Handbook of the Equity Risk Premium

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Edited by Rajnish Mehra, this volume focuses on the equity risk premium puzzle, a term coined by Mehra and Prescott in 1985 which encompasses a number of empirical regularities in the prices of capital assets that are at odds with the predictions of standard economic theory.This handbook is indispensable for any serious assessment of the state of the art on the famous equity premium puzzle. I had already read most of its content in previous working papers available in the internet, but having the peer-reviewed version reunited in a unique volume ready for consultation at any time is an invaluable...

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HANDBOOK OF THE EQUITY RISK PREMIUM ebook3600.com
HANDBOOKS IN FINANCE Series Editor WILLIAM T. ZIEMBA Advisory Editors KENNETH J. ARROW GEORGE C. CONSTANTINIDES B. ESPEN ECKBO HARRY M. MARKOWITZ ROBERT C. MERTON STEWART C. MYERS PAUL A. SAMUELSON WILLIAM F. SHARPE amsterdam • boston • heidelberg • london new york • oxford • paris • san diego san francisco • singapore • sydney • tokyo
HANDBOOK OF THE EQUITY RISK PREMIUM By Rajnish Mehra amsterdam • boston • heidelberg • london new york • oxford • paris • san diego san francisco • singapore • sydney • tokyo
Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands Linacre House, Jordan Hill, Oxford OX2 8DP, UK First edition 2008 Copyright c 2008 Elsevier B.V. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: permissions@elsevier.com. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-444-50899-7 For information on all Elsevier publications visit our website at books.elsevier.com Printed and bound in the USA 08 09 10 11 10 9 8 7 6 5 4 3 2 1
Dedicated to my parents to Jyoti and Ravi to Neeru and to Chaitanya
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Contents List of Contributors xvii Preface xix Introduction to the Series xxiii 1 The Equity Premium: ABCs 1 Rajnish Mehra (UCSB) and Edward C. Prescott (Arizona State) 1. Introduction 2 1.1. An Important Preliminary Issue 2 1.2. Data Sources 3 1.3. Estimates of the Equity Premium 6 1.4. Variation in the Equity Premium Over Time 9 2. Is the Equity Premium Due to a Premium for Bearing Non-Diversiﬁable Risk? 11 2.1. Standard Preferences 14 References 25 Appendix A 29 Appendix B 29 Appendix C 35 Appendix D 35 2 Risk-Based Explanations of the Equity Premium 37 John B. Donaldson (Columbia) and Rajnish Mehra (UCSB) Introduction 39 1. Alternative Preference Structures 41 1.1. Preliminaries 41 1.2. Coincidence of Risk and Time Preferences in CRRA utility 44 1.3. Separating Risk and Time Preferences: Epstein–Zin and others 46 1.4. Variation in the CRRA and EIS 52 vii
viii Contents 1.5. Habit Formation 55 1.6. Behavioral Models 61 1.7. Beyond One Good and a Representative Agent 71 2. Production Economies 78 3. Disaster Events and Survivorship Bias 81 4. Market Incompleteness and Trading Frictions 86 4.1. Restricted Participation 86 5. Model Uncertainty 91 6. Concluding Comments 93 References 94 3 Non-Risk-based Explanations of the Equity Premium 101 Rajnish Mehra (UCSB) and Edward C. Prescott (Arizona State) Introduction 102 1. The Inappropriateness of Using T-Bills as a Proxy for the Intertemporal Marginal Rate of Substitution of Consumption 102 1.1. Liquidity 104 1.2. Transaction Balances 104 2. The Eﬀect of Government Regulations and Rules 106 3. Taxes 107 4. Borrowing Constraints 110 5. The Impact of Agent Heterogeneity and Intermediation Costs 113 6. Concluding Comments 114 References 114 4 Equity Premia with Benchmark Levels of Consumption: Closed-Form Results 117 Andrew B. Abel (Wharton) 1. Preferences 120 2. The Canonical Asset 126 2.1. The Price of the Canonical Asset 127 2.2. The Rate of Return on the Canonical Asset 129 3. Risk, Term, and Equity Premia 131 4. Log-Normality 134 5. Risk, Term, and Equity Premia Under Log-Normality with Consumption Externalities and Without Habit Formation 135 6. Linear Approximations to Risk, Term, and Equity Premia 137 7. Second Moments 138 7.1. Linear Approximations to Second Moments 140 8. Correlation of Dividend-Price Ratio and the Rate of Return on Stock 142 8.1. Correlation of Dividend-Price Ratio and the Excess Rate of Return on Stock 144
