NBER WORKING PAPER SERIES THE EQUITY PREMIUM IN RETROSPECT Rajnish Mehra Edward C.Prescott Working Paper 9525 http://www.nber.org/papers/w9525 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge,MA 02138 February 2003 Forthcoming in the Handbook of the Economics of Finance,edited by G.M Contantinides,M.Harris and R. Stulz,North Holland,Amsterdam.We thank George Constantinides,John Donaldson,Ellen R.McGrattan and Mark Rubinstein for helpful discussions.Mehra acknowledges financial support from the Academic Senate of the University of California.Prescott acknowledges financial support from the National Science Foundation.The views expressed herein are those of the author and not necessarily those of the National Bureau of Economic Research. 2003 by Rajnish Mehra and Edward C.Prescott.All rights reserved.Short sections of text not to exceed two paragraphs,may be quoted without explicit permission provided that full credit including Onotice,is given to the source
NBER WORKING PAPER SERIES THE EQUITY PREMIUM IN RETROSPECT Rajnish Mehra Edward C. Prescott Working Paper 9525 http://www.nber.org/papers/w9525 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 February 2003 Forthcoming in the Handbook of the Economics of Finance, edited by G.M Contantinides, M. Harris and R. Stulz, North Holland, Amsterdam. We thank George Constantinides, John Donaldson, Ellen R. McGrattan and Mark Rubinstein for helpful discussions. Mehra acknowledges financial support from the Academic Senate of the University of California. Prescott acknowledges financial support from the National Science Foundation. The views expressed herein are those of the author and not necessarily those of the National Bureau of Economic Research. ©2003 by Rajnish Mehra and Edward C. Prescott. All rights reserved. Short sections of text not to exceed two paragraphs, may be quoted without explicit permission provided that full credit including ©notice, is given to the source
The Equity Premium in Retrospect Rajnish Mehra and Edward C.Prescott NBER Working Paper No.9525 February 2003 JEL No.D91,E2,E60,G0,G11,G12,G13,H2,H55 ABSTRACT This article takes a critical look at the literature on equity premium puzzle-the inability of standard intertemporal economic models to rationalize the statistics that have characterized U.S.financial markets over the past century.A summary of historical returns for the United States and other industrialized countries and an overview of the economic construct itselfare provided.The intuition behind the discrepancy between model prediction and empirical data is explained and the research efforts to enhance the model's ability to replicate the empirical data are summarized. Rajnish Mehra Edward C.Prescott Department of Economics Research Department University of California Federal Reserve Bank of Minneapolis Santa Barbara,CA 93106 90 Hennepin Avenue and NBER Minneapolis,MN 55480 mehra@econ.ucsb.edu and NBER prescott@econ.umn.edu
The Equity Premium in Retrospect Rajnish Mehra and Edward C. Prescott NBER Working Paper No. 9525 February 2003 JEL No. D91, E2, E60, G0, G11, G12, G13, H2, H55 ABSTRACT This article takes a critical look at the literature on equity premium puzzle - the inability of standard intertemporal economic models to rationalize the statistics that have characterized U.S. financial markets over the past century. A summary of historical returns for the United States and other industrialized countries and an overview of the economic construct itself are provided. The intuition behind the discrepancy between model prediction and empirical data is explained and the research efforts to enhance the model’s ability to replicate the empirical data are summarized. Rajnish Mehra Edward C. Prescott Department of Economics Research Department University of California Federal Reserve Bank of Minneapolis Santa Barbara, CA 93106 90 Hennepin Avenue and NBER Minneapolis, MN 55480 mehra@econ.ucsb.edu and NBER prescott@econ.umn.edu
2 More than two decades ago,we demonstrated that the equity premium(the return earned by a risky security in excess of that earned by a relatively risk-free T-bill),was an order of mag- nitude greater than could be rationalized in the context of the standard neoclassical paradigms of financial economics as a premium for bearing risk.We dubbed this historical regularity 'the eq- uity premium puzzle.'(Mehra and Prescott(1985)).Our challenge to the profession has spawned a plethora of research efforts to explain it away. In this paper,we take a retrospective look at the puzzle,critically examine the data sources used to document the puzzle,attempt to clearly explain it and evaluate the various at- tempts to solve it.The paper is organized into four 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 the data sources.Part 2 examines the question,'Is the equity premium due to a premium for bearing non-diversifiable risk?'Part 3 examines the related ques- tion,'Is the equity premium due to borrowing constraints,a liquidity premium or taxes?' Finally,part 4 examines the equity premium expected to prevail in the future. We conclude that research to date suggests that the answer to the first question is 'no', unless one is willing to accept that individuals are implausibly risk averse.In answer to the sec- ond question McGratten and Prescott(2001)found that,most likely,the high equity premium observed in the postwar period was indeed the result of a combination of the factors that included borrowing constraints and taxes. 1.1 Facts Any discussion of the equity premium over time confronts the question of which average returns are more useful in summarizing historical information:arithmetic or geometric?It is well
