Risk Prices Vary in the Cross Section

We introduce new methods for cross-sectional asset pricing with unobserved heterogeneity in compensation for risk. We develop an expectation maximization approach to group assets by risk prices, extending the k-means clustering approach, and a formal test for whether di erences 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 135 combinations of test assets, factor models, and time periods. Variation in risk prices is comparably important to variation in risk exposures for explaining the cross-section of expected returns. JEL: G12, G14, C21, C55