The Gerber Statistic: A Robust Co-Movement Measure for Portfolio Optimization
介绍Gerber统计量，一种稳健的协同变动度量，用于估计协方差矩阵以构建投资组合。它通过计数序列中超过数据依赖阈值的同步协同变动比例，不受极端值影响，特别适合含噪声和极端波动的金融时间序列。实证表明，在30年九资产组合中，其收益优于历史协方差和Ledoit-Wolf收缩法。
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 <i>historical covariance matrix</i>) 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.