)
an instrument that has already been going up (or down) for some time,
market impact costs are also likely to be more severe in this case. For these
reasons, intraday trend following is less common than mean reversion oriented trading strategies, and requires low latency capabilities.

HFT Risk Management and Portfolio Construction
HFT strategies most often have a different approach to risk management
from their slower peers, even for strategies (such as those in the fast alpha

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275

category) that share similar underlying themes. Accounting for risk factors,
transaction cost models, and various other inputs to an optimizer, for example, takes precious computing time. This would slow down the process
of implementing the alpha strategy. Furthermore, most of the kinds of risk
factors that longer‐term strategies would want to hedge rarely apply to security movements from one moment to the next intraday. For example, some
longer‐term traders care about neutralizing their exposure to the size factor
(market capitalization, essentially). They don’t want to have a bias of being
long small capitalization companies and short large caps (or vice versa).
Intraday, this is a dramatically less useful distinction, because the way that
this risk factor expresses itself in the markets simply doesn’t take place at an
(often very short‐term) intraday timescale. Another way of thinking of this
effect is that statistical correlations are much weaker at shorter timescales
than at longer ones, while idiosyncratic (primarily liquidity‐driven) considerations are more significant.
There is a further question of applicability of risk models to three
of the four types of HFT strategies described above. Arbitrage strategies,
for example, clearly require a different type of risk management from
what is provided by a risk factor model. By design, long positions and
short positions are in essentially identical instruments. This leaves no
room for conventional risk factor exposures. The kinds of considerations that apply to arbitrageurs relate to sizing their bets to ensure that
the temporary variances in the spread between their longs and shorts do
not put them out of business. For CMMs and NCMMs, the goal is to
unload inventory as quickly as possible, not to worry about risk factor
exposures.
The most common approach to risk management for HFT strategies
is to control a very small number of very simple‐to‐calculate risks. For
example, limiting the maximum order size on a given ticker, the maximum accumulated position size for a given instrument, the maximum
aggregate portfolio size, or the maximum number of open orders on an
instrument (or in aggregate) are all very simple risk checks that add virtually no latency. Many will automatically unwind their portfolios and
stop trading if they reach a certain predefined loss level. Some HFTs will
elect to control their directional exposure as well, limiting their net long
or short percentages. Most HFT strategies are concerned with ensuring that hedging trades are put on extremely quickly, and before prices
move adversely. For example, if an arbitrage trader sees an opportunity
to buy the S&P 500 index and short the underlying stocks, locking in
some small profit, it is possible that both legs of this trade will not be
implemented at precisely the same moment. After one leg is executed, the
trader simply owns a directional bet on the stock market. It is not until

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the second leg is executed that the trade becomes an arbitrage (and risk
free). As such, if the market moves adversely to the first leg of the trade
before the second leg can be put on, not only might the opportunity disappear, but money can easily be lost. This is known as legging risk, and
many HFTs try to manage it.
Portfolio construction, too, looks very different for HFTs from what it
is for longer‐term quants. The most obvious example of this is in the case
of arbitrage trades. If you have an opportunity to make riskless profits, you
should do that trade as large as the market will allow you to do. For both
kinds of market makers, they have little control over how many of their
passive orders end up being lifted by more active participants. For them, it
comes down to simply ensuring that they diversify their risk across names,
or to limiting the maximum size of inventory that can be accumulated (since
whatever is accumulated must soon thereafter be dispensed). In the case of
fast alpha strategies, there is no particularly common theme to how traders size positions. But they tend to use the simpler ideas from among those
discussed in Chapter 6. Equal weighting positions, or weighting them based
simply on the expected return, are common approaches. But considerations
of covariance and volatility rarely factor in, and there is almost no sense in
running an optimization or even accounting for risk and transaction cost
modeling. All of these things add time to the process of making trades, and
so simplifying the calculation of the strategy (as we discussed in Chapter 14)
is an important way to reduce latency.
The most surprising thing about HFTs is that, while they trade (hyper)
actively, they most often do not account for transaction cost models in their
strategies. This seems paradoxical: If transaction cost models are supposed
to help you trade in a smarter way, why would the very active traders eschew
them? In some sense, the transaction costs that other investors are paying
(bid/offer spreads and liquidity taking fees) are often the main sources of
alpha for many HFTs. As such, transaction costs as typically defined are very
often negative: They are sources of profit. Obviously, it then becomes desirous to trade as often as possible. This is outside of a passive HFT’s control,
because she cannot cause someone else to trade actively, but it is an objective
for a passive HFT nonetheless.
Active HFT strategies, by contrast, must overcome the same transaction
costs as apply to other investors, but without the benefit of holding the position for a very long time. As you can imagine, not nearly as many opportunities exist to hold a position for a short amount of time, say a few minutes,
and generate a profit net of transaction costs. HFTs, thus, tend to consider
commissions, regulatory fees, and taxes, and the economics of providing or
taking liquidity more than market impact and slippage.

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Summary
We have now explored the kinds of strategies that HFTs utilize. You may
notice that there are some significant differences between HFT strategies
and the kinds of alpha strategies that we described in Chapter 3. Indeed,
many HFT practitioners, privately, will tell you they don’t think about alpha
at all. Even for those that do, it is most often at best secondary to technology concerns. A major risk is losing a speed advantage. And, when you look
at both the kinds of strategies being employed and the penalties that accrue
to being slow (which we described in Chapter 14), it begins to be clear why
this is the case.
It does not take someone particularly clever to say that the S&P 500
index should have basically the same value in every instrument that tracks
it. This is a tautology, in fact. S&P 500 = S&P 500. But it is something else
entirely to be able to profit from the extremely fleeting instances where there
is a divergence. It is specifically a technological problem, and many of the
strategies that HFTs employ are at least as much driven by technology as by
a better way of forecasting the future.

Note
1. This practice is called payment for order flow. It carries quite a bit of controversy, because the beneficiary of the payment for order flow is generally the broker, not the broker’s customers. It is, of course, the customers who send orders.
As a result of the well‐deserved controversy around this practice, it has become
less common as the years have gone by. But it has been a feature of the capital
markets for much longer than HFTs have existed.

Chapter

Controversy Regarding
High-Frequency Trading
The major advances in speed of communication and ability to
interact took place more than a century ago. The shift from sailing
ships to telegraph was far more radical than that from telephone
to email!
—Noam Chomsky

s we described at the beginning of Part Four, HFT came into the public’s
consciousness through controversies surrounding it. Most of the arguments against HFT strike me as being arguments made by people who are
either ignorant of the facts or motivated by self‐interest to present biased
and flawed information to the public. The kinds of criticisms generally ignore the differences between the various types of HFTs, confuse various elements of market structure with the practice of HFT, and conflate high-speed
trading (and, often, quant trading in general) with HFT.
The criticisms of HFT seem to gravitate around four major ideas. According to detractors, HFT:
1. Represents unfair competition, creating a two‐tiered system of haves
and have‐nots.
2. Manipulates markets and/or engages in front‐running other investors.
3. Causes structural instability and/or creates additional volatility in

markets.
4. Has no social value.

We will address each of these arguments in order, with the primary goal
of separating fact from fiction.

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High-Speed and High-Frequency Trading

Does HFT Create Unfair Competition?
In 2009, Andrew Brooks, head of U.S. equity trading for T. Rowe Price, said,
“But we’re moving toward a two‐tiered marketplace of the high‐frequency
arbitrage guys, and everyone else. People want to know they have a legitimate shot at getting a fair deal. Otherwise, the markets lose their integrity.”1
The idea behind this argument is that superfast computers, algorithms, and
telecomm setups are all very expensive and unavailable to the average person, and they create a two‐tiered system where HFTs have a huge advantage. This is not an accurate assessment of the current state of the markets.
There are three reasons why, and we will go through each of them here.

The Role of Speed in Market Making
Markets need market makers, just as manufacturers and consumers need
distributors. There have always been market makers, and you can’t have
a properly functioning market without them. Furthermore, market makers have always had to be fast, because of the adverse selection problem
associated with passive trading, which we covered in Chapter 14. In the
past, speed advantages were obtained by a privileged tier of traders who
were allowed to be insiders of the exchange. They used to be called locals, floor traders, specialists, and so on. Now, speed advantages are earned
competitively on a level playing field, and this represents serious progress
in leveling the playing field dramatically compared to the state of markets
in years gone by.
The markets are more egalitarian today than they ever have been in
their history. We have already given the examples from the early 1800s,
when a carrier pigeon was winning technology, providing those that invested in it a serious speed advantage. In the early days of Wall Street, firms
who were more proximate to the physical exchange had superior speed and
access advantages. Later, those that had telephones before others had an
advantage. And so on. The advantage that a big bank had over the average
investor was bigger by orders of magnitude in 1929 than in 2009. In 2009,
the advantage of Getco, among the very fastest in the HFT world, over
the average online brokerage customer was on the order of a fraction of a
second. Even on a very busy day, the advantage gained by such an edge in
speed is trivially small. Compare that with the advantage of a firm that had
personnel on the exchange floor 30 years ago, trading in real time, while a
typical retail investor would check end‐of‐day prices the next morning in
the newspaper!
When advantages are gained in a fair game, on a level playing field,
this is not an unfair competition issue, nor is it a two‐tiered system

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issue. It is a competitive advantage. Brooks’ comments can be taken to
mean that people who are smarter, and who invest capital in expensive
infrastructure that makes them better able to compete, have an unfair
advantage over everyone else. But by that standard, Warren Buffett has
an unfair advantage over everyone else by being earlier to the table on
a good idea. He has extra access to information, he is smarter, and he
has analysts who do a better job than others are able to do of processing information. Why wouldn’t that reduce the integrity of the markets?
This analogy extends to all fields where competition is present. The New
York Yankees can afford to pay any player any amount they want to in
order to acquire his services, thereby building a more talented team than
many others. Not all players choose to play for them, and the Yankees are
clearly not assured of success by virtue of having the highest payroll in
their sport. Formula One racing teams are not all equal in funding or talent. Some have better drivers and engineers, they engage in better R&D,
and they end up winning more races as a result. The reality is that none
of this is unfair. It is basic capitalism: If you are willing to take a risk, you
might get a reward.
It would be unfair if some players were being prevented from taking
risks and having a chance at rewards. But this is clearly not the case with
HFT. Anyone can get colocation space for servers. Anyone can get top‐of‐
the‐line hardware and fast communications networks. There was an incident
in 2012, in which the NYSE was justly punished for making certain datasets
available only to some HFTs. But the point is that NYSE was in violation
of extant rules (Rule 603(a) of Reg NMS, specifically), which make it clear
that anyone who wants this special data can get it. They were fined, and the
issue has been put to bed.2 It is clear that firms that wish to compete must
invest a lot of capital in infrastructure. They also have to acquire the skills
to compete. But that’s true for almost any venture.
Moreover, investment in massively expensive infrastructure does not
guarantee success. I won’t name names, but I know many HFTs that have
sunk millions of their own and investors’ money into infrastructure and
have absolutely nothing to show for it except red ink. This demonstrates
that paying for the kind of speed we discussed in Chapter 14 does not
guarantee profits. It merely puts a trader on a level playing field with other
traders attempting to do similar things. And, as is the case in any fair competition, there are winners and losers. But it’s instructive when we see losers,
because it demonstrates that there is no “club membership” that an HFT
receives by spending large sums of money, which entitle it to low‐risk profits. Investment in good real estate, good technology, smart people, and other
sources of potential advantage are exactly that: an investment that might
pay off or might not.

