THE FRANK J. FABOZZI SERIES QUANTITATIVE EQUITY INVESTING. Techniques and Strategies FRANK J. FABOZZI, SERGIO M. FOCARDI, PETTER N.

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1 THE FRANK J. FABOZZI SERIES QUANTITATIVE EQUITY INVESTING Techniques and Strategies FRANK J. FABOZZI, SERGIO M. FOCARDI, PETTER N. KOLM

3 Quantitative Equity Investing

4 The Frank J. Fabozzi Series Fixed Income Securities, Second Edition by Frank J. Fabozzi Focus on Value: A Corporate and Investor Guide to Wealth Creation by James L. Grant and James A. Abate Handbook of Global Fixed Income Calculations by Dragomir Krgin Managing a Corporate Bond Portfolio by Leland E. Crabbe and Frank J. Fabozzi Real Options and Option-Embedded Securities by William T. Moore Capital Budgeting: Theory and Practice by Pamela P. Peterson and Frank J. Fabozzi The Exchange-Traded Funds Manual by Gary L. Gastineau Professional Perspectives on Fixed Income Portfolio Management, Volume 3 edited by Frank J. Fabozzi Investing in Emerging Fixed Income Markets edited by Frank J. Fabozzi and Efstathia Pilarinu Handbook of Alternative Assets by Mark J. P. Anson The Global Money Markets by Frank J. Fabozzi, Steven V. Mann, and Moorad Choudhry The Handbook of Financial Instruments edited by Frank J. Fabozzi Collateralized Debt Obligations: Structures and Analysis by Laurie S. Goodman and Frank J. Fabozzi Interest Rate, Term Structure, and Valuation Modeling edited by Frank J. Fabozzi Investment Performance Measurement by Bruce J. Feibel The Handbook of Equity Style Management edited by T. Daniel Coggin and Frank J. Fabozzi The Theory and Practice of Investment Management edited by Frank J. Fabozzi and Harry M. Markowitz Foundations of Economic Value Added, Second Edition by James L. Grant Financial Management and Analysis, Second Edition by Frank J. Fabozzi and Pamela P. Peterson Measuring and Controlling Interest Rate and Credit Risk, Second Edition by Frank J. Fabozzi, Steven V. Mann, and Moorad Choudhry Professional Perspectives on Fixed Income Portfolio Management, Volume 4 edited by Frank J. Fabozzi The Handbook of European Fixed Income Securities edited by Frank J. Fabozzi and Moorad Choudhry The Handbook of European Structured Financial Products edited by Frank J. Fabozzi and Moorad Choudhry The Mathematics of Financial Modeling and Investment Management by Sergio M. Focardi and Frank J. Fabozzi Short Selling: Strategies, Risks, and Rewards edited by Frank J. Fabozzi The Real Estate Investment Handbook by G. Timothy Haight and Daniel Singer Market Neutral Strategies edited by Bruce I. Jacobs and Kenneth N. Levy Securities Finance: Securities Lending and Repurchase Agreements edited by Frank J. Fabozzi and Steven V. Mann Fat-Tailed and Skewed Asset Return Distributions by Svetlozar T. Rachev, Christian Menn, and Frank J. Fabozzi Financial Modeling of the Equity Market: From CAPM to Cointegration by Frank J. Fabozzi, Sergio M. Focardi, and Petter N. Kolm Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies edited by Frank J. Fabozzi, Lionel Martellini, and Philippe Priaulet Analysis of Financial Statements, Second Edition by Pamela P. Peterson and Frank J. Fabozzi Collateralized Debt Obligations: Structures and Analysis, Second Edition by Douglas J. Lucas, Laurie S. Goodman, and Frank J. Fabozzi Handbook of Alternative Assets, Second Edition by Mark J. P. Anson Introduction to Structured Finance by Frank J. Fabozzi, Henry A. Davis, and Moorad Choudhry Financial Econometrics by Svetlozar T. Rachev, Stefan Mittnik, Frank J. Fabozzi, Sergio M. Focardi, and Teo Jasic Developments in Collateralized Debt Obligations: New Products and Insights by Douglas J. Lucas, Laurie S. Goodman, Frank J. Fabozzi, and Rebecca J. Manning Robust Portfolio Optimization and Management by Frank J. Fabozzi, Peter N. Kolm, Dessislava A. Pachamanova, and Sergio M. Focardi Advanced Stochastic Models, Risk Assessment, and Portfolio Optimizations by Svetlozar T. Rachev, Stogan V. Stoyanov, and Frank J. Fabozzi How to Select Investment Managers and Evaluate Performance by G. Timothy Haight, Stephen O. Morrell, and Glenn E. Ross Bayesian Methods in Finance by Svetlozar T. Rachev, John S. J. Hsu, Biliana S. Bagasheva, and Frank J. Fabozzi Structured Products and Related Credit Derivatives by Brian P. Lancaster, Glenn M. Schultz, and Frank J. Fabozzi

