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Article Excerpt
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. If so, the changes in excess return and volatility of these magnitudes over business cycles may have important implications for investors' risk aversion. As such, time-varying volatility feedback (or investors' attitudes toward the risk) over business cycles emerges as an appealing idea. The "volatility feedback" effect has been studied by several financial economists including Pindyck (1984); French, Schwert, and Stambaugh (1987); and Campbell and Hentschel (1992), but they have not explored the role of business cycles in the relation explicitly.
In estimating the relation between excess return and volatility, we use an asymmetric generalized autoregressive conditional hetero-skedasticity (AGARCH) model. The model is analytically tractable and captures the asymmetric volatility movement. (4) Further, in an attempt to avoid using the hindsight National Bureau of Economic Research (NBER) information about business cycles, we estimate a regime switching model, where a Markov switching model is estimated simultaneously with a generalized autoregressive conditional heteroskedasticity (GARCH) model. To investigate and confirm potential state-dependent risk aversion, we employ a simple equilibrium asset pricing model with its calibration.
For our sample period 1926-2001, we fail to find a significant relation between risk and excess return in the simple GARCH models without allowing for the business cycle effect. However, once we allow for a business cycle factor (boom and recession), the risk premium coefficient becomes significantly positive for boom periods, whereas it remains insignificantly negative for recession periods. Since the coefficient of volatility in the excess return equation is usually characterized as measuring the time-varying risk aversion parameter as in Merton (1980), this suggests that our finding is in favor of increased risk aversion in the boom period (i.e., procyclical risk aversion).
Using a simple equilibrium asset pricing model with its calibration, we confirm that risk aversion is state dependent and procyclical. We also find that asymmetric volatility movement is weakened during boom periods. Our finding of procyclical risk aversion helps us understand not only the observed larger risk premium for a given risk in the boom periods but also the observed weakened asymmetric volatility during the boom periods.
The remainder of the article is organized as follows. In Section II, we briefly review related literature. In Section III, we describe our data and classification of business cycles. In Section IV, we introduce empirical models of the relation between excess return and volatility--generalized autoregressive conditional heteroskedasticity in mean (GARCH-M) model and Markov switching model--and discuss estimation results. In Section V, we further discuss the implications of the estimation results regarding state-dependent risk aversion over business cycles. In Section VI, we provide several robustness checks. We conclude in Section VII.
II. RELATED LITERATURE
The intertemporal relation between risk and return has been examined extensively; however, empirical evidence is mixed. For example, French, Schwert, and Stambaugh (1987) and Campbell and Hentschel (1992) found that the data are consistent with a positive relation between conditional expected excess stock return and conditional variance, whereas Fama and Schwert (1977); Campbell (1987); Breen, Glosten, and Jagannathan (1989); Turner, Startz, and Nelson (1989); Pagan and Hong (1991); Nelson (1991); Glosten, Jagannathan, and Runkle (1993); and Whitelaw (2000) found a negative relation. Harvey (1989) provided empirical evidence suggesting that there may be some time variation in the relation between risk and return.
Regarding the effect of real economic activity (or business cycle) on market volatility, Schwert (1990) and Fama (1990) argued that future production growth rates explain a large fraction of the variation in stock returns over 1889-1988. McQueen and Roley (1993) found that after allowing for different stages of the business cycle, a stronger relationship between stock prices and economic news becomes evident. They found that when the economy is strong, the stock market responds negatively to news about higher real economic activity. Using a two-variable Markov chain model, Hamilton and Lin (1996) found that economic recessions are a primary factor that drive fluctuations in the volatilities of stock returns.
Whitelaw (1994) found a weak, unconditional, contemporaneous relation between the two moments of stock market returns but a strong, noncontemporaneous relation between the conditional volatility and the conditional expected return. Specifically, he found that volatility appears to lead expected returns over the course of the business cycle. Using a simulated method of moments in a two-state economy, Wu (2001) found that both leverage effect and volatility feedback effect are important to asymmetric volatility movements. Using daily return data and multivariate GARCH models, DeGoeij and Marquering (2002) explained the asymmetric volatility movement of the Treasury bond market with macroeconomic news announcement shocks. By extending these studies and allowing for a business cycle factor (boom and recession) in models of GARCH-M and Markov regime switching, we find that the risk premium coefficient becomes significantly positive for boom periods, whereas it remains insignificantly negative for recession periods.
A number of authors have explored investors' attitudes toward risk by studying the volatility feedback effect. Brown, Harlow, and Tinic (1988) showed that stock price reactions to unfavorable news events tend to be larger than those to favorable events. They attribute this finding to volatility feedback. Poterba and Summers (1986), on the other hand, argued that volatility feedback cannot be important because changes in volatility are too short-lived to have a major effect on stock prices. French, Schwert, and Stambaugh (1987) regressed stock returns on innovations in volatility and found a negative coefficient, which they attribute to volatility feedback. Haugen, Talmor, and Walter (1991) reported a similar result.
An interesting feature of return volatility is its asymmetric movement. Volatility is typically higher after the stock market falls than after it rises, so stock returns are negatively correlated with future volatility. Black (1976), who argued that this could be due to the increase in leverage that occurs when the market value of a firm declines, first discussed this correlation, or predictive asymmetry. However, subsequent studies tended to show...
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