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High dimensional Global Minimum Variance Portfolio

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  • Li, Hua
  • Bai, Zhi Dong
  • Wong, Wing Keung

Abstract

This paper proposes the spectral corrected methodology to estimate the Global Minimum Variance Portfolio (GMVP) for the high dimensional data. In this paper, we analysis the limiting properties of the spectral corrected GMVP estimator as the dimension and the number of the sample set increase to infinity proportionally. In addition, we compare the spectral corrected estimation with the linear shrinkage and nonlinear shrinkage estimations and obtain that the performance of the spectral corrected methodology is best in the simulation study.

Suggested Citation

  • Li, Hua & Bai, Zhi Dong & Wong, Wing Keung, 2015. "High dimensional Global Minimum Variance Portfolio," MPRA Paper 66284, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:66284
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    File URL: https://mpra.ub.uni-muenchen.de/66284/1/MPRA_paper_66284.pdf
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    References listed on IDEAS

    as
    1. Dominik Wied & Daniel Ziggel & Tobias Berens, 2013. "On the application of new tests for structural changes on global minimum-variance portfolios," Statistical Papers, Springer, vol. 54(4), pages 955-975, November.
    2. Taras Bodnar & Wolfgang Schmid, 2008. "A test for the weights of the global minimum variance portfolio in an elliptical model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(2), pages 127-143, March.
    3. repec:hal:journl:peer-00741629 is not listed on IDEAS
    4. Frahm, Gabriel & Memmel, Christoph, 2010. "Dominating estimators for minimum-variance portfolios," Journal of Econometrics, Elsevier, vol. 159(2), pages 289-302, December.
    5. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
    6. 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.
    7. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    8. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    9. Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
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    Cited by:

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    More about this item

    Keywords

    Global Minimum Variance Portfolio; Spectral Corrected Covariance; Sample Covariance;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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