MODERN PORTFOLIO

THEORY AND

NVESTMENT ANALYSIS

FOURTH EDITION

EDWIN J. ELTON MARTIN J. GRUBER

Leonard N. Stern School of Business New York University

JOHN WILEY & SONS, INC. New York • Chichester • Brisbane • Toronto • Singapore

Contents

Chapter 1 INTRODUCTION

Outline of the Book The Economic Theory of Choice: An Illustration Under Certainty Conclusion Multiple Assets and Risk Questions and Problems Bibliography

1 1

3 a a э

10

Part 1 PORTFOLIO ANALYSIS

Section 1 MEAN VARIANCE PORTFOLIO THEORY

Chapter 2 THE CHARACTERISTICS OF THE OPPORTUNITY SET UNDER RISK

Determining the Average Outcome A Measure of Dispersion Variance of Combinations of Assets Characteristics of Portfolios in General Conclusion Questions and Problems Bibliography

Chapter 3 DELINEATING EFFICIENT PORTFOLIOS

Combination of Two Risky Assets Revisited: Short Sales Not Allowed

11 13

15 16 18 20 24 32 34 ЗБ

38

38 IX

X CONTENTS

The Shape of the Portfolio Possibilities Curve 49 The Efficient Frontier with Riskiess Lending and Borrowing 57 Conclusion 61 Questions and Problems 61 Bibliography 62

Chapter 4 TECHNIQUES FOR CALCULATING THE EFFICIENT FRONTIER 65

Short Sales Allowed with Riskiess Lending and Borrowing 66 Short Sales Allowed: No Riskiess Lending and Borrowing 71 Riskiess Lending and Borrowing with Short Sales not Allowed 72 No Short Selling and No Riskiess Lending and Borrowing 72 The Incorporation of Additional Constraints 73 Conclusion 74 Appendix A An Alternative Definition of Short Sales 74 Appendix В Determining the Derivative 75 Appendix С Solving Systems of Simultaneous Equations 79 Appendix D A General Solution- 82 Appendix E Quadratic Programming and Kuhn-Tucker Conditions 88 Questions and Problems 90 Bibliography 91

Section 2 SIMPLIFYING THE PORTFOLIO SELECTION PROCESS 95

Chapter 5 THE CORRELATION STRUCTURE OF SECURITY RETURNS: THE SINGLE-INDEX MODEL 97

The Inputs to Portfolio Analysis 98 Single-Index Models: An Overview 99 Characteristics of the Single-Index Model 105 , Estimating Beta 107 The Market Model 123 Questions and Problems 123 Bibliography 125

CONTENTS XI

Chapter 6 THE CORRELATION STRUCTURE OF SECURITY RETURNS: MULTI-INDEX MODELS AND GROUPING TECHNIQUE

Multi-Index Models Average Correlation Models Mixed Models Fundamental Multi-Index Models* Conclusion Appendix A Procedure for Reducing Any Multi-Index Model to a Multi-Index Model with Orthogonal Indices Appendix В Mean Return, Variance, and Covariance of a Multi-Index Model Questions and Problems Bibliography

132 133 141 142 143 148

148 149 151 152

Chapter 7 SIMPLE TECHNIQUES FOR DETERMINING THE EFFICIENT FONTIER

The Single-Index Model The Constant Correlation Model Other Return Structures Conclusions Appendix A Single-Index Model—Short Sales Allowed Appendix В Constant Correlation Coefficient—Short Sales Allowed Appendix С Single-Index Model with Short Sales Not Allowed Appendix D Constant Correlation Coefficient—Short Sales Not Allowed Questions and Problems Bibliography

157 158 171 175 175 175 178 179 182 183 184

Section 3 SELECTING THE OPTIMUM PORTFOLIO 187

Chapter 8 UTILITY ANALYSIS

An Introduction to Preference Functions The Economic Properties of Utility Functions Empirical Evidence on the Suitability of Alternative Preference Functions Appendix A An Axiomatic Derivation of the Expected Utility Function Appendix В Absolute and Relative Risk Aversion

189 190 194 201 202 206

XII CONTENTS

Questions and Problems 209 Bibliography 210

Chapter 9 OTHER PORTFOLIO SELECTION MODELS 212

Maximizing the Geometric Mean Return 213 Safety First 21В Stochastic Dominance 222 Skewness and Portfolio Analysis 230 Conclusion 231 Appendix A Safety First with Riskless Lending and Borrowing 231 Appendix В Proof of the Sufficiency of the Stochastic Theorems 23B Questions and Problems 238 Bibliography 239

Section 4 WIDENING THE SELECTION UNIVERSE 245

Chapter 10 INTERNATIONAL DIVERSIFICATION* 247

The World Portfolio 247 Calculating the Return on Foreign Investments 249 The Risk of Foreign Securities 252 Returns from International Diversification 258 The Effect of Exchange Risk 261 Return Expectations and Portfolio Performance 262 Other Evidence on Internationally Diversified Portfolios 266 Models for Managing International Portfolios 270 Conclusion 274 Questions and Problems 274 Bibliography 276

