World Scientific - Nobel Laureate Series: Vol 1 HARRY MARKOWITZ. Selected Works

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2 World Scientific - Nobel Laureate Series: Vol 1 HARRY MARKOWITZ Selected Works

3 World Scientific - Nobel Laureate Series Vol. 1 Harry Markowitz: Selected Works edited by Harry M Markowitz

4 World Scientific - Nobel Laureate Series: Vol 1 HARRY MARKOWITZ Selected Works edited by HARRY M MARKOWITZ University of California, San Diego, USA,Ii» World Scientific NEW JERSEY. LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI

5 Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore USA office: 27 Warren Street, Suite , Hackensack, NJ UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. World Scientific - Nobel Laureate Series: Vol. 1 HARRY MARKOWITZ Selected Works Copyright 2008 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN ISBN-I ISBN (Pbk) ISBN-IO (pbk) Printed in Singapore by World Scientific Printers

6 In Memory of Alan S Manne Alan Manne was about my age and played polo. He did not die in a polo accident but blacked out while on his horse. He woke up briefly and was told that he would not be able to use his arms or legs. He said he would rather go. He asked his family whether his horse had stepped on him. He was assured that his horse had been a lady and just stood there. He asked his children to take care of their mother. He said that he had been working on a joint paper, told in which drawer the latest draft was located, and asked one of his children to give it to his coauthor. This book is also dedicated to George B. Dantzig who was Alan and my mentor, and to all our spouses who waited patiently while we played our favourite competitive game: research. v

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8 Foreword I remember very clearly the day I met Harry. I walked into his office where he sat writing a response to a letter that arrived on his desk. I knew nothing about financial economics. He was generous with his time. After a brief conversation we headed to dinner to meet his wife, Barbara. That dinner lasted for many hours as he patiently explained the finer details and mathematics of diversification, utility functions, optimization algorithms, and of course, portfolio selection. As we finished dinner, he listed a few articles he thought would help improve my understanding. I read all those references soon after that dinner and many times in the years since. New students to the field of financial economics will find the foundation of our discipline in these works. Portfolio Section in Chapter 2 explains "risk", "diversification", and "portfolio selection". The companion article, The Utility of Wealth, speaks to the idea of measuring wealth. More advanced readers will find support for efficient market theory and behavioral finance in these classic articles. Students and practitioners in the field of Operations Research will find the "Markowitz Rule" which today often aids the speed of determination of large matrix inversion problems in Chapter 3. Practitioners will find not only supporting logic for the pursuit of diversification in their client's portfolios through optimizations in this chapter but a detailed discussion of a solution algorithm. Chapter 4 again reaches into the field of Operations Research with its articles about the SIMSCRIPT language one of several computer languages that traces its origin to Harry. Readers will also find lessons on research methodology in these articles. The first works in Chapter 5 speak to ideas either directly mentioned in or alluded to in Harry's first book. Several of these ideas remain a source of contention. Economic theorists still argue that all forms of utility functions hold value for empirical uses and practitioners spend countless hours trying to select a representative utility function in their portfolio construction problems. Approximating Expected Utility by a Function of Mean and Variance serves as the touch point for this argument while Mean-Variance Versus Direct Utility Maximization provides good empirical evidence to reject many utility maximization exercises as unnecessary. Later articles in this chapter return to the topic of computer programming languages with application to portfolio problems. This chapter concludes with entries about the topic of long run investment. Chapters 6 and 7 are a collection of papers that comfortably are at rest in the world of theoretical financial economics or the world of the practitioner. vii

9 viii Foreword Several of articles in these chapters offer good guidance to practitioners as well as sound theoretical arguments. A few weeks ago Harry, Barbara and I again sat at dinner discussing this volume. Once again he was patient and generous with his time. As he explained which articles he included in the different chapters, I found myself thinking about the concepts contained in many of these classic pieces - about how freely the ideas in these papers move between theory and practice. And just what these ideas mean to so many people in the operations research field, simulation teams, the financial services industry as well as different academy departments. The ideas in these pages have spawned industries, helped companies and governments address complex problems, and launched the careers of many professionals. What more can be said, enjoy! Bernard V. Tew October 2007

10 Contents Foreword Acknowledgements vii ix Chapter 1 Overview 1 Trains of Thought 3 Chapter Portfolio Selection 15 The Early History of Portfolio Theory The Utility of Wealth 43 Chapter 3 Rand [I] and The Cowles Foundation 51 Industry-wide, Multi-industry and Economy-wide 53 Process Analysis Alternate Methods of Analysis 85 The Elimination Form of the Inverse and its Application 99 to Linear Programming The Optimization of a Quadratic Function Subject to 115 Linear Constraints The General Mean-variance Portfolio Selection Problem 139 Chapter 4 Rand [II] and CACI 147 Simulating with SIMSCRIPT 155 Programming by Questionnaire 165 SIMSCRIPT 211 Barriers to the Practical Use of Simulation Analysis 271 Chapter 5 IBM's T. J. Watson Research Center 279 Approximating Expected Utility by a Function of 281 Mean and Variance Mean-variance Versus Direct Utility Maximization The Value of a Blank Check The "Two beta" Trap Portfolio Analysis with Factors and Scenarios Sparsity and Piecewise Linearity in Large Portfolio Optimization Problems ix

