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Linear statistical inference for global and local minimum variance portfolios


  • Frahm, Gabriel


Traditional portfolio optimization has been often criticized since it does not account for estimation risk. Theoretical considerations indicate that estimation risk is mainly driven by the parameter uncertainty regarding the expected asset returns rather than their variances and covariances. This is also demonstrated by several numerical studies. The global minimum variance portfolio has been advocated by many authors as an appropriate alternative to the traditional Markowitz approach since there are no expected asset returns which have to be estimated and thus the impact of estimation errors can be substantially reduced. But in many practical situations an investor is not willing to choose the global minimum variance portfolio, especially in the context of top down portfolio optimization. In that case the investor has to minimize the variance of the portfolio return by satisfying some specific constraints for the portfolio weights. Such a portfolio will be called 'local minimum variance portfolio'. Some finite sample hypothesis tests for global and local minimum variance portfolios are presented as well as the unconditional finite sample distribution of the estimated portfolio weights and the first two moments of the estimated expected portfolio returns.

Suggested Citation

  • Frahm, Gabriel, 2007. "Linear statistical inference for global and local minimum variance portfolios," Discussion Papers in Econometrics and Statistics 1/07, University of Cologne, Institute of Econometrics and Statistics.
  • Handle: RePEc:zbw:ucdpse:107

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    References listed on IDEAS

    1. Klein, Roger W. & Bawa, Vijay S., 1976. "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics, Elsevier, vol. 3(3), pages 215-231, June.
    2. 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.
    3. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
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    Cited by:

    1. Alexander Bade & Gabriel Frahm & Uwe Jaekel, 2009. "A general approach to Bayesian portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 337-356, October.


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