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

Sander Gerber, Harry M. Markowitz, Philip A. Ernst, Yinsen Miao, Babak Javid and Paul Sargen
The Journal of Portfolio Management February 2022, jpm.2021.1.316; DOI: https://doi.org/10.3905/jpm.2021.1.316
Sander Gerber
is chief executive officer at Hudson Bay Capital Management in New York, NY
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Harry M. Markowitz
is an adjunct professor of finance and accounting at Rady School of Management at University of California in La Jolla, CA
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Philip A. Ernst
is an associate professor of statistics at Rice University in Houston, TX
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Yinsen Miao
is a senior data scientist at Fidelity Investments in Boston, MA
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Babak Javid
is a senior analyst at Hudson Bay Capital Management in New York, NY
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Paul Sargen
is chief risk officer at Hudson Bay Capital Management in New York, NY
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Abstract

The purpose of this article 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. Because the statistic is not affected by extremely large or extremely small movements, it is especially well suited for financial time series, which often exhibit extreme movements and a great amount of noise. Operating within the mean–variance portfolio optimization framework of Markowitz, 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 given by Ledoit and Wolf. Using a well-diversified portfolio of nine assets over a 30-year period (January 1990–December 2020), we find, empirically, that for almost all investment scenarios considered, the Gerber statistic’s returns dominate those achieved by both historical covariance and by the shrinkage method of Ledoit and Wolf.

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The Journal of Portfolio Management: 48 (5)
The Journal of Portfolio Management
Vol. 48, Issue 5
April 2022
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The Gerber Statistic: A Robust Co-Movement Measure for Portfolio Optimization
Sander Gerber, Harry M. Markowitz, Philip A. Ernst, Yinsen Miao, Babak Javid, Paul Sargen
The Journal of Portfolio Management Dec 2021, jpm.2021.1.316; DOI: 10.3905/jpm.2021.1.316

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The Gerber Statistic: A Robust Co-Movement Measure for Portfolio Optimization
Sander Gerber, Harry M. Markowitz, Philip A. Ernst, Yinsen Miao, Babak Javid, Paul Sargen
The Journal of Portfolio Management Dec 2021, jpm.2021.1.316; DOI: 10.3905/jpm.2021.1.316
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  • Article
    • Abstract
    • THE GERBER STATISTIC
    • EMPIRICAL STUDY
    • EMPIRICAL RESULTS
    • CONCLUSION
    • ACKNOWLEDGMENTS
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