Dominating estimators for the global minimum variance portfolio

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 are derived. 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 and also their large-sample properties for fixed d but n -> infinity as well as n,d -> infinity but n/d -> q <= infinity are investigated. Further, a small-sample test for the question whether it is better to completely ignore time series information in favor of naive diversification is presented.