Using a flexible modeling approach that avoids imposing restrictive parametric assumptions, we find evidence of a clear non-monotonic relation between conditional volatility and expected stock returns: At low-to-medium levels of conditional volatility there is a positive trade-off between risk and expected returns, but this relationship gets inverted at high levels of conditional volatility as observed during the recent financial crisis. We next propose a novel measure of risk based on the conditional covariance between daily observations on a broad economic activity index and stock returns. Using this measure, we find clear evidence of a monotonically increasing risk-return trade-off. Our finding that the conditional volatility-expected return relation is non-monotonic, while the conditional covariance-expected return is monotonically rising helps explain why some empirical studies find a negative risk-return relation, while others find a positive risk-return trade-off and also suggests that a positive risk-return relationship can be established once a better measure of risk is used.