A Large-Dimensional Test for Cross-Sectional Anomalies: Efficient Sorting Revisited

44 Pages Posted: 15 Apr 2020 Last revised: 14 Oct 2020

See all articles by Gianluca De Nard

Gianluca De Nard

University of Zurich - Department of Banking and Finance

Zhao Zhao

Huazhong University of Science and Technology - Department of Economics

Date Written: March 24, 2020

Abstract

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

De Nard, Gianluca and Zhao, Zhao, A Large-Dimensional Test for Cross-Sectional Anomalies: Efficient Sorting Revisited (March 24, 2020). Available at SSRN: https://ssrn.com/abstract=3560178 or http://dx.doi.org/10.2139/ssrn.3560178

Gianluca De Nard (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Zürichbergstrasse 14
Zürich, Zürich CH-8032
Switzerland

HOME PAGE: http://denard.ch

Zhao Zhao

Huazhong University of Science and Technology - Department of Economics ( email )

Wuhan, Hubei 430074
China

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