Statistical Arbitrage E-Book

Andrew Pole

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Finance Editions
• Sprache: Englisch

Seitenzahl: 317

Veröffentlichungsjahr: 2011

Beschreibung

While statistical arbitrage has faced some tough times?as markets experienced dramatic changes in dynamics beginning in 2000?new developments in algorithmic trading have allowed it to rise from the ashes of that fire. Based on the results of author Andrew Pole?s own research and experience running a statistical arbitrage hedge fund for eight years?in partnership with a group whose own history stretches back to the dawn of what was first called pairs trading?this unique guide provides detailed insights into the nuances of a proven investment strategy. Filled with in-depth insights and expert advice, Statistical Arbitrage contains comprehensive analysis that will appeal to both investors looking for an overview of this discipline, as well as quants looking for critical insights into modeling, risk management, and implementation of the strategy.

Leseprobe

Contents

Preface

Foreword

Acknowledgments

Chapter 1: Monte Carlo or Bust

1.1 Beginning

1.2 Whither? and Allusions

Chapter 2: Statistical Arbitrage

2.1 Introduction

2.2 Noise MODELS

2.3 Popcorn Process

2.4 Identifying Pairs

2.5 Portfolio Configuration and Risk Control

2.6 Dynamics and Calibration

Chapter 3: Structural Models

3.1 Introduction

3.2 Formal Forecast Functions

3.3 Exponentially Weighted Moving Average

3.4 Classical Time Series Models

3.5 Which Return?

3.6 A Factor Model

3.7 Stochastic Resonance

3.8 Practical Matters

3.9 Doubling: A Deeper Perspective

3.10 Factor Analysis Primer

Chapter 4: Law of Reversion

4.1 Introduction

4.2 Model and Result

4.3 Inhomogeneous Variances

4.4 First-Order Serial Correlation

4.5 Nonconstant Distributions

4.6 Applicability of the Result

4.7 Application to U.S. Bond Futures

4.8 Summary

Appendix 4.1: Looking Several Days Ahead

Chapter 5: Gauss Is Not the God of Reversion

5.1 Introduction

5.2 Camels and Dromedaries

5.3 Some Bells Clang

Chapter 6: Interstock Volatility

6.1 Introduction

6.2 Theoretical Explanation

Chapter 7: Quantifying Reversion Opportunities

7.1 Introduction

7.2 Reversion in a Stationary Random Process

7.3 Nonstationary Processes: Inhomogeneous Variance

7.4 Serial Correlation

Appendix 7.1: Details of the Lognormal Case in Example 6

Chapter 8: Nobel Difficulties

8.1 Introduction

8.2 Event Risk

8.3 Rise of a New Risk Factor

8.4 Redemption Tension

8.5 The Story of Regulation Fair Disclosure (FD)

8.6 Correlation During Loss Episodes

Chapter 9: Trinity Troubles

9.1 Introduction

9.2 Decimalization

9.3 Stat. Arb. Arbed Away

9.4 Competition

9.5 Institutional Investors

9.6 Volatility Is the Key

9.7 Temporal Considerations

9.8 Truth in Fiction

9.9 A Litany of Bad Behavior

9.10 A Perspective on 2003

9.11 Realities of Structural Change

9.12 Recap

Chapter 10: Arise Black Boxes

10.1 Introduction

10.2 Modeling Expected Transaction Volume and Market Impact

10.3 Dynamic Updating

10.4 More Black Boxes

10.5 Market Deflation

Chapter 11: Statistical Arbitrage Rising

11.1 Catastrophe Process

11.2 Catastrophic Forecasts

11.3 Trend Change Identification

11.4 Catastrophe Theoretic Interpretation

11.5 Implications for Risk Management

11.6 Sign Off

Appendix 11.1 Understanding the Cuscore

Bibliography

Index

Copyright © 2007 by Andrew Pole. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Pole, Andrew, 1961–

Statistical arbitrage: algorithmic trading insights and techniques / Andrew Pole.

p. cm. — (Wiley finance series)

Includes bibliographical references and index.

