Stock Market Risk and Return: An Equilibrium Approach

Abstract

Empirical evidence that expected stock returns are weakly related to volatility at the market level appears to contradict the intuition that risk and return are positively related. We investigate this issue in a general equilibrium exchange economy characterized by a regime-switching consumption process with time-varying transition probabilities between regimes. When estimated using consumption data, the model generates a complex, nonlinear and time-varying relation between expected returns and volatility, duplicating the salient features of the risk/return trade-off in the data. The results emphasize the importance of time-varying investment opportunities and highlight the perils of relying on intuition from static models. Understanding the risk/return trade-off is fundamental to equilibrium asset pricing. In this context, the stock market is one of the most natural starting points since it serves as a proxy for the wealth portfolio that is studied in finance theory. It is perhaps surprising, therefore, that there is still a good deal of controversy around the issue of how to measure risk at the market level. Recent empirical studies [e.g., Glosten, Jagannathan, and Runkle (1993), Whitelaw (1994), and Boudoukh, Richardson, and Whitelaw (1997)] document two puzzling results with regard to the intertemporal relation between equity risk and return at the market level. 1 First, they provide evidence of a weak, or even negative, relation between conditional expected returns and the conditional volatility of returns. 2 Second, they document significant time variation in this relation. Specifically, in a modified GARCH-M framework using post-World War II monthly data, Glosten, Jagannathan, and Runkle (1993) find that the estimated coefficient on volatility in the expected return regression is negative. In a similar dataset, when both conditional moments are estimated as functions of predetermined financial variables, Whitelaw (1994)