5 Quantitative Equity Investing Techniques and Strategies FRANK J. FABOZZI SERGIO M. FOCARDI PETTER N. KOLM with the assistance of Joseph A. Cerniglia and Dessislava Pachamanova John Wiley & Sons, Inc.

6 Copyright 2010 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. 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) , fax (978) , or on the web at Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) , fax (201) , or online at Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. 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) , outside the United States at (317) , or fax (317) 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 Library of Congress Cataloging-in-Publication Data: Fabozzi, Frank J. Quantitative equity investing : techniques and strategies / Frank J. Fabozzi, Sergio M. Focardi, Petter N. Kolm ; with the assistance of Joseph A. Cerniglia and Dessislava Pachamanova. p. cm. (The Frank J. Fabozzi series) Includes index. ISBN (cloth) 1. Portfolio management. 2. Investments. I. Focardi, Sergio. II. Kolm, Petter N. III. Title. HG F dc Printed in the United States of America

7 FJF To my wife Donna, and my children Francesco, Patricia, and Karly SMF To my mother and in memory of my father PNK To my wife and my daughter, Carmen and Kimberly, and in memory of my father-in-law, John

9 Contents Preface About the Authors xi xv CHAPTER 1 Introduction 1 In Praise of Mathematical Finance 3 Studies of the Use of Quantitative Equity Management 9 Looking Ahead for Quantitative Equity Investing 45 CHAPTER 2 Financial Econometrics I: Linear Regressions 47 Historical Notes 47 Covariance and Correlation 49 Regressions, Linear Regressions, and Projections 61 Multivariate Regression 76 Quantile Regressions 78 Regression Diagnostic 80 Robust Estimation of Regressions 83 Classification and Regression Trees 96 Summary 99 CHAPTER 3 Financial Econometrics II: Time Series 101 Stochastic Processes 101 Time Series 102 Stable Vector Autoregressive Processes 110 Integrated and Cointegrated Variables 114 Estimation of Stable Vector Autoregressive (VAR) Models 120 Estimating the Number of Lags 137 Autocorrelation and Distributional Properties of Residuals 139 Stationary Autoregressive Distributed Lag Models 140 vii

10 viii CONTENTS Estimation of Nonstationary VAR Models 141 Estimation with Canonical Correlations 151 Estimation with Principal Component Analysis 153 Estimation with the Eigenvalues of the Companion Matrix 154 Nonlinear Models in Finance 155 Causality 156 Summary 157 CHAPTER 4 Common Pitfalls in Financial Modeling 159 Theory and Engineering 159 Engineering and Theoretical Science 161 Engineering and Product Design in Finance 163 Learning, Theoretical, and Hybrid Approaches to Portfolio Management 164 Sample Biases 165 The Bias in Averages 167 Pitfalls in Choosing from Large Data Sets 170 Time Aggregation of Models and Pitfalls in the Selection of Data Frequency 173 Model Risk and its Mitigation 174 Summary 193 CHAPTER 5 Factor Models and Their Estimation 195 The Notion of Factors 195 Static Factor Models 196 Factor Analysis and Principal Components Analysis 205 Why Factor Models of Returns 219 Approximate Factor Models of Returns 221 Dynamic Factor Models 222 Summary 239 CHAPTER 6 Factor-Based Trading Strategies I: Factor Construction and Analysis 243 Factor-Based Trading 245 Developing Factor-Based Trading Strategies 247 Risk to Trading Strategies 249 Desirable Properties of Factors 251 Sources for Factors 251

