RT Journal Article
SR Electronic
T1 The Gerber Statistic: A Robust Co-Movement Measure for Portfolio Optimization
JF The Journal of Portfolio Management
FD Institutional Investor Journals
SP 87
OP 102
DO 10.3905/jpm.2021.1.316
VO 48
IS 3
A1 Sander Gerber
A1 Harry M. Markowitz
A1 Philip A. Ernst
A1 Yinsen Miao
A1 Babak Javid
A1 Paul Sargen
YR 2022
UL https://pm-research.com/content/48/3/87.abstract
AB 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.