Beta-Sorted Portfolios

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 rationalizes the well-known estimation algorithm with precise economic and statistical assumptions on the general data generating process. We provide conditions that ensure consistency and asymptotic normality along with new uniform inference procedures allowing for uncertainty quantification and general hypothesis testing for financial applications. We show that the rate of convergence of the estimator is non-uniform and depends on the beta value of interest. We also show that the widely used Fama-MacBeth variance estimator is asymptotically valid but is conservative in general and can be very conservative in empirically relevant settings. We propose a new variance estimator, which is always consistent and provide an empirical implementation which produces valid inference. In our 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.