Since the equity premium is a compensation for bearing systematic risk, it should depend on macroeconomic conditions. Expected risk premiums should be countercyclical. In other words, when economic prospects are good expected risk premiums should be low. On the other hand, high risk premiums are required to induce investors to take risks during challenging economic times. Fama and French (1989) provide empirical evidence for this argument. In the same line of research, Chen (1991) finds that the default spread, the term spread, the dividend yield and industrial production growth are important determinants of the future equity premium. He argues that the significance of these variables stems from their correlation with macroeconomic conditions. This argument is empirically supported by Estrella and Hardouvelis (1991) who document that the term spread is a strong predictor of changes in the economic activity. Lettau et al. (2008) explore the link between the equity premium and macroeconomic risks or the volatility of the aggregate economy. They find that the decline in the equity premium at the end of the last century can be explained by the decline of macroeconomic risks.
Another critical determinant of the equity premium is the risk aversion of investors. If risk aversion increases, the investors will demand a higher compensation for the risk exposure, which would lead to lower asset prices and thus a higher risk premium. In the opposite case, a decrease in the risk aversion would put upward pressure on the asset prices and lower the risk premiums. Building on this argument to model the equity premium has been challenging. While estimating the direction of the relationship between the risk aversion and the risk premium is straightforward, a full specification of this relationship requires knowledge of the utility function of investors. By investing
equilibrium, therefore, assets should be priced to make equal the current loss and the expected future gain in investors’ marginal utility, conditioned on the expected future level of consumption. This conditioning is necessary because the marginal utility of consumption may be different when the investment is made and when it is liquidated. The value of additional consumption is inversely related to the level of consumption. In other words, the marginal utility of consumption is low in good times when the level of consumption is high and vice versa. It follows that the assets, which pay off during the good times or when the level of consumption is high, are less desirable and therefore have to offer a higher rate of return to attract investors. This prediction corresponds to the prediction of the CAPM, implying that high-beta assets should offer higher expected rate of return to compensate investors for exposure to the risk of disproportionate loss in market downturns.
Building on the consumption pricing framework, Mehra and Prescott (2008) show that, under the assumption of a perfect correlation between the equity return and consumption growth rate, the equity premium is given by:
2
lnR
E-lnr
rf=as
X (3.15)where:
α is the risk aversion coefficient
σ2
x is the variance of the growth rate in consumption
Variations in the growth rate of consumption are not large enough to justify the historically observed equity premium with a reasonable value of the risk aversion coefficient. Mehra and Prescott (1985) were the first to discover and emphasize this fact. Their model generates the equity premium below 0.5 per cent, which is significantly lower than the observed value of about six per cent. This finding can be interpreted as the equity premium not being a compensation for a non-diversifiable risk.
The large proportion of unexplained equity premium reported by Mehra and Prescott (1985) has stimulated a large number of theoretical and empirical studies. Rietz (1988) argues that accounting for low-probability events that have highly negative
consequences can explain the observed levels of the equity premium. In other words, a significant portion of the equity premium is the compensation for exposure to risk of rare market crashes that, when they happen, have disastrous effects on the wealth of investors. Barro (2005) suggests that incorporating stochastic variations in disaster probabilities is a natural way to extend this approach, and that far-out-of-the-money options can be used to measure disaster probabilities.
Longstaff and Piazesi (2004) propose a model with three components. The first component is the variance of the consumption growth as in Mehra and Prescott (1985). The second component is the probability of a jump in asset prices and the consumption level which is in line with Rietz (1988) and Barro (2005). Finally, the third component is the firm-risk premium which is the most important because the cash flows of firms are highly correlated with consumption growth. Longstaff and Piazesi (2004) show that their model explains about a half of the historically observed equity premium, which is high when compared to other studies but is still far from a complete understanding of the equity premium.
Finally, an important determinant of the equity premium appears to be liquidity. Based on data spanning a century, Jones (2002) finds the variation in the aggregate liquidity to be an important determinant of equity returns. Bekaert, Harvey and Lundblad (2007) reach the same conclusion for emerging markets.