Dominating estimators for minimum-variance portfolios

In this paper, we derive two shrinkage estimators for minimum-variance portfolios 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 assets d≥4$d\ge 4$ and number of observations n≥d+2$n\ge d+2$. The small-sample properties of the shrinkage estimators as well as their large-sample properties for fixed d$d$ but n→∞$n\to \infty$ and n,d→∞$n,d\to \infty$ but n/d→q≤∞$n/d\to q\le \infty$ 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.