Earning the Right Premium on the Right Factor in Portfolio Planning

The optimal portfolio as well as the utility from trading stocks and derivatives depends on the risk factors and on their market prices of risk. We analyze this dependence for a CRRA investor in a model setup with stochastic volatility and stochastic jumps in the stock price and its volatility. We find that both the decomposition of the variance and the decomposition of the equity risk premium into a diffusion component and a jump risk component matter. We furthermore show that the same holds true for the compartment of the latter into its various elements. Additionally, we show that the structure of the optimal exposures to jump risk crucially depends on which elements of jump risk are priced. In a complete market, changing the assumption on whether jump intensity risk, jump size risk, or jump variance risk are priced reverses the dependence of the optimal jump risk exposures on the jump size (in the stock price) completely. The function changes from flat to increasing to (inversely) U-shaped.