ISBN 978-0-470-13844-1 (cloth)

1. Pairs trading. 2. Arbitrage—Mathematical models. 3. Speculation–Mathematical models. I. Title.

HG4661.P65 2007

332.64'5 — dc22

2007026257

ISBN 978-0-470-13844-1

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To Eliza and Marina

Preface

These pages tell the story of statistical arbitrage. It is both a history, describing the first days of the strategy’s genesis at Morgan Stanley in the 1980s through the performance challenging years of the early twenty-first century, and an exegesis of how and why it works. The presentation is from first principles and largely remains at the level of a basic analytical framework. Nearly all temptation to compose a technical treatise has been resisted with the goal of contributing a work that will be readily accessible to the larger portion of interested readership. I say “nearly all”: Chapter 7 and the appendix to Chapter 11 probably belong to the category of “temptation not resisted.” Much of what is done by more sophisticated practitioners is discussed in conceptual terms, with demonstrations restricted to models that will be familiar to most readers. The notion of a pair trade—the progenitor of statistical arbitrage—is employed to this didactic end rather more broadly than actual trading utility admits. In adopting this approach, one runs the risk of the work being dismissed as a pairs trading manual; one’s experience, intent, and aspirations for the text are more extensive, but the inevitability of the former is anticipated. In practical trading terms, the simple, unelaborated pair scheme is no longer very profitable, nonetheless it remains a valuable tool for explication, retaining the capacity to demonstrate insight, modeling, and analysis while not clouding matters through complexity. After a quarter century in the marketplace, for profitable schemes beyond paper understanding and illustration, one needs to add some structural complexity and analytical subtlety.

One elaboration alluded to in the text is the assembling of a set of similar pairs (without getting into much detail on what metrics are used to gauge the degree of similarity), often designated as a group. Modeling such groups can be done in several ways, with some practitioners preferring to anchor a group on a notional archetype, structuring forecasts in terms of deviation of tradable pairs from the archetype; others create a formal implementation of the cohort as a gestalt or a synthetic instrument. Both of those approaches, and others, can be formally analyzed as a hierarchical model, greatly in vogue (and greatly productive of insight and application) in mainstream statistical thinking for two decades; add to the standard static structure the dynamic element in a time series setting and one is very quickly building an analytical structure of greater sophistication than routinely used as the didactic tool in this book. Nonetheless, all such modeling developments rely on the insight and techniques detailed herein.

Those readers with deeper knowledge of mathematical and statistical science will, hopefully, quickly see where the presentation can be taken.

Maintaining focus on the structurally simple pair scheme invites readers to treat this book as an explicit “how to” manual. From this perspective, one may learn a reasonable history of the what and the how and a decent knowledge of why it is possible. Contemporary successful execution will require from the reader some additional thought and directed exploration as foregoing remarks have indicated. For that task, the book serves as a map showing major features and indicating where the reader must get out a compass and notebook. The old cartographers’ device “Here be dragons” might be usefully remembered when you venture thus.

The text has, unashamedly, a statistician’s viewpoint: Models can be useful. Maintaining a model’s utility is one theme of the book. The statistician’s preoccupation with understanding variation—the appreciation of the knowledge that one’s models are wrong, though useful, and that the nature of the wrongness is illuminated by the structure of “errors” (discrepancies between observations and what a model predicts) is another theme of the book. Or, rather, not a distinct theme, but an overriding, guiding context for the material.

The notion of a pair trade is introduced in Chapter 1 and elaborated upon in Chapter 2. Following explication and exemplification, two simple theoretical models for the underlying phenomenon exploited by pairs, reversion, are proposed. These models are used throughout the text to study what is possible, illuminate how the possibilities might be exploited, consider what kinds of change would have negative impact on exploitation, and characterize the nature of the impact. Approaches for selecting a universe of instruments for modeling and trading are described. Consideration of change is introduced from this first toe dipping into analysis, because temporal dynamics underpin the entirety of the project. Without the dynamic there is no arbitrage.

