Stock Returns, Asymmetric Volatility, Risk Aversion, and Business Cycle: Some New Evidence,

I. INTRODUCTION Most asset pricing models, starting with Intertemporal Capital Asset Pricing Model of Merton (1973), suggest a positive relation between risk and return for the aggregate stock market. There is an extensive empirical literature that has tried to establish the existence of such a trade-off between risk and return for stock market indexes. Unfortunately, the results have been inconclusive. Often the relation between risk and return has been found insignificant and, sometimes, even negative. Recently, it has been debated whether risk aversion is state dependent and whether it is procyclical or countercyclical. In this article, we explore the role of the business cycle in the relation between risk and return for the aggregate stock market. Specifically, by employing asymmetric generalized autoregressive conditional heteroskedasticity in mean models (AGARCH-M), Markov switching models, and a simple theoretical equilibrium framework, we explore how these three related issues--excess stock returns, volatility, and risk aversion--are affected by business cycles. As noted by Fama (1990), of many possible forces that drive the stock market, real economic activities, represented by business cycles, could be an important one since they are highly related to major stock pricing factors; market volatility; and the psychology of investors, particularly investors' attitude toward risk. An interesting observation about excess stock return is that it is time varying over business cycles and significantly higher in boom periods. (1) According to our estimates for the sample period 1926-2001 presented in Table 1, the mean excess stock return is 0.8963%/mo in boom periods and -0.3247%/mo in recession periods. The excess stock return tends to be very high in the boom period because stock returns remain relatively high with increasing dividend payments. Another interesting observation about the stock market is that the volatility of excess stock return is also time varying over business cycles and significantly lower in boom periods. Our estimates of standard deviation of monthly stock excess return for the sample period 1926-2001 are 4.6% in the boom period and 8.2% in the recession period. These estimates imply that the excess return-risk relation is time varying over the business cycle. Since the coefficient of variance or standard deviation in the conditional mean equation is usually interpreted as being closely related to the coefficient of relative risk aversion as argued by Merton (1980), our finding suggests a potential time-varying risk aversion. (2) There is a general agreement that investors, within a given time period, require a larger expected return from a security that is riskier. However, there seems to be no relationship between risk and return over time. As such, whether or not investors require a larger risk premium, for investing in a security during periods when the security is more risky relatively remains inconclusive. At first glance, it may appear that rational, risk-averse investors would require a relatively larger risk premium during times when the payoff from the security is more risky. A larger risk premium may not be required, however, because times that are relatively more risky could coincide with times in which investors are better able to bear particular types of risk. Further, a larger risk premium may not be required because investors may want to save relatively more during periods when the future is more risky. (3) Hence, a positive as well as a negative sign for the correlation between the conditional mean and the conditional variance of the excess return on stocks would be consistent with existing theories. Since there are conflicting predictions about the intertemporal trade-off between risk and return, it is important to empirically characterize the nature of this relation. According to Merton (1980), the coefficient of variance or the standard deviation in the conditional mean equation, which is called volatility feedback, is usually interpreted as the coefficient of relative risk aversion. …