This paper analyzes a class of stochastic endogenous growth models with uninsurable idiosyncratic income risk. The model economy is populated by infinitely-lived households who own and operate their own business, work for a stock company, and participate in stock and bond markets. Households have time- and state-additive log-utility preferences and production functions exhibit constant returns to scale with respect to produced input factors (physical and human capital). This paper shows that if the idiosyncratic component of productivity and depreciation shocks is unpredictable, then there exists an equilibrium in which households choose not to trade bonds. This no-trade result implies that equilibria can be found by solving a one-agent decision problem. The paper also analyzes the asset return implications of a calibrated model economy with an individual income process that displays realistic variations in idiosyncratic income risk. The calibrated model economy generates a sizable mean equity premium (1%) if the volatility of implied stock returns matches the volatility of observed U.S. stock returns.