In Chapter 3 we increase the depth and breadth of the analysis, expanding the modeling scope from simple observational rules1 for pairs to formal statistical models for more general portfolios. Several popular models for time series are described but detailed focus is on weighted moving averages at one extreme of complexity and factor analysis at another, these extremes serving to carry the message as clearly as we can make it. Pair spreads are referred to throughout the text serving, as already noted, as the simplest practical illustrator of the notions discussed. Where necessary to make our urgencies sensible, direct mention is made of other aspects of the arbitrageur’s concern, including portfolio optimization and factor exposures. For the most part though, incursions into multivariate territory are avoided. Volatility modeling (and the fascinating idea of stochastic resonance) are treated separately here and in Chapter 6; elsewhere discussion is subsumed in that of the mean forecast process.

Chapter 4 presents a probability theorem that illuminates the prevalence of price moves amenable to exploitation by the simple rules first applied in the late 1980s. The insight of this result guides evaluation of exploitation strategies. Are results borne of brilliance on the part of a modeler or would a high school graduate perform similarly because the result is driven by structural dynamics, long in the public domain, revealed by careful observation alone? Many a claim of a “high” proportion of winning bets by a statistical arbitrageur has more to do with the latter than any sophistication of basic spread modeling or (importantly) risk management. When markets are disrupted and the conditions underlying the theoretical result are grossly violated, comparative practitioner performance reveals much about basic understanding of the nature of the process being exploited. Knowledge of the theoretical results often reveals itself more when assumptions are violated than when things are hunky dory and managers with solid understanding and those operating intellectually blind generate positive returns in equal measure. (Tony O’Hagan suggested that the basic probability result is long known, but I have been unable to trace it. Perhaps the result is too trivial to be a named result and exists as a simple consequence, a textbook exercise, of basic distribution theory. No matter, the implication remains profoundly significant to the statistical arbitrage story.)

Chapter 5 critiques a published article (whose authors remain anonymous here to protect their embarrassment) to clarify the broad conditions under which the phenomenon of reversion occurs. A central role for the normal distribution is dismissed. The twin erroneous claims that (a) a price series must exhibit a normal marginal distribution for reversion to occur, and (b) a series exhibiting a normal marginal distribution necessarily exhibits reversion are unceremoniously dispelled. There is reversion anywhere and everywhere, as Chapter 4 demonstrates.

Chapter 6 answers the question, important for quantifying the magnitude of exploitable opportunities in reversion gambits, “How much volatility is there in a spread?”

Chapter 7 is for the enthusiast not easily dissuaded by the presence of the many hieroglyphs of the probability calculus. Anyone with a good first course in probability theory can follow the arguments, and most can manage the detailed derivations, too. The mechanics are not enormously complicated. Some of the conceptual distinctions may be challenging at first—read it twice! The effort will be repaid as there is significant practical insight in the examples considered at length. Knowledge of how close theoretical abstractions come to reflecting measurable features of actual price series is invaluable in assessing modeling possibilities and simulation or trading results. Notwithstanding that remark, it is true that the remainder of the book does not rely on familiarity with the material in Chapter 7. While you may miss some of the subtlety in the subsequent discussions, you will not lack understanding for omitting attention to this chapter.

Chapters 8 through 10 might have been labeled “The Fall,” as they characterize the problems that beset statistical arbitrage beginning in 2000 and directly caused the catastrophic drop in return during 2002–2004. An important lesson from this history is that there was not a single condition or set of conditions that abruptly changed in 2000 and thereby eliminated forecast performance of statistical arbitrage models. What a story that would be! Far more dramatic than the prosaic reality, which is a complex mix of multiple causes and timings. All the familiar one liners, including decimalization, competition, and low volatility, had (and have) their moment, but none individually, nor the combination, can have delivered a blow to financial markets. Fundamentally altering the price dynamics of markets in ways that drastically diminish the economic potential in reversion schemes, mining value across the spectrum from the very high frequency hare of intra-day to the venerable tortoise of a month or more, requires a more profound explanation.

Change upon change upon change cataloged in Chapter 9 is at the root of the dearth of return to statistical arbitrage in 2002–2004. (Performance deterioration in 2000–2002 was evident but limited to a subset of practitioners.) This unusual episode in recent U.S. macroeconomic history is over, but the effects linger in the financial markets reflecting emergent properties of the collective behavior of millions of investors; and surely those investors continue to embody, no matter how lingering, those changes and the causes thereof.

