Beta-Sorted Portfolios

TL;DR

This paper analyzes the statistical properties of beta-sorted portfolios, providing a formal framework, consistency conditions, and new inference procedures to improve empirical finance research.

Contribution

It introduces a nonparametric two-step estimator framework for beta-sorted portfolios, with methods for inference and hypothesis testing, addressing limitations of current practices.

Findings

Beta-sorted portfolios are shown to be consistent under certain conditions.

New uniform inference procedures enable uncertainty quantification.

Limitations of empirical practices are highlighted and addressed.

Abstract

Beta-sorted portfolios -- portfolios comprised of assets with similar covariation to selected risk factors -- are a popular tool in empirical finance to analyze models of (conditional) expected returns. Despite their widespread use, little is known of their statistical properties in contrast to comparable procedures such as two-pass regressions. We formally investigate the properties of beta-sorted portfolio returns by casting the procedure as a two-step nonparametric estimator with a nonparametric first step and a beta-adaptive portfolios construction. Our framework rationalize the well-known estimation algorithm with precise economic and statistical assumptions on the general data generating process and characterize its key features. We study beta-sorted portfolios for both a single cross-section as well as for aggregation over time (e.g., the grand mean), offering conditions that ensure consistency and asymptotic normality along with new uniform inference procedures allowing for uncertainty quantification and testing of various relevant hypotheses in financial applications. We also highlight some limitations of current empirical practices and discuss what inferences can and cannot be drawn from returns to beta-sorted portfolios for either a single cross-section or across the whole sample. Finally, we illustrate the functionality of our new procedures in an empirical application.