2 More than two decades ago, we demonstrated that the equity premium (the return earned by a risky security in excess of that earned by a relatively risk-free T-bill), was an order of magnitude greater than could be rationalized in the context of the standard neoclassical paradigms of financial economics as a premium for bearing risk. We dubbed this historical regularity ‘the equity premium puzzle.’(Mehra and Prescott(1985)). Our challenge to the profession has spawned a plethora of research efforts to explain it away. In this paper, we take a retrospective look at the puzzle, critically examine the data sources used to document the puzzle, attempt to clearly explain it and evaluate the various attempts to solve it. The paper is organized into four 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 the data sources. Part 2 examines the question, ‘Is the equity premium due to a premium for bearing non-diversifiable risk?’ Part 3 examines the related question, ‘Is the equity premium due to borrowing constraints, a liquidity premium or taxes?’ Finally, part 4 examines the equity premium expected to prevail in the future. We conclude that research to date suggests that the answer to the first question is ‘no’, unless one is willing to accept that individuals are implausibly risk averse. In answer to the second question McGratten and Prescott (2001) found that, most likely, the high equity premium observed in the postwar period was indeed the result of a combination of the factors that included borrowing constraints and taxes. 1.1 Facts Any discussion of the equity premium over time confronts the question of which average returns are more useful in summarizing historical information: arithmetic or geometric? It is well
3 known that the arithmetic average return exceeds the geometric average return and that if the re- turns 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 premium is about 20 percent,this can result in a difference of about 2 percent between the two measures,which is non-trivial since the phenomena under consideration has an arithmetic mean of between 2 and 8 percent.In Mehra and Prescott(1985),we reported arithmetic averages,since the best available evidence indicated that stock returns were uncorrelated over time.When this is the case,the expected future value of a S1 investment is obtained by compounding the arithmetic average of the sample return,which is the correct statistic to report if one is interested in the mean value of the investment.If,how- ever,the objective is to obtain the median future value of the investment,then the initial invest- ment should be compounded at the geometric sample average.When returns are serially corre- lated,then the arithmetic average2can lead to misleading estimates and thus the geometric aver- age may be the more appropriate statistic to use.In this paper,as in our 1985 paper,we report arithmetic averages.However,in instances where we cite the results of research when arithmetic averages are not available,we clearly indicate this.3 1.2 Data Sources A second crucial consideration in a discussion of the historical equity premium has to do with the reliability of early data sources.The data documenting the historical equity premium in the United States can be subdivided into three distinct sub-periods,1802-1871,1871-1926 and We present a simple proof in appendix A. 2The point is well illustrated by the textbook example where an initial investment of $100 is worth $200 after one year and $100 after two years.The arithmetic average return is 25%whereas the geometric average return is 0%.The latter coincides with the true return. 3In this case an approximate estimate of the arithmetic average return can be obtained by adding one-half the variance of the returns to the geometric average
