Statistical Arbitrage
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Statistical Arbitrage Algorithmic Trading Insights and Techniques ANDREW POLE John Wiley & Sons, Inc. Statistical Arbitrage Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States. With offices in North America, Europe, Australia, and Asia. Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding. The Wiley Finance series contains books written specifically for finance and investment professionals as well as sophisticated indi- vidual investors and their financial advisors. Book topics range from portfolio management to e-commerce, risk management, financial engineering, valuation, and financial instrument analysis, as well as much more. For a list of available titles, visit our Web site at www.Wiley Finance.com. Statistical Arbitrage Algorithmic Trading Insights and Techniques ANDREW POLE John Wiley & Sons, Inc. Copyright c 2007 by Andrew Pole. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. Wiley Bicentennial logo: Richard J. Pacifico. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the Web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. 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For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our Web site at www.wiley.com. 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 Printed in the United States of America 10987654321 To Eliza and Marina Contents Preface xiii Foreword xix Acknowledgments xxiii CHAPTER 1 Monte Carlo or Bust 1 Beginning 1 Whither? And Allusions 4 CHAPTER 2 Statistical Arbitrage 9 Introduction 9 Noise Models 10 Reverse Bets 11 Multiple Bets 11 Rule Calibration 12 Spread Margins for Trade Rules 16 Popcorn Process 18 Identifying Pairs 20 Refining Pair Selection 21 Event Analysis 22 Correlation Search in the Twenty-First Century 26 Portfolio Configuration and Risk Control 26 Exposure to Market Factors 29 Market Impact 30 Risk Control Using Event Correlations 31 Dynamics and Calibration 32 Evolutionary Operation: Single Parameter Illustration 34 vii viii CONTENTS CHAPTER 3 Structural Models 37 Introduction 37 Formal Forecast Functions 39 Exponentially Weighted Moving Average 40 Classical Time Series Models 47 Autoregression and Cointegration 47 Dynamic Linear Model 49 Volatility Modeling 50 Pattern Finding Techniques 51 Fractal Analysis 52 Which Return? 52 A Factor Model 53 Factor Analysis 54 Defactored Returns 55 Prediction Model 57 Stochastic Resonance 58 Practical Matters 59 Doubling: A Deeper Perspective 61 Factor Analysis Primer 63 Prediction Model for Defactored Returns 65 CHAPTER 4 Law of Reversion 67 Introduction 67 Model and Result 68 The 75 percent Rule 68 Proof of the 75 percent Rule 69 Analytic Proof of the 75 percent Rule 71 Discrete Counter 73 Generalizations 73 Inhomogeneous Variances 74 Volatility Bursts 75 Numerical Illustration 76 First-Order Serial Correlation 77 Analytic Proof 79 Examples 82 Nonconstant Distributions 82 Applicability of the Result 84 Application to U.S. Bond Futures 85 Contents ix Summary 87 Appendix 4.1: Looking Several Days Ahead 87 CHAPTER 5 Gauss Is Not the God of Reversion 91 Introduction 91 Camels and Dromedaries 92 Dry River Flow 95 Some Bells Clang 98 CHAPTER 6 Interstock Volatility 99 Introduction 99 Theoretical Explanation 103 Theory versus Practice 105 Finish the Theory 105 Finish the Examples 106 Primer on Measuring Spread Volatility 108 CHAPTER 7 Quantifying Reversion Opportunities 113 Introduction 113 Reversion in a Stationary Random Process 114 Frequency of Reversionary Moves 117 Amount of Reversion 118 Movements from Quantiles Other Than the Median 135 Nonstationary Processes: Inhomogeneous Variance 136 Sequentially Structured Variances 136 Sequentially Unstructured Variances 137 Serial Correlation 138 Appendix 7.1: Details of the Lognormal Case in Example 6 139 CHAPTER 8 Nobel Difficulties 141 Introduction 141 Event Risk 142 Will Narrowing Spreads Guarantee Profits? 144 Rise of a New Risk Factor 145 x CONTENTS Redemption Tension 148 Supercharged Destruction 150 The Story of Regulation Fair Disclosure (FD) 150 Correlation During Loss Episodes 151 CHAPTER 9 Trinity Troubles 155 Introduction 155 Decimalization 156 European Experience 157 Advocating the Devil 158 Stat. Arb. Arbed Away 159 Competition 160 Institutional Investors 163 Volatility Is the Key 163 Interest Rates and Volatility 165 Temporal Considerations 166 Truth in Fiction 174 A Litany of Bad Behavior 174 A Perspective on 2003 178 Realities of Structural Change 179 Recap 180 CHAPTER 10 Arise Black Boxes 183 Introduction 183 Modeling Expected Transaction Volume and Market Impact 185 Dynamic Updating 188 More Black Boxes 189 Market Deflation 189 CHAPTER 11 Statistical Arbitrage Rising 191 Catastrophe Process 194 Catastrophic Forecasts 198 Trend Change Identification 200 Using the Cuscore to Identify a Catastrophe 202 Is It Over? 204 Catastrophe Theoretic Interpretation 205 Implications for Risk Management 209 Contents xi Sign Off 211 Appendix 11.1: Understanding the Cuscore 211 Bibliography 223 Index 225 Preface hese pages tell the story of statistical arbitrage. It is both a history, T 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 xiii xiv PREFACE a gestalt or a synthetic instrument. Both of those