Focused Shrinkage Estimators for the Global Minimum Variance Portfolio

Abstract

We propose a shrinkage estimator for covariance matrices designed to minimize estimation error of the Global Minimum Variance (GMV) portfolio. Implementing the GMV portfolio requires estimating the asset covariance matrix and using this to obtain variance-minimizing portfolio weights. Standard estimation approaches for this application utilize shrinkage. These estimators use shrinkage weights that are not designed to directly minimize estimation error of the final object of interest: GMV portfolio weights. We develop a focused shrinkage approach to the problem. This method utilizes the form of the trading rule to derive a shrinkage estimator that directly controls estimation error of GMV portfolio weights. Extensive simulations are conducted to compare performance with nine standard competitors. Our estimator uniformly outperformed all competitors across portfolios of various sizes. The methods are applied to several standard portfolios of US and international assets. Similar improvements are found. Our estimator achieves the smallest out-of-sample portfolio variance in 25 of 28 data sets considered.