11 x Contents The ER and EAS Formalisms for System Modeling and 357 the EAS-E Language EAS-E: An Integrated Approach to Application 377 Development The System Architecture of EAS-E: An Integrated 405 Programming and Database Language Samuelson and Investment for the Long Run 417 Investment for the Long Run: New Evidence for an 429 Old Rule Chapter 6 Baruch College (CUNY) and Daiwa Securities 443 Investment Rules, Margin and Market Volatility 445 Risk Adjustment 453 Normative Portfolio Analysis: Past, Present and Future 467 Individual versus Institutional Investing 473 Foundations of Portfolio Theory 481 Fast Computation of Mean-variance Efficient Sets Using 491 Historical Covariances Computation of Mean-semivariance Efficient Sets by 507 the Critical Line Algorithm Data Mining Corrections 519 Chapter 7 Harry Markowitz Company 529 The Likelihood of Various Stock Market Return 531 Distributions: Part 1: Principles of Inference The Likelihood of Various Stock Market Return 545 Distributions: Part 2: Empirical Results Resampled Frontiers Versus Diffuse Bayes: 573 An Experiment On Socks Ties and Extended Outcomes 591 Single-Period Mean-variance Analysis in a Changing 601 World Financial Market Simulation 615 Portfolio Optimization with Factors, Scenarios and 627 Realistic Short Positions Market Efficiency: A Theoretical Distinction and So What? 641 Efficient Portfolios, Sparse Matrices, and Entities: 661 A Retrospective DeFinetti Scoops Markowitz 669 CAPM Investors Do Not Get Paid for Bearing Risks: 697 A Linear Relation Does not Imply Payment for Risk

12 Acknowledgements I would like to thank the publishers of the various articles that are reproduced herein for permission to do so. I would also like to express my gratitude to my many coauthors for the fun and interesting times we have had collaborating on these works. Further, I would like to express special thanks to Sandhya of World Scientific Publishing for guidance and encouragement in preparing the enclosed collection and my introductory comments on them. Almost last but definitely not least, I wish to acknowledge the tireless and good-spirited labors of my secretary Mary Schultz a.k.a. Midge. Finally I want to warmly acknowledge the role of Bernie Tew who was personally authorized by my wife, Barbara Markowitz, to bug me until I finished my part of all this. Chapter 1 Trains of Thought Reprinted with permission from Markowitz, H. M. (1993). Trains of Thought. The American Economist, 37(1), 3-9. Chapter 2 Portfolio Selection Reprinted with permission from Markowitz, H. M. (1952). Portfolio Selection. The Journal of Finance, 7(1), The Early History of Portfolio Theory: Reproduced and republished from Markowitz, H. M. (1999). The Early History of Portfolio Theory: Financial Analysts Journal, with permission from CFA Institute. All rights reserved. The Utility of Wealth Reprinted with permission from Markowitz, H. M. (1952). The Utility of Wealth. The Journal of Political Economy, 60, Chapter 3 Industry-wide, Multi-industry and Economy-wide Process Analysis The publisher has attempted to identify the rightful owner of this paper. Anyone else who claims rights is requested to contact World Scientific Publishing Co. at editor@wspc.com.sg. xi

13 xii Acknowledgements The Elimination Form of the Inverse and its Application to Linear Programming Reprinted with permission, Markowitz, H. M. (1957). The Elimination Form of the Inverse and its Application to Linear Programming. Management Science, 3, 1957, Copyright 2008, the Institute for Operations Research and the Management Sciences, 7240 Parkway Drive, Suite 310, Hanover, MD USA. Alternate Methods of Analysis Reprinted with permission from Manne, A., Markowitz, H. M., (1963). Alternate Methods of Analysis in Studies in Process Analysis: Economy-Wide Production Capabilities, pp Reprinted with permission of the Cowles Foundation, which retains all rights under the original copyright. The Optimization of a Quadratic Function Subject to Linear Constraints Reprinted with permission from Markowitz, H. M. (1956). Naval Research Logistics Quarterly, Vol. 3, pp The General Mean-Variance Portfolio Selection Problem Reprinted with permission, Philosophical Transactions of the Royal Society A, Markowitz, H. M. (1994). The General Mean-Variance Portfolio Selection Problem, 347A, 1994, Chapter 4 Barriers to the Practical use of Simulation Analysis 1981 IEEE. Reprinted, with permission, from Markowitz, H. M. Barriers to the Practical use of Simulation Analysis Winter Simulation Conference Proceedings, 1, 3-9. Simulating with Simscript Reprinted with permission, Markowitz, H. M. (1966). Simulating with Simscript. Management Science, 12(10), 1966, B396-B405. Copyright 2008, the Institute for Operations Research and the Management Sciences, 7240 Parkway Drive, Suite 310, Hanover, MD USA. Simscript Reprinted with permission from Markowitz, H. M. (1979). Simscript. Encyclopedia of Computer Science and Technology, 13, Programming by Questionnaire Reprinted with permission of the RAND Corporation, Ginsberg, A. S., Markowitz, H. M. and Oldfather, P. M. (1965). Programming by Questionnaire. Memo RM PR, 1-42.

