Characteristic-Sorted Portfolios: Estimation and Inference

Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies. Despite its popularity, little attention has been paid to the statistical properties of the procedure. We develop a general framework for portfolio sorting by casting it as a nonparametric estimator. We present valid asymptotic inference methods and a valid mean square error expansion of the estimator leading to an optimal choice for the number of portfolios. In practical settings, the optimal choice may be much larger than the standard choices of five or ten. To illustrate the relevance of our results, we revisit the size and momentum anomalies.