What is the Shape of the Risk-Return Relation?†

Using a novel and flexible regression approach that avoids imposing restrictive modeling assumptions, we find evidence of a nonmonotonic relation between conditional volatility and expected stock market returns. At low and medium levels of conditional volatility there is a positive risk-return trade-off, but this relation is inverted at high levels of volatility. This finding helps explain the absence of a consensus in the empirical literature on the sign of the risk-return trade-off. We propose a new measure of risk based on the conditional covariance between observations of a broad economic activity index and stock market returns. Using this broader covariancebased risk measure, we find clear evidence of a positive and monotonic risk-return trade-off.