10 Table 5 Equity Premium:30 Year Moving Averages Time Period real return real return on a relatively %equity pre- on a market riskless security mium index Mean Mean Mean 1900-1950 6.51 2.01 4.50 1951-2000 8.98 1.41 7.58 Source:Mehra and Prescott (1985).Updated by the authors Although the premium has been increasing over time,this is largely due to the diminish- ing return on the riskless asset,rather than a dramatic increase in the return on equity,which has been relatively constant.The low premium in the nineteenth centaury is largely due to the fact that the equity premium for the period 1802-1861 was zero.If we exclude this period,we find that difference in the premium in the second half of the nineteenth century relative to average values in the twentieth century is less striking. We find a dramatic change in the equity premium in the post 1933 period-the premium rose from 3.92 percent to 8.93 percent,an increase of more than 125 percent.Since 1933 marked the end of the period when the US was on the gold standard,this break can be seen as the change in the equity premium after the implementation of the new policy. 1.4 Variation in the Equity Premium over Time The equity premium has varied considerably over time,as illustrated in Figures 1 and 2, below.Furthermore,the variation depends on the time horizon over which it is measured.There See the earlier discussion on data
10 Table 5 Equity Premium: 30 Year Moving Averages Time Period % real return on a market index % real return on a relatively riskless security % equity premium Mean Mean Mean 1900–1950 6.51 2.01 4.50 1951–2000 8.98 1.41 7.58 Source: Mehra and Prescott (1985). Updated by the authors Although the premium has been increasing over time, this is largely due to the diminishing return on the riskless asset, rather than a dramatic increase in the return on equity, which has been relatively constant. The low premium in the nineteenth centaury is largely due to the fact that the equity premium for the period 1802–1861 was zero.11 If we exclude this period, we find that difference in the premium in the second half of the nineteenth century relative to average values in the twentieth century is less striking. We find a dramatic change in the equity premium in the post 1933 period – the premium rose from 3.92 percent to 8.93 percent, an increase of more than 125 percent. Since 1933 marked the end of the period when the US was on the gold standard, this break can be seen as the change in the equity premium after the implementation of the new policy. 1.4 Variation in the Equity Premium over Time The equity premium has varied considerably over time, as illustrated in Figures 1 and 2, below. Furthermore, the variation depends on the time horizon over which it is measured. There 11 See the earlier discussion on data
11 have even been periods when it has been negative. duwu 60 0 TTTTTTTTTTTT 1925 194 1955 1965 1975 1985 19952000 Year.end Figure 1 196d 1g54 1984 1974 1934 a 20-Year Period Ending Figure 2 Source:Ibbotson 2001 The low frequency variation has been counter-cyclical.This is shown in Figure 3 where we have plotted stock market value as a share of national incomeand the mean equity premium averaged over certain time periods.We have divided the time period from 1929 to 2000 into sub- periods,where the ratio market value of equity to national income was greater than 1 and where it was less than 1.Historically,as the figure illustrates,subsequent to periods when this ratio was In Mehra(199)it is argued that the variation in this ratio is difficult to rationalize in the standard neoclassical framework since over the same period after tax cash flows to equity as a share of national income are fairly constant.Here we do not address
11 have even been periods when it has been negative. Figure 1 Figure 2 Source: Ibbotson 2001 The low frequency variation has been counter- cyclical. This is shown in Figure 3 where we have plotted stock market value as a share of national income12 and the mean equity premium averaged over certain time periods. We have divided the time period from 1929 to 2000 into subperiods, where the ratio market value of equity to national income was greater than 1 and where it was less than 1. Historically, as the figure illustrates, subsequent to periods when this ratio was 12 In Mehra (1998) it is argued that the variation in this ratio is difficult to rationalize in the standard neoclassical framework since over the same period after tax cash flows to equity as a share of national income are fairly constant. Here we do not address