Contents ix 9. Special Cases 146 9.1. Rational Expectations 146 9.2. Distorted Beliefs 151 10. Accuracy of Approximations 153 11. Summary 156 References 156 Discussion: Francisco Gomes (LBS) 158 1. Introduction 158 2. Preferences with Benchmark Levels of Consumption 159 3. Changing the “Benchmark Level” of the Explanation 161 3.1. Aggregate Moments 161 3.2. Micro-Economic Implications 162 3.3. Micro-Economic Foundations and Aggregation 163 4. Leverage, Correlation between Dividends and Consumption, and distorted Beliefs 163 4.1. Levered Equity Claims and Correlation Between Dividends and Consumption 163 4.2. Non-Rational Expectations 164 5. Final Remarks 165 References 165 5 Long-Run Risks and Risk Compensation in Equity Markets 167 Ravi Bansal (Duke) 1. Introduction 168 2. Long-Run Risks Model 170 2.1. Preferences and the Environment 170 2.2. Long-Run Growth Rate Risks 171 2.3. Long-Run Growth and Uncertainty Risks 174 2.4. Data and Model Implications 176 3. Cross-Sectional Implications 185 3.1. Value, Momentum, Size, and the Cross-Sectional Puzzle 185 4. Conclusion 191 References 191 Discussion: John C. Heaton (Chicago) 194 1. Summary 194 2. A Low-Frequency Component in Consumption? 194 3. Preferences 195 4. Returns and Long-Run Cash Flows 197 5. Conclusion 198 References 198
x Contents 6 The Loss Aversion/Narrow Framing Approach to the Equity Premium Puzzle 199 Nicholas Barberis (Yale) and Ming Huang (Cornell) 1. Introduction 201 2. Loss Aversion and Narrow Framing 203 3. The Equity Premium 207 3.1. Modeling Loss Aversion and Narrow Framing 207 3.2. Quantitative Implications 212 3.3. Attitudes to Large Monetary Gambles 216 3.4. Attitudes to Small Monetary Gambles 218 3.5. The Importance of Narrow Framing 220 4. Other Applications 224 5. Further Extensions 225 5.1. Dynamic Aspects of Loss Aversion 225 5.2. Other Forms of Narrow Framing 226 6. Conclusion and Future Directions 227 References 228 Discussion: Xavier Gabaix (New York) 230 1. Work Out More Systematically the Preferences of PT vs. EU Investors—The “Equity Protection Puzzle” 230 2. Make Quantitative Predictions, Particularly About Equilibrium Market Phenomena, Rather than Just about Individual Trading Behavior 232 3. Do a Version of the Model in Continuous Time 233 References 234 Discussion: Ravi Jagannathan (Northwestern) 235 7 Financial Markets and the Real Economy 237 John H. Cochrane (Chicago) 1. Introduction 239 1.1. Risk Premia 239 1.2. Who Cares? 242 1.3. The Mimicking Portfolio Theorem and the Division of Labor 243 2. Facts: Time Variation and Business Cycle Correlation of Expected Returns 244 2.1. Variation over Time 244 2.2. Variation Across Assets 245 2.3. Return Forecasts—Variation over Time 246 2.4. The Cross Section of Returns—Variation Across Assets 251 3. Equity Premium 257 3.1. Mehra and Prescott and the Puzzle 261 3.2. The Future of the Equity Premium 266
Contents xi 4. Consumption Models 267 4.1. Hansen and Singleton; Power Utility 267 4.2. New Utility Functions 270 4.3. Empirics with New Utility Functions 273 4.4. Consumption and Factor Models 286 5. Production, Investment, and General Equilibrium 290 5.1. “Production-Based Asset Pricing” 290 5.2. General Equilibrium 294 6. Labor Income and Idiosyncratic Risk 302 6.1. Labor and Outside Income 302 6.2. Idiosyncratic Risk, Stockholding, and Micro Data 307 7. Challenges for the Future 314 References 314 Appendix 322 Discussion: Lars Peter Hansen (Chicago) 326 References 329 8 Understanding the Equity Risk Premium Puzzle 331 George M. Constantinides (Chicago) 1. Introduction 332 2. Habit Persistence 337 3. Limited Stock Market Participation and Per Capita Consumption 345 4. Incomplete Markets and Idiosyncratic Income Shocks 349 5. Concluding Remarks 355 References 356 Discussion: Hanno Lustig (UCLA) 360 1. Introduction 360 1.1. Environment 361 1.2. Preferences and Endowments 361 2. Complete Markets 362 2.1. Equilibrium 363 2.2. Equity Premium Puzzle 364 3. Missing Markets 364 3.1. Equilibrium 365 3.2. Mankiw’s Recipe for Generating Risk Premia 365 3.3. Constantinides and Duﬃe 366 3.4. Independence of Idiosyncratic Shocks from Aggregate Conditions 368 4. Missing Markets and State-Dependent Solvency Constraints 370 4.1. Incomplete Markets 370 4.2. Complete Markets 371
