THE FRANK J. FABOZZI SERIES

QUANTITATIVEEQUITYINVESTING

FRANK J. FABOZZI, SERGIO M. FOCARDI, PETTER N. KOLM

Techniques and Strategies

In 1952, Harry Markowitz introduced a critical innovation in investment management—popularly referred to as modern portfolio theory—in which

he suggested that investors should decide the allocation of their investment funds on the basis of the trade-off between portfolio risk, as measured by the standard deviation of investment returns, and portfolio return, as measured by the expected value of the investment return. Entire new research areas grew from his groundbreaking idea, which, with the spread of low-cost powerful computers, found important practical applications in several fi elds of fi nance. Developing the necessary inputs for constructing portfolios based on modern portfolio theory has been facilitated by the development of Bayesian statistics, shrinkage techniques, factor models, and robust portfolio optimization. Modern quantitative techniques have now made it possible to manage large investment portfolios with computer programs that look for the best risk-return trade-off available in the market.

This book shows you how to perform quantitative equity portfolio management using these modern techniques. It skillfully presents state-of-the-art advances in the theory and practice of quantitative equity portfolio management. Page by page, the expert authors—who have all worked closely with hedge fund and quantitative asset management fi rms—cover the most up-to-date techniques, tools, and strategies used in the industry today.

They begin by discussing the role and use of mathematical techniques in fi nance, offering sound theoretical arguments in support of fi nance as a rigorous science. They go on to provide extensive background material on one of the principal tools used in quantitative equity management—fi nancial econometrics—covering modern regression theory, applications of Random Matrix Theory, dynamic time series models, vector autoregressive models, and cointegration analysis. The authors then look at fi nancial engineering, the pitfalls of estimation, methods to control model risk, and the modern theory of factor models, including approximate and dynamic factor models. After laying a fi rm theoretical foundation, they provide practical advice on optimization techniques and trading strategies based on factors and factormodels, offering a modern view on how to construct factor models.

$95.00 USA/$114.00 CAN

FRANK J. FABOZZI is Professor in the Practice of Finance and Becton Fellow at the Yale School of Management and Editor of the Journal of Portfolio Management. He is a Chartered Financial Analyst and earned a doctorate in economics from the City University of New York.

SERGIO M. FOCARDI is Professor of Finance at EDHEC Business School in Nice and a founding partner of the Paris-based consulting f irm The Intertek Group. He is also a member of the Editorial Board of the Journal of Portfolio Management. Sergio holds a degree in electronic engineering from the University of Genoa and a PhD in mathematical f inance from the University of Karlsruhe as well as a postgraduate degree in communications from the Galileo Ferraris Electrotechnical Institute (Turin).

PETTER N. KOLM is the Deputy Director of the Mathematics in Finance Master’s Program and Clinical Associate Professor of Mathematics at the Courant Institute of Mathematical Sciences, New York University; and a founding Partner of the New York–based f inancial consulting f irm the Heimdall Group, LLC. Previously, Petter worked in the Quantitative Strategies Group at Goldman Sachs Asset Management. He received an MS in mathematics from ETH in Zurich; an MPhil in applied mathematics from the Royal Institute of Technology in Stockholm; and a PhD in applied mathematics from Yale University.

Jacket Illustration: Jupiter Images

QUANTITATIVE EQUITY INVESTING

Quantitative equity portfolio management is a fundamental building block of investment management. This hands-on guide closes the gap between theory and practice by presenting state-of-the-art quantitative techniques and strategies for managing equity portfolios.

Authors Frank Fabozzi, Sergio Focardi, and Petter Kolm—all of whom have extensive experience in this area—address the essential elements of this discipline, including fi nancial model building, fi nancial engineering, static and dynamic factor models, asset allocation, portfolio models, transaction costs, trading strategies, and much more. They provide numerous illustrations and thorough discussions of implementation issues facing those in the investment management business and include the necessary background material in fi nancial econometrics to make the book self-contained. For many of the advanced topics, they also provide the reader with references to the most recent applicable research in this rapidly evolving fi eld.

In today’s fi nancial environment, you need the skills to analyze, optimize, and manage the risk of your quantitative equity portfolio. This guide offers you the best information available to achieve this goal.

