Dominating estimators for the global minimum variance portfolio

Gabriel Frahm and Christoph Memmel

No 2/08, Discussion Papers in Econometrics and Statistics from University of Cologne, Institute of Econometrics and Statistics

Abstract: 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 → ∞ 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.

Keywords: Covariance matrix estimation; Global minimum variance portfolio; James-Stein estimation; Naive diversification; Shrinkage estimator (search for similar items in EconPapers)
JEL-codes: C13 G11 (search for similar items in EconPapers)
Date: 2008
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Related works:
Working Paper: Dominating estimators for the global minimum variance portfolio (2009)
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