xii Contents 5. Conclusion 372 References 372 A. Second-Order Taylor Expansion 373 B. Constantinides and Duﬃe 374 9 Cash Flow Risk, Discounting Risk, and the Equity Premium Puzzle 377 Gurdip Bakshi (Maryland) and Zhiwu Chen (Yale) 1. Introduction 379 2. Economic Determinants of Equity Premium 381 2.1. Cash Flow Process 381 2.2. The Discounting Process 382 2.3. Dynamics of the Market Portfolio 383 2.4. Dynamics of the Equity Premium 385 3. Time-Series Data on S&P500 EPS, EPS Growth, and the Interest Rate 387 4. Implications of the Model for Equity Premium 389 4.1. How Large Is the Interest-Rate Risk Premium? 389 4.2. Maximum-Likelihood Estimation of the (Physical) Gt Process 391 4.3. Compensation for Cash Flow Risk and the Equity Premium 392 5. Concluding Remarks and Extensions 396 Appendix 398 References 400 Discussion: Vito D. Gala (LBS) 403 1. Discussion 403 1.1. Calibration and Estimation 404 1.2. Where Is the Equity Premium Puzzle? 405 References 407 Discussion: Lior Menzly (Proxima) 409 1. Introduction 410 2. The Model 410 2.1. Pricing Kernel 410 2.2. Cash Flow Process 411 2.3. The Model—Solutions 411 3. Calibration 412 3.1. Calibrating the Model 412 3.2. Estimation Results 412 4. Two-Stage Procedure—An Empirical Concern 412 5. Conclusion 414 References 414
Contents xiii 10 Distribution Risk and Equity Returns 415 Jean-Pierre Danthine (Lausanne), John B. Donaldson (Columbia), and Paolo Siconolﬁ (Columbia) 1. Introduction 417 2. The Business Cycle and the Labor Market 418 2.1. The Stylized Facts of the Business Cycle 418 2.2. The Labor Market 421 3. The Model Economy 423 3.1. Workers 423 3.2. Shareholders 424 3.3. The Firm 425 3.4. Equilibrium 427 3.5. Numerical Procedures and Calibration 429 4. An Economy with Distribution Risk Only 430 5. Adding Aggregate Uncertainty 432 6. Comparative Dynamics and Welfare Assessment 436 6.1. Changes in the Correlation of Productivity and Distribution Shocks 437 6.2. Changes in Risk Aversion and the Conditional Mean Distribution Shock 438 6.3. Other Comparative Dynamic Tests 440 6.4. Welfare Considerations 441 6.5. Explaining the Market Value to National Income Ratio 442 7. Technology-Driven Variations in Factor Shares 443 8. Robustness 446 9. An Alternative Interpretation of the Sharing Mechanism 448 10. Related Literature 452 11. Concluding Comments 459 References 460 Discussion: Urban J. Jermann (Wharton) 463 References 466 11 The Worldwide Equity Premium: A Smaller Puzzle 467 Elroy Dimson (LBS), Paul Marsh (LBS), and Mike Stauhton (LBS) 1. Introduction 469 2. Prior Estimates of the Equity Premium 471 2.1. Expert Opinion 472 3. Long-Run International Data 474 3.1. The DMS Global Database: Composition and Start Date 475 3.2. The DMS Global Database: General Methodology and Guiding Principles 477 4. Long-Run Historical Rates of Return 479 4.1. Extremes of History 480 4.2. The Long-Run Perspective 483