FABOZZIFOCARDI

KOLM

QU

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TITATIVE EQU

ITY INVESTIN

GTechniques and Strategies

Techniques and strategies for successfulquantitative equity management

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QuantitativeEquity

Investing

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The Frank J. Fabozzi SeriesFixed Income Securities, Second Edition by Frank J. FabozziFocus on Value: A Corporate and Investor Guide to Wealth Creation by James L. Grant and James A. AbateHandbook of Global Fixed Income Calculations by Dragomir KrginManaging a Corporate Bond Portfolio by Leland E. Crabbe and Frank J. FabozziReal Options and Option-Embedded Securities by William T. MooreCapital Budgeting: Theory and Practice by Pamela P. Peterson and Frank J. FabozziThe Exchange-Traded Funds Manual by Gary L. GastineauProfessional Perspectives on Fixed Income Portfolio Management, Volume 3 edited by Frank J. FabozziInvesting in Emerging Fixed Income Markets edited by Frank J. Fabozzi and Efstathia PilarinuHandbook of Alternative Assets by Mark J. P. AnsonThe Global Money Markets by Frank J. Fabozzi, Steven V. Mann, and Moorad ChoudhryThe Handbook of Financial Instruments edited by Frank J. FabozziCollateralized Debt Obligations: Structures and Analysis by Laurie S. Goodman and Frank J. FabozziInterest Rate, Term Structure, and Valuation Modeling edited by Frank J. FabozziInvestment Performance Measurement by Bruce J. FeibelThe Handbook of Equity Style Management edited by T. Daniel Coggin and Frank J. FabozziThe Theory and Practice of Investment Management edited by Frank J. Fabozzi and Harry M. MarkowitzFoundations of Economic Value Added, Second Edition by James L. GrantFinancial Management and Analysis, Second Edition by Frank J. Fabozzi and Pamela P. PetersonMeasuring and Controlling Interest Rate and Credit Risk, Second Edition by Frank J. Fabozzi,

Steven V. Mann, and Moorad ChoudhryProfessional Perspectives on Fixed Income Portfolio Management, Volume 4 edited by Frank J. FabozziThe Handbook of European Fixed Income Securities edited by Frank J. Fabozzi and Moorad ChoudhryThe Handbook of European Structured Financial Products edited by Frank J. Fabozzi and

Moorad ChoudhryThe Mathematics of Financial Modeling and Investment Management by Sergio M. Focardi and

Frank J. FabozziShort Selling: Strategies, Risks, and Rewards edited by Frank J. FabozziThe Real Estate Investment Handbook by G. Timothy Haight and Daniel SingerMarket Neutral Strategies edited by Bruce I. Jacobs and Kenneth N. LevySecurities Finance: Securities Lending and Repurchase Agreements edited by Frank J. Fabozzi and

Steven V. MannFat-Tailed and Skewed Asset Return Distributions by Svetlozar T. Rachev, Christian Menn, and

Frank J. FabozziFinancial Modeling of the Equity Market: From CAPM to Cointegration by Frank J. Fabozzi, Sergio M.

Focardi, and Petter N. KolmAdvanced Bond Portfolio Management: Best Practices in Modeling and Strategies edited by

Frank J. Fabozzi, Lionel Martellini, and Philippe PriauletAnalysis of Financial Statements, Second Edition by Pamela P. Peterson and Frank J. FabozziCollateralized Debt Obligations: Structures and Analysis, Second Edition by Douglas J. Lucas, Laurie S.

Goodman, and Frank J. FabozziHandbook of Alternative Assets, Second Edition by Mark J. P. AnsonIntroduction to Structured Finance by Frank J. Fabozzi, Henry A. Davis, and Moorad ChoudhryFinancial 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. ManningRobust Portfolio Optimization and Management by Frank J. Fabozzi, Peter N. Kolm,

Dessislava A. Pachamanova, and Sergio M. FocardiAdvanced Stochastic Models, Risk Assessment, and Portfolio Optimizations by Svetlozar T. Rachev,

Stogan V. Stoyanov, and Frank J. FabozziHow to Select Investment Managers and Evaluate Performance by G. Timothy Haight,

Stephen O. Morrell, and Glenn E. RossBayesian Methods in Finance by Svetlozar T. Rachev, John S. J. Hsu, Biliana S. Bagasheva, and

Frank J. FabozziStructured Products and Related Credit Derivatives by Brian P. Lancaster, Glenn M. Schultz, and

Frank J. Fabozzi

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John Wiley & Sons, Inc.

