Conventional asset pricing theory suggests that investors receive no compensation for idiosyncratic risk, but several studies indicate that it may play an important role. This paper makes clear exactly when these risks affect asset prices in a comprehensive framework with jumps and heterogeneous recursive preferences. While cross-sectional endowment risk always affects the riskfree rate and equity volatility, it is irrelevant to risk premia given exogenous returns if and only if all agents have additively separable preferences. It is irrelevant to risk premia given endogenous returns if and only if all agents have identical, time-additive power utility and cross-sectional risk is uncorrelated with aggregate consumption risk. The framework admits explicit asset pricing solutions that directly apply to a broad set of economic settings. The applicability of the framework is demonstrated in a general equilibrium model with recursive-utility agents who can invest in a riskfree bond, the stock market, and their own inalienable human capital, which is subject to risk of an idiosyncratic disaster.