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CHAPMAN & HALL/CRC Financial Mathematics Series Aims and scope: The field of financial mathematics forms an ever-expanding slice of the financial sector. This series aims to capture new developments and summarize what is known over the whole spectrum of this field. It will include a broad range of textbooks, reference works, and handbooks that are meant to appeal to both academics and practitioners. This series encourages the inclusion of numerical code and concrete real-world examples. Series Editors M.A.H. Dempster Centre for Financial Research Judge Business School University of Cambridge Dilip B. Madan Robert H. Smith School of Business University of Maryland Rama Cont Center for Financial Engineering Columbia University New York Published Titles American-Style Derivatives; Valuation and Computation, Jerome Detemple Financial Modelling with Jump Processes, Rama Cont and Peter Tankov An Introduction to Credit Risk Modeling, Christian Bluhm, Ludger Overbeck, and Christoph Wagner Portfolio Optimization and Performance Analysis, Jean-Luc Prigent Quantitative Equity Portfolio Management: Modern Techniques and Applications, Edward E. Qian, Ronald H. Hua, and Eric H. Sorensen Robust Libor Modelling and Pricing of Derivative Products, John Schoenmakers Structured Credit Portfolio Analysis, Baskets & CDOs, Christian Bluhm and Ludger Overbeck Proposals for the series should be submitted to one of the series editors above or directly to: CRC Press, Taylor and Francis Group 24-25 Blades Court Deodar Road London SW15 2NU UK C5580.indb 2 4/6/07 9:16:11 AM

CHAPMAN & HALL/CRC FINANCIAL MATHEMATICS SERIES Quantitative Equity Portfolio Management Modern Techniques and Applications Edward E. Qian, Ronald H. Hua, and Eric H. Sorensen Boca Raton London New York Chapman & Hall/CRC is an imprint of the Taylor & Francis Group, an informa business C5580.indb 3 4/6/07 9:16:12 AM

Chapman & Hall/CRC Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487‑2742 © 2007 by Taylor & Francis Group, LLC Chapman & Hall/CRC is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid‑free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number‑10: 1‑58488‑558‑0 (Hardcover) International Standard Book Number‑13: 978‑1‑58488‑558‑0 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the conse‑ quences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978‑750‑8400. CCC is a not‑for‑profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Qian, Edward E. Quantitative equity portfolio management : modern techniques and applications / Edward E. Qian, Ronald H. Hua, and Eric H. Sorensen. p. cm. ‑‑ (Chapman & Hall/CRC financial mathematics series ; 6) Includes bibliographical references and index. ISBN‑13: 978‑1‑58488‑558‑0 ISBN‑10: 1‑58488‑558‑0 1. Portfolio management‑‑Mathematical models. I. Hua, Ronald H. II. Sorensen, Eric H. III. Title. IV. Series. HG4529.5.Q25 2007 332.6‑‑dc22 2006100572 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com C5580.indb 4 4/6/07 9:16:12 AM

Contents Preface, xi Abstract, xiii About the Authors, xv Chapter 1 < Introduction: Beliefs, Risk, and Process INfORMATION CAPTURe 1.1 BelIefs 1.2 RIsk 1.3 QUANTITATIVe INVesTMeNT PROCess 1.4 1.5 The ChAPTeRs APPeNDIX: PsYChOlOGY AND BehAVIOR fINANCe A1.1 ADVANCes IN PsYChOlOGY A1.2 BehAVIORAl fINANCe A1.3 BehAVIORAl MODels RefeReNCes eNDNOTes Part I Chapter 2 < Portfolio Theory 2.1 DIsTRIBUTIONs Of INVesTMeNT ReTURNs 2.2 OPTIMAl PORTfOlIOs 2.3 CAPITAl AsseT PRICING MODel 1 1 3 5 8 11 11 12 12 14 16 18 23 24 28 38 C5580.indb 5 4/6/07 9:16:13 AM

