This paper explores the ability of theoretically-based asset pricing models, such as the Capital Asset Pricing Model (CAPM) and the Consumption CAPM (CCAPM), to explain the cross-section of average stock returns. Unlike previous empirical tests, the authors specify the pricing kernel as a conditional linear factor model, assuming that risk premia vary over time. Central to their approach is the use of a conditioning variable that proxies for fluctuations in the log consumption-aggregate wealth ratio, which is expected to summarize conditional expectations of excess returns. The authors find that such conditional factor models can explain a substantial fraction of the cross-sectional variation in portfolio returns, performing better than unconditional (C)CAPM specifications and comparable to the three-factor Fama-French model on portfolios sorted by size and book-to-market ratios. The scaled multifactor consumption CAPM, using aggregate consumption data, accounts for the difference in returns between low and high book-to-market firms and exhibits little evidence of residual size or book-to-market effects. The choice of conditioning variable is crucial, and the authors find that movements in $cay$ (the difference between log consumption and a weighted average of log asset wealth and log labor income) are a good proxy for movements in the consumption-aggregate wealth ratio. The paper concludes by discussing the implications of these findings for the value premium and the role of human capital in asset pricing.This paper explores the ability of theoretically-based asset pricing models, such as the Capital Asset Pricing Model (CAPM) and the Consumption CAPM (CCAPM), to explain the cross-section of average stock returns. Unlike previous empirical tests, the authors specify the pricing kernel as a conditional linear factor model, assuming that risk premia vary over time. Central to their approach is the use of a conditioning variable that proxies for fluctuations in the log consumption-aggregate wealth ratio, which is expected to summarize conditional expectations of excess returns. The authors find that such conditional factor models can explain a substantial fraction of the cross-sectional variation in portfolio returns, performing better than unconditional (C)CAPM specifications and comparable to the three-factor Fama-French model on portfolios sorted by size and book-to-market ratios. The scaled multifactor consumption CAPM, using aggregate consumption data, accounts for the difference in returns between low and high book-to-market firms and exhibits little evidence of residual size or book-to-market effects. The choice of conditioning variable is crucial, and the authors find that movements in $cay$ (the difference between log consumption and a weighted average of log asset wealth and log labor income) are a good proxy for movements in the consumption-aggregate wealth ratio. The paper concludes by discussing the implications of these findings for the value premium and the role of human capital in asset pricing.