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The Purpose of Speed
The second reason that the claim of a two‐tiered system is wrong is that
HFTs do not use their fairly earned competitive advantage to compete with
investors, but rather with each other. HFTs (particularly market makers) are
in the business of facilitating investor orders, which means that they take
the opposite side of these orders. As demonstrated in Chapter 14, obtaining
a speed advantage over other HFTs is important to managing the adverse
selection problems associated with passive trading.
It is incorrect to claim that a trader who does not want to accumulate a
significant net position, and who prefers to end the day with no positions at
all would be competing with an investor who has a time horizon measured
in weeks, months, or years. Indeed, HFTs are enormous net providers of
liquidity, while investors are net consumers of it.
This is borne out by the numbers. The enormous energy and cost expended on speed by HFTs can yield a strategy with a speed that can be measured. It comes to around $0.001 per share in U.S. equities, as mentioned
earlier. The fastest traders in the market can earn profits in that range. Yes,
of course they trade a lot of shares, but as we showed in Chapter 13, even
in aggregate, HFT profits in U.S. equities are just over half of what even a
single medium‐sized retail U.S. equity brokerage firm earns.
Let’s contrast these economics with those of a good statistical arbitrage trader. Such a firm can earn approximately $0.01 to $0.02 per share.
In this case, the extra $0.001 per share earned by having better infrastructure is useful, but only at the margin. In the case of a longer‐term investor,
one with a return target measured in several (or many) dollars and tens
of percentage points, earning an extra $0.001 per share on a typical trade
does not move the needle. This is especially true because they don’t trade
all that often.
Comparing the economics of HFT to the economics of longer‐term investors is another way to demonstrate that there is little or no competition
across these types of participants. Instead, each has a role in the market’s
ecosystem. The competition among HFTs exists because they are competing with each other to interact in the least adverse way with non‐HFT
order flow.

A Philosophical Point
Every advantage in investing, in particular in alpha‐driven investing, is about
speed. Whether it is getting data faster, processing the information faster (or
even processing the information better), or executing orders more quickly,
investment ideas make money only if other people have similar ideas, after

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you have implemented yours. This is true of deep value investing as much as
it is true of HFT investing.
This is a fundamental statement about alpha, and it ties in with the
definition of alpha given in Chapter 3: Alpha is all about timing. In particular, it is about realizing value before others. Whether you are a long‐term
active investor like Warren Buffett, a statistical arbitrageur, a trend‐follower
in futures markets, or an HFT, you make money only when your longs go
up and/or your shorts go down. This is only the case when other investors,
in aggregate, follow in your footsteps. Perhaps this is the most important
point to consider of all: Successful investing and trading rely inherently on a
correct anticipation of the future aggregate behavior of other investors and
traders. There is nothing special about anticipating someone’s trading versus
anticipating someone’s longer‐term bets.
In sum, it’s hard to see any merit in the idea that HFT is unfair or creates
a two‐tiered marketplace. HFTs do have some advantages over the average
person, but then again, so does every person with an above‐average IQ, or
even an above‐average expenditure of time and money on analysis of investment or trading decisions. That advantage, in every class of active investing
from long‐term money management to HFT, is fundamentally about speed.
Specifically, it is about getting into positions before other people get the
same ideas, and getting out before it is too late to retain profits. This leads
directly to the second question about HFTs.

Does HFT Lead to Front-Running or
Market Manipulation?
HFTs are accused of front‐running investors. This is a topic that understandably generates a lot of heat. But unfortunately, it also generates very little by
way of credible examples to examine. As far as market manipulation, in the
rare cases that the arguments get specific, detractors point to such practices
as quote stuffing, which involves placing and canceling huge numbers of orders in order to confound others into making mistakes. Another favorite of
critics is that “their [HFTs’] computers can essentially bully slower investors
into giving up profits—and then disappear before anyone even knows they
were there,”3 which usually doesn’t get further explanation. Events that are
entirely unrelated to HFT, such as Facebook’s troubled IPO in 2012, have
been deemed by some in the press and public to be an HFT manipulation
problem.
The manipulation claim seems to have its roots in the case of Goldman
Sachs sending the Feds after Sergey Aleynikov (as we described in
Chapter 13). That case (until Aleynikov’s conviction was dismissed and

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vacated) gave people who were suspicious about how anyone could make
money in 2008 an aha moment. In their statements about the sensitivity
of the code that was alleged to have been stolen, the indubitable Goldman
claimed that “there is a danger that somebody who knew how to use this
program could use it to manipulate markets in unfair ways.”4 We will address both claims here.

Front-Running
Let’s be really explicit: Front‐running occurs when a fiduciary uses knowledge of his customer’s order to buy or sell to perform that same action
before the customer has the opportunity to do so. But HFTs aren’t looking at customer orders and then deciding whether to front‐run them. They
are forecasting into the extremely near‐term future, and sometimes they are
speculating about what other traders might do next. As we pointed out
in the section entitled “Does HFT Create Unfair Competition?,” timing is
everything for all kinds of alpha‐driven investors, and much of the exercise
in timing relates to anticipating what others might do later. But most HFTs
are not getting information about customer orders before they go out to the
market. Mostly, they are responding to such orders, but that’s what most
traders have always done, with or without computers.
Some HFTs (arbitrageurs and HFT alpha traders) are reacting to fleeting inefficiencies caused by others’ orders to reap profits. Noncontractual
market makers (NCMMs) react to the limit order book and other information to place passive orders. They have no knowledge of the trades that
others plan to make, and they do not see orders before those orders hit
the market. Contractual market makers (CMMs) actually do see customer
order flow and have requirements to provide liquidity on that order flow.
Ironically, it is here where front‐running is actually theoretically possible,
in contrast to the other scenarios just mentioned. However, it is rare that
a CMM is the subject of the public’s ire against HFTs. In fact, some critics
want all HFTs to become CMMs, with obligations like those CMMs have.
This would have the perverse consequence of giving all HFTs a look at order
flow before it hits the tape.
A pet phrase of HFT’s detractors is latency arbitrage, which is a stylized
strategy that is supposed to demonstrate how an HFT can utilize a predatory algorithm to front‐run an institutional trader’s execution algorithm. It
is a story that begins with a premise that an HFT can see a customer order
before it hits the tape, and then walks through how this information would
be used to front‐run an order. It is further claimed that this kind of predatory practice generates $1.5 to $3 billion in profits annually for HFTs in the
U.S. equity market alone.

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It is true that, if an HFT could actually see the order before it hits the
tape, it would be able to front‐run a customer order. If we grant the premise,
the rest of the argument is trivial and follows directly. However, the premise
is completely false.
The scenario imagined is that, when this order is placed, it takes some
time to be reflected in the national best bid‐offer (NBBO), due to the latency
we have described already in updating this centralized data feed. As we have
also pointed out, to combat this latency, many HFTs establish direct data
feeds from the exchanges. Thus, it is true that they can see the customer’s
order before it is reflected in the centralized tape. However—and this is
the central flaw in the claim being addressed—the customer’s order has to
already be in the queue at a given exchange for an HFT with a direct data
feed to see it.
There is no conceivable way that an HFT could see the order before
it happens. It is true that, relative to someone relying on the consolidated
tape, the HFT will be able to be better aware of the actual current order
book. And there are clearly advantages to having timely information, or
else it would be stupid for an HFT to bother establishing expensive and
hard‐to‐manage direct feeds. But this advantage comes at a cost, and it is a
cost any participant is welcome to bear for himself to compete. If a trader’s
strategy requires feeds to be as timely as an HFT, then it is probable he will
go through all the trouble. If not, then he will not. But this is no different
from establishing any other kind of competitive advantage in any industry
(see “Does HFT Create Unfair Competition?”).
It seems to me that HFT’s opponents have misunderstood the difference
between being faster than others and front‐running them. Front‐running is
illegal, and it basically doesn’t occur insofar as HFT is concerned. HFTs are,
however, faster than most other market participants. Usain Bolt is faster
than most other sprinters. He wins medals, and we marvel at his speed. We
are not surprised that a marathoner cannot run 100 meters as quickly as
Bolt, and we do not attempt to compare the “fastest man in the world” with
the “fastest marathoner in the world.” This is because it would be strange
to do so: They are competing in different games. Bolt is not trying to outrun
Patrick Makau (record‐holder for fastest marathon). Just so, HFTs are not
trying to front‐run pension investors (nor could they, given the basic fact
that the pension fund’s orders go directly to the market). They are competing in different games.
Imagine a world in which there are no computerized trading strategies, no execution algorithms. In such a world, some traders would still
have the ability to access and process information faster and more accurately than others. And those traders would outwit the less capable and
make a profit doing so. This is completely normal and acceptable. And

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the analogy is identical in the case of HFTs. They do not have access to
customer order flow before the fact. They can find out what the customer
flow was as soon as possible after the fact, and they can attempt to react
very quickly to that information. This, too, is completely normal and
totally acceptable.

