Authors: Matias D. Cattaneo, Richard K. Crump, Yingjie Feng, and Weining Wang
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Staff Reports
Beta-Sorted Portfolios
Number 1068
July 2023 Revised September 2026
July 2023 Revised September 2026
JEL classification: C14, C12, G12
Beta-sorted portfolios—portfolios comprised of assets with similar covariation with 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 portfolio 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 drawbacks of the widely used Fama-MacBeth variance estimator. To address these limitations, we propose a new variance estimator. We demonstrate the usefulness of our theoretical results in two empirical applications, including one in which we introduce a novel risk factor that captures the business credit cycle and show that it predicts both the cross-sectional and time-series behavior of U.S. stock returns.
Author Disclosure Statement(s)
Matias D. Cattaneo
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Beta-Sorted Portfolios,” joint with Richard Crump and Weining Wang.
Richard K. Crump
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Beta-Sorted Portfolios,” joint with Matias Cattaneo and Weining Wang.
Weining Wan
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Beta-Sorted Portfolios,” joint with Matias Cattaneo and Richard Crump.
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Beta-Sorted Portfolios,” joint with Richard Crump and Weining Wang.
Richard K. Crump
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Beta-Sorted Portfolios,” joint with Matias Cattaneo and Weining Wang.
Weining Wan
I declare that I have no relevant or material financial interests that relate to the research described in my paper entitled “Beta-Sorted Portfolios,” joint with Matias Cattaneo and Richard Crump.
Suggested Citation:
Cattaneo, Matias, Richard K. Crump, Yingjie Feng, and Weining Wang. 2023. “Beta-Sorted Portfolios.” Federal Reserve Bank of New York Staff Reports, no. 1068, revised September 2026. https://doi.org/10.59576/sr.1068
Cattaneo, Matias, Richard K. Crump, Yingjie Feng, and Weining Wang. 2023. “Beta-Sorted Portfolios.” Federal Reserve Bank of New York Staff Reports, no. 1068, revised September 2026. https://doi.org/10.59576/sr.1068
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