14 Acknowledgements xiii Chapter 5 Approximating Expected Utility by a Function of Mean and Variance Reprinted with permission from Markowitz, H. M. (1979). Approximating Expected Utility by a Funcion of Mean and Variance. The American Economic Review, 69(3), Investment for the Long Run: New Evidence for an Old Rule Reprinted with permission from Levy, H. and Markowitz, H. M. (1976). Investment for the Long Run: New Evidence for an Old Rule. The Journal of Finance, 31(5), Portfolio Analysis with Factors and Scenarios Reprinted with permission from Markowitz, H. M. and Perold, A. F. (1981). Portfolio Analysis with Factors and Scenarios. The Journal of Finance, 36(14), Mean-Variance Versus Direct Utility Maximization Reprinted with permission from Kroll, Y., Levy, H. and Markowitz, H. M. (1984). Mean-Variance Versus Direct Utility Maximization. The Journal of Finance, 39(1), EAS-E: An Integrated Approach to Application Development Reprinted with permission from Malhotra, A., Markowitz, H. M. and Pazel, D. P. (1983). EAS-E: An Integrated Approach to Application Development. ACM Transactions and Database Systems, 8(4), The ER and EAS Formalisms for System Modeling, and the EAS-E Language This article was published in Proceedings of the 2 nd International Conference on Entity-Relationship Approach to Modeling and Analysis, Markowitz, H. M., Malhotra, A. and Pazel, D. P., The ER and EAS Formalisms for System Modeling, and the EAS-E Language, 29-47, Copyright Elsevier (1983). Sparsity and Piecewise Linearity in Large Portfolio Optimization Problem This article was published in Sparse Matrices and Their Uses, Markowitz, H. M. and Perold, A. F., Sparsity and Piecewise Linearity in Large Portfolio Optimization Problems, , Copyright Elsevier (1981).

15 xiv Acknowledgements The System Architecture of EAS-E: An Integrated Programming and Data Base Language Reprinted with permission from Markowitz, H. M. (1983). The System Architecture of EAS-E: An Integrated Programming and Data Base Language. IBM Systems Journal, 22(3), The Two Beta Trap Reprinted with permission from Markowitz, H. M. (1984). The Two Beta Trap. The Journal of Portfolio Management, 11(1), The Value of a Blank Check Reprinted with permission from Markowitz, H. M., Reid, D. W. and Tew, B. V. (1994). The Value of a Blank Check. The Journal of Portfolio Management, 21, Samuelson and Investment for the Long Run By permission of Oxford University Press. Chp. "Samuelson and Investment for the Long Run" by Harry Markowitz from "Samuelsonian Economics and the Twenty-First Century" edited by Szenberg, Ramrattan, & Gottesman (2006). Chapter 6 Individual versus Institutional Investing Reproduced with the permission of the Academy of Financial Services and Financial Services Review. Reprinted with permission from Markowitz, H. M. (1991). Individual versus Institutional Investing. Financial Service Review, 1(1), 1-9. Foundations of Portfolio Theory Reprinted with permission from Markowitz, H. M. (1991). Foundations of Portfolio Theory. The Journal of Finance, 46(2), Normative Portfolio Analysis: Past, Present, and Future This article was published in Journal of Economics and Business, Markowitz, H. M., Normative Portfolio Analysis: Past, Present, and Future, 99-lO3, Copyright Elsevier (1990). Risk Adjustment RiskAdjustment, Harry Markowitz. Copyright (1990) by Journal of Accounting, Auditing and Finance. Reproduced with permission of Greenwood Publishing Group, Inc., Westport, CT.

Mathematical Modeling and Methods of Option Pricing

Mathematical Modeling and Methods of Option Pricing This page is intentionally left blank Mathematical Modeling and Methods of Option Pricing Lishang Jiang Tongji University, China Translated by Canguo