Manipulation and Cancellation Rates
Focusing now on manipulation, some have claimed that HFTs manipulate
markets, either by moving prices or as a result of their high order cancellation rates. The troubled Facebook IPO in 2012 has been used as an example
of this supposed manipulation by some observers. As it turns out, the problems at the opening of Facebook’s IPO were specifically driven by technology problems at Nasdaq. What this has to do with HFTs is not something
I have the ability to imagine. It also appears lost on those pointing to the
Facebook IPO as evidence of an HFT manipulation problem that the price
dropped and remained well below the IPO price at least up until the time of
this writing (five months to the day after the IPO date, FB is approximately
50 percent below its IPO price).
But let’s imagine that some bad actor in the HFT world does decide to
manipulate markets or engage in quote stuffing. Should someone using a
powerful tool for illegal purposes bring judgment on himself or on the tool
he used? Should speculative trading be banned because the Hunt brothers
cornered and manipulated the silver markets beginning in the 1970s (without the use of any technology more sophisticated than a telephone)? For
that matter, should telephones be banned, since they can and have been used
for evil purposes?
But we need not grant that HFTs engage in manipulative practices. Manipulation usually requires a trader to acquire a large enough inventory of
a position to move the market. But considering our definition of an HFT,
this is not in line with an HFT’s requirement to get out of positions by the
end of the day. Inventory, as we’ve seen, is generally not desirable to an
HFT. So there is a logical inconsistency between the contention that HFTs
manipulate markets and the fact that they dislike holding positions. The
reality is that anyone with sufficient means and motivation can attempt to
manipulate markets.
Critics have also pointed to the frequency with which HFTs cancel their
orders (known as cancellation rates) as a way to manipulate markets at
a micro level. A high rate of entering and cancelling orders is referred to
as quote stuffing. Opponents of HFT claim that there are two problems
with high cancellation rates: first, that high cancellation rates imply that
the liquidity that we think we see is either not there at all or it is of inferior

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quality; second, that HFTs manipulate markets by overwhelming exchanges
with massive message volumes due to placing and canceling too many orders. There are a number of problems with these arguments, but first, let’s
understand why cancellation rates are and should be high, if the market is
functioning correctly.
We demonstrated in Chapter 14 the importance of queue placement in
placing and canceling passive orders. Time priority markets (such as the U.S.
equity markets) require that a passive trader be fast on his feet if he doesn’t
want to get picked off. Since much of the HFT world is passive, there is a
great deal of competition to provide liquidity to active traders. This competition is good for the active trader, because it means that her trade will get
done at a good price. Every time the price changes in a market, every time
there is a trade, this is new information that must be accounted for by the
market maker. This usually means canceling a previously resting passive
order and placing a new one. Decimalization of stocks led to an increased
frequency of price changes, and this has in turn meant a permanently higher
rate of cancellations.
Fragmentation in the U.S. equity market is another important contributor. Because there are over a dozen official exchanges under Reg NMS, and
because the formation of the NBBO is so slow (as described in Chapter 14),
many HFTs post orders directly to each exchange. But they are posting far
more liquidity than they actually want to provide, and once they get filled
on the size they are willing to trade, they must cancel the extra orders or risk
being run over by active traders. This is some of the basic risk management
that we described in Chapter 15, and it is a good thing that HFTs are careful
about managing risk.
Finally, many new orders reach the market too late to be at or near the
front of the queue. In these cases, allowing those orders to remain in the
order book is very risky for market makers, for all the reasons we described
in Chapter 14. As such, seeing that an order arrived too late is sufficiently
good reason to cancel it.
Opponents of HFT claim that the liquidity being provided is merely a
mirage, or if it is real, it is inferior. Unfortunately, there is no evidence to
support these claims. But the facts are what they are: The average NBBO
quote on SPY, which is the highest volume stock in the world, had an average duration of over three seconds in the first half of 2010.4 A typical stock
has lower volumes and longer NBBO quote durations. These numbers are
not different from what opponents claim to have been true in the pre‐HFT
days of 2004.5
HFT’s opponents also contend that high message rates (which occur
when there is a high volume of orders and cancellations) cause delays for
exchanges, which buys the HFT time (to do what, I’m not sure). It is true

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that, when message volumes spike, exchanges must deal with the same
microbursting problem (Chapter 14) as HFTs have to solve, and at the
extremes, the exchanges do see delays. But slowing down message traffic
would serve no economic purpose for an HFT. Indeed, during the Flash
Crash, many HFTs who stopped trading did so specifically because data
latencies were getting to such a level that they felt their data quality had
deteriorated so much that they couldn’t responsibly continue trading. Data
latency is an enemy to an HFT, not a friend.
Furthermore, if exchanges were being hampered by HFTs, it is easy
enough for them to do something about it. Indeed, exchanges do monitor
the message traffic from each participant that connects to them, and they
warn, sanction, and if necessary ban traders who generate excess traffic.
This is a completely rational and acceptable way to handle the situation,
because not all exchanges have the same capacity to handle messages. An
artificial message limit would be too low for some and too high for others, and would add an arbitrary element to the healthy competition among

exchanges.
A minimum resting time, which would disallow the immediate cancellation of an order, has also been suggested. The proximate effect of such
a change would be that a large proportion of all orders would be very
stale, and that such stale orders would offer new and very fruitful arbitrage
opportunities to HFTs. For example, imagine that the NBBO on the SPY
shows 1,000 shares bid at $144.20 and 1,000 shares offered at $144.21,
and if these are freshly made orders that must rest for some time. Now
imagine that the S&P futures move rapidly downward just at that time. The
trader whose 1,000 share bid at $144.20 is stuck because of a minimum
resting time would see it get filled happily by an active order from an index
arbitrageur, who would subsequently be able, quite possibly, to immediately
buy back the short position at a lower price. Remember, based on what we
showed in Chapter 14, the main reason a passive order would get canceled
is to avoid being picked off. Requiring that a liquidity-providing passive trader allow himself to be picked off, in order to solve a nonexistent
problem, doesn’t seem likely to be an effective improvement to the current
market structure.
As a final note, an academic paper published in September 2012 took
the first-ever detailed, empirical look at the impact of HFTs on market manipulation.6 The authors analyzed 22 stock exchanges around the world
from January 2003 through June 2011. Their findings:
Controlling for country, market, legal and other differences across
exchanges and over time, and using a variety of robustness checks including difference‐in‐differences tests, we show that the presence of

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high frequency trading in some markets has significantly mitigated
the frequency and severity of end‐of‐day manipulation, counter to
recent concerns expressed in the media. The effect of HFT is more
pronounced than the role of trading rules, surveillance, enforcement
and legal conditions in curtailing the frequency and severity of end‐
of‐day manipulation. We show our findings are robust to different
measures of end‐of‐day manipulation, including but not limited to
option expiry dates, among other things.

Does HFT Lead to Greater Volatility or
Structural Instability?
Occasionally, computer software has glitches. When one of those glitches
leads to millions of erroneous orders, causing huge instability in market
prices, people feel that they should be worried. Furthermore, even without
the presence of bugs in someone’s code, events like the Flash Crash of 2010
lead to speculation that HFTs are to blame for extreme market volatility.
Indeed, it remains fairly widely asserted that the Flash Crash was a computer‐driven event, despite both an abundance of evidence to the contrary
and none in favor of such a theory. Even an SEC report on the event, which
exonerated HFTs about as clearly as could be done by a government report,
made no dent in the perception that HFTs were to blame.
Aside from the Flash Crash, other events have not helped the public
relations efforts for HFT. For example, an HFT firm named Infinium was
probed in August 2010 for a bug in its HFT programs that led to a $1 increase in the price of crude oil in about one second. So are HFTs responsible
for instability and volatility?
As was the case with the arguments already discussed, HFTs are accused
of things that are equally or more applicable to other forms of trading. For
every HFT problem or computer hiccup, there is a Mizuho securities trader
who accidentally sold 600,000 shares of a stock at 1 yen each, instead of
1 share at 600,000 yen. Not to pick on the Japanese, but another fat finger error only a few months later had another trader buy 2,000 shares of
a stock that traded at 510,000 yen, instead of 2 shares, costing his firm
$10 million in losses. An entertaining article in the Financial News, a Dow
Jones publication, from March 20077 listed 10 human‐driven trading errors of breathtaking scope, including one for more than $100 billion worth
of stock in a European pharmaceutical; another involving a trader whose
elbow touched an Instant Sell key on his keyboard, leading to a massive
futures order in French government bonds; another order where a trader

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carelessly attempted to transact more than £8.1 billion worth of shares
(nearly four times the company’s market capitalization); and another where
someone wrongly entered the 6‐digit SEDOL identifier for a stock in the size
field of an order, leading to a £60 million loss; and so on.
Whether HFTs cause volatility even in the absence of glitches is a different question, which we will address empirically. However, this question is
worth putting in context. It is clearly a matter of real concern if investors are
systematically overpaying for their transactions. Such overpayment could
certainly occur if an investor transacts due to heightened short-term volatility. And if HFTs are a driver of heightened short-term volatility, then there is
both a fair and a very real concern to be addressed. But common sense gives
us the same answer as a thorough empirical analysis.
We have had, and we continue to have, serious economic and geopolitical problems weighing on the markets. The 1929 market crash that kicked
off the Great Depression, the spike in inflation and bond yields that crushed
most assets in the 1970s, the decades‐long stagnation in Japan’s economy
and capital markets, the 1998 LTCM/Russian‐driven crash, the dot‐com
bubble and the subsequent 50 percent decline in stocks that took years to
recover, the financial debacle of 2008 (from which we still haven’t fully recovered), and the problems in Greek and other Eurozone sovereigns are all
by orders of magnitude more significant drivers of volatility than HFT will
likely ever be. Neither computers nor HFTs play any role in these real economic issues, which seem to be the kinds of things with which real money
investors are (and should be) primarily concerned.

