Dominating estimators for the global minimum variance portfolio

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