《金融投资学》教学资源（英文文献）The Equity Premium in Retrospect

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 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

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 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 $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, 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 average2 can 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 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 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.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 ‘mar￾ket,’ 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

J Return on a Risk-free Security Since there were no Treasury bills at the time,researchers have used the data set con- structed by Siegel(1998)for this period,using highly rated securities with an adjustment for the default premium.It is interesting to observe,as mentioned earlier,that based on this data set the equity premium for the period 1802-1862 was zero.We conjecture that this may be due to the fact that since most financing in the first half of the nineteenth century was done through debt, the distinction between debt and equity securities was not very clear-cut. Sub-period 1871-1926 Equity Return Data Shiller(1989)is the definitive source for the equity return data for this period.His data is based on the work of Cowles(1939),which covers the period 1871-1938.Cowles used a value- weighted portfolio for his index,which consisted of 12 stocks'in 1871 and ended with 351 in 1938.He included all stocks listed on the New York Stock Exchange,whose prices were re- ported in the Commercial and Financial Chronicle.From 1918 onward he used the Standard and Poor's(S&P)industrial portfolios.Cowles reported dividends,so that,unlike the earlier indexes for the period 1802-1871,a total return calculation was possible. Return on a Risk Free Security There is no definitive source for the short-term risk-free rate in the period before 1920, when Treasury certificates were first issued.In our 1985 study,we used short-term commercial 6 The first actively traded stock was floated in the U.S in 1791 and by 1801 there were over 300 corporations,although less than 10 were actively traded.Siegel (1998)). It was only from Feb.16,1885,that Dow Jones began reporting an index,initially composed of 12 stocks.The S&P index dates back to 1928,though for the period 1928-1957 it consisted of 90 stocks.The S&P 500 debuted in March 1957

5 Return on a Risk-free Security Since there were no Treasury bills at the time, researchers have used the data set con￾structed by Siegel (1998) for this period, using highly rated securities with an adjustment for the default premium. It is interesting to observe, as mentioned earlier, that based on this data set the equity premium for the period 1802–1862 was zero. We conjecture that this may be due to the fact that since most financing in the first half of the nineteenth century was done through debt, the distinction between debt and equity securities was not very clear-cut.6 Sub-period 1871–1926 Equity Return Data Shiller (1989) is the definitive source for the equity return data for this period. His data is based on the work of Cowles (1939), which covers the period 1871–1938. Cowles used a value￾weighted portfolio for his index, which consisted of 12 stocks7 in 1871 and ended with 351 in 1938. He included all stocks listed on the New York Stock Exchange, whose prices were re￾ported in the Commercial and Financial Chronicle. From 1918 onward he used the Standard and Poor’s (S&P) industrial portfolios. Cowles reported dividends, so that, unlike the earlier indexes for the period 1802–1871, a total return calculation was possible. Return on a Risk Free Security There is no definitive source for the short-term risk-free rate in the period before 1920, when Treasury certificates were first issued. In our 1985 study, we used short-term commercial 6 The first actively traded stock was floated in the U.S in 1791 and by 1801 there were over 300 corporations, although less than 10 were actively traded. ( Siegel (1998)). 7 It was only from Feb. 16, 1885, that Dow Jones began reporting an index, initially composed of 12 stocks. The S&P index dates back to 1928, though for the period 1928–1957 it consisted of 90 stocks. The S&P 500 debuted in March 1957

6 paper as a proxy for a riskless short-term security prior to 1920 and Treasury certificates from 1920-1930.Our data prior to 1920,was taken from Homer(1963).Most researchers have either used our data set or Siegel's. Sub-period 1926-present Equity Return Data This period is the"Golden Age"in regards to accurate financial data.The NYSE data- base at the Center for Research in Security Prices(CRSP)was initiated in 1926 and provides re- searchers with high quality equity return data.The Ibbotson Associates Yearbooks are also a very useful compendium of post-1926 financial data. Return on a Risk-free Security Since the advent of Treasury bills in 1931,short maturity bills have been an excellent proxy for a"real"risk-free security since the innovation in inflation is orthogonal to the path of real GNP growth.Of course,with the advent of Treasury Inflation Protected Securities(TIPS) on January 29,1997,the return on these securities is the real risk-free rate. 1.3 Estimates of the Equity Premium Historical data provides us with a wealth of evidence documenting that for over a cen- tury,stock returns have been considerably higher than those for Treasury-bills.This is illustrated in Table 1,which reports the unconditional estimates for the US equity premium based on the 8 Ibbotson Associates."Stocks,Bonds,Bills and Inflation."2000 Yearbook.Chicago.Ibbotson Associates.2001. See Litterman(1980)who also found that that in post war data the innovation in inflation had a standard deviation of one half of nconditional estimates we use the cntire data set to fomm our estimate.The Mchra-Prescott data sct covers the ong est time period for which both consumption and stock return data is available.The former is necessary to test the implication of consumption based asset pricing models