An Empirical Analysis of HFTs and Volatility
Empirical analysis supports the claim that HFTs are not responsible for
volatility. Critics point out that volatility in the S&P 500 has climbed since
HFTs have gained prominence. A September 2011 article in the New York
Times was titled “Market Swings Are Becoming New Standard.”8 It argues
that the stock market is more likely to “make large swings—on the order
of 3 percent or 4 percent—than it has been any other time in recent stock
market history.” It goes on to list HFT as one of the probable causes. In an
article for the High Frequency Traders website, Manoj Narang dissects this
argument and provides an empirical study of the sources of volatility.9 Let’s
update and build on that analysis here.
The S&P 500 goes through two distinct phases in any given 24‐hour
period. The first is the period during which the market is open. We can
measure the behavior of the S&P while it’s open by comparing the opening
price and a closing price. The second period is when the market is closed.
To understand the behavior of the market during this period, we can look at

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one day’s closing price and the next day’s opening price. These two mutually
exclusive segments (open:close and close:open) add up to the behavior of
the index from one day’s close to the next day’s close.
HFTs are active during the trading day. They are almost all dormant
overnight (remember, they tend to take home no overnight positions). Much
of the news that impacts markets comes out overnight (though some, for
example, the Federal Open Market Committee’s announcements, are intraday phenomena). As such, we can take as a rule of thumb that overnight
(close:open) volatility is unrelated to HFTs, while intraday volatility could
be related to HFTs (or other news and events that occur intraday). One
of the errors that the aforementioned New York Times article makes is to
point out that close‐to‐close volatility has gone up since HFTs have gained
prominence. But we can do a better job of understanding the sources of this
increase by examining the behavior of the market while it is closed, versus
when HFTs are active (while the market is open).
For this analysis, we look at four quantities and compare them during
two distinct periods. The first quantity is the absolute value of the percent
change in the S&P from one day’s close to the next (close:close). The second
quantity is the absolute value of the percent change in the S&P from the
open to the close of a single day (open:close). The third compares the absolute value of the percent change in the S&P from one day’s close to the
next day’s open (close:open). The final quantity is the absolute value of the
percent change from the intraday high to the intraday low for a single day.
We took data from January 1, 2000, through September 2012, and drew a
dividing line at January 1, 2007. This is because Reg NMS was enacted during 2007, which changed market structure to what it is today. Furthermore,
the post‐2007 period is clearly when HFTs became most active. If the critics
are right, we should see the open:close volatility increase at least as much as
the close:close volatility, since that’s the only time that HFTs could possibly
affect prices.
Comparing the close:close results, we find that the S&P 500 (as measured using the SPY ETF) averaged 0.84 percent changes from 2000 to 2006,
and 1.03 percent changes from 2007 to 2012. This is a 23 percent increase
in the magnitude of the index’s movements, and is the primary evidence
used to support the contention that HFTs have caused increased volatility. However, if we divide the data into the natural partitions we described
(close:open and open:close), we see a different picture. This is shown in
Exhibit 16.1.
What is clear from this table is that, while volatility (measured in this
way) has increased overall from 2007 onward, the increase is actually much
smaller intraday than it is overnight. The increase in the average of the
gap from high to low within a day is also much smaller than the increase

292
Exhibit 16.1

High-Speed and High-Frequency Trading

Average Price Movement in SPY

close:close

2000–2006

2007–2012

% Difference

0.84%

1.03%

+23%

open:close (intraday)

0.76%

0.82%

+8%

close:open (overnight)

0.37%

0.59%

+59%

high:low

1.47%

1.72%

+17%

in overnight volatility. These data clearly indicate that market volatility has
increased for reasons that have nothing to do with HFTs.
Examining the median movements of the S&P instead of the averages
shows an even more stark contrast, as shown in Exhibit 16.2. Here, we see
that volatility has actually not increased all that much, and that intraday
volatility has actually contracted somewhat since the rise of HFTs! By contrast, and consistent with what we saw from the analysis of average movements, overnight volatility has spiked according to this measure as well.
We can also examine whether larger moves have become more frequent.
To answer this question, we looked at the frequency of moves of 3 percent
or greater in the same way, as shown in Exhibit 16.3. Here, we see an increase in volatility measured in each way, but the pattern of increases in
overnight volatility far outstripping intraday volatility holds.
It becomes more interesting as we examine even larger moves. What we
see is that, when counting the frequency of larger moves (4 percent or more),
the instances have become more common in the intraday period than from
close to close, while the high versus low volatility increase continues to lag.
This is shown in Exhibit 16.4.
At these more extreme levels, it appears that overnight volatility plays
less of a role than intraday volatility in explaining the increase in the frequency of very large moves since 2007. However, even here, the picture is
mixed. First, while the intraday volatility increases more as the magnitude
of the move goes up, we see that the high versus low volatility increases at
a slower pace overall. Second, as we begin to examine these outlier events,
Exhibit 16.2

Median Price Movement in SPY
2000–2006

2007–2012

% Difference

close:close

0.62%

0.67%

+8%

open:close (intraday)

0.55%

0.53%

–3%

close:open (overnight)

0.26%

0.39%

+51%

high:low

1.26%

1.33%

+5%

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Controversy Regarding High-Frequency Trading

Exhibit 16.3

Frequency of 3% or Greater Moves in SPY
2000–2006

2007–2012

% Difference

close:close

2.56%

5.87%

+129%

open:close (intraday)

1.53%

2.69%

+75%

close:open (overnight)

0.11%

0.83%

+629%

high:low

6.20%

10.91%

+76%

we are dealing with events that happen very infrequently. For example, out
of the 1,448 trading days since January 1, 2007, we have seen only 20 instances where intraday moves were at least 4 percent. As such, it would be
unwise to draw any serious conclusions from these data.
However, one could contend that HFTs’ association with market volatility is as follows: Most of the time their activities coincide with lower
volatility, but in the most extreme cases, their activities coincide with higher
volatility. Even if we make a grave statistical error and mistake coincidence
for causation, the most damning argument against HFTs could be that, in
the 20 instances where the market moved at least 4 percent in an intraday
period over the last five and a half years, HFTs may have contributed to
those large moves to some unknowable degree. Other investors surely will
also bear some of the blame. But for the other 1,428 days, HFTs reduced
volatility.
One major reason that the data support the claim that HFTs reduce
volatility is that a strategy that buys and sells roughly the same amount
during a fixed time period cannot cause any net price impact on the instrument being traded. Whatever price impact was generated on the buying of
a position is realized in the opposite direction when selling it. And without impact, the probability that volatility, even measured on the slowest
timescale attributable to HFTs (one day), is related to HFTs is effectively
nil. The definition of HFTs logically precludes one from drawing such a
conclusion.
Exhibit 16.4

Frequency of 4% or Greater Moves in the SPY
2000–2006

2007–2012

% Difference

close:close

0.68%

2.97%

+335%

open:close (intraday)

0.28%

1.38%

+386%

close:open (overnight)

0.11%

0.48%

+325%

high:low

1.65%

5.73%

+248%

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High-Speed and High-Frequency Trading

Furthermore, it is a basic fact of capital markets that posting limit orders, which is a huge part of the activity of HFTs, does not cause volatility,
but rather reduces it. Every single order in the order book represents a friction that must be overcome before the market can move through the price
levels presented in the order book. Illiquidity breeds volatility, not an abundance of liquidity. This fact seems lost on HFT’s opponents. Even in times of
duress, when HFTs must trade actively, it is most often to liquidate positions
that were acquired passively. This implies that even in stress scenarios, such
as the one we will cover in depth next, HFTs are probably no worse than
neutral to liquidity. In aggregate, it is extremely clear that they are liquidity
providers.

The Flash Crash
It took less than 20 minutes for many blue‐chip shares to drop by about 5
percent. In smaller capitalization companies, the moves were worse. Brunswick Corp fell 9.3 percent in 12 minutes (more than 22 percent from its
opening price). There was massive volume, enough to cause the NYSE to
take almost two and a half hours after the market close to finish reporting floor transactions. Market makers were found to have exacerbated the
downdraft by turning from buyers to sellers. There was chaos in the prices
of some executions relative to what they should probably have been, given
the prevailing market. There was widespread disgust and disappointment
in the integrity of capital markets, and many brokerage firms saw reduced
volumes and earnings in the wake of this event. These events occurred on
May 29, 1962.10 But they hold some important parallels and equally important lessons in considering the Flash Crash of 2010. The reality is that, just
as real, deep crises occur in markets without any help from computers or
HFTs, so do rapid fluctuations in prices.
The causes of the 2010 Flash Crash are several. First, and most importantly, the markets were already jittery from a brewing sovereign debt crisis
in Europe and a very tentative economic recovery in the United States. The
stock market was already down several percentage points for the day before the first spike down around 2:40 p.m. The role of negative short‐term
sentiment on the part of a wide array of market participants should not be
discounted. It was the single largest cause of the Flash Crashes of both 1962
and 2010.
Second, Waddell & Reed, an established mutual fund manager, entered
a large (somewhat inelegant, and fully discretionary) order to sell S&P futures.11 The face value of this order was approximately $4.1 billion, and
at a time when the market was already down, this order exacerbated price
movements enough to trigger further selling, for example from stop‐losses

Controversy Regarding High-Frequency Trading

295

and other kinds of stop‐orders. The order was entered around 2:30 p.m. on
May 6, 2010, and at that point, the S&P 500 was already down 2.5 percent
for the day. There is little doubt that this 75,000 contract order, which took
20 minutes to execute, was a driver of the volatility that ensued. In particular, their trading algorithm was designed to ignore price movements and
merely focus on volume levels as the determinant of the size of each order
placed. But since their own order was causing others to panic, volumes increased, and their 75,000 contract order became the center of a snowball. It
is important to point out that there is no judgment assigned to these facts.
Waddell’s order was perfectly legitimate, with no evil intent behind it. It
was their right to enter it, and what transpired afterward has no bearing on
that fact.
Third, the interconnectedness of instruments across various exchanges
and instrument classes (e.g., S&P futures to S&P exchange‐traded funds
[ETFs] to the constituents of these ETFs, to the names that are peers of those
constituents) in U.S. equities had a role in the propagation of these volatile
moves across the marketplace. As we described in talking about index arbitrage in Chapter 15, the prices of structurally correlated instruments will
tend to move together. So, when S&P futures fell, the ETFs that track the
same index moved in lockstep. So did the stocks that are constituents of the
S&P 500 (and the ETFs that contain those). Then, statistical correlations
dictated that other, similar stocks should follow suit. There is little judgment on this fact, either. It is generally a good thing to have many ways to
express an investment idea. Each structure offers some benefits and some
drawbacks, and that they tend to move lockstep with one another does not
mean that there is some problem that needs to be solved.
Fourth, the fragmentation of the U.S. equity market played a role.
The fragmentation itself was a procustomer change in market structure
that really picked up steam in the late 1990s with the propagation of
electronic communication networks (ECNs). The increased competition
with the previously monopolistic stock exchanges drove costs lower and
liquidity higher. But in this case, fragmentation did have a hand in the
breakdown in liquidity due to the declaration of Self Help. Reg NMS allows an exchange to cease participating and sharing information with the
other market centers if there is a problem with one or more of them. The
NYSE Arca exchange, for example, was alleged to have had problems with
its technology, resulting from the huge increase in message traffic. (Remember our discussion about microbursts in Chapter 14? This is why they
matter!) Several exchanges pointed to what they viewed as Arca’s problems and declared Self Help, which they are allowed to do if they find that
some member of the market system is having problems. This exacerbated
the fragmentation problem and reduced liquidity. It was a contributor to

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the stub quotes issue that led to some shares being executed at obviously
ridiculous prices.
Finally, the Flash Crash was exacerbated by the extremely reasonable
decision by some (not nearly all) HFT speculators to cease trading. They
are not required to make markets, and data latency times coming out of
exchanges were severe. At a time when the market was clearly broken in
several places, there is no judgment that should be cast against any trader
who simply wants no part of some craziness in the markets. Note that, nevertheless, volumes during the flash crash were spectacularly high, so either
non‐HFT traders were doing many multiples of their normal order size, or
else HFT traders weren’t as absent as is widely believed.
In sum, HFTs were not responsible for the Flash Crash, nor are they
responsible for the very real economic problems we face currently. Can HFT
cause market problems through glitches or misbehavior? Absolutely. But so
can a lot of other things that aren’t HFTs. No one is talking about banning
human traders because they often screw up spectacularly once in a while.
Why should we have a double standard on computerized traders? Regulation is useful here, and there should always be repercussions for costly and
careless errors. The first and most appropriate repercussion is that people
who make dumb trades tend to lose money for themselves (e.g., Knight
Capital). They have their investors to face, as well. But that sort of natural
punishment, coupled with any required ex post enforcement, seems perfectly
legitimate given the total lack of other valid options.