11 Contents ix Building Factors from Company Characteristics 253 Working with Data 253 Analysis of Factor Data 261 Summary 266 CHAPTER 7 Factor-Based Trading Strategies II: Cross-Sectional Models and Trading Strategies 269 Cross-Sectional Methods for Evaluation of Factor Premiums 270 Factor Models 278 Performance Evaluation of Factors 288 Model Construction Methodologies for a Factor-Based Trading Strategy 295 Backtesting 306 Backtesting Our Factor Trading Strategy 308 Summary 309 CHAPTER 8 Portfolio Optimization: Basic Theory and Practice 313 Mean-Variance Analysis: Overview 314 Classical Framework for Mean-Variance Optimization 317 Mean-Variance Optimization with a Risk-Free Asset 321 Portfolio Constraints Commonly Used in Practice 327 Estimating the Inputs Used in Mean-Variance Optimization: Expected Return and Risk 333 Portfolio Optimization with Other Risk Measures 342 Summary 357 CHAPTER 9 Portfolio Optimization: Bayesian Techniques and the Black-Litterman Model 361 Practical Problems Encountered in Mean-Variance Optimization 362 Shrinkage Estimation 369 The Black-Litterman Model 373 Summary 394 CHAPTER 10 Robust Portfolio Optimization 395 Robust Mean-Variance Formulations 396 Using Robust Mean-Variance Portfolio Optimization in Practice 411

12 x CONTENTS Some Practical Remarks on Robust Portfolio Optimization Models 416 Summary 418 CHAPTER 11 Transaction Costs and Trade Execution 419 A Taxonomy of Transaction Costs 420 Liquidity and Transaction Costs 427 Market Impact Measurements and Empirical Findings 430 Forecasting and Modeling Market Impact 433 Incorporating Transaction Costs in Asset-Allocation Models 439 Integrated Portfolio Management: Beyond Expected Return and Portfolio Risk 444 Summary 446 CHAPTER 12 Investment Management and Algorithmic Trading 449 Market Impact and the Order Book 450 Optimal Execution 452 Impact Models 455 Popular Algorithmic Trading Strategies 457 What Is Next? 465 Some Comments about the High-Frequency Arms Race 467 Summary 470 APPENDIX A Data Descriptions and Factor Defi nitions 473 The MSCI World Index 473 One-Month LIBOR 482 The Compustat Point-in-Time, IBES Consensus Databases and Factor Definitions 483 APPENDIX B Summary of Well-Known Factors and Their Underlying Economic Rationale 487 APPENDIX C Review of Eigenvalues and Eigenvectors 493 The SWEEP Operator 494 Index 497

13 Preface Quantitative equity portfolio management is a fundamental building block of investment management. The basic principles of investment management have been proposed back in the 1950s in the pathbreaking work of Harry Markowitz. For his work, in 1990 Markowitz was awarded the Nobel Memorial Prize in Economic Sciences. Markowitz s ideas proved to be very fertile. Entire new research areas originated from it which, with the diffusion of low-cost powerful computers, found important practical applications in several fields of finance. Among the developments that followed Markowitz s original approach we can mention: The development of CAPM and of general equilibrium asset pricing models. The development of multifactor models. The extension of the investment framework to a dynamic multiperiod environment. The development of statistical tools to extend his framework to fattailed distributions. The development of Bayesian techniques to integrate human judgment with results from models. The progressive adoption of optimization and robust optimization techniques. Due to these and other theoretical advances it has progressively become possible to manage investments with computer programs that look for the best risk-return trade-off available in the market. People have always tried to beat the market, in the hunt for a free lunch. This began by relying on simple observations and rules of thumb to pick the winners, and later with the advent of computers brought much more complicated systems and mathematical models within common reach. Today, so-called buy-side quants deploy a wide range of techniques ranging from econometrics, optimization, and computer science to data mining, machine learning, and artificial intelligence to trade the equity markets. Their strategies may range from intermediate and long-term strategies, six months to xi

