15 Real Annual Return on S&P 500,1889-2000 (percent) 60 40 1889 697 91 g17 2 41 -20 .40 60 Year Source:Mehra and Prescott (1985).Data updated by the authors. Figure 5
15 Real Annual Return on S&P 500, 1889-2000 (percent) -60 -40 -20 0 2 0 4 0 6 0 1889 1893 1897 1901 1905 1909 1913 1917 1921 1925 1929 1933 1937 1941 1945 1949 1953 1957 1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 Year Percent Source: Mehra and Prescott (1985). Data updated by the authors. Figure 5
16 Real Annual Return on a Relatively Riskless Security,1889-2000 (percent) 20 15 0 1889 -5 .10 .15 .20 Year Source:Mehra and Prescott(1985).Data updated by the authors Figure 6 To enhance and deepen our understanding of the risk-return trade-off in the pricing of financial assets,we take a detour into modern asset pricing theory and look at why different assets yield different rates of return.The deus ex machina of this theory is that assets are priced such that,ex- ante,the loss in marginal utility incurred by sacrificing current consumption and buying an asset at a certain price is equal to the expected gain in marginal utility,contingent on the anticipated increase in consumption when the asset pays off in the future. The operative emphasis here is the incremental loss or gain of utility of consumption and should be differentiated from incremental consumption.This is because the same amount of con-
16 Real Annual Return on a Relatively Riskless Security, 1889-2000 (percent) -20 -15 -10 - 5 0 5 1 0 1 5 2 0 1889 1893 1897 1901 1905 1909 1913 1917 1921 1925 1929 1933 1937 1941 1945 1949 1953 1957 1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 Year Percent Source: Mehra and Prescott (1985). Data updated by the authors. Figure 6 To enhance and deepen our understanding of the risk-return trade-off in the pricing of financial assets, we take a detour into modern asset pricing theory and look at why different assets yield different rates of return. The deus ex machina of this theory is that assets are priced such that, exante, the loss in marginal utility incurred by sacrificing current consumption and buying an asset at a certain price is equal to the expected gain in marginal utility, contingent on the anticipated increase in consumption when the asset pays off in the future. The operative emphasis here is the incremental loss or gain of utility of consumption and should be differentiated from incremental consumption. This is because the same amount of con-
17 sumption may result in different degrees of well-being at different times.As a consequence,as- sets that pay off when times are good and consumption levels are high-when the marginal util- ity of consumption is low-are less desirable than those that pay off an equivalent amount when times are bad and additional consumption is more highly valued.Hence consumption in period t has a different price if times are good than if times are bad. Let us illustrate this principle in the context of the standard,popular paradigm,the Capi- tal Asset Pricing Model(CAPM).The model postulates a linear relationship between an asset's 'beta,'a measure of systematic risk,and its expected return.Thus,high-beta stocks yield a high expected rate of return.That is because in the CAPM,good times and bad times are captured by the return on the market.The performance of the market,as captured by a broad-based index, acts as a surrogate indicator for the relevant state of the economy.A high-beta security tends to pay off more when the market return is high-when times are good and consumption is plentiful; it provides less incremental utility than a security that pays off when consumption is low,is less valuable and consequently sells for less.Thus higher beta assets that pay off in states of low marginal utility will sell for a lower price than similar assets that pay off in states of high mar- ginal utility.Since rates of return are inversely proportional to asset prices,the lower beta assets will,on average,give a lower rate of return than the former. Another perspective on asset pricing emphasizes that economic agents prefer to smooth patterns of consumption over time.Assets that pay off a larger amount at times when consump- tion is already high "destabilize"these patterns of consumption,whereas assets that pay off when consumption levels are low "smooth"out consumption.Naturally,the latter are more valuable and thus require a lower rate of return to induce investors to hold these assets.(Insurance policies are a classic example of assets that smooth consumption.Individuals willingly purchase and hold
17 sumption may result in different degrees of well-being at different times. As a consequence, assets that pay off when times are good and consumption levels are high – when the marginal utility of consumption is low – are less desirable than those that pay off an equivalent amount when times are bad and additional consumption is more highly valued. Hence consumption in period t has a different price if times are good than if times are bad. Let us illustrate this principle in the context of the standard, popular paradigm, the Capital Asset Pricing Model (CAPM). The model postulates a linear relationship between an asset’s ‘beta,’ a measure of systematic risk, and its expected return. Thus, high-beta stocks yield a high expected rate of return. That is because in the CAPM, good times and bad times are captured by the return on the market. The performance of the market, as captured by a broad-based index, acts as a surrogate indicator for the relevant state of the economy. A high-beta security tends to pay off more when the market return is high – when times are good and consumption is plentiful; it provides less incremental utility than a security that pays off when consumption is low, is less valuable and consequently sells for less. Thus higher beta assets that pay off in states of low marginal utility will sell for a lower price than similar assets that pay off in states of high marginal utility. Since rates of return are inversely proportional to asset prices, the lower beta assets will, on average, give a lower rate of return than the former. Another perspective on asset pricing emphasizes that economic agents prefer to smooth patterns of consumption over time. Assets that pay off a larger amount at times when consumption is already high “destabilize” these patterns of consumption, whereas assets that pay off when consumption levels are low “smooth” out consumption. Naturally, the latter are more valuable and thus require a lower rate of return to induce investors to hold these assets. (Insurance policies are a classic example of assets that smooth consumption. Individuals willingly purchase and hold
