Earning the right premium on the right factor in portfolio planning

•The utility from derivatives depends on the compartment of the equity risk premium.•The investor does not prefer a premium on jump risk to a premium on diffusion risk or vice versa.•The more extreme the market prices of risk, the larger the utility of the investor.•The optimal exposures to jump risk crucially depend on which elements of jump risk are priced.

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 models with stochastic volatility, jumps in the stock price, and jumps in volatility. We find that the compartment of the total variance into diffusion risk and jump risk has a small impact on the utility in an incomplete market only. In contrast, the decomposition of the equity risk premium into a diffusion component and a jump risk component and the compartment of the latter into its various elements has a huge impact on the utility in a complete market. The more extreme the market prices of risk, i.e. the more they deviate from their equilibrium values, the larger the utility of the investor. Additionally, we show that the structure of the optimal exposures to jump risk crucially depends on which elements of jump risk are priced.