Andrew Pole - Statistical Arbitrage

Contents

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. ArbitrageMathematical models. 3. SpeculationMathematical 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 strategys 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 tradethe progenitor of statistical arbitrageis 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; ones 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 statisticians viewpoint: Models can be useful. Maintaining a models utility is one theme of the book. The statisticians preoccupation with understanding variationthe appreciation of the knowledge that ones 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.