Modeling Financial Return Dynamics by Decomposition

While the predictability of excess stock returns is statistically small, their sign and volatility exhibit a substantially larger degree of dependence over time. We capitalize on this observation and consider prediction of excess stock returns by decomposing the equity premium into a product of sign and absolute value components and carefully modeling the marginal predictive densities of the two parts. Then we construct the joint density of a positively valued (absolute returns) random variable and a discrete binary (sign) random variable by copula methods and discuss computation of the conditional mean predictor. Our empirical analysis of US stock return data shows among other interesting ndings that despite the large unconditional correlation between the two multiplicative components they are conditionally very weakly dependent.