3 known that the arithmetic average return exceeds the geometric average return and that if the 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 premium is about 20 percent, this can result in a difference of about 2 percent between the two measures, which is non - trivial since the phenomena under consideration has an arithmetic mean of between 2 and 8 percent. In Mehra and Prescott (1985), we reported arithmetic averages, since the best available evidence indicated that stock returns were uncorrelated over time. When this is the case, the expected future value of a $1 investment is obtained by compounding the arithmetic average of the sample return, which is the correct statistic to report if one is interested in the mean value of the investment.1 If, however, the objective is to obtain the median future value of the investment, then the initial investment should be compounded at the geometric sample average. When returns are serially correlated, then the arithmetic average2 can lead to misleading estimates and thus the geometric average may be the more appropriate statistic to use. In this paper, as in our 1985 paper, we report arithmetic averages. However, in instances where we cite the results of research when arithmetic averages are not available, we clearly indicate this.3 1.2 Data Sources A second crucial consideration in a discussion of the historical equity premium has to do with the reliability of early data sources. The data documenting the historical equity premium in the United States can be subdivided into three distinct sub-periods, 1802–1871, 1871–1926 and 1 We present a simple proof in appendix A. 2 The point is well illustrated by the textbook example where an initial investment of $100 is worth $200 after one year and $100 after two years. The arithmetic average return is 25% whereas the geometric average return is 0%. The latter coincides with the true return. 3 In this case an approximate estimate of the arithmetic average return can be obtained by adding one-half the variance of the returns to the geometric average
4 1926-present.The quality of the data is very different for each subperiod.Data on stock prices for the nineteenth century is patchy,often necessarily introducing an element of arbitrariness to compensate for its incompleteness. Subperiod 1802-1871 Equity Return Data We find that 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(1990)constructs a "spliced"index for the period 1802-1987;his index for the period 1802-1862 is based on the work of Smith and Cole(1935),who constructed a number of early stock indexes.For the period 1802-1820,their index was constructed from an equally weighted portfolio of seven bank stocks,while another index for 1815-1845 was com- posed of six bank stocks and one insurance stock.For the period 1834-1862 the index consisted of an equally weighted portfolio of(at most)27 railroad stocks.They used one price quote,per stock,per month,from local newspapers.The prices used were the average of the bid and ask prices,rather than transaction prices,and their computation of returns ignores dividends.For the period 1863-1871,Schwert uses data from Macaulay(1938),who constructed a value-weighted index using a portfolio of about 25 North-east and mid-Atlantic railroad stocks;this index also excludes dividends.Needless to say,it is difficult to assess how well this data proxies the 'mar- ket,'since undoubtedly there were other industry sectors that were not reflected in the index. 4They chose stocks in hindsight.the sample selection bias caused by including only stocks that survived and were actively quoted for the whole period is obvious."(Schwert(1990)) "It is unclear what sources Macaulay used to collect individual stock prices but he included all railroads with actively traded stocks.”Ibid
4 1926 – present. The quality of the data is very different for each subperiod. Data on stock prices for the nineteenth century is patchy, often necessarily introducing an element of arbitrariness to compensate for its incompleteness. Subperiod 1802-1871 Equity Return Data We find that 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 (1990) constructs a “spliced” index for the period 1802–1987; his index for the period 1802–1862 is based on the work of Smith and Cole (1935), who constructed a number of early stock indexes. For the period 1802–1820, their index was constructed from an equally weighted portfolio of seven bank stocks, while another index for 1815–1845 was composed of six bank stocks and one insurance stock. For the period 1834–1862 the index consisted of an equally weighted portfolio of (at most) 27 railroad stocks.4 They used one price quote, per stock, per month, from local newspapers. The prices used were the average of the bid and ask prices, rather than transaction prices, and their computation of returns ignores dividends. For the period 1863–1871, Schwert uses data from Macaulay (1938), who constructed a value-weighted index using a portfolio of about 25 North-east and mid-Atlantic railroad stocks;5 this index also excludes dividends. Needless to say, it is difficult to assess how well this data proxies the ‘market,’ since undoubtedly there were other industry sectors that were not reflected in the index. 4 “They chose stocks in hindsight … the sample selection bias caused by including only stocks that survived and were actively quoted for the whole period is obvious.” (Schwert (1990)) 5 “It is unclear what sources Macaulay used to collect individual stock prices but he included all railroads with actively traded stocks.” Ibid