The Investors' Belief in Stock Returns and Volatilities

Abstract

Motivated by the asset pricing implications of the regime-switching equilibrium models in the literature, this paper investigates empirically the effects of regime switches in aggregate stock returns and volatilities. The investors' belief, defined as the posterior probability of the bear regime, is estimated based on a regime-switching model where the regime of the economy follows a two-state hidden Markov process. Veronesi (1999) shows that both the expected excess return and the volatility of the returns are the concave, bell-shaped functions of the investors' belief if risk aversion is a constant.The empirical findings in this paper suggest that the expected excess return and the volatility are monotonically increasing functions of the investors' belief. Therefore, a reasonable explanation for the empirical finding is that risk aversion is time-varying and the representative agent is more risk averse in the bear regime so that a higher expected excess return and higher volatility in the bad regime are generated. A second empirical finding is that the stock return predictors, such as the term spread, the in flation rate, and the T-bill rate, have significant business cycle patterns in the predictive regressions. For example, the term spread is positively related to the stock market returns in the boom regime, but is negatively related to the stock market returns in the bear regime. This suggests that the increasing term spread is good news in the bear regime because it indicates that the economy is improving and will recover soon, thus the investors require a lower equity premium. In addition, the equity premium is more sensitive to the predictors in the bear regime because the bear regime is short lived. Similar results are also found in the predictive regressions for the variance of the stock market returns.