vi < Contents 2.4 ChARACTeRIsTIC PORTfOlIOs PROBleMs RefeReNCes Chapter 3 < Risk Models and Risk Analysis 3.1 ARBITRAGe PRICING TheORY AND APT MODels 3.2 RIsk ANAlYsIs 3.3 CONTRIBUTION TO VAlUe AT RIsk PROBleMs RefeReNCes Part II Chapter 4 < evaluation of Alpha factors 45 47 51 53 54 64 72 74 76 81 4.1 AlPhA PeRfORMANCe BeNChMARks: The RATIOs 81 4.2 sINGle-PeRIOD skIll: INfORMATION COeffICIeNT 83 4.3 MUlTIPeRIOD Ex AntE INfORMATION RATIO 94 100 4.4 eMPIRICAl eXAMPles PROBleMs 108 110 RefeReNCes Chapter 5 < Quantitative factors 5.1 VAlUe fACTORs 5.2 QUAlITY fACTORs 5.3 MOMeNTUM fACTORs APPeNDIX A5.1: APPeNDIX A5.2: NeT OPeRATING AsseTs (NOA) RefeReNCes eNDNOTes fACTOR DefINITION Chapter 6 < Valuation Techniques and Value Creation 6.1 VAlUATION fRAMewORk 111 111 125 135 145 148 150 153 155 156 C5580.indb 6 4/6/07 9:16:13 AM

Contents < vii 162 6.2 fRee CAsh flOw 6.3 MODelING The BUsINess eCONOMICs Of A fIRM 167 6.4 COsT Of CAPITAl 172 6.5 eXPlICIT PeRIOD, fADe PeRIOD, AND TeRMINAl VAlUe 6.6 AN eXAMPle: CheeseCAke fACTORY, INC. (CAke) 6.7 MUlTIPATh DIsCOUNTeD CAsh flOw ANAlYsIs 6.8 MUlTIPATh DCf ANAlYsIs (MDCf) 6.9 sUMMARY PROBleMs RefeReNCes eNDNOTes Chapter 7 < Multifactor Alpha Models 7.1 sINGle-PeRIOD COMPOsITe IC Of A MUlTIfACTOR MODel 7.2 OPTIMAl AlPhA MODel: AN ANAlYTICAl DeRIVATION 7.3 fACTOR CORRelATION Vs. IC CORRelATION 7.4 COMPOsITe AlPhA MODel wITh ORThOGONAlIzeD fACTORs 7.5 fAMA–MACBeTh ReGRessION AND OPTIMAl AlPhA MODel PROBleMs APPeNDIX A7.1: APPeNDIX A7.2: RefeReNCes INVeRse Of A PARTITIONeD MATRIX DeCOMPOsITION Of MUlTIVARIATe ReGRessION Part III Chapter 8 < Portfolio Turnover and Optimal Alpha Model 8.1 PAssIVe PORTfOlIO DRIfT 8.2 TURNOVeR Of fIXeD-weIGhT PORTfOlIOs 173 175 180 184 192 193 194 194 195 196 200 207 214 217 225 226 227 229 233 234 236 C5580.indb 7 4/6/07 9:16:13 AM

viii < Contents 8.3 TURNOVeR DUe TO fOReCAsT ChANGe 8.4 TURNOVeR Of COMPOsITe fOReCAsTs INfORMATION hORIzON AND lAGGeD 8.5 fOReCAsTs 8.6 OPTIMAl AlPhA MODel UNDeR TURNOVeR CONsTRAINTs 8.7 sMAll TRADes AND TURNOVeR PROBleMs APPeNDIX A8.1: ReDUCTION IN AlPhA eXPOsURe RefeReNCes eNDNOTes Chapter 9 < Advanced Alpha Modeling Techniques 9.1 The ReTURN-GeNeRATING eQUATION 9.2 CONTeXTUAl MODelING 9.3 MATheMATICAl ANAlYsIs Of CONTeXTUAl MODelING 9.4 eMPIRICAl eXAMINATION Of CONTeXTUAl APPROACh 9.5 PeRfORMANCe Of CONTeXTUAl MODels 9.6 seCTOR Vs. CONTeXTUAl MODelING 9.7 MODelING NONlINeAR effeCTs 9.8 sUMMARY PROBleMs APPeNDIX A9.1: MODel DIsTANCe TesT RefeReNCes Chapter 10 < factor Timing Models 241 247 252 257 267 274 276 278 279 281 282 283 287 290 300 303 306 313 313 314 315 317 318 10.1 CAleNDAR effeCT: BehAVIORAl ReAsONs 10.2 CAleNDAR effeCT: eMPIRICAl ResUlTs 323 10.3 seAsONAl effeCT Of eARNINGs ANNOUNCeMeNT 336 C5580.indb 8 4/6/07 9:16:14 AM

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