State-Dependent Volatility and the Market Risk Premium

Abstract

The market risk premium is estimated based on the equilibrium relationship between risk and expected returns in an intertemporal setting characterized by periods of distinctly different levels of risk. In this environment of discrete volatility states, expected returns compensate investors for current volatility risk as well as the risk associated with a change in the level of market volatility. More importantly, expected returns include the expected change in market value associated with a change in the level of market risk. For this reason, average realized returns within each volatility state do not reflect the risk premium required by investors for state specific risk. By explicitly modelling the process governing the evolution of volatility states, I recover the required risk premium for each volatility state. The dynamic nature of the volatility process implies a term structure of expected forward risk premia that is dependent upon the current level of market volatility. During the period from 1926 to 1997, my estimates indicate that the economy is likely to have been in the high-volatility state approximately 13 percent of the time and that there is a strong statistical relationship between these high-volatility episodes and business cycle contraction periods. In addition, I find evidence of a structural shift in the volatilty process corresponding to the end of the Great Depression Era. As a result of this structural change, the likelihood of being in the high-volatility state decreases dramatically after 1940, implying a significant decrease in the level of market risk. Consistent with this reduction in risk, I find evidence of an abnormal increase in market values during the period from 1940 to 1960. After controlling for this windfall capital gain, my analysis suggests that the long-run market risk premium for the period after 1940 is substantially less than that implied by the simple historical average of excess market returns.