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Dominating estimators for the global minimum variance portfolio

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  • Frahm, Gabriel
  • Memmel, Christoph

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. --

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Bibliographic Info

Paper provided by University of Cologne, Department for Economic and Social Statistics in its series Discussion Papers in Statistics and Econometrics with number 2/08.

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Date of creation: 2008
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Handle: RePEc:zbw:ucdpse:208

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Keywords: Covariance matrix estimation; Global minimum variance portfolio; James-Stein estimation; Naive diversification; Shrinkage estimator;

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References

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  1. Vasyl Golosnoy & Yarema Okhrin, 2007. "Multivariate Shrinkage for Optimal Portfolio Weights," The European Journal of Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 13(5), pages 441-458.
  2. Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 2(02), pages 76-84, June.
  3. Alexander Kempf & Christoph Memmel, 2006. "Estimating the global Minimum Variance Portfolio," Schmalenbach Business Review (sbr), LMU Munich School of Management, LMU Munich School of Management, vol. 58(4), pages 332-348, October.
  4. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, Elsevier, vol. 134(1), pages 235-256, September.
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Cited by:
  1. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2014. "$L_p$ regularized portfolio optimization," Papers 1404.4040, arXiv.org.
  2. Taras Bodnar & Wolfgang Schmid & Taras Zabolotskyy, 2013. "Asymptotic behavior of the estimated weights and of the estimated performance measures of the minimum VaR and the minimum CVaR optimal portfolios for dependent data," Metrika, Springer, Springer, vol. 76(8), pages 1105-1134, November.
  3. Gabriel Frahm & Tobias Wickern & Christof Wiechers, 2012. "Multiple tests for the performance of different investment strategies," AStA Advances in Statistical Analysis, Springer, Springer, vol. 96(3), pages 343-383, July.

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