Part 2 MODELS OF EQUILIBRIUM IN THE CAPITAL MARKETS

Chapter 11 THE STANDARD CAPITAL ASSET PRICING MODEL

The Assumptions Underlying the Standard Capital Asset Pricing Model CCAPM) The Capital Asset Pricing Model Prices and the CAPM Conclusion Questions and Problems Bibliography

281

283

284 285 295 296 299 300

CONTENTS xiii

Chapter 12 NONSTANDARD FORMS OF CAPITAL ASSET PRICING MODELS

Short Sales Disallowed Modifications of Riskless Lending and Borrowing Personal Taxes Nonmarketable Assets Heterogeneous Expectations Non-Price-Taking Behavior Multiperiod CAPM The Consumption-Oriented CAPM Inflation Risk and Equilibrium The Multi Beta CAPM Conclusion Appendix Derivation of the General Equilibrium with Taxes Questions and Problems Bibliography

302

303

303 315 317 319 320 321 322 323 324 325

325 328 329

Chapter 13 EMPIRICAL TESTS OF EQUILIBRIUM MODELS

The Models—Ex-Ante Expectations and Ex-Post Tests Empirical Tests of the CAPM Testing Some Alternative Forms of the CAPM Model Testing the Post-Tax Form of the CAPM Model Testing the Consumption Based CAPM CCCAPM) Some Reservations About Traditional Tests of General Equilibrium Relationships and Some New Research Conclusion Appendix Random Errors in Beta and Bias in the Parameters of the CAPM Questions and Problems Bibliography

337

337 339

352 353

354

357 359

360 362 362

Chapter 14 THE ARBITRAGE PRICING MODEL OF APT— A NEW APPROACH TO EXPLAINING ASSET PRICES

APT—What Is It? Estimating and Testing APT APT and CAPM Conclusions

368

369 375 386 387

XIV CONTENTS

Appendix Specification of the APT with an Unobserved Market Factor Questions and Problems Bibliography

388 389 390

Part 3 SECURITY ANALYSIS AND PORTFOLIO THEORY 3 9 7

Chapter 15 EFFICIENT MARKETS 399

Chapter 16

Chapter 17

Some Background Weak Form Tests Empirical Tests of Weak Form Efficiency Semi-Strong Form Tests Strong Form Tests Implications of Efficiency Market Anomalies Market Rationality Questions and Problems Bibliography

THE VALUATION PROCESS

Discounted Cash Flow Models Cross-sectional Regression Analysis An Ongoing System Conclusion Questions and Problems Bibliography

EARNINGS ESTIMATION

The Elusive Number Called Earnings The Importance of Earnings Characteristics of Earnings and Earnings Forecasts Conclusion Questions and Problems Bibliography

402 403 405 418 425 427 428 432 433 433

449

450 464 469 475 476 477

482

482 484

489 498 498 498

Chapter 18 INTEREST RATE THEORY AND THE PRICING OF BONDS 501

An Introduction to Debt Securities 502 The Many Definitions of Rates 504 Bond Prices and Spot Rates 510 Determining Spot Rates 511

CONTENTS XV

The Determinants of Bond Prices 514 Conclusion 533 Appendix A Special Considerations in Bond Pricing 533 Appendix В Estimating Spot Rates 534 Questions and Problems 536 Bibliography 537

Chapter 19 THE MANAGEMENT OF BOND PORTFOLIOS 542

Duration 542 Protecting Against Term Structure Shifts 549 Indexation 553 Actively Managed Bond Portfolios 553 Management Styles 561 Appendix A Duration Measures 562 Appendix В Exact Matching Programs 565 Appendix С Bond-Swapping Techniques 567 Appendix D Convexity 568 Questions and Problems 569 Bibliography 570

Chapter 20 OPTION PRICING THEORY 573

Types of Options 573 Some Basic Characteristics of Option Values 579 Valuation Models 585 Implicit Estimates of Stock's Own Variance from Option Formulas 596 Use of Options 599 Conclusion 603 Appendix A Derivation of the Binomial Formula 603 Appendix В Derivation of the Black—Scholes Formula 606 Questions and Problems 608 Bibliography 609

Chapter 21 THE VALUATION AND USES OF FINANCIAL FUTURES 617

Description of Financial Futures 618 Valuation of Financial Futures 622 The Uses of Financial Futures 629 Nonfinancial Futures and Commodity Funds 633 Questions and Problems 634 Bibliography 635

xvi CONTENTS

Part 4 EVALUATING THE INVESTMENT PROCESS 6 3 9

Chapter 22 EVALUATION OF PORTFOLIO PERFORMANCE 641

Evaluation Techniques 642 Decomposition of Overall Evaluation Б61 Problems in Portfolio Measurement 671 Mutual Fund Performance 675 Conclusion 680 Questions and Problems 681 Bibliography 682

Chapter 23 EVALUATION OF SECURITY ANALYSIS

Why the Emphasis on Earnings? The Evaluation of Earnings Forecasts Evaluating the Valuation Process Conclusion Questions and Problems Bibliography

Chapter 24 PORTFOLIO MANAGEMENT REVISITED

Managing Stock Portfolios Active Management Passive Versus Active International Diversification Bond Management Bond and Stock Investment with a Liability Stream Bibliography

686 687 688 697 700 701 702 703 704 708 709 710 710 714 720

Index 721