xiv Contents 5. New Global Evidence on the Equity Premium 486 5.1. The Equity Premium Around the World 487 5.2. A Smaller Risk Premium 489 5.3. Survivorship of Markets 490 5.4. Survivorship Bias Is Negligible 492 6. Decomposing the Historical Equity Premium 493 6.1. Unanticipated Success 493 6.2. Decomposition of the Equity Premium 495 6.3. From the Past to the Future 497 7. Conclusion 500 References 501 Appendix 1: Decomposition of the Equity Premium 505 Appendix 2: Data Sources for the DMS Database 507 12 History and the Equity Risk Premium 515 William N. Goetzmann (Yale) and Roger G. Ibbotson (Yale) 1. Introduction 516 2. Historical Conception and Measurement of the Equity Risk Premium 517 3. Stocks, Bonds, Bills, and Inﬂation 521 4. History as Written by the Winners? 523 5. The Equity Premium Over the Very Long Term 524 6. Conclusion 527 References 528 Discussion: Stephen F. LeRoy (UCSB) 530 References 534 13 Can Heterogeneity, Undiversiﬁed Risk, and Trading Frictions Solve the Equity Premium Puzzle 535 John C. Heaton (Chicago) and Deborah Lucas (Northwestern) 1. Introduction 537 2. Labor Income as Background Risk 539 2.1. Calibrating the Income Process 544 2.2. Adding Trading Frictions 547 3. Entrepreneurial Income as Background Risk 552 4. Limited Participation and Limited Diversiﬁcation 555 5. Conclusions 556 References 556 Discussion: Kjetil Storesletten (U Oslo) 558 1. Introduction 558 2. Labor Income Risk 559
Contents xv 3. Transaction Costs 560 4. Concentrating Aggregate Risk on Fewer Hands 560 4.1. Entrepreneurial Risk 560 4.2. Limited Participation 561 5. Conclusion 562 References 563 14 Asset Prices and Intergenerational Risk Sharing: The Role of Idiosyncratic Earnings Shocks 565 Kjetil Storesletten (U Oslo), Chris Telmer (CMU), and Amir Yaron (Wharton) 1. Introduction 567 2. An Analytical Example of the Constantinides–Duﬃe Model 569 2.1. Calibration of the Constantinides–Duﬃe Economy 570 2.2. Model Implications 571 3. Incorporating the Life Cycle 573 3.1. Calibration 576 4. Quantitative Results 577 4.1. Asset Pricing Implications 580 4.2. Sensitivity Analysis 581 5. Conclusions 581 References 584 A. Calibration Appendix 587 B. Asset Pricing 590 Discussion: Darrell Duﬃe (Stanford) 591 References 592 Index 593
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List of Contributors Andrew B. Abel, Department of Finance, 2315 Steinberg Hall-Dietrich Hall, The Wharton School, University of Pennsylvania, 3620 Locust Walk, Philadelphia, PA 19104-6367, USA Gurdip Bakshi, Department of Finance, Smith School of Business, University of Maryland, College Park, MD 20742, USA Ravi Bansal, Fuqua School of Business, Duke University, 1 Towerview Drive, Durham, NC 27708, USA Nicholas Barberis, Yale School of Management, 135 Prospect Street, New Haven CT 06511, USA Zhiwu Chen, Yale School of Management, 135 Prospect Street, New Haven, CT 06520, USA John H. Cochrane, Graduate School of Business, University of Chicago, 5807 S. Woodlawn, Chicago IL 60637, USA George M. Constantinides, Graduate School of Business, The University of Chicago, 5807 South Woodlawn Avenue, Chicago IL 60637, USA Jean-Pierre Danthine, University of Lausanne, Bldg Extranef, Dorigny, CH-1015 Lausanne, Switzerland Elroy Dimson, London Business School, Regents Park, London NW1 4SA, UK John B. Donaldson, Graduate School of Business, Columbia University, 3022 Broad- way, New York, NY 10027-6989, USA Darrell Duﬃe, Graduate School of Business, Stanford University, 518 Memorial Way, Stanford, CA 94305-5015, USA Xavier Gabaix, Department of Finance, Stern School of Business, New York Univer- sity, 44 West 4th Street, Suite 9-190, New York, NY 10012, USA Vito Gala, London Business School, Regent’s Park, London, NW1 4SA, UK xvii
xviii List of Contributors William N. Goetzmann, Yale School of Management, 135 Prospect Street, New Haven, CT 06511-3729, USA Francisco Gomes, Department of Finance, London Business School, Regent’s Park, London NW1 4SA, UK Lars Peter Hansen, Department of Economics, University of Chicago, 1126 East 59th St., Chicago, Illinois. 