Does HFT Lack Social Value?
This is perhaps the most disappointing argument I’ve heard against HFT.
Actually its being infuriating has nothing to do with HFT at all. It is
problematic in the philosophical outlook it implies, and disappointing in
the writers who have furthered its acceptance by many. Paul Krugman,
a brilliant Nobel‐laureate economist, actually made the argument in an
op‐ed piece in the New York Times that HFT is generally a game of “bad
actors,” and that it’s “hard to see how traders who place their orders
one‐thirtieth of a second faster than anyone else do anything to improve
that social function.”12 Allow me to state this explicitly. This is a catastrophically bad point of view, most especially for a self‐described liberal
economist.
I don’t care about the fact, and it is a clear and indisputable fact despite
all the rhetoric to the contrary, that HFTs actually provide an enormous
amount of liquidity to the marketplace, which facilitates the trading activities of a great number of other types of players that are judged as having

Controversy Regarding High-Frequency Trading

297

social value by those interested in casting such judgments. It’s irrelevant. The
problem is far deeper with this argument.
The first question that is begged when someone raises the banner of social value is this: Who gets to decide what has social value and what doesn’t?
What is the minimum holding period for an investor to be judged favorably
as improving the social function of markets? Where do we stop with this
analysis of social value? What about short‐sellers, who were indeed questioned and blamed heavily for the failures of Bear Stearns, AIG, and others
in 2008? What about the makers of Bubble‐Yum, Snickers bars, Coca‐Cola,
cigarettes, guns, fighter jets, and nuclear weapons? It seems like kind of a
fascist line of thinking to raise the question of social value. What’s the social
value of an economist? What’s the social value of a tobacco company or a
gun manufacturer? Who gets to decide? It’s a free country, so people can
say and do what they want, so long as they do not impinge on the rights of
others. And this type of thinking leads directly to the impingement of others’
pursuits via its fallacious presumptions.

Regulatory Considerations
It’s true that computers are powerful tools, and that the more powerful a
tool is, the greater amount of damage (or good) that it can do. But while that
calls for scrutiny and sensible regulation, it does not call for the banning of
the use of powerful tools.
Despite the hot‐headed talk from some outmoded corners of the marketplace, U.S. regulators have been surprisingly even‐headed and downright
thoughtful about all this. So far, every real step they’ve taken with regard to
HFT has actually seemed pretty fair. Banning naked access was a reasonable
thing to do. The SEC’s report on the Flash Crash was even‐keeled, pretty
accurate, and placed the responsibility (not the blame, which is something
needed when there’s a real disaster) more or less in the right camps.
One of the most controversial measures being considered in the United
States is a financial transaction tax (FTT). It is also one of the most stupid
ideas regarding HFT and potential improvements to market structure. If the
tax is not universal and global, then trading will simply move to markets
where taxes are lower or are not applied at all. If taxes are universal and
global, and if HFT becomes unprofitable as a result, volumes are likely to
plummet, which reduces both the amount collected by the FTT and follow‐
on impacts to capital gains taxes. Declining volumes will also damage banks
and brokerage firms severely, and it is probable that their least risky and
most profitable units will be the hardest hit. Banks’ prime brokerage units
are nearly riskless operations that generate large revenues from customers’

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High-Speed and High-Frequency Trading

commissions. If customers are trading less, banks will make less. This probably implies a substantial loss in jobs, not just at the banks, but also at various trading entities associated with the markets.
None of this has stopped 11 countries in the EU from adopting an FTT,
but it will not be surprising if they follow the path Sweden has already been
down. In 1984, Sweden enacted an FTT. Trading volumes across various asset classes in Sweden fell dramatically. Futures volumes were off 98 percent,
bond volumes dropped 80 percent, and the options market in Sweden disappeared entirely. By 1990, Sweden’s equity markets lost more than half
of their volumes to London’s exchanges. The fees collected were just over
3 percent of what the Swedish Finance Ministry had forecasted, and the
FTT actually cost the Swedish Treasury revenue in aggregate, because other
taxable revenues on capital gains fell, more than offsetting the minuscule
revenues that were achieved. It was repealed in 1991.13 Needless to say,
Sweden did not join the 11 countries that adopted the FTT in October 2012.
The irony is that the tax is designed to “make the financial firms that
got us into this mess pay their share for the recovery.” But customers of
financial firms (e.g., hedge funds and HFTs) certainly did not cause lax
mortgage lending practices, CDOs, bogus AAA ratings, and so on. And it is
customers of financial firms, not the financial firms, who will be paying this
tax. It’s one thing if it’s just HFTs and hedge funds paying the tax. Maybe
most people wouldn’t care. But the Dutch Central Bank (DCB) “opposes the
introduction of a European financial transaction tax that it estimated would
cost the nation’s lenders, pension funds and insurers about €4 billion and
hurt economic growth.” The DCB concluded that more than 40 percent of
the annual cost of an FTT in the Netherlands would be borne by pensions
(€1.7 billion).14
I don’t care much about the bluster in the press. I’ve been involved in
hedge funds for over 16 years now, and when I got started, few knew what
a hedge fund even was. When they did, it was in the form of vilification
(Soros for attacking Asian currencies, LTCM for nearly destroying the financial markets, and so on). We get paid pretty well, and if not being liked
by someone who trusts what he reads in the news to be the whole story is
the cost of that compensation, I’ll take that trade every day. I only hope that
those with the power to actually make changes continue to take constructive steps, rather than heeding the biased and/or uninformed voices of a very
loud minority with regard to HFT. And certainly, we should be very, very
wary of the unintended consequences of taking bad advice from ignorant,
shortsighted, or biased people.
Some reasonable ideas to improve market structure do exist. Circuit
breakers, which have long been proposed (and used, in markets like futures)
are an effective way to cool down overheated markets. Ending the ban on

Controversy Regarding High-Frequency Trading

299

locked markets would go a very long way toward eliminating one of the
most severe inefficiencies in the U.S. equity market, which would further
eliminate the need for ISO orders (which are, for all practical purposes, unavailable to most investors, since the broker must determine that the investor
is capable of complying with Reg NMS, which most investors cannot do).
Liquidity provision rebates are currently tiered, so that the most active participants get the best rebate tiers. While rebates themselves are a good thing
(as they make it worthwhile to accept the risk of providing liquidity), tiered
rebates make it impossible for lower‐volume customers to profitably post
passive orders. Moving toward a much flatter (or entirely flat) rebate structure would solve this problem. And, finally, it behooves regulators to begin
to arm themselves with technology that will enable them to properly monitor and police the markets. This appears to be well understood by now, and
we are beginning to see the SEC take significant steps in the right direction.

Summary
In general, and let me say this clearly, HFTs are not run by evil people. They
stay well within both the rules of the markets and the boundaries of common ethics and good sense. They often self‐report any irregularities caused
by their trading to the authorities. That the powerful computers and fast
communication lines they possess might be used to manipulate the market
doesn’t mean that legitimate activities undertaken with these tools must be
stopped. Just as people are prosecuted for calling in fake bomb threats, so
should people be prosecuted for manipulation, front‐running, and other bad
behaviors in the markets. But there has been no evidence that computerized
traders are especially guilty of such activities, and there is certainly no logic
to a call to ban their activities because of a few examples of corruption.
Let us remember that some people have to be told what’s right and
wrong, and they have to be punished for ignoring the rules. We Americans
had to be told it was wrong to hold slaves, and wrong to force our children
to work as coal miners and chimney sweeps, and so on. That doesn’t make
farming or all farmers bad. It doesn’t make families or all parents bad. It
unfortunately makes regulations and their proper enforcement absolutely
required, because otherwise some people will go too far. Even with good
regulations and enforcement, this still happens. But there’s no cure for the
vices of humanity.
HFT isn’t evil any more than walking your dog is evil. Nor should it be
banned any more than walking one’s dog should be banned. Yes, some dog
owners will let their dog crap on your lawn and simply walk away, leaving
the souvenir behind. That doesn’t make dogs bad; it makes the dog’s owner

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sort of antisocial, and well‐deserving of some punishment. Computers, even
when used for trading, are programmed by people. If those people are malicious or careless, they will hurt others, and they should be prosecuted.
But people have been hurting others through malice and carelessness for
far longer than we’ve had computers, ECNs, or dark fiber. To take the attention off of the humans that engage in the activities that are harmful, and to
focus on the instrument they use to cause harm, is folly. Furthermore, nearly
every single serious academic study undertaken has either demonstrated
that HFTs have empirically added liquidity and improved price discovery, or
demonstrated that there is no evidence to support the idea that HFTs have
created additional volatility or decreased market efficiency. The most critical
papers often remark that problems can arise from HFT, but they are quick
to note that such problems have arisen before HFT, and continue to arise
due to other factors since the advent of HFT. An excellent and recent summary, which is also full of further references, can be found at the Foresight
Project, which was conducted by the UK Government Office for Science,
using leading academics from 20 countries.15

Notes
1. Charles Duhigg, “Stock Traders Find Speed Pays, in Milliseconds,” www
.nytimes.com, July 23, 2009.
2. http://sec.gov/litigation/admin/2012/34‐67857.pdf.
3. http://topics.nytimes.com/topics/reference/timestopics/subjects/h/high_frequency_algorithmic_trading/index.html, September 26, 2012. This article starts by
conflating high speed and high frequency trading. It is a case study in confusing
cause and effect, in confusing anything to do with computers with HFT, and
with creating a tempest in a teacup (e.g., Knight Capital’s near collapse). It’s a
pretty shabby article, and I say this as someone who likes the New York Times.
4. Manoj Narang, “What’s All the Fuss About High‐Frequency Trading Cancellation Rates?,” www.institutionalinvestor.com, June 24, 2010.
5. David Glovin and Christine Harper, “Goldman Trading‐Code Investment Put at
Risk by Theft (Update3),” www.bloomberg.com, July 6, 2009.
6. Douglas Cumming, Feng Zhan, and Michael Aitken, “High Frequency Trading and End‐of‐Day Manipulation,” available at SSRN 2145565September 12,
2012.
7. Stacy‐Marie Ishmael, “The Curse of the Fat‐fingered Trader,” FT Alphaville,
March 16, 2007, http://ftalphaville.ft.com.
8. Louise Story and Graham Bowley, “Market Swings Are Becoming New Standard,” New York Times, September 11, 2011, www.nytimes.com.
9. Manoj Narang, “HFT Is NOT Responsible for Market Volatility—You Are!”
September 15, 2011, www.highfrequencytraders.com.