6 paper as a proxy for a riskless short-term security prior to 1920 and Treasury certificates from 1920–1930. Our data prior to 1920, was taken from Homer (1963). Most researchers have either used our data set or Siegel’s. Sub-period 1926–present Equity Return Data This period is the “Golden Age” in regards to accurate financial data. The NYSE data￾base at the Center for Research in Security Prices (CRSP) was initiated in 1926 and provides re￾searchers with high quality equity return data. The Ibbotson Associates Yearbooks8 are also a very useful compendium of post–1926 financial data. Return on a Risk-free Security Since the advent of Treasury bills in 1931, short maturity bills have been an excellent proxy for a “real” risk-free security since the innovation in inflation is orthogonal to the path of real GNP growth.9 Of course, with the advent of Treasury Inflation Protected Securities (TIPS) on January 29, 1997, the return on these securities is the real risk-free rate. 1.3 Estimates of the Equity Premium Historical data provides us with a wealth of evidence documenting that for over a cen￾tury, stock returns have been considerably higher than those for Treasury-bills. This is illustrated in Table 1, which reports the unconditional estimates10 for the US equity premium based on the 8 Ibbotson Associates. “Stocks, Bonds, Bills and Inflation.” 2000 Yearbook. Chicago. Ibbotson Associates. 2001. 9 See Litterman (1980) who also found that that in post war data the innovation in inflation had a standard deviation of one half of one percent. 10 To obtain unconditional estimates we use the entire data set to form our estimate. The Mehra-Prescott data set covers the long￾est time period for which both consumption and stock return data is available. The former is necessary to test the implication of consumption based asset pricing models

various data sets used in the literature,going back to 1802.The average annual real return,(the inflation adjusted return)on the U.S.stock market over the last 110 years has been about 8.06 percent.Over the same period,the return on a relatively riskless security was a paltry 1.14 per- cent.The difference between these two returns,the"equity premium,"was 6.92 percent. Furthermore,this pattern of excess returns to equity holdings is not unique to the U.S.but is observed in every country with a significant capital market.The U.S.together with the U.K., Japan,Germany and France accounts for more than 85 percent of the capitalized global equity value. The annual return on the British stock market was 5.7 percent over the post war period, an impressive 4.6 percent premium over the average bond return of 1.1 percent.Similar statisti- cal differentials are documented for France,Germany and Japan.Table 2 illustrates the equity premium in the post war period for these countries. Table 1 U.S.Equity Premium Using Different Data Sets Data Set real return on a real return on a relatively equity pre- market index riskless security mium Mean Mean Mean 1802-1998 7.0 2.9 4.1 (Siegel) 1871-199 6.99 1.74 5.75 (Shiller) 1889-2000 8.06 1.14 6.92 (Mehra-Prescott) 1926-2000 8.8 0.4 8.4 (Ibbotson)

7 various data sets used in the literature, going back to 1802. The average annual real return, (the inflation adjusted return) on the U.S. stock market over the last 110 years has been about 8.06 percent. Over the same period, the return on a relatively riskless security was a paltry 1.14 per￾cent. The difference between these two returns, the “equity premium,” was 6.92 percent. Furthermore, this pattern of excess returns to equity holdings is not unique to the U.S. but is observed in every country with a significant capital market. The U.S. together with the U.K., Japan, Germany and France accounts for more than 85 percent of the capitalized global equity value. The annual return on the British stock market was 5.7 percent over the post war period, an impressive 4.6 percent premium over the average bond return of 1.1 percent. Similar statisti￾cal differentials are documented for France, Germany and Japan. Table 2 illustrates the equity premium in the post war period for these countries. Table 1 U.S. Equity Premium Using Different Data Sets Data Set % real return on a market index % real return on a relatively riskless security % equity pre￾mium Mean Mean Mean 1802-1998 (Siegel) 7.0 2.9 4.1 1871-199 (Shiller) 6.99 1.74 5.75 1889-2000 (Mehra-Prescott) 8.06 1.14 6.92 1926-2000 (Ibbotson) 8.8 0.4 8.4

