Stochastic models with economywide shocks imply that the welfare costs of aggregate volatility are negligible. Empirical evidence suggests that the volatility of idiosyncratic shocks is several times that of aggregate shocks. This paper introduces both types of shocks. We find that if in the process of eliminating aggregate risk the policymaker can reduce idiosyncratic risk by an amount suggested by available empirical evidence, the welfare gains from stabilization can become significant. The introduction of idiosyncratic risk has important implications for asset pricing, and in particular may reduce the risk-free rate substantially, through the precautionary savings motive. Many of our results are sensitive both to the degree of risk aversion and to the flexibility of labor supply. The paper highlights the trade-offs involved in analyzing the effects of risk on growth and welfare and on asset pricing, clarifying the need to examine these issues within a unified stochastic general equilibrium framework.