Agents who place greater weight on the risk of downside losses than they are attach to upside gains demand greater compensation for holding stocks with high downside risk. We show that the cross-section of stock returns reflects a premium for downside risk. Stocks that covary strongly with the market when the market declines have high average returns. We estimate that the downside risk premium is approximately 6% per annum and demonstrate that the compensation for bearing downside risk is not simply compensation for market beta. Moreover, the reward for downside risk is not subsumed by coskewness or liquidity risk, and is robust to controlling for momentum and other cross-sectional effects.