Handbook of the Equity Risk Premium

Rajnish Mehra

• Publisher: Elsevier Science
• Year: 2011
• ISBN:
  9780080555850
• Topic: Business
• Subtopic: Corporate Finance
• Index: Business

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.

CHAPTER 1 The Equity Premium: ABCs

Rajnish Mehra

University of California, Santa Barbara, and NBER

Edward C. Prescott

Arizona State University and Federal Reserve Bank of Minneapolis

1. Introduction

1.1. An Important Preliminary Issue

1.2. Data Sources

1.3. Estimates of the Equity Premium

1.4. Variation in the Equity Premium over Time

2. Is the Equity Premium due to a Premium for Bearing Non-Diversifiable Risk?

2.1. Standard Preferences

References

Appendix A

Appendix B

Appendix C

Appendix D

JEL Classification: G10, G12, D9

Keywords: asset pricing, equity risk premium, CAPM, consumption CAPM, risk free rate puzzle

We thank George Constantinides, John Donaldson and Viral Shah for helpful comments and Francisco Azeredo for excellent research assistance.

1. INTRODUCTION

The year 1978 saw the publication of Robert Lucas’ seminal paper “Asset Prices in an Exchange Economy” in Econometrica. Its publication transformed asset pricing and substantially raised the level of discussion, providing a theoretical construct to study issues that could not be addressed within the dominant paradigm at the time, the Capital Asset Pricing Model.¹ A crucial input parameter for using the latter is the equity premium² (the return earned by a broad market index in excess of that earned by a relatively risk-free security). Lucas’ asset pricing model allowed one to pose questions about the magnitude of the equity premium.³ In our paper, “The Equity Premium: A Puzzle,”⁴ we decided to address this issue.

In this chapter we take a retrospective look at our original paper and show why we concluded that the equity premium is not a premium for bearing non-diversifiable risk.⁵ We critically evaluate the data sources used to document the puzzle and touch on other issues that may be of interest to the researcher who did not have a ringside seat 20 years ago. We stress that the perspective here captures the spirit of our original paper and not necessarily our current thinking on these issues.⁶

This and the subsequent two chapters are motivated by the intention to make this volume a self-contained reference for the beginning researcher in the field. The chapters that follow address the research efforts that have preoccupied the profession in an effort to explain the equity premium.

This chapter is organized into two parts. Part 1 documents the historical equity premium in the United States and in selected countries with significant capital markets (in terms of market value) and comments on data sources. Part 2 examines the question, “Is the equity premium a premium for bearing non-diversifiable risk?”

1.1. An Important Preliminary Issue

Any discussion of the equity premium raises the question of whether arithmetic or geometric returns should be used for summarizing historical return data. In Mehra and Prescott (1985), we used arithmetic averages. If returns are uncorrelated over time, the appropriate statistic is the arithmetic average because the expected future value of a $1 investment is obtained by compounding the mean returns. Thus, this is the appropriate statistic to report if one is interested in the mean terminal value of the investment.⁷

The arithmetic average return exceeds the geometric average return. If returns are log-normally distributed, the difference between the two is one-half the variance of the returns. Since the annual standard deviation of the equity returns is about 20 percent, there is a difference of about 2 percent between the two measures. Using geometric averages significantly underestimates the expected future value of an investment. In this chapter, as in our 1985 paper, we report arithmetic averages. In instances where we cite the results of research when arithmetic averages are not available, we clearly indicate this.⁸

1.2. Data Sources

A crucial consideration in a discussion of the historical equity premium has to do with the reliability of early data sources. The data we used in documenting the historical equity premium in the United States can be subdivided into three distinct subperiods, 1802–1871, 1871–1926, and 1926–present, with wide variation in the quality of the data over each subperiod. Data on stock prices for the 19th century is patchy, often necessarily introducing an element of arbitrariness to compensate for its incompleteness.

1.2.1. Subperiod 1802–1871

Equity Return Data

The equity return data prior to 1871 is not particularly reliable. To the best of our knowledge, the stock return data used by all researchers for the period 1802–1871 is due to Schwert (1990), who gives an excellent account of the construction and composition of early stock market indexes. Schwert...

Table of contents

• Cover image
• Title page
• Table of Contents
• HANDBOOKS IN FINANCE
• Copyright
• Dedication
• List of Contributors
• Preface
• Introduction to the Series
• Chapter 1: The Equity Premium: ABCs
• Chapter 2: Risk-Based Explanations of the Equity Premium
• Chapter 3: Non-Risk-based Explanations of the Equity Premium
• Chapter 4: Equity Premia with Benchmark Levels of Consumption: Closed-Form Results
• Discussion: Equity Premia with Benchmark Levels of Consumption: Closed-Form Results
• Chapter 5: Long-Run Risks and Risk Compensation in Equity Markets
• Discussion: Long-Run Risks and Risk Compensation in Equity Markets
• Chapter 6: The Loss Aversion/Narrow Framing Approach to the Equity Premium Puzzle
• Discussion: The Loss Aversion/Narrow Framing Approach to the Equity Premium Puzzle
• Discussion: The Loss Aversion/Narrow Framing Approach to the Equity Premium Puzzle
• Chapter 7: Financial Markets and the Real Economy
• Discussion: Financial Markets and the Real Economy
• Chapter 8: Understanding the Equity Risk Premium Puzzle
• Discussion: Understanding the Equity Risk Premium Puzzle
• Chapter 9: Cash Flow Risk, Discounting Risk, and the Equity Premium Puzzle
• Discussion: Cash Flow Risk, Discounting Risk, and the Equity Premium Puzzle
• Discussion: Cash Flow Risk, Discounting Risk, and the Equity Premium Puzzle
• Chapter 10: Distribution Risk and Equity Returns
• Discussion: Distribution Risk and Equity Returns
• Chapter 11: The Worldwide Equity Premium: A Smaller Puzzle
• Chapter 12: History and the Equity Risk Premium
• Discussion: “The Worldwide Equity Premium: A Smaller Puzzle” and “History and the Equity Risk Premium”
• Chapter 13: Can Heterogeneity, Undiversified Risk, and Trading Frictions Solve the Equity Premium Puzzle?
• Discussion: Can Heterogeneity, Undiversified Risk, and Trading Frictions Solve the Equity Premium Puzzle?
• Chapter 14: Asset Prices and Intergenerational Risk Sharing: The Role of Idiosyncratic Earnings Shocks
• Discussion: Asset Prices and Intergenerational Risk Sharing: The Role of Idiosyncratic Earnings Shocks
• Index