Beta-Sorted Portfolios

Matias D. Cattaneo, Richard K. Crump, Weining Wang

The framework

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 rationalises 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 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 conservative in general, and can lead to substantial power loss in empirically-relevant settings. We propose a new variance estimator which is always consistent and provide an empirical implementation which produces more powerful inference. 

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.

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