# investandmarket

INVESTORS AND MARKETS PRINCETONLECTURES INFINANCE Yacine Ait-Sahalia, Series Editor The Princeton Lectures in Finance, published by arrangement with the Bendheim Center for Finance of Princeton University, are based on annual lectures offered at Princeton University. Each year, the Bendheim Center invites a leading fi gure in the fi eld of fi nance to deliver a set of lectures on a topic of major signifi cance to researchers and professionals around the world. Stephen A. Ross, Neoclassical Finance William F. Sharpe, Investors and Markets: Portfolio Choices, Asset Prices, and Investment Advice INVESTORS AND MARKETS PORTFOLIO CHOICES, ASSET PRICES, AND INVESTMENT ADVICE William F. Sharpe This work is published by arrangement with the Bendheim Center for Finance of Princeton University princeton university press princeton and oxford Copyright ? 2007 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Third printing, and fi rst paperback printing, 2008 Paperback ISBN: 978-0-691-13850-3 The Library of Congress has cataloged the cloth edition of this book as follows Sharpe, William F. Investors and markets : portfolio choices, asset prices, and investment advice / William F. Sharpe. p.cm. Includes bibliographical references and index. ISBN-13: 978-0-691-12842-9 (hardcover : alk. paper) ISBN-10: 0-691-12842-1 (hardcover : alk. paper) 1. Portfolio management.2. Securities—Prices.3. Capital asset pricing model. 4. Investment analysis.5. Investments.I. Title. HG4529.5.S532007 332.6—dc222006015387 British Library Cataloging-in-Publication Data is available This book has been composed in Goudy and Swiss 911 Extra Compressed by Princeton Editorial Associates, Inc., Scottsdale, Arizona Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 3 5 7 9 10 8 6 4 CONTENTS PREFACEvii ONE Introduction1 TWO Equilibrium9 THREE Preferences35 FOUR Prices63 FIVE Positions111 SIX Predictions129 SEVEN Protection149 EIGHT Advice185 REFERENCES213 INDEX215 PREFACE T HIS BOOK IS based on the Princeton University Lectures in Finance that I gave in May 2004. The invitation to present these lectures pro- vided me a chance to address old issues in new ways and to bring to- gether a number of interrelated topics in fi nancial economics with an emphasis on individuals’ saving and investment decisions. I am grateful to Professor Yacine Ait-Sahalia of Princeton, the series editor, and to Peter Dougherty of Princeton University Press for inviting me to under- take this project and for giving me valuable advice throughout. This work follows a tradition with strong Princeton roots. In the fi rst (2001) Princeton Lectures in Finance, Stephen Ross masterfully addressed the central issues associated with asset pricing. That work is now available as the fi rst book in this series: Neoclassical Finance (Ross 2005). In 2001 Princeton University Press published the fi rst edition of John Cochrane’s marvelous book, Asset Pricing (Cochrane 2001), which is fast be- coming a standard text for its target audience—“economics and fi nance Ph.D. students, advanced MBA students, and professionals with similar background.” My goal is to continue down the path set by Ross and Cochrane, using a somewhat different approach and providing several extensions. However, this book differs substantially from the work of Ross and Cochrane in both approach and motivation. I am primarily concerned with helping individual investors make good saving and investment decisions—usually with the assis- tance of investment professionals such as fi nancial planners, mutual fund man- agers, advisory services, and personal asset managers. This requires more than just an understanding of the determinants of asset prices. But for many other applications in fi nance, it suffi ces to understand asset pricing. For example, a corporation desiring to maximize the value of its stock can, in principle, simply consider the pricing of the potential outcomes associated with its ac- tivities. A fi nancial engineer designing a fi nancial product may need only to determine a way to replicate the desired outcomes and compute the cost of doing so. Appropriately, Ross concentrated on the ability to price assets using only information about other assets’ prices in his fi rst chapter: “No Arbitrage: The Fundamental Theorem of Finance.” The title of Cochrane’s book indicates a similar focus, as does his statement in the preface that “we now go to asset prices directly. One can then fi nd optimal portfolios, but it is a side issue for the asset pricing question.” However, to determine the best investment portfolio for an individual, one needs more than asset prices. To use the standard economic jargon, individuals should maximize expected utility, not just portfolio value. To do so effi ciently requires an understanding of the ways in which asset prices refl ect investors’ diverse situations and views of the future. I thus