Volatility Components, Leverage Effects, and the Return-Volatility Relations

This paper investigates the return-volatility relation by taking into account the model specification problem. The market volatility is modeled to have two components, one due to the diffusion risk and the other due to the jump risk. The model indicates that under the absence of leverage effects, it becomes a variant of Merton's ICAPM, while under the existence of leverage effects, the return-volatility relations are determined by interactions between risk premia and leverage effects. Empirically, I find a robust negative relationship between the excess return and the jump volatility, whereas the relationship between the excess return and the diffusion volatility is hard to identify notwithstanding that the indirect evidence of the positive relationship exists