Dominating Estimators for the Global Minimum Variance Portfolio

Gabriel Frahm, Christoph Memmel
2008 Social Science Research Network  
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more » ... von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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. 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. JEL classification: C13, G11. We would like to thank Alexander Kempf and Julia Nasev for their helpful comments on the manuscript. The opinions expressed in this paper are those of the authors and do not necessarily reflect the opinions of the Deutsche Bundesbank. †
doi:10.2139/ssrn.1272969 fatcat:7spofpr53bbsdbawuwiac77aym