Controversy Regarding High-Frequency Trading

301

10. Jason Zweig, “Back to the Future: Lessons From the Forgotten ‘Flash Crash’ of
1962,” online.wsj.com, May 29, 2010.
11. Marcy Gordon and Daniel Wagner, “‘Flash Crash’ Report: Waddell & Reed’s
$4.1 Billion Trade Blamed for Market Plunge,” www.huffingtonpost.com,
October 1, 2010, www.huffingtonpost.com.
12. Paul Krugman, “Rewarding Bad Actors,” www.nytimes.com, August 2, 2009.
13. http://publications.gc.ca/collections/Collection‐R/LoPBdP/BP/bp419‐e.htm.
14. Maud van Gaal, “EU Transaction Tax Is ‘Undesirable,’ Dutch Central Bank
Says,” www.bloomberg.com, February 6, 2012.
15. www.bis.gov.uk/foresight/our‐work/projects/current‐projects/computer‐trading/
working‐paper.

Chapter

Looking to the Future
of Quant Trading
All evolution in thought and conduct must at first appear as heresy
and misconduct.
—George Bernard Shaw

o‐called black‐box trading has existed for more than three decades. It is
hopefully clearer to the reader that these strategies are not so much black
boxes as much as systematic implementations of the kinds of things that
human traders and investors have always done. Unfortunately, automation
is most often received with a great deal of distress. Sometimes, this is very
understandable, as in the case of job displacement where a person’s occupation is being obviated by automation. Other times, ignorance is a sufficient
reason for fear. In either case, I believe that the backlash against quants is,
at its core, a generational issue. We are just past a point of transition in our
marketplace. Automation and computerization in the markets have pretty
much happened. But it’s still a recent enough phenomenon that companies
and individuals who are poorly equipped to participate profitably in the
modern markets are bitter and vocal. But as these types of players adapt,
move into other lines of work, or retire, newer participants who are perfectly happy to participate in these markets are abundant.
Looking ahead, I see a couple of interesting trends that bear watching.
Markets today are undoubtedly and categorically more fair and egalitarian
than they have ever been in their history. However, the level of transparency
available today, coupled with the level of technology at the disposal of even
less sophisticated market participants and observers, has led to a continuous pressure to ensure that markets are simply fair, not merely less unfair.

303

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High-Speed and High-Frequency Trading

I think that at least some of the elements that cause problems (e.g., the ban
on locked markets) will be addressed.
At the same time, there is light at the end of tunnel in this low‐latency
arms race. We are rapidly converging on that asymptotic limit of minimal
latency. Most practitioners welcome such a state for the markets, because it
will cause the focus of market participants back onto the more interesting
challenges of outsmarting one another, rather than simply outrunning one
another. It also seems likely that, once we reach this point, firms will have
less reason to each rebuild the same standard, highest‐performance infrastructure. This standardization of the platform will also deal with many of
the (unfounded) criticisms of HFT, because everyone will have access to the
same infrastructure.
Since the time I wrote the first edition of this book, I have seen little progress in the areas of research I highlighted then. Relatively naive,
frequently ineffective approaches remain in place to blend alpha models
together, to size positions correctly, and to manage risk. These are fields of
research in which little useful literature has been published, and the landscape remains wide open for innovation. And some fields of study within
the quant trading industry have been ignored almost entirely. Models that
predict whether certain strategies are likely to perform well or poorly in the
future are also somewhat uncommon, though they are increasingly being
explored by various systematic trading firms.
The manner in which quant trading systems are used can also evolve.
There are already examples of hybrid quant‐discretionary strategies, which
utilize quant systems to screen for opportunities while allowing discretion
to rule the rest of the process. But more work can be done to ascertain
whether certain other parts of the investment process can combine human
subjectivity with the objectivity and consistency of machines. For example,
it is easy to imagine analysts inputting their views into a computer system
and allowing the system to determine the portfolio. In other words, instead
of using machines to support human decisions, human input could support
systematic decisions. At least one very prominent discretionary equity trading firm has established an effort in this area, and the initial results have
apparently been very promising.
On the opposite end of the spectrum, and due largely to the ever‐
increasing power of computer processors, sophisticated machine learning
approaches are becoming more and more feasible. There remains the challenge of extremely noisy, dirty data. But for those who can tackle this challenge, there may be interesting temporal inefficiencies to exploit for profit,
particularly with regard to shorter‐term trading strategies.
Big data is a term borrowed from the tech industry, relating to datasets
so large as to outstrip the capabilities of standard database tools. In quant

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305

trading, it refers to large datasets that usually come from the Internet and
that may give insight into sentiment. For example, numerous strategies have
cropped up that analyze Twitter, blogs, and other Internet content sources
to try to determine if sentiment readings can predict near‐term stock price
movements.
There appears to be an interesting opportunity set at the intersection of
high frequency and more traditional quant trading strategies. These “mid‐
frequency” strategies have shorter holding periods than traditional quant
strategies and are focused heavily on alpha. But the kinds of opportunities they pursue—for example, using the limit order book to predict price
behavior with a time horizon of an hour or longer—require the technical
infrastructure needed to do well in high-frequency trading. As such, these
mid‐frequency strategies are at the borderline between two equally difficult‐to‐master styles, and the opportunity set is interesting perhaps specifically because the barriers to entry are so high. As high-frequency trading
has become more challenging in many markets, with volumes declining and
competition at a fierce level, this may become an interesting area to observe.
So far, we have seen a few HFT firms venture into the asset management
business, and the success of these ventures has not been heartening (though
it is extremely early yet). That said, the demand for short‐term quant strategies appears to be high, and capital has been allocated aggressively in this
area at a time when it has been difficult to generate profits.
It has been interesting to see an increased acceptance of systematic trading strategies by investors who had felt them too opaque previously. During
2012, I know of billions of dollars allocated to quant funds specifically by
pensions and large, traditional fund‐of‐funds who historically would have
said, “We don’t invest in quant.” However, far too much of this money is
going to bulge‐bracket asset gathering outfits who care more about asset
gathering than generating alpha.
Indeed, and at least partially because of this trend to allocate money
primarily to the largest managers, the last five years have seen enormous
turnover at the company and individual level among boutiques. A great
many well‐respected quant trading outfits have closed down, while a large
number more have entered the space. The quant liquidation of 2007,
Lehman’s collapse in 2008, and the hedge fund industry’s institutionalization
have all contributed to this trend. The implementation of the Dodd‐Frank
prohibition on proprietary trading by banks has also led to a large flow of
talent out of the industry. Many quants, like many other people around the
world, are simply unemployed and have few prospects. I expect that a collectivist approach to some of the more tiresome and expensive aspects of
building a quant strategy will be centralized and shared. Prime candidates
for such a business structure include data acquisition and management,

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operations and compliance management, and execution. However, raising
trading capital remains a huge challenge for smaller firms and any startups
that are not headed by brand name quants.
In addition to the general requirement to evolve in order to survive,
great challenges face the quant trader today. Regulations are becoming increasingly hostile as both quant trading and hedge funds are demonized in
the popular press. The economic problems that were exacerbated by large
investment banks, failed IPOs, and a host of other ailments have been foisted onto quants and HFTs without any regard for the facts. Ironically, the
causality is actually in the opposite direction. Rather than causing problems, quants have mainly suffered because of the innumerable government
interventions and geopolitical events that have rattled markets ever since
late 2008. Many alternative investment professionals are turning away from
quant trading in disgust after years of repeated once‐in‐a‐lifetime events.
For quants, this may be a period of natural selection, in which the weaker or
less lucky firms are forced out of the business while the stronger or luckier
firms can survive only if they evolve.

About the Author

ishi K Narang is the founder and portfolio manager of Telesis Capital
LLC, a boutique alternative investment manager specializing in short‐
term quantitative alpha strategies. He has been involved in the hedge fund
industry variously as an investor in and practitioner of quantitative trading
strategies since 1996.
When he isn’t working, Rishi enjoys playing his guitar, writing essays
and poems, making pencil sketches, arguing with people, playing tennis, doing yoga, and hiking. Rishi completed his undergraduate degree in economics
at the University of California at Berkeley. He lives in Los Angeles with his
wife, Dr. Carolyn Wong, and their son, Solomon.

307

Index

Accuracy of information, 15–16
Active Portfolio Management (Grinold and
Kahn), 109
Adverse selection, 247, 267, 270
Adverse selection bias, 95, 122
Aggressive orders, 120–124, 244–245,
250–252
Aite Group, 6
Aleynikov, Sergey, 237
Algorithmic execution, 4–5, 119–128
Algorithmic trading, 7, 239
Algorithms, order execution, 7, 18, 119–128
aggressive vs. passive, 121–124
hidden orders, 124–125
high-speed trading, 253–256 (see also
High-speed trading)
Intermarket sweep orders (ISOs), 125–126
large vs. small orders, 127
market and limit orders, 125
smart order routing, 127–128
All-or-none order, 125
Alpha, 15
defined, 23
fast alpha, 273–274, 276
portfolio, 229–230
time decay of, 160–162
Alpha-driven weighting, 97–98
Alpha models, 23–64
bet structure, 49–51
blending of, 56–62
characteristics of, 17–18, 20, 68
conditioning variables, 53–55
data-driven, 24–26, 42–45
definition in, 52–53
forecast target, 46
investment universe, 51–52
permutations of, 56
risk management elements, 72–73
run frequency, 55
strategy implementation, 45–56

theory-driven, 26–42
time horizon, 47–49
types of, 24–26
American Recovery Act, 202
Arbitrage:
in high-frequency trading, 271–273
index arbitrage, 260, 271–272
latency arbitrage, 284
merger arbitrage, 186–187
statistical arbitrage, 7, 14, 31–32, 191
venue arbitrage, 272
Arms race to zero, 256
Assessment of quants. See Evaluation of
quants and strategies
Asset class, and investment universe, 51
ATM effect, 186, 188
Average rate of return, 154
AXA Rosenberg, 180
Axcom, 30
Backwardation, 39
Bad prints, 140
Ball, Ray, 37
Bamberger, Gerry, 31
Bank of America, 15
Barclay Hedge, 6
Bayesian statistics, 62–63
Bear Stearns bailout, 185–186
Beller, Mark, 262
Berlekamp, Elwyn, 30
Beta, 23, 35
Bet structure:
characteristics of, 49–51
importance of, 230
Big data, 304
Black box:
origination of term, 14
schematics of, 17, 64, 77, 90, 114, 131,
146, 171
trading system characteristics, 19

