IDEAS home Printed from
   My bibliography  Save this paper

Dominating estimators for the global minimum variance portfolio


  • Frahm, Gabriel
  • Memmel, Christoph


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.

Suggested Citation

  • Frahm, Gabriel & Memmel, Christoph, 2008. "Dominating estimators for the global minimum variance portfolio," Discussion Papers in Econometrics and Statistics 2/08, University of Cologne, Institute of Econometrics and Statistics.
  • Handle: RePEc:zbw:ucdpse:208

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Alexander Kempf & Christoph Memmel, 2006. "Estimating the global Minimum Variance Portfolio," Schmalenbach Business Review (sbr), LMU Munich School of Management, vol. 58(4), pages 332-348, October.
    2. Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 76-84, June.
    3. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
    4. Vasyl Golosnoy & Yarema Okhrin, 2007. "Multivariate Shrinkage for Optimal Portfolio Weights," The European Journal of Finance, Taylor & Francis Journals, vol. 13(5), pages 441-458.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Gabriel Frahm & Tobias Wickern & Christof Wiechers, 2012. "Multiple tests for the performance of different investment strategies," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 343-383, July.
    2. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2014. "$L_p$ regularized portfolio optimization," Papers 1404.4040,
    3. 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: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1105-1134, November.

    More about this item


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

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:ucdpse:208. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.