deal here with both asset pric- ing and portfolio choice. And, as will be seen, I treat them more as one subject than as two. Over the past year and a half I have benefi ted greatly from comments and suggestions made by a number of friends and colleagues. Without implicating any of them in the fi nal results, I wish to thank Yacine Ait-Sahalia, Princeton University; Geert Bekaert, Columbia University; Phillip Dolan, Macquarie University; Peter Dougherty, Princeton University Press; Ed Fine, Financial Engines, Inc.; Steven Grenadier, Stanford University; Christopher Jones, Financial Engines, Inc.; Haim Levy, Hebrew University; Harry Markowitz, Harry Markowitz Associates; André Perold, Harvard University; Steven Ross, Massachusetts Institute of Technology; and Jason Scott, Jim Shearer, John Watson, and Robert Young, Financial Engines, Inc. Finally, I express my gratitude to my wife Kathy for her support and encour- agement. We are proof that a professional artist and a fi nancial economist can live happily and productively together. viiiPREFACE INVESTORS AND MARKETS ONE INTRODUCTION 1.1. The Subject of This Book T HIS IS A BOOK about the effects of investors interacting in capital mar- kets and the implications for those who advise individuals concerning savings and investment decisions. The subjects are often considered separately under titles such as portfolio choice and asset pricing. Portfolio choice refers to the ways in which investors do or should make de- cisions concerning savings and investments. Applications that are intended to describe what investors do are examples of positive economics. Far more common, however, are normative applications, designed to prescribe what investors should do. Asset pricing refers to the process by which the prices of fi nancial assets are determined and the resulting relationships between expected returns and the risks associated with those returns in capital markets. Asset pricing theories or models are examples of positive or descriptive economics, since they at- tempt to describe relationships in the real world. In this book we take the view that these subjects cannot be adequately understood in isolation, for they are inextricably intertwined. As will be shown, asset prices are deter- mined as part of the process through which investors make portfolio choices. Moreover, the appropriate portfolio choice for an individual depends crucially on available expected returns and risks associated with different investment strategies, and these depend on the manner in which asset prices are set. Our goal is to approach these issues more as one subject than as two. Accordingly, the book is intended for those who are interested in descriptions of the oppor- tunities available in capital markets, those who make savings and investment decisions for themselves, and those who provide such services or advice to others. Academic researchers will fi nd here a series of analyses of capital market con- ditions that go well beyond simple models that imply portfolio choices clearly inconsistent with observed behavior. A major focus throughout is on the effects on asset pricing when more realistic assumptions are made concerning investors’ situations and behavior. Investment advisors and investment managers will fi nd a set of possible frameworks for making logical decisions, whether or not they believe that as- set prices well refl ect future prospects. It is crucial that investment professionals differentiate between investing and betting. We show that a well thought out model of asset pricing is an essential ingredient for sound investment practice. Without one, it is impossible to even know the extent and nature of bets in- corporated in investment advice or management, let alone ensure that they are well founded. 1.2. Methods This book departs from much of the previous literature in the area in two im- portant ways. First, the underlying view of the uncertain future is not based on the mean/variance approach advocated for portfolio choice by Markowitz (1952) and used as the basis for the original Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965), Mossin (1966), and Treynor (1999). Instead, we base our analyses on a straightforward version of the state/preference approach to uncertainty developed by Arrow (1953) extending the work of Arrow (1951) and Debreu (1951). Second, we rely extensively on the use of a program that simulates the process by which equilibrium can be reached in a capital market and provides extensive analysis of the resulting relationships between asset prices and future prospects. 