309

310
Black Box, The (film), 14
Black-Litterman optimization, 108–109
Bollerslev, Tim, 102
Bond market, 37–38, 73–75
Book-to-price ratio, 38–39
Book yield, 38
Breakout trading, 205
Brokers, functions of, 117, 118–119, 129
Buffett, Warren, 24
Calmar ratio, 159–160
Cancellation rates, 286–288
Carry trades, 37–38
Chhikara, Sudhir, 145
Circuit breakers, 298
Clearing, 80
CMMs (contractual market makers),
265–269
Colocation, 129
Commodity trading advisors (CTAs),
6, 28
Common investor risk, 186–193
Competition, unfair, 280–283
Conditional models, 60–61
Conditioning, 28
Conditioning variables, 53–55
Constrained optimization, 106–108
Constraints, hard, 69
Contagion risk, 186–193
Contango, 39
Contractual market makers (CMMs),
265–269, 284
Contrarians, 31, 35
Correlation coefficients, 177
Correlation matrix, 103–105
Credit crisis beginning in 2007, 10
Criticisms of quant trading, 197–213
art/science debate, 197–198
data mining, 210–213
handling of market changes, 204–205
quant similarities/differences, 206–207
underestimation of risk, 199–204
vulnerability of small quants vs. large,
207–210
CRM (customer relationship management)
software, 211
Cross-connects, 253
CTAs (commodity trading advisors),
6, 28
Cumulative profits, 154

Index

Currency trading, 38
Current market conditions, 44
Dark exchanges, 128
Dark liquidity, 128
Dark pools, 81, 84, 128
Data, 133–146
asynchronicity in, 142–144
cleaning, 139–144, 218, 219
fundamental, 135–137 (see also
Fundamental data strategies)
importance of, 19, 133–135
incorrect, 135, 139–144
missing, 139–140
sources of, 137–138
storing, 144–145
types of, 135–137
Data burning, 169
Data bursts, 254, 257–259
Data cubes, 145
Data-driven alpha models:
applications, 24–26, 42–45
compared with theory-based alpha
model, 43
implementation of, 42–56
Data-driven risk models, 70
Data edge, 225–226
Data feed handlers, 133
Data miners/mining, 25, 43–44, 111,
210–213
Data sourcing, 218, 219
Data vendors, 137–138
Defining trends, 52–53
Dennis, Richard, 150
D. E. Shaaw, 150
Directional bets, 50
Directional forecasts, 101
Direct market access (DMA), 117, 129
Discretionary investment style, 9, 11, 16, 151
Dispersion, 70
Diversity:
in alpha models, 56
of revenue sources, 41
Dividends, 141
Dividend yield, 36
DMA (direct market access), 117, 129
Dodd, David, 37
Donchian, Richard, 28–29, 149
Dot-com bubble, 24, 30, 200, 290. See also
Internet Bubble

311

Index

Drawdowns, 100, 114, 155–156, 164,
200, 226
Dutch tulip mania, 30
Earnings quality signal, 41
Earnings yield (E/P), 36, 60
EBITDA (earnings before interest, taxes,
depreciation, and amortization), 38
Eckhardt, William, 150
ECNs (electronic communication
networks), 84
Edge, 223–227
Efficient Asset Management (Michaud), 110
Efficient frontier, 99
Einstein, Albert, 148, 164
Electronic communication networks
(ECNs), 84
Empirical risk models, 74–75
Empirical scientists, 25–26
Enterprise value (EV), 38
Equal position weighting, 94–96
Equal risk weighting, 96–97
Equal-weighted model, 59–60
Equity risk premium, 153–154
Evaluation of quants and strategies. See
Quant strategies evaluation; Quant
trader evaluation
Exchange fees, 81
Execution, 117–131
components of, 117–119
evaluating, 219, 220
monitoring, 194
order execution algorithms (see
Algorithms, order execution)
trading infrastructure, 128–130
Execution models, 17–18
Exogenous shock risk, 184–186
Expected correlation matrix, 99, 103–105
Expected returns, 101
Expected volatility, 101
Exposure monitoring tools, 193–194
Facebook IPO, 286
Factor portfolios, 109–110
Fairness of price, 247
Falsification, 148
Fama, Eugene, 35
Fama-French three factor model, 35
Fast alpha, 273–274, 276
Fat tails, 177

Fill-or-kill order, 125
Filtering, 28
Financial crises, 176–177, 185–186, 290
bear market of 2000-2002, 204
Credit crisis beginning in 2007, 10
economic crisis starting in 2008, 201–204
October 1987 market crash, 5, 204
quant liquidation crisis of 2007, 186–193,
199, 200, 247
Russian debt crisis, 10, 187, 200
summer of 1998, 204
Financial engineering, 203
Financial Information eXchange (FIX)
protocol, 129–130
Financial transaction tax (FTT), 297–298
FIX (Financial Information eXchange)
protocol, 129–130
Flash Crash, 5, 238, 247, 288, 289, 294–296
Flat files, 144
Flat transaction cost models, 86–87
Flight-to-quality environments, 40
Forecasting, 24, 82, 101
Forecast targets, 46
Foreign exchange markets, 6
Fragmentation, 287, 295
Francioni, Reto, 7
Fraud risk, 41
French, Kenneth, 35
Frequentist statistics, 63
Front-running, 283–286
FTT (financial transaction tax), 297–298
Fundamental data, 135–137
Fundamental data strategies:
growth/sentiment, 39–40
quality, 40–42
value/yield, 35–39
Futures contracts, 39, 140–141, 149, 255,
263, 271
Futures markets, 6, 17, 28–29, 39, 46
Futures trading, 28, 129
Generalized Autoregressive Conditional
Heteroskedasticity (GARCH), 102
Geography, and investment universe, 51
Global Alpha Fund, 5
Goldman Sachs, 5, 150, 237
Good-till-cancelled order, 125
Graham, Benjamin, 37
Great Depression, 200
Greater fools theory, 28

312
Griffin, Ken, 202
Growth stocks, 182
Growth strategies, 39–40
Hard constraints, 69
Hard-to-borrow list, 99, 170
Hardware, 130
Hedge funds, 6, 29, 163, 188, 190, 201–202,
208, 298, 305–306
Hibernia Atlantic, 256
Hidden orders, 124–125
High-frequency trading/traders (HFT), 5,
259–260, 265–277
and advantage of speed, 280–283
arbitrage, 271–273
contractual market making, 265–269
controversy regarding (see High-frequency
trading (HFT) controversies)
defining, 239–240
fast alpha, 273–274
and high-speed trading (see High-speed
trading)
index arbitrage, 260, 271–272
noncontractual market making, 269–271
overview, 237–241
and portfolio construction, 276
revenues from, 240–241
and risk checks, 261–262
risk management approaches, 274–276
venue arbitrage, 272
High-frequency trading (HFT) controversies:
front-running and market manipulation,
283–286
market manipulation, 283–284, 286–289
regulatory considerations, 297–299
social value of, 296–297
unfair competition, 280–283
volatility and structural instability,
289–296
High-speed trading, 243–263
aggressive orders, 244–245, 250–252
data bursts, 257–259
defining, 243
delays in order transmission, 253–256
order books, 256–257
passive orders, 244, 247–250, 252
risk checks, 260–262
signal construction, 259–260
sources of latency, 252–262
why speed matters, 244–252

Index

Historical data, 9, 35, 44, 70, 74–75, 109,
139, 152, 170, 180–181, 204, 210–213
Historical regression, 59
Historical trends, 180–181
Hite, Larry, 29
Hit rate, 194
Hop, 261
Housing bubble, 202–203
Human Genome Project, 25
Iceberging, 125
Idea generation, 149–151
Implied volatilities, 42
Improving, defined, 246
Index arbitrage, 260, 271–272
Information ratio, 159
In-sample research, 152–153
Instrument class, 51
Interest rate risk, 74
Intermarket sweep orders (ISOs), 125
Internet Bubble, 74, 168, 182. See also Dotcom bubble
Interrogator, The (Toliver), 216–217
Inventory risk, 270
Investment process edge, 224–225
Investments, evaluating, 219
Investment universe, 51–52
Investor sentiment, 34
Iraq War, 185
ISOs (intermarket sweep orders), 125
Joining, defined, 246
Knight Capital, 263
Knight Trading, 179–180
Krugman, Paul, 296
Lack-of-competition edge, 226
Latency arbitrage, 284
Latency trading. See High-speed trading
Legging risk, 276
Leverage, 16, 41–42, 71–72, 187–190, 192
Limit order book, 121
Limit orders, 122, 123. See also Passive
orders
Linear models, 58–60
Linear transaction cost models, 87
Liquidity:
defining, 247
implications of, 51–52, 246–247

313

Index

quant liquidation crisis of 2007, 186–193
in rule-based portfolio construction, 96
and transaction costs, 83, 84
Liquidity pools, 127–128
Liquidity provision, 123
Lit exchanges, 128, 269
Live production trading system, 19
Long Term Capital Management (LTCM), 4,
9, 187, 208
Long-term strategies, 49, 230, 238
Look-ahead bias, 142–144
Low-latency trading. See High-speed trading
LTCM. See Long Term Capital Management
(LTCM)
Lumpiness, 155
Machine learning models, 58, 61, 111, 304
Madoff, Bernie, 229
Managed futures, 28
Management quality, 41
Man Group, 29
Market Access Rule, 261
Market crash of 1987, 5, 204
Market inefficiencies, 7–8
Market makers, 266, 280–283
Market manipulation, 283–284, 286–289
Market-on-close orders, 125
Market orders, 245, 251–252
Markowitz, Harry, 98, 150
Mars Climate Orbiter (MCO), 134–135
Matching engines, 253
McKay Brothers, 256
Mean reversion strategies, 30–33, 95,
181–182
Mean variance optimization, 98, 99, 150
Medallion Fund, 5
Medium-frequency traders (MFTs), 239
Medium-term strategies, 49
Merger arbitrage, 186–187
Merrill Lynch, 15
Michaud, Richard, 110
Microsoft (MSFT), 41
Mid-market, 120
Millenium Partners, 151
Mint Investments, 29
Model definition, 52–53
Model risk:
implementation errors, 179–180
inapplicability of modeling, 176–178
model misspecification, 179

