Characteristic-Sorted Portfolios: Estimation and Inference

TL;DR

This paper develops a statistical framework for portfolio sorting in empirical finance, providing inference methods and optimal portfolio number choices, which can significantly differ from traditional standards.

Contribution

It introduces a nonparametric estimator framework for portfolio sorting, with valid inference and optimal portfolio number selection, enhancing analysis of financial anomalies.

Findings

Optimal number of portfolios can be much larger than standard choices.

Provides valid asymptotic inference methods for portfolio sorting.

Revisits size and momentum anomalies with improved methodology.

Abstract

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 5 or 10. To illustrate the relevance of our results, we revisit the size and momentum anomalies.