1.2.1. The State/Preference Approach We utilize a state/preference approach with a discrete-time, discrete-outcome setting. Simply put, uncertainty is captured by assigning probabilities to alter- native future scenarios or states of the world, each of which provides a different set of investment outcomes. This rules out explicit reliance on continuous- time formulations and continuous distributions (such as normal or log-normal), although one can use discrete approximations of such distributions. Discrete formulations make the mathematics much simpler. Many standard results in fi nancial economics can be obtained almost trivially in such a set- ting. At least as important, discrete formulations can make the underlying economics of a situation more obvious. At the end of the day, the goal of the (social) science of fi nancial economics is to describe the results obtained when individuals interact with one another. The goal of fi nancial economics as a prescriptive tool is to help individuals make better decisions. In each case, the better we understand the economics of an analysis, the better equipped we are to evaluate its usefulness. The term state/preference indicates both that discrete states and times are involved, and that individuals’ preferences for consump- tion play a key role. Also included are other aspects, such as securities repre- senting production outputs. 2CHAPTER 1 1.2.2. Simulation Simulation makes it possible to substitute computation for derivation. Instead of formulating complex algebraic models, then manipulating the resulting equations to obtain a closed-form solution equation, one can build a computer model of a marketplace populated by individuals, have them trade with one another until they do not wish to trade any more, then examine the charac- teristics of the resulting portfolios and asset prices. Simulations of this type have both advantages and disadvantages. They can be relatively easy to understand. They can also refl ect more complex situations than must often be assumed if algebraic models are to be used. On the other hand, the relationship between the inputs and the outputs may be diffi cult to fully comprehend. Worse yet, it is hard if not impossible to prove a relationship via simulation, although it is possible to disprove one. Consider, for example, an assertion that when people have preferences of type A and securities of type B are available, equilibrium asset prices have char- acteristics of type C; that is, A + B ? C. One can run a simulation with some people of type A and securities of type B and observe that the equilibrium asset prices are of type C. But this does not prove that such will always be the case. One can repeat the experiment with different people and securities, but always with people of type A and securities of type B. If in one or more cases the equilibrium is not of type C, the proposition (A + B ? C) is disproven. But even if every simulation conforms with the proposition, it is not proven. The best that can be said is that if many simulations give the same result, one’s confi dence in the truth of the proposition is increased. Simulation is thus at best a brute force way to derive propositions that may hold most or all of the time. But equilibrium simulation can be a powerful device. It can produce ex- amples of considerable complexity and help people think deeply about the determinants of asset prices and portfolio choice. It can also be a powerful ally in bringing asset pricing analysis to more people. 1.2.3. The APSIM Program The simulation program used for all the examples in this book is called APSIM, which stands for Asset Pricing and Portfolio Choice Simulator. It is available without charge at the author’s Web site: www.wsharpe.com, along with work- books for each of the cases covered. The program, associated workbooks, in- structions, and source code can all be downloaded. Although the author has made every attempt to create a fast and reliable simulation program, no war- ranty can be given that the program is without error. Although reading C++ programming code for a complex program is not rec- ommended for most readers, the APSIM source code does provide documen- tation for the results described here. In a simulation context, this can serve a INTRODUCTION3 function similar to that of formal proofs of results obtained with traditional algebraic models. 1.3. Pedagogy If you were to attend an MBA fi nance class at a modern university you would learn about subjects such as portfolio optimization, asset allocation analysis, the Capital Asset Pricing Model, risk-adjusted performance analysis, alpha and beta values, Sharpe Ratios, and index funds. All this material was built from Harry Markowitz’s view that an investor should focus on the expected return and risk of his or her overall portfolio and from the original Capital Asset Pricing Model that assumed that investors followed Markowitz’s ad- vice. Such mean/variance analysis provides the foundation for many of the quantitative methods used by those who manage investment portfolios or as- sist individuals with savings and investment decisions. If you were to attend a Ph.D. fi nance class at the same university you woul