Economists have long recognized that investors care differently about downside losses versus upside gains. Agents who place greater weight on downside risk demand additional compensation for holding stocks with high sensitivities to downside market movements. We show that the cross-section of stock returns reflects a premium for downside risk. Specifically, 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. The reward for bearing downside risk is not simply compensation for regular market beta, nor is it explained by coskewness or liquidity risk, or size, book-to-market, and momentum characteristics.