Beta-Sorted Portfolios

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 econometric 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 rationalizes the well-known estimation algorithm with precise economic and statistical assumptions on the general data generating process. We provide conditions which ensure valid estimation and inference allowing for a range of hypotheses of interest in financial applications. We show that the rate of convergence of the estimator changes depending on the value of beta. We demonstrate that valid inference depends critically on the object of interest and discuss shortcomings of the widely-used Fama-MacBeth variance estimator. To address these limitations, we propose a new variance estimator. In an empirical application, we introduce a novel risk factor—a measure of the business credit cycle—and show that it is strongly predictive of both the cross-section and time-series behavior of U.S. stock returns.