A Large-Dimensional Test for Cross-Sectional Anomalies: Efficient Sorting Revisited
47 Pages Posted: 15 Apr 2020 Last revised: 23 Feb 2023
Date Written: July 10, 2021
Many researchers seek factors that predict the cross-section of stock returns. In finance, the key is to replicate anomalies by long-short portfolios based on their factor scores, with microcaps alleviated via New York Stock Exchange (NYSE) breakpoints and value-weighted returns. In econometrics, the key is to include a covariance matrix estimator of stock returns for the (mimicking) portfolio construction. This paper marries these two strands of literature in order to test the zoo of cross-sectional anomalies by injecting size controls, basically NYSE breakpoints and value-weighted returns, into efficient sorting. Thus, we propose to use a covariance matrix estimator for ultra-high dimensions (up to 5,000) taking into account large, small and microcap stocks. We demonstrate that using a nonlinear shrinkage estimator of the covariance matrix substantially enhances the power of tests for cross-sectional anomalies: On average, ‘Student’ t-statistics more than double.
Keywords: Anomalies, cross-section of returns, efficient sorting, large dimensions, Markowitz portfolio selection, nonlinear shrinkage
JEL Classification: C13, C58, G11
Suggested Citation: Suggested Citation