QuantitativeEquity

InvestingTechniques and Strategies

FRANK J. FABOZZISERGIO M. FOCARDI

PETTER N. KOLM

with the assistance of Joseph A. Cerniglia and Dessislava Pachamanova

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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 transmit-ted in any form or by any means, electronic, mechanical, photocopying, recording, scan-ning, 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) 646-8600, 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/permissions.

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 specifi cally disclaim any implied warranties of merchantability or fi tness 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 profi t 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) 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:

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 Pacha-manova. p. cm. — (The Frank J. Fabozzi series)Includes index.ISBN 978-0-470-26247-4 (cloth)

1. Portfolio management. 2. Investments. I. Focardi, Sergio. II. Kolm, Petter N. III. Title. HG4529.5.F3346 2010 332.63’2042—dc22 2009050962

Printed in the United States of America.

10 9 8 7 6 5 4 3 2 1

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FJFTo my wife Donna, and my children

Francesco, Patricia, and Karly

SMFTo my mother and in memory of my father

PNKTo my wife and my daughter, Carmen and Kimberly,

and in memory of my father-in-law, John

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Contents

vii

Preface xiAbout the Authors xv

CHAPTER 1 Introduction 1

In Praise of Mathematical Finance 3Studies of the Use of Quantitative Equity Management 9Looking Ahead for Quantitative Equity Investing 45

CHAPTER 2Financial Econometrics I: Linear Regressions 47

Historical Notes 47Covariance and Correlation 49Regressions, Linear Regressions, and Projections 61Multivariate Regression 76Quantile Regressions 78Regression Diagnostic 80Robust Estimation of Regressions 83Classifi cation and Regression Trees 96Summary 99

CHAPTER 3Financial Econometrics II: Time Series 101

Stochastic Processes 101Time Series 102Stable Vector Autoregressive Processes 110Integrated and Cointegrated Variables 114Estimation of Stable Vector Autoregressive (VAR) Models 120Estimating the Number of Lags 137Autocorrelation and Distributional Properties of Residuals 139Stationary Autoregressive Distributed Lag Models 140

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viii CONTENTS

Estimation of Nonstationary VAR Models 141Estimation with Canonical Correlations 151Estimation with Principal Component Analysis 153Estimation with the Eigenvalues of the Companion Matrix 154Nonlinear Models in Finance 155Causality 156Summary 157

CHAPTER 4Common Pitfalls in Financial Modeling 159

Theory and Engineering 159Engineering and Theoretical Science 161Engineering and Product Design in Finance 163Learning, Theoretical, and Hybrid Approaches to

Portfolio Management 164Sample Biases 165The Bias in Averages 167Pitfalls in Choosing from Large Data Sets 170Time Aggregation of Models and Pitfalls in the

Selection of Data Frequency 173Model Risk and its Mitigation 174Summary 193

CHAPTER 5Factor Models and Their Estimation 195

The Notion of Factors 195Static Factor Models 196Factor Analysis and Principal Components Analysis 205Why Factor Models of Returns 219Approximate Factor Models of Returns 221Dynamic Factor Models 222Summary 239

CHAPTER 6 Factor-Based Trading Strategies I: Factor Construction and Analysis 243

Factor-Based Trading 245Developing Factor-Based Trading Strategies 247Risk to Trading Strategies 249Desirable Properties of Factors 251Sources for Factors 251

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Contents ix

Building Factors from Company Characteristics 253Working with Data 253Analysis of Factor Data 261Summary 266

CHAPTER 7Factor-Based Trading Strategies II: Cross-Sectional Models and Trading Strategies 269

Cross-Sectional Methods for Evaluation of Factor Premiums 270Factor Models 278Performance Evaluation of Factors 288Model Construction Methodologies for a

Factor-Based Trading Strategy 295Backtesting 306Backtesting Our Factor Trading Strategy 308Summary 309

