Economists generally accept that, even after adjusting for risk, average stock returns are substantially higher than average returns on short-term debt instruments. The failure of financial theory to explain the magnitude of these excess returns has led to this phenomenon being labeled as the “equity premium puzzle” by Mehra and Prescott (1985). Standard asset pricing models can only match the data if investors are extremely risk averse. In particular, the coefficient of relative risk aversion must be implausibly large for traditional models to reconcile the large differential between real equity returns and real returns available on short-term debt instruments. Of course, we expect different financial assets to deliver large variations in returns, but typically financial economists have explained such differentials by attributing them to differences among the covariances of asset returns and investors consumption, e.g. the Consumption Capital Asset Pricing Model of Lucas (1978) and Breeden (1979). The more traditional version of CAPM assumes a perfect correlation between the stock market return and the consumption path of the typical investor.
This allows us to measure asset risk as its covariance with the market return. However, in their path breaking work, Mehra and Prescott (1985), using annual US data from 1889 to 1978, showed that the covariance of equity returns with consumption growth was insufficient to explain the observed equity premium of over 6%. In fact, they could only account for a premium of approximately 0.35%. Much of the resulting empirical literature has focused on the US markets where longer data series exist, but Campbell (1996, 2003) focuses on some smaller stock markets and finds evidence that an equity premium is also a feature of these markets.
Our analysis investigates the robustness of the equity premium across high-and low-volatility regimes for both stock market returns and consumption growth. The prevailing economic conditions can have a strong influence on stock market performance. Schwert (1989) finds increased volatility of equity returns during economic recessions, while Campbell et al. (2001) show that this result extends to more recent time periods. Lettau et al (2006) show that, at low frequency, the equity premium is related to macroeconomic risk, as measured by the volatility of consumption growth. Sill (2006) develops a link between macroeconomic volatility and stock market returns. Given that there is substantial empirical evidence that both financial and economic markets are characterized by time-varying volatility, we argue that the risk aversion of investors may also vary across regimes and hence over time.
Campbell and Cochrane (1999) find that the coefficient of risk aversion varies, in a nonlinear manner, with the state of surplus consumption. Many studies take long run averages that encompass differing market conditions and consequently the implied levels of risk aversion may hide important differences in risk attitudes across regimes. This is the area that we wish to address.
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