Cross-sectional expected returns: new Fama–MacBeth regressions in the era of machine learning

Abstract

We extend the Fama–MacBeth regression framework for cross-sectional return prediction to incorporate big data and machine learning. Our extension involves a three-step procedure for generating return forecasts based on Fama–MacBeth regressions with regularization and predictor selection as well as forecast combination and encompassing. As a by-product, it provides estimates of characteristic payoffs. We also develop three performance measures for assessing cross-sectional return forecasts, including a generalization of the popular time-series out-of-sample R 2 statistic to the cross section. Applying our extension to over 200 firm characteristics, our cross-sectional return forecasts significantly improve out-of-sample predictive accuracy and provide substantial economic value to investors. Overall, our results suggest that a relatively large number of characteristics matter for determining cross-sectional expected returns. Our new method is straightforward to implement and interpret, and it performs well in our application.