Intertemporal risk–return relationships in bull and bear markets

This paper examines whether the intertemporal risk–return relationship in the U.S. stock market varies with bull and bear markets. Based on the non-parametric Bry–Boschan approach for identifying bull and bear markets and the non-parametric Bartlett-kernel based realized variance as a proxy for the conditional variance, our empirical findings reveal that the risk–return relationship is significantly positive in bull markets, but significantly negative in bear markets. Even when the macroeconomic variables reflecting business cycle fluctuations are taken into account, these empirical results remain the same. The rolling regression results also reveal that our findings are quite robust over time; in particular, the range of the rolling estimates is much smaller, suggesting that the time-varying risk–return relationship can be appropriately explained by bull and bear markets.