Modern portfolio theory (MPT), 99
Modifying conditioner, 54
Momentum strategies, 95
Monte Carlo Simulation, 110
Mortgages, securitized, 176–177
Moving average crossover indicator, 28
MPT (modern portfolio theory), 99
Multiple regression, 59
Naked access, 261, 297
Naked short sale, 170
Newedge Alternative Investment Solutions, 6
Newton, Isaac, 148
Noncontractual market makers (NCMMs),
269–271, 284
Nonlinear models, 58, 60–61
Objective function, 93, 99
Occam’s razor, 163–164
Opaqueness, 14
Optimization techniques. See Portfolio
optimization techniques
Optimizers. See Portfolio optimizers
Options markets, 34
Order books, 244–245, 256–257
Order execution. See Execution
Order execution algorithms. See Algorithms,
order execution
Order flow internalizers. See CMMs
(contractual market makers)
Order transmission:
data bursts, 257–259
between market centers (see also
Algorithms, order execution)
to and from market centers, 253–254
between market centers, 254–256
Organization of information, 218
Out-of-sample testing, 167–169
Overfitting, 162–167, 211–213
Pairs trading, 7, 14
Parameter fitting, 165–166
Parameters:
determining, 53
sensitivity to, 162
Parsimony, 163
Passive orders, 120–124, 244, 267
canceling, 252
in contractual market makers (CMMs),
266–267

314
Passive orders (continued)
need for speed with, 247–250, 252
in noncontractual market making
(NCMM), 269–270
placing, 247–250, 287
PCA (pricipal component analysis), 74
Penalty functions, for size limits, 69
Percentage winning trades, 159
Piecewise-linear transaction cost models, 87–88
Pioneering Portfolio Management
(Swenson), 13
Popper, Karl, 148, 164
Portfolio bidding, 118
Portfolio construction, 229–231
elements of, 64
evaluating, 219, 220
in high-frequency trading, 276
Portfolio construction models, 62, 93–113
choosing, 113
elements of, 17–18, 20
goal of, 93
optimizers, 93–94, 98–112
output of, 112–113
rule-based, 93, 94–98
Portfolio insurance, 197
Portfolio of strategies, 160
Portfolio optimization techniques, 105–111
Black-Litterman optimization, 108–109
constrained optimization, 106–108
data-mining approaches, 111
factor portfolios, 109–110
resampled efficiency, 110–111
unconstrained optimization, 106
Portfolio optimizers, 98–114
inputs to optimization, 101–105
optimization techniques, 105–111 (see
also Portfolio optimization techniques)
“Portfolio Selection” (Markowitz), 150
Predictive power, 157–158
Price data, 135–137
Price/earnings-to-growth (PEG) ratio, 39
Price-related data strategies:
mean reversion, 30–33
technical sentiment, 34–35
trend-following, 27–30
Price-to-earnings (P/E) ratio, 35–36
Primary data vendors, 137–138
Principal component analysis (PCA), 74
Profit-and-loss monitors, 194
Profit-targets, 54

Index

Proximity hosting, 253
Pulte Homes, 190–191
Quadratic transaction cost models, 89–90
Quality investing, 40–42
Quantitative Investment Management, 4
Quantitative risk-modeling approaches, 77
Quantitative trading system:
benefits of, 8–9
high frequency of, 4
implementation of, 6–7, 10–11
long/short positions, 38–40
performance of, 4–5
risk measurement/mismeasurement, 9–10
strategy intervention in, 15–16
structure of, 16–19
volume, 6
Quant liquidation crisis of 2007, 186–193,
199, 200, 247
Quant long/short (QLS), 38–40
Quants:
characteristics of, 14–16
defining, 13, 14
equity investments, 38–40
evaluation of (see Evaluation of quants
and strategies)
future direction for, 303–306
trading strategies (see Quant strategies
evaluation)
Quant strategies evaluation:
goals and importance of, 215–216
information gathering, 216–218
investment process, 218–221
Quant trader evaluation:
edge, 223–227
integrity, 227–229
portfolio fit, 230–231
skill and experience, 221–223
Quant traders/trading:
criticisms of (see Criticisms of quant trading)
evaluation of (see Quant trader evaluation)
future direction for, 303–306
interviewing, 218–221
negative perceptions of, 4–5
quasi-quant traders, 16
types of, 25–26
Quote stuffing, 286
Refitting, 53
Regime change risk, 180–184

Index

Regime changes, impact of, 204–205
Regulation, 260–262, 297–299
Regulation National Market System (NMS),
125–126, 287, 291, 295
Relational databases, 144–145
Relative bets, 49, 50
Relative value, 51
Renaissance Technologies, 4, 30, 151
Resampled efficiency, 110–111
Resampling, 156
Research, 147–171
evaluation methods, 218, 219
idea generation, 149–151
scientific method, 147–149
testing, 151–170 (see also Testing, in
research)
Returns:
ratios of, vs. risk, 159–160
variability of, 155
Risk, 175–195
common investor/contagion risk,
186–193
exogenous shock risk, 184–186
interest rate risk, 74
inventory risk, 270
legging risk, 276
model risk, 176–180
monitoring tools, 193–195
regime change risk, 180–184
systematic risk, 73
underestimation of, 199–201
Risk-adjusted returns, 99, 159–160
Risk checks, 260–262
Risk exposures:
measuring, 67
monitoring tools, 193–194
Risk management, 67–68, 219, 220
and HFT strategies, 274–276
size limiting, 69–72
Risk models, 67–77
characteristics of, 17–18, 68
choosing, 74–76
in constrained optimization, 106
empirical, 74–75
evaluating, 219
limiting amounts of risk, 69
limiting types of risk, 71–76
measuring risk, 70
theory-driven, 73, 74–76
Risk targeting, 189

315
Roll yield, 39
Rotational models, 60, 61
Rothman, Matthew, 206
Royal Dutch, 187
R-squared, 157
Rube Goldberg device, 13
Rule-based portfolio construction models,
93, 94–98
alpha-driven weighting, 97–98
equal position weighting, 94–96
equal risk weighting, 96–97
Run frequency, 55
Russian debt crisis, 10, 187, 200
S&P E-Mini futures contract (ES), 255, 271
Sample bias, 156
Scharff, Hanns Joachim, 216
Scientific method, 147–149
Scientists, types of, 25
Secondary conditioner, 54
Secondary data vendors, 138
Secrecy, 217
Securitized mortgages, 176–177
Security Analysis (Graham and Dodd), 37
Sensitivity, 162
Sentiment-based strategies, 40, 41–42
Sentiment data, 34
Settlement, 80–81
Seykota, Ed, 28
Sharpe, William, 98
Sharpe ratio, 159
Shaw, David, 31
Shell, 187
Short selling, 170, 186, 190, 201–202
Short-term strategies, 49, 230–231, 238
The Signal and the Noise (Silver), 62
Signal-mixing models (of alphas), 61–62
Signal strength, 46
Silver, Nate, 62, 63
Simons, James, 8, 30
Size-limited models, 69–72
Slippage, 81–82, 83, 85, 169, 251–252
Smart order routing, 127–128
Software programs:
alpha model (see Alpha models)
back-testing, 176
CRM, 211
data errors in, 143
FIX protocol, 129–130
implementation errors, 179–180

316
Soros, George, 200
Speed. See also high-speed trading
in high-frequency trading (HFT), 280–283
Spike filter, 140–141
Spread Networks, 255–256
Statistical arbitrage, 7, 14, 31–32, 191
Statistical risk models, 74
Statistical techniques, 62–63
Sterling ratio, 159
Stochastic volatility modeling, 101–102
Stocks/stock market. See also Highfrequency trading/traders (HFT); Highspeed trading
asynchronicity in, 143–144
fundamental data, 136
splits and dividends, 141
stock picking, 224
stop limit orders, 125
stop-losses, 54
stop-loss policy, 151
Stop limit orders, 125
Stop-losses, 54
Stop-loss policy, 151
Structural correlation, 271
Structural edge, 226–227
Structured products, 202–203
Stub quotes, 296
Substitution effect, 112
Sullenberger, Chelsey, 223–227
Swenson, David, 13
Systematic approach, abandoning of, 15–16
Systematic risk, 73
Systematic strategies, vs. discretionary
strategies, 16
Systems performance monitors, 195
TABB Group, 6
Tartaglia, Nunzio, 31
Technical sentiment strategies, 34–35
Technical traders, 151
Terrorist attacks, 16, 185
Tertiary data vendors, 138
Testing, in research:
assumptions of, 169–170
importance of, 151
in-sample (training), 152–153
model “goodness”, 153–162
out-of-sample testing, 167–169
overfitting, 162–167

Index

Teza, 237
Theoretical scientists, 25–26
Theory development. See Idea generation
Theory-driven alpha models:
applications, 25–26
fundamental data, 35–42
implementation of, 26–42
price-related data, 26–35
Theory-driven risk models, 69–70, 73,
74–76
Theory of gravity, 148
Thesys technologies, 256
Thorp, Ed, 31
Tick-to-trade latency, 261
Time decay, 160–162
Time horizon, 47–49, 53, 230–231, 238
Timestamps, 142, 256
Toliver, Raymond, 216
Trade execution. See Execution
Tradeworkx, 262
Trading assumptions, 169–170
Transaction cost models, 79–89
characteristics of, 17–18, 20
costs overview, 80–85
role of, 79–80, 90
types of, 85–89
Transaction costs, 107
commissions, 80, 169
fees, 80–81, 169
with high-frequency trading, 169–170
market impact, 82–85, 169
minimizing, 79–80
models (see Transaction cost models)
slippage, 81–82, 83, 169, 251–252
Trend-following strategies, 27–30, 32–34,
52–53
Trends, 148
Trust, building, 217
Ultra high-frequency traders (UHFTs), 239
Unconstrained optimization, 106
Value at risk (VaR), 71, 177, 189, 199
Value strategies, 35–39
Variability of returns, 155
Venue arbitrage, 272
Volatility:
defined, 70
and equal risk weighting, 96–97

317

Index

expected, 101
in high-frequency trading, 289–294
implied, 42
of revenues, 41
value at risk (VaR) model, 71
Volume-weighted average price (VWAP), 120

Wasserman, Larry, 63
Weinstein, Boaz, 202
When Genius Failed (Lowenstein), 187
Worst peak-to-valley drawdowns, 155–156
Yield, 35–39, 60

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Wiley Finance : Inside The Black Box A Simple Guide To Quantitative And High Frequency Trading (2nd Edition) Rishi K. Narang

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