This paper examines the effects of time-varying volatility on welfare. I construct a tractable endogenous growth model with recursive preferences, stochastic volatility, and capital adjustment costs. The model shows that a rise in volatility can decelerate growth in the absence of any level shocks. In contrast to level risk, which is always welfare reducing for a risk-averse household, volatility risk can increase or decrease welfare, depending on model parameters. When calibrated to U.S. data, the model finds that the welfare cost of volatility risk is largely negligible under plausible model parameterizations.