P Table 2 Equity Premium in Different Countries Country real return real return on a relatively %equity pre- on a market riskless security mium index Mean Mean Mean UK 5.7 1.1 4.6 (1947-1999) Japan 4.7 1.4 3.3 (1970-1999) Germany 9.8 3.2 6.6 (1978-1997 France 9.0 2.7 6.3 (1973-1998) Source:U.K from Siegel (1998),the rest are from Campbell (2001) The dramatic investment implications of this differential rate of return can be seen in Table 3,which maps the capital appreciation of $1 invested in different assets from 1802 to 1997 and from 1926 to 2000. Table3 Terminal value of $1 invested in Stocks and Bonds Investment Period Stocks T-bills Real Nominal Real Nominal 1802-1997 $558,945 $7.470,000 $276 $3,679 1926-2000 $266.47 $2,586.52 $1.71 $16.56 Source:Ibbotson(2001)and Siegel(1998) As Table 3 illustrates,$1 invested in a diversified stock index yields an ending wealth of $558,945 versus a value of $276,in real terms,for $1 invested in a portfolio of T-bills for the period 1802-1997.The corresponding values for the 75-year period,1926-2000,are $266.47 and $1.71.We assume that all payments to the underlying asset,such as dividend payments to

8 Table 2 Equity Premium in Different Countries Country % real return on a market index % real return on a relatively riskless security % equity pre￾mium Mean Mean Mean UK (1947-1999) 5.7 1.1 4.6 Japan (1970-1999) 4.7 1.4 3.3 Germany (1978-1997) 9.8 3.2 6.6 France (1973-1998) 9.0 2.7 6.3 Source: U.K from Siegel (1998), the rest are from Campbell (2001) The dramatic investment implications of this differential rate of return can be seen in Table 3, which maps the capital appreciation of $1 invested in different assets from 1802 to 1997 and from 1926 to 2000. Table 3 Terminal value of $1 invested in Stocks and Bonds Investment Period Stocks T-bills Real Nominal Real Nominal 1802-1997 $558,945 $7,470,000 $276 $3,679 1926-2000 $266.47 $2,586.52 $1.71 $16.56 Source: Ibbotson (2001) and Siegel (1998) As Table 3 illustrates, $1 invested in a diversified stock index yields an ending wealth of $558,945 versus a value of $276, in real terms, for $1 invested in a portfolio of T-bills for the period 1802–1997. The corresponding values for the 75-year period, 1926–2000, are $266.47 and $1.71. We assume that all payments to the underlying asset, such as dividend payments to

9 stock and interest payments to bonds are reinvested and that there are no taxes paid. This long-term perspective underscores the remarkable wealth building potential of the equity premium.It should come as no surprise therefore,that the equity premium is of central importance in portfolio allocation decisions,estimates of the cost of capital and is front and cen- ter in the current debate about the advantages of investing Social Security funds in the stock market. In Table 4 we report the premium for some interesting sub-periods:1889-1933,when the United States was on a gold standard;1933-2000,when it was off the gold standard;and 1946-2000,the postwar period.Table 5 presents 30 year moving averages,similar to those re- ported by the US meteorological service to document'normal'temperature. Table4 Equity Premium in Different Sub-Periods Time Period real return real return on a relatively %equity pre- on a market riskless security mium index Mean Mean Mean 1889-1933 7.01 3.09 3.92 19342000 8.76 -0.17 8.93 1946-2000 9.03 0.68 8.36 Source:Mehra and Prescott(1985).Updated by the authors

9 stock and interest payments to bonds are reinvested and that there are no taxes paid. This long-term perspective underscores the remarkable wealth building potential of the equity premium. It should come as no surprise therefore, that the equity premium is of central importance in portfolio allocation decisions, estimates of the cost of capital and is front and cen￾ter in the current debate about the advantages of investing Social Security funds in the stock market. In Table 4 we report the premium for some interesting sub-periods: 1889–1933, when the United States was on a gold standard; 1933–2000, when it was off the gold standard; and 1946–2000, the postwar period. Table 5 presents 30 year moving averages, similar to those re￾ported by the US meteorological service to document ‘normal’ temperature. Table 4 Equity Premium in Different Sub-Periods Time Period % real return on a market index % real return on a relatively riskless security % equity pre￾mium Mean Mean Mean 1889–1933 7.01 3.09 3.92 1934–2000 8.76 -0.17 8.93 1946–2000 9.03 0.68 8.36 Source: Mehra and Prescott (1985). Updated by the authors