14 xii PREFACE several years out, to so-called ultra-high or high-frequency strategies, at the sub-millisecond level. The modern quantitative techniques have replaced good old-fashioned experience and market insight, with the scientific rigor of mathematical and financial theories. This book is about quantitative equity portfolio management performed with modern techniques. One of our goals for this book is to present advances in the theory and practice of quantitative equity portfolio management that represent what we might call the state of the art of advanced equity portfolio management. We cover the most common techniques, tools, and strategies used in quantitative equity portfolio management in the industry today. For many of the advanced topics, we provide the reader with references to the most recent applicable research in the field. This book is intended for students, academics, and financial practitioners alike who want an up-to-date treatment of quantitative techniques in equity portfolio management, and who desire to deepen their knowledge of some of the most cutting-edge techniques in this rapidly developing area. The book is written in an almost self-contained fashion, so that little background knowledge in finance is needed. Nonetheless, basic working knowledge of undergraduate linear algebra and probability theory are useful, especially for the more mathematical topics in this book. In Chapter 1 we discuss the role and use of mathematical techniques in finance. In addition to offering theoretical arguments in support of finance as a mathematical science, we discuss the results of three surveys on the diffusion of quantitative methods in the management of equity portfolios. In Chapters 2 and 3, we provide extensive background material on one of the principal tools used in quantitative equity management, financial econometrics. Coverage in Chapter 2 includes modern regression theory, applications of Random Matrix Theory, and robust methods. In Chapter 3, we extend our coverage of financial economics to dynamic models of times series, vector autoregressive models, and cointegration analysis. Financial engineering, the many pitfalls of estimation, and methods to control model risk are the subjects of Chapter 4. In Chapter 5, we introduce the modern theory of factor models, including approximate factor models and dynamic factor models. Trading strategies based on factors and factor models are the focus of Chapters 6 and 7. In these chapters we offer a modern view on how to construct factor models based on fundamental factors and how to design and test trading strategies based on these. We offer a wealth of practical examples on the application of factor models in these chapters. The coverage in Chapters 8, 9, and 10 is on the use of optimization models in quantitative equity management. The basics of portfolio optimization are reviewed in Chapter 9, followed by a discussion of the Bayesian approach to investment management as implemented in the Black-Litterman

15 Preface xiii framework in Chapter 9. In Chapter 10 we discuss robust optimization techniques because they have greatly enhanced the ability to implement portfolio optimization models in practice. The last two chapters of the book cover the important topic of trading costs and trading techniques. In Chapter 11, our focus is on the issues related to trading cost and implementation of trading strategies from a practical point of view. The modern techniques of algorithmic trading are the subject of the final chapter in the book, Chapter 12. There are three appendixes. Appendix A provides a description of the data and factor definitions used in the illustrations and examples in the book. A summary of the factors, their economic rationale, and references that have supported the use of each factor is provided in Appendix B. In Appendix C we provide a review of eigenvalues and eigenvectors. TEACHING USING THIS BOOK Many of the chapters in this book have been used in courses and workshops on quantitative investment management, econometrics, trading strategies and algorithmic trading. The topics of the book are appropriate for undergraduate advanced electives on investment management, and graduate students in finance, economics, or in the mathematical and physical sciences. For a typical course it is natural to start with Chapters 1 3, 5, and 8 where the quantitative investment management industry, standard econometric techniques, and modern portfolio and asset pricing theory are reviewed. Important practical considerations such as model risk and its mitigation are presented in Chapter 4. Chapters 6 and 7 focus on the development of factor-based trading strategies and provide many practical examples. Chapters 9 12 cover the important topics of Bayesian techniques, robust optimization, and transaction cost modeling by now standard tools used in quantitative portfolio construction in the financial industry. We recommend that a more advanced course covers these topics in some detail. Student projects can be based on specialized topics such as the development of trading strategies (in Chapters 6 and 7), optimal execution, and algorithmic trading (in Chapters 11 and 12). The many references in these chapters, and in the rest of the book, provide a good starting point for research. ACKNOWLEDGMENTS We would like to acknowledge the assistance of several individuals who contributed to this book. Chapters 6 and 7 on trading strategies were co-

The Basics of Finance

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