The shift of trading from the floor of the New York Stock Exchange to internal exchanges, in the guise of computer algorithms designed by large brokerage houses and investment banks, has cumulatively become a change with glacier-like implacability. Slow. Massive. Irresistible. Crushing. Reforming.2 A frequently remarked facet of the evolving dynamics is the decline of market volatility. Where has market volatility gone? In large part the algorithms have eaten it. Reduce the voice of a single participant yelling in a crowd and the babel is unaffected. Quite a significant proportion of participants and the reduced babel is oddly deafening. Now that computer programs (Chapter 10) “manage” over 60 percent of U.S. equity trades among “themselves” the extraodinary result is akin to administering a dose of ritalin to the hyperactive market child. In the commentary on low volatility two themes stand out: one is a lament over the lack of Keynes’ animal spirits, a concern that the entrepreneurial genius of America is subdued even as Asian giants are stirring; the other is a fear that investors have forgotten the risks inherent in investment decisions, that inadvisable decisions are therefore being made that will have negative consequences in the near future. The inconsistency in those two characterizations is stark, but it can be rationalized. Contrary to the first notion, the spirit is quite animated—with a billion and a half shares changing ownership daily on the NYSE mart alone, what other conclusion should one draw? There is plenty of spirit: simply its animus is satisfied with less overt fuss. Algorithms don’t have emotions. So there is plenty of innovative risk taking, but low volatility by historical standards, induced by trading technologies, has not yet been properly internalized by many market participants. Viewing contemporary volatility levels in the manner to which historical experience has been accustomed ineluctably leads to excessive risk taking.

Chapter 10 is interesting in its own right, notwithstanding any relationship to the evolution of statistical arbitrage opportunities. Algorithms and computer driven trading are changing the financial world in many ways. Electronic exchanges have already been seen off most of the world’s peopled trading places—and who among us believes that the floor of the NYSE will be more than a museum, parking lot, or memory in a year or two?

Chapter 11 describes the phoenix of statistical arbitrage, rising out of the ashes of the fire created and sustained by the technological developments in algorithmic trading. New, sustained patterns of stock price dynamics are emerging. The story of statistical arbitrage has returned to a new beginning. Will this fledgling fly?

The renaissance predicted in Chapter 11, drafted in 2005, is already coming to pass. Since at least early 2006 there has been a resurgence of performance from those practitioners who persisted through the extremely challenging dynamic changes of 2003–2005. Interestingly, while there are new systematic patterns in the movements of relative equity prices, some old patterns have also regained potency. Adoption of algorithmic trading is accelerating, with tools now offered by more than 20 vendors. In another technology driven development, beginning with Goldman Sachs in late 2006, at least two offerings of general hedge fund replication by algorithmic means have been brought to market. This is an exciting as well as exacting time for statistical arbitrageurs.

1There is no pejorative intent in the use of the term: The rules were effective. Statistical content was limited to measurement of range of variation; no distributional study, model formulation, estimation, error analysis, or forecasting was undertaken prior to milking the observational insight. Those activities came soon enough—after the profits were piling up. With the expanded statistical study, adding trading experience to historical data, came insight into subtleties of the stock price motions exploited and the market forces driving repetitious occurrence of opportunities.

2One major structural consequence, fed also by technical advance in the credit markets and the development of Exchange Traded Funds, is literally the forming anew of patterns of price behavior detemined by the interaction of computer algorithms as agents for share dealings. In addition to this re-forming, reform is simultaneously underway with changes to Securities Exchange Commission regulations and NYSE rules.

Foreword

Mean reversion in prices, as in much of human activity, is a powerful and fundamental force, driving systems and markets to homeostatic relationships. Starting in the early 1980s, statistical arbitrage was a formal and successful attempt to model this behavior in the pursuit of profit. Understanding the arithmetic of statistical arbitrage (sometimes abbreviated as stat. arb.) is a cornerstone to understanding the development of what has come to be known as complex financial engineering and risk modeling.