Downside Variance Risk Premium

We propose a new decomposition of the variance risk premium in terms of upside and downside variance risk premia. The difference between upside and downside variance risk premia is a measure of skewness risk premium. We establish that the downside variance risk premium is the main component of the variance risk premium, and that the skewness risk premium is a priced factor with significant prediction power for aggregate excess returns. Our empirical investigation highlights the positive and significant link between the downside variance risk premium and the equity premium, as well as a positive and significant relation between the skewness risk premium and the equity premium. Finally, we document the fact that the skewness risk premium fills the time gap between one quarter ahead predictability, delivered by the variance risk premium as a short term predictor of excess returns and traditional long term predictors such as price-dividend or price-earning ratios. Our results are supported by a simple equilibrium consumption-based asset pricing model.