12 high the realized equity premium was low.A similar results holds when stock valuations are low relative to national income.In this case the subsequent equity premium is high. Since After Tax Corporate Profits as a share of National Income are fairly constant over Market Value/National Income and Mean Equity Premium (Averaged over time periods when MV/NI>1 and MV/NI<1) 14 2.5 12 2 10 1.5 0.5 0 0 Time Figure 3 time,this translates into the observation that the realized equity premium was low subse- quent to periods when the Price/Earnings ratio is high and vice versa.This is the basis for the returns predictability literature in Finance.(Campbell and Shiller(1988)and Fama and French (1988). this issue and simply utilize the fact that this ratio has varied considerably over time
12 high the realized equity premium was low. A similar results holds when stock valuations are low relative to national income. In this case the subsequent equity premium is high. Since After Tax Corporate Profits as a share of National Income are fairly constant over Figure 3 time, this translates into the observation that the realized equity premium was low subsequent to periods when the Price/ Earnings ratio is high and vice versa. This is the basis for the returns predictability literature in Finance. (Campbell and Shiller (1988) and Fama and French (1988)). this issue and simply utilize the fact that this ratio has varied considerably over time. Market Value/National Income and Mean Equity Premium (Averaged over time periods when MV/NI>1 and MV/NI<1) 0 2 4 6 8 1 0 1 2 1 4 1929 1931 1933 1935 1937 1939 1941 1943 1945 1947 1949 1951 1953 1955 1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 Time 0 0.5 1 1.5 2 2.5
13 In Figure 4we have plotted stock market value as a share of national income and the sub- sequent three-year mean equity premium.This provides further conformation that historically, Market Value/National Income and 3 Year Ahead Mean Equity Premium (Averaged over time periods when MV/NI>1 and MV/NI<1) 18 2.5 16 12 1.5 70 IN/AW 0.5 0 。eg8 BSSOS B OELG8BsotoG8GR GRE BEOML OO Time Figure 4 periods of relatively high market valuation have been followed by periods when the equity premium was relatively low
13 In Figure 4we have plotted stock market value as a share of national income and the subsequent three-year mean equity premium. This provides further conformation that historically, Figure 4 periods of relatively high market valuation have been followed by periods when the equity premium was relatively low. Market Value/National Income and 3 Year Ahead Mean Equity Premium (Averaged over time periods when MV/NI>1 and MV/NI<1) 0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 1929 1932 1935 1938 1941 1944 1947 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 Time EP % 0 0.5 1 1.5 2 2.5 MV/NI
14 2. Is The Equity Premium Due To A Premium For Bearing Non- diversifiable Risk? In this section,we examine various models that attempt to explain the historical equity premium.We start with a model with standard(CRRA)preferences,then examine models incor- porating alternative preference structures,idiosyncratic and uninsurable income risk,and models incorporating a disaster state and survivorship bias. Why have stocks been such an attractive investment relative to bonds?Why has the rate of return on stocks been higher than on relatively risk-free assets?One intuitive answer is that since stocks are 'riskier'than bonds,investors require a larger premium for bearing this addi- tional risk;and indeed,the standard deviation of the returns to stocks (about 20 percent per an- num historically)is larger than that of the returns to T-bills(about 4 percent per annum),so,ob- viously they are considerably more risky than bills!But are they? Figures 5 and 6 below illustrate the variability of the annual real rate of return on the S&P 500 index and a relatively risk-free security over the period 1889-2000.Of course,the index did not consist of 500 stocks for the entire period
14 2. Is The Equity Premium Due To A Premium For Bearing Non- diversifiable Risk? In this section, we examine various models that attempt to explain the historical equity premium. We start with a model with standard (CRRA) preferences, then examine models incorporating alternative preference structures, idiosyncratic and uninsurable income risk, and models incorporating a disaster state and survivorship bias. Why have stocks been such an attractive investment relative to bonds? Why has the rate of return on stocks been higher than on relatively risk-free assets? One intuitive answer is that since stocks are ‘riskier’ than bonds, investors require a larger premium for bearing this additional risk; and indeed, the standard deviation of the returns to stocks (about 20 percent per annum historically) is larger than that of the returns to T-bills (about 4 percent per annum), so, obviously they are considerably more risky than bills! But are they? Figures 5 and 6 below illustrate the variability of the annual real rate of return on the S&P 500 index and a relatively risk-free security over the period 1889–2000.Of course, the index did not consist of 500 stocks for the entire period