Dominating Estimators for the Global Minimum Variance Portfolio

44 Pages Posted: 8 Jun 2016

See all articles by Gabriel Frahm

Gabriel Frahm

Helmut Schmidt University

Christoph Memmel

Deutsche Bundesbank

Date Written: 2009

Abstract

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.

Keywords: Covariance matrix estimation, global minimum variance portfolio, James-Stein estimation, naive diversification, shrinkage estimator

JEL Classification: C13, G11

Suggested Citation

Frahm, Gabriel and Memmel, Christoph, Dominating Estimators for the Global Minimum Variance Portfolio (2009). Bundesbank Series 2 Discussion Paper No. 2009,01, Available at SSRN: https://ssrn.com/abstract=2794024 or http://dx.doi.org/10.2139/ssrn.2794024

Gabriel Frahm (Contact Author)

Helmut Schmidt University ( email )

Holstenhofweg 85
Hamburg, 22008
Germany
+49 40 6541-2791 (Phone)
+49 40 6541-2023 (Fax)

HOME PAGE: http://www.hsu-hh.de/stochastik/

Christoph Memmel

Deutsche Bundesbank ( email )

Wilhelm-Epstein-Str. 14
Frankfurt/Main, 60431
Germany

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