60637, USA John C. Heaton, The University of Chicago, Graduate School of Business, 5807 South Woodlawn Avenue, Chicago, IL 60637, USA Ming Huang, Johnson Graduate School of Management, Cornell University, 319 Sage Hall, Ithaca, NY 14853-6201, USA Roger G. Ibbotson, Yale School of Management, 135 Prospect Street, New Haven, CT 06511-3729, USA Ravi Jagannathan, Kellogg School of Management, Northwestern University, 2001 Sheridan Rd, Evanston, IL 60208, USA Urban J. Jermann, Department of Finance, The Wharton School of the University of Pennsylvania, 3620 Locust Walk, Philadelphia, PA 19104-6367, USA Stephen F. LeRoy, Department of Economics, University of California, Santa Barbara, CA 93106, USA Deborah Lucas, Kellogg School of Management, 2001 Sheridan Rd, Evanston, IL 60208, USA Hanno Lustig, Department of Economics, University of California at Los Angeles, Bunche Hall 8357, Box 951477, Los Angeles, CA 90095-1477, USA Paul Marsh, London Business School, Regents Park, London NW1 4SA, UK Rajnish Mehra, Department of Economics, 3014 North Hall, University of California, Santa Barbara, CA 93106-9210, USA Lior Menzly, Director of Quantitative Research and Risk Management, Proxima Alfa Investment (USA), 623 Fifth Ave, 14th Floor, New York, NY 10022, USA Edward C. Prescott, Department of Economics, W. P. Carey School of Business, Arizona State University, Tempe, AZ 85287-3806, USA Paolo Siconolﬁ, Columbia Business School, 3022 Broadway, Uris Hall 820, New York, NY 10027, USA Mike Staunton, London Business School, Regents Park, London NW1 4SA, UK Kjetil Storesletten, Department of Economics, University of Oslo, PO Box 1095 Blindern, N-0317 Oslo, Norway Chris Telmer, Tepper School of Business, Carnegie Mellon University, Posner Hall, Room 350, Tech and Frew Streets, Pittsburgh, PA 15213, USA Amir Yaron, The Wharton School, University of Pennsylvania, 2325 Steinberg Hall-Dietrich Hall, 3620 Locust Walk, Philadelphia, PA 19104-6367, USA
Preface Historical data provide a wealth of evidence documenting that for more than a century, U.S. stock returns have been considerably higher than the returns for Treasury bills. The average annual real return (that is, the inﬂation-adjusted return) on the U.S. stock market for the past 110 years has been about 7.9 percent. In the same period, the real return on a relatively riskless security was a paltry 1.0 percent. The diﬀerence between these two returns, 6.9 percentage points, is the equity premium. The generally accepted tenet of the neoclassical paradigm has been that the observed diﬀerences in the rates of return to ﬁnancial assets, in particular, the large diﬀerence between the average returns on corporate equity and T-bills, is a premium for bear- ing non-diversiﬁable aggregate risk. What came as a surprise to many economists and researchers in ﬁnance was the conclusion of a research paper that Edward Prescott and I wrote in 1979. We found that stocks and bonds pay oﬀ in approximately the same states of nature or economic scenarios and hence, they should command approximately the same rate of return. The historical U.S. equity premium was an order of magnitude greater than could be rationalized in the context of the standard neoclassical paradigm of ﬁnancial economics. In fact, using standard theory to estimate risk-adjusted returns, we found that stocks on average should command, at most, a 1 percent return premium over bills. Since, for as long as we had reliable data, (about a hundred years), the mean premium on stocks over bills was considerably and consistently higher, we realized that we had a puzzle on our hands. It took us six more years to convince a skeptical profession and for “The Equity Premium: A Puzzle” to be published. I want to emphasize that the equity premium puzzle is a quantitative puzzle; standard theory is consistent with our notion of risk that, on average, stocks should return more than bonds. The puzzle cannot be dismissed lightly because much of our economic intuition is based on the very class of models that fall short so dramatically when confronted with ﬁnancial data. It underscores the failure of paradigms central to ﬁnancial and economic modelling to capture the characteristic that appears to make stocks comparatively riskier. Hence, the viability of using this class of models for any quantitative assessment—for instance, to gauge the welfare implications of alternative stabilization policies—is thrown open to question. xix