A risk perspective of estimating portfolio weights of the global minimum-variance portfolio

Abstract

The problem of how to determine portfolio weights so that the variance of portfolio returns is minimized has been given considerable attention in the literature, and several methods have been proposed. Some properties of these estimators, however, remain unknown, and many of their relative strengths and weaknesses are therefore difficult to assess for users. This paper contributes to the field by comparing and contrasting the risk functions used to derive efficient portfolio weight estimators. It is argued that risk functions commonly used to derive and evaluate estimators may be inadequate and that alternative quality criteria should be considered instead. The theoretical discussions are supported by a Monte Carlo simulation and two empirical applications where particular focus is set on cases where the number of assets (p) is close to the number of observations (n). Keywords Global minimum-variance portfolio • Portfolio theory • High dimensional • Risk functions JEL Classification C13 • C18 • C44 • G11 We thank two anonymous reviewers for their insightful comments and helpful suggestions and the session participants at the German Statistical Society conference in Augsburg 2016 and those attending the seminar at the European University Viadrina in January 2017 for useful suggestions. The usual disclaimer applies.

Statistical Inference for the Expected Utility Portfolio in High Dimensions

“…Moreover, the rejection of the null hypothesis in (40) ensures the rejection of the null hypothesis in (36) meaning that w 0 is not the EU optimal portfolio. Let α * c (w 0 ) be the consistent estimator of α * (w 0 ) as constructed in (25) when the shrinkage target is b = w 0 . Then the application of Theorem 2 shows that…”

“…Similarly as in the low-dimensional case, the first line of the research deals with deriving improved estimators for the mean vector and the covariance matrix of asset returns. These are used to obtain improved plug-in estimators of the optimal portfolio weights (see, [24], [25]). The second possibility is to improve the estimators of the optimal portfolio weights directly.…”

Statistical inference for the EU portfolio in high dimensions

“…Similarly as in the low-dimensional case, the first line of the research deals with deriving improved estimators for the mean vector and the covariance matrix of asset returns. These are used to obtain improved plug-in estimators of the optimal portfolio weights (see, Ledoit and Wolf (2017), Holgersson et al (2020)). The second possibility is to improve the estimators of the optimal portfolio weights directly.…”