This paper studies the importance of idiosyncratic endowment shocks for aggregate asset prices in a generalized continuous-time framework that accommodates both jumps and recursive preferences. I show that, regardless of the presence of jumps, counter-cyclical cross-sectional risk is irrelevant to risk premia if and only if (i) all agents have time-additive power utility and (ii) cross-sectional risk is uncorrelated with aggregate consumption risk. To quantify the relevance of these conditions, I calibrate a general-equilibrium model with a continuum of recursive-utility agents who face uninsurable idiosyncratic human-capital disasters. The model explains both asset pricing moments and cross-sectional income moments from Social Security Administration income data.