Dominating estimators for the global minimum variance portfolio
by Gabriel Frahm ; Christoph Memmel
In this paper, we derive two shrinkage estimators for the global minimum variance portfolio that dominate the traditional estimator with respect to the out-of-sample variance of the portfolio return. The presented results hold for any number of observations n >= d + 2 and number of assets d >= 4 . The small-sample properties of the shrinkage estimators as well as their large-sample properties for fixed d but n --> as well as n/ d ! 1 but n/d -->q <= are investigated. Furthermore, we present a small-sample test for the question of whether it is better to completely ignore time series information in favor of naive diversification. -- Covariance matrix estimation ; Global minimum variance portfolio ; James-Stein estimation ; Naive diversification ; Shrinkage estimator