18 them,despite of their very low rates of return). To return to the original question:are stocks that much riskier than T-bills so as to justify a six percentage differential in their rates of return? What came as a surprise to many economists and researchers in finance was the conclu- sion of a paper by Mehra and Prescott,written in 1979.Stocks and bonds pay off in approxi- mately the same states of nature or economic scenarios and hence,as argued earlier,they should command approximately the same rate of return.In fact,using standard theory to estimate risk- adjusted returns,we found that stocks on average should command,at most,a one percent return premium over bills.Since,for as long as we had reliable data (about 100 years),the mean pre- mium 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 our pa- per "The Equity Premium:A Puzzle"to be published.(Mehra and Prescott(1985)). 2.1 Standard Preferences The neoclassical growth model and its stochastic variants are a central construct in con- temporary finance,public finance,and business cycle theory.It has been used extensively by, among others,Abel et al.(1989),Auerbach and Kotlikoff(1987),Barro and Becker(1988). Brock(1979),Cox,Ingersoll and Ross(1985),Donaldson and Mehra(1984),Lucas(1978), Kydland and Prescott(1982),and Merton(1971).In fact,much of our economic intuition is de- rived from this model class.A key idea of this framework is that consumption today and con- sumption in some future period are treated as different goods.Relative prices of these different goods are equal to people's willingness to substitute between these goods and businesses'ability to transform these goods into each other
18 them, despite of their very low rates of return). To return to the original question: are stocks that much riskier than T-bills so as to justify a six percentage differential in their rates of return? What came as a surprise to many economists and researchers in finance was the conclusion of a paper by Mehra and Prescott, written in 1979. Stocks and bonds pay off in approximately the same states of nature or economic scenarios and hence, as argued earlier, they should command approximately the same rate of return. In fact, using standard theory to estimate riskadjusted returns, we found that stocks on average should command, at most, a one percent return premium over bills. Since, for as long as we had reliable data (about 100 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 our paper “The Equity Premium: A Puzzle” to be published. (Mehra and Prescott (1985)). 2.1 Standard Preferences The neoclassical growth model and its stochastic variants are a central construct in contemporary finance, public finance, and business cycle theory. It has been used extensively by, among others, Abel et al. (1989), Auerbach and Kotlikoff (1987), Barro and Becker (1988), Brock (1979), Cox, Ingersoll and Ross (1985), Donaldson and Mehra (1984), Lucas (1978), Kydland and Prescott (1982), and Merton (1971). In fact, much of our economic intuition is derived from this model class. A key idea of this framework is that consumption today and consumption in some future period are treated as different goods. Relative prices of these different goods are equal to people’s willingness to substitute between these goods and businesses’ ability to transform these goods into each other
19 The model has had some remarkable successes when confronted with empirical data, particularly in the stream of macroeconomic research referred to as Real Business Cycle Theory, where researchers have found that it easily replicates the essential macroeconomic features of the business cycle.See,in particular,Kydland and Prescott (1982).Unfortunately,when confronted with financial market data on stock returns,tests of these models have led,without exception,to their rejection.Perhaps the most striking of these rejections is contained in our 1985 paper. To illustrate this we employ a variation of Lucas'(1978)pure exchange model.Since per capita consumption has grown over time,we assume that the growth rate of the endowment fol- lows a Markov process.This is in contrast to the assumption in Lucas'model that the endowment level follows a Markov process.Our assumption,which requires an extension of competitive equilibrium theory,enables us to capture the non-stationarity in the consumption series associ- ated with the large increase in per capita consumption that occurred over the last century. We consider a frictionless economy that has a single representative 'stand-in'household. This unit orders its preferences over random consumption paths by 0<B<1 (1) where c,is the per capita consumption and the parameter Bis the subjective time discount factor, which describes how impatient households are to consume.If Bis small,people are highly im- patient,with a strong preference for consumption now versus consumption in the future.As modeled,these households live forever,which implicitly means that the utility of parents de- pends on the utility of their children.In the real world,this is true for some people and not for others.However,economies with both types of people-those who care about their children's
19 The model has had some remarkable successes when confronted with empirical data, particularly in the stream of macroeconomic research referred to as Real Business Cycle Theory, where researchers have found that it easily replicates the essential macroeconomic features of the business cycle. See, in particular, Kydland and Prescott (1982). Unfortunately, when confronted with financial market data on stock returns, tests of these models have led, without exception, to their rejection. Perhaps the most striking of these rejections is contained in our 1985 paper. To illustrate this we employ a variation of Lucas' (1978) pure exchange model. Since per capita consumption has grown over time, we assume that the growth rate of the endowment follows a Markov process. This is in contrast to the assumption in Lucas' model that the endowment level follows a Markov process. Our assumption, which requires an extension of competitive equilibrium theory13, enables us to capture the non-stationarity in the consumption series associated with the large increase in per capita consumption that occurred over the last century. We consider a frictionless economy that has a single representative 'stand-in' household. This unit orders its preferences over random consumption paths by E Uc t t 0 t 0 b b 0 1 = • Â Ï Ì Ó ¸ ˝ ˛ ( ) , < < (1) where ct is the per capita consumption and the parameter bis the subjective time discount factor, which describes how impatient households are to consume. If bis small, people are highly impatient, with a strong preference for consumption now versus consumption in the future. As modeled, these households live forever, which implicitly means that the utility of parents depends on the utility of their children. In the real world, this is true for some people and not for others. However, economies with both types of people—those who care about their children’s