Risk price variation : the missing half of empirical asset pricing

Equal compensation across assets for the same risk exposures is a bedrock of asset pricing theory and empirics. Yet real-world frictions can violate this equality and create high-Sharpe ratio opportunities. We develop new methods for asset pricing with cross-sectional heterogeneity in compensation for risk. We extend k-means clustering to group assets by risk prices and introduce a formal test for whether differences in risk premia across market segments are too large to occur by chance. Using portfolios of US stocks, international stocks, and assets from multiple classes, we find significant evidence of cross-sectional variation in risk prices for all 159 combinations of test assets, factor models, and time periods. Variation in risk prices is as important as variation in risk exposures for explaining the cross-section of expected returns