CHAPTER 8Portfolio Optimization: Basic Theory and Practice 313

Mean-Variance Analysis: Overview 314Classical Framework for Mean-Variance Optimization 317Mean-Variance Optimization with a Risk-Free Asset 321Portfolio Constraints Commonly Used in Practice 327Estimating the Inputs Used in Mean-Variance Optimization:

Expected Return and Risk 333Portfolio Optimization with Other Risk Measures 342Summary 357

CHAPTER 9Portfolio Optimization: Bayesian Techniques and the Black-Litterman Model 361

Practical Problems Encountered in Mean-Variance Optimization 362

Shrinkage Estimation 369The Black-Litterman Model 373Summary 394

CHAPTER 10Robust Portfolio Optimization 395

Robust Mean-Variance Formulations 396Using Robust Mean-Variance Portfolio Optimization

in Practice 411

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x CONTENTS

Some Practical Remarks on Robust Portfolio Optimization Models 416

Summary 418

CHAPTER 11Transaction Costs and Trade Execution 419

A Taxonomy of Transaction Costs 420Liquidity and Transaction Costs 427Market Impact Measurements and Empirical Findings 430Forecasting and Modeling Market Impact 433Incorporating Transaction Costs in Asset-Allocation Models 439Integrated Portfolio Management:

Beyond Expected Return and Portfolio Risk 444Summary 446

CHAPTER 12Investment Management and Algorithmic Trading 449

Market Impact and the Order Book 450Optimal Execution 452Impact Models 455Popular Algorithmic Trading Strategies 457What Is Next? 465Some Comments about the High-Frequency Arms Race 467Summary 470

APPENDIX AData Descriptions and Factor Defi nitions 473

The MSCI World Index 473One-Month LIBOR 482The Compustat Point-in-Time, IBES Consensus Databases

and Factor Defi nitions 483

APPENDIX BSummary of Well-Known Factors and Their Underlying Economic Rationale 487

APPENDIX C Review of Eigenvalues and Eigenvectors 493

The SWEEP Operator 494

Index 497

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Preface

xi

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 Me-morial Prize in Economic Sciences. Markowitz’s ideas proved to be very fer-tile. Entire new research areas originated from it which, with the diffusion of low-cost powerful computers, found important practical applications in several fi elds of fi nance.

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 fat-tailed distributions.The development of Bayesian techniques to integrate human judgment with results from models.The progressive adoption of optimization and robust optimization tech-niques.

Due to these and other theoretical advances it has progressively become pos-sible 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 com-plicated 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 artifi cial intelligence to trade the equity markets. Their strate-gies may range from intermediate and long-term strategies, six months to

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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 scientifi c rigor of mathematical and fi nancial theories.

This book is about quantitative equity portfolio management per-formed with modern techniques. One of our goals for this book is to present advances in the theory and practice of quantitative equity portfolio manage-ment 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 fi eld.

This book is intended for students, academics, and fi nancial practitio-ners 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 back-ground knowledge in fi nance is needed. Nonetheless, basic working knowl-edge 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 fi nance. In addition to offering theoretical arguments in support of fi nance as a mathematical science, we discuss the results of three surveys on the dif-fusion 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, fi nancial economet-rics. Coverage in Chapter 2 includes modern regression theory, applications of Random Matrix Theory, and robust methods. In Chapter 3, we extend our coverage of fi nancial economics to dynamic models of times series, vec-tor 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 optimi-zation are reviewed in Chapter 9, followed by a discussion of the Bayesian approach to investment management as implemented in the Black-Litterman

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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 trad-ing costs and trading techniques. In Chapter 11, our focus is on the issues related to trading cost and implementation of trading strategies from a prac-tical point of view. The modern techniques of algorithmic trading are the subject of the fi nal chapter in the book, Chapter 12.

There are three appendixes. Appendix A provides a description of the data and factor defi nitions 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 under-graduate advanced electives on investment management, and graduate stu-dents in fi nance, 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 economet-ric 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 fac-tor-based trading strategies and provide many practical examples. Chapters 9–12 cover the important topics of Bayesian techniques, robust optimiza-tion, and transaction cost modeling—by now standard tools used in quanti-tative portfolio construction in the fi nancial 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 devel-opment of trading strategies (in Chapters 6 and 7), optimal execution, and algorithmic trading (in Chapters 11 and 12). The many references in these chap-ters, 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-

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