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Multivariate Shrinkage for Optimal Portfolio Weights


  • Vasyl Golosnoy
  • Yarema Okhrin


This paper proposes a multivariate shrinkage estimator for the optimal portfolio weights. The estimated classical Markowitz weights are shrunk to the deterministic target portfolio weights. Assuming log asset returns to be i.i.d. Gaussian, explicit solutions are derived for the optimal shrinkage factors. The properties of the estimated shrinkage weights are investigated both analytically and using Monte Carlo simulations. The empirical study compares the competing portfolio selection approaches. Both simulation and empirical studies show that the proposed shrinkage estimator is robust and provides significant gains to the investor compared to benchmark procedures.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:eurjfi:v:13:y:2007:i:5:p:441-458
    DOI: 10.1080/13518470601137592

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    Cited by:

    1. repec:eee:ejores:v:266:y:2018:i:1:p:371-390 is not listed on IDEAS
    2. Taras Bodnar & Yarema Okhrin & Nestor Parolya, 2016. "Optimal shrinkage-based portfolio selection in high dimensions," Papers 1611.01958,, revised May 2017.
    3. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2018. "Estimation of the global minimum variance portfolio in high dimensions," European Journal of Operational Research, Elsevier, vol. 266(1), pages 371-390.
    4. Sourish Das & Aritra Halder & Dipak K. Dey, 2014. "Regularizing Portfolio Risk Analysis: A Bayesian Approach," Papers 1404.3258,, revised Oct 2015.
    5. Fabio Caccioli & Imre Kondor & G'abor Papp, 2015. "Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error," Papers 1510.04943,
    6. 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.
    7. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2014. "$L_p$ regularized portfolio optimization," Papers 1404.4040,
    8. Imre Kondor & G'abor Papp & Fabio Caccioli, 2017. "Analytic approach to variance optimization under an $\ell_1$ constraint," Papers 1709.08755,
    9. Imre Kondor, 2014. "Estimation Error of Expected Shortfall," Papers 1402.5534,
    10. Yarema Okhrin & Wolfgang Schmid, 2007. "Comparison of different estimation techniques for portfolio selection," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 91(2), pages 109-127, August.
    11. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2016. "Liquidity Risk And Instabilities In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-28, August.
    12. Taras Bodnar & Solomiia Dmytriv & Nestor Parolya & Wolfgang Schmid, 2017. "Tests for the weights of the global minimum variance portfolio in a high-dimensional setting," Papers 1710.09587,, revised Nov 2017.
    13. Bodnar, Taras & Mazur, Stepan & Okhrin, Yarema, 2017. "Bayesian estimation of the global minimum variance portfolio," European Journal of Operational Research, Elsevier, vol. 256(1), pages 292-307.
    14. Takuya Kinkawa & Nobuo Shinozaki, 2010. "Dominance of a Class of Stein type Estimators for Optimal Portfolio Weights When the Covariance Matrix is Unknown," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 17(1), pages 19-50, March.
    15. Li, Hua & Bai, Zhi Dong & Wong, Wing Keung, 2015. "High dimensional Global Minimum Variance Portfolio," MPRA Paper 66284, University Library of Munich, Germany.
    16. repec:hal:journl:peer-00741629 is not listed on IDEAS
    17. Bauder, David & Bodnar, Taras & Mazur, Stepan & Okhrin, Yarema, 2018. "Bayesian inference for the tangent portfolio," Working Papers 2018:2, Örebro University, School of Business.
    18. Golosnoy, Vasyl & Okhrin, Yarema, 2009. "Flexible shrