The Gerber Statistic: A Robust Co-Movement Measure for Portfolio Optimization

22 Pages Posted: 19 Jul 2021

See all articles by Sander Gerber

Sander Gerber

Hudson Bay Capital Management, LP

Harry Markowitz

University of California at San Diego

Philip Ernst

Rice University

Yinsen Miao

Fidelity Investments, Inc.

Babak Javid

Hudson Bay Capital Management, LP

Paul Sargen

Hudson Bay Capital Management, LP

Date Written: July 4, 2021

Abstract

The purpose of this paper is to introduce the Gerber statistic, a robust co-movement measure for covariance matrix estimation for the purpose of portfolio construction. The Gerber statistic extends Kendall's Tau by counting the proportion of simultaneous co-movements in series when their amplitudes exceed data-dependent thresholds. Since the statistic is neither affected by extremely large or extremely small movements, it is especially well-suited for financial time series, which often exhibit extreme movements as well as a great amount of noise. Operating within the mean-variance portfolio optimization framework of Markowitz (1952,1959) we consider the performance of the Gerber statistic against two other commonly used methods for estimating the covariance matrix of stock returns: the sample covariance matrix (also called the historical covariance matrix) and shrinkage of the sample covariance matrix as formulated in Ledoit and Wolf (2004). Using a well-diversified portfolio of nine assets over a thirty year time period (January 1990-December 2020), we empirically find that, for almost all scenarios considered, the Gerber statistic's returns dominate those achieved by both historical covariance and by the shrinkage method of Ledoit and Wolf (2004).

Keywords: Gerber statistic, co-movement; robust covariance estimation, Markowitz mean-variance optimization, shrinkage method, historical covariance

JEL Classification: C13, C61, G11

Suggested Citation

Gerber, Sander and Markowitz, Harry and Ernst, Philip and Miao, Yinsen and Javid, Babak and Sargen, Paul, The Gerber Statistic: A Robust Co-Movement Measure for Portfolio Optimization (July 4, 2021). Available at SSRN: https://ssrn.com/abstract=3880054 or http://dx.doi.org/10.2139/ssrn.3880054

Sander Gerber (Contact Author)

Hudson Bay Capital Management, LP ( email )

777 Third Avenue
New York, NY NY 10017
United States

Harry Markowitz

University of California at San Diego ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
(858) 534-3383 (Phone)

Philip Ernst

Rice University ( email )

6100 South Main Street
Houston, TX 77005-1892
United States

Yinsen Miao

Fidelity Investments, Inc. ( email )

United States

Babak Javid

Hudson Bay Capital Management, LP ( email )

777 Third Avenue
New York, NY NY 10017
United States

Paul Sargen

Hudson Bay Capital Management, LP ( email )

777 Third Avenue
New York, NY NY 10017
United States

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