Characteristic-Sorted Portfolios: Estimation and Inference

53 Pages Posted: 15 Aug 2016 Last revised: 11 Jan 2018

See all articles by Matias D. Cattaneo

Matias D. Cattaneo

University of Michigan at Ann Arbor - Department of Economics

Richard K. Crump

Federal Reserve Banks - Federal Reserve Bank of New York

Max Farrell

University of Chicago - Booth School of Business - Econometrics and Statistics

Ernst Schaumburg

Federal Reserve Banks - Federal Reserve Bank of New York

Date Written: January 2018

Abstract

Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies in different asset classes. Despite the popularity of portfolio sorting, little attention has been paid to the statistical properties of the procedure or the conditions under which it produces valid inference. We develop a general, formal framework for portfolio sorting by casting it as a nonparametric estimator. We give precise conditions under which the portfolio-sorting estimator is consistent and asymptotically normal, and also establish consistency of both the Fama-MacBeth variance estimator and a new plug-in estimator. Our framework bridges the gap between portfolio sorting and cross-sectional regressions by allowing for linear conditioning variables when sorting. In addition, we obtain a valid mean square error expansion of the sorting estimator, which we employ to develop optimal choices for the number of portfolios. We show that the choice of the number of portfolios is crucial to drawing accurate conclusions from the data and we provide a simple, data-driven procedure that balances higher-order bias and variance. In many practical settings the optimal number of portfolios varies substantially across applications and subsamples and is, in many cases, much larger than the standard choices of five or ten portfolios used in the literature. We give formal and intuitive justifications for this finding based on the bias-variance trade-off underlying the portfolio sorting estimator. To illustrate the relevance of our results, we revisit the size and momentum anomalies..

Keywords: portfolio sorts, stock market anomalies, firm characteristics, nonparametric estimation, partitioning, cross-sectional regressions

JEL Classification: C12, C14

Suggested Citation

Cattaneo, Matias D. and Crump, Richard K. and Farrell, Max and Schaumburg, Ernst, Characteristic-Sorted Portfolios: Estimation and Inference (January 2018). FRB of NY Staff Report No. 788. Available at SSRN: https://ssrn.com/abstract=2822686

Matias D. Cattaneo (Contact Author)

University of Michigan at Ann Arbor - Department of Economics ( email )

611 Tappan Street
Ann Arbor, MI 48109-1220
United States
734-763-1306 (Phone)

HOME PAGE: http://www.umich.edu/~cattaneo/

Richard K. Crump

Federal Reserve Banks - Federal Reserve Bank of New York ( email )

33 Liberty Street
New York, NY 10045
United States

Max Farrell

University of Chicago - Booth School of Business - Econometrics and Statistics ( email )

Chicago, IL 60637
United States

Ernst Schaumburg

Federal Reserve Banks - Federal Reserve Bank of New York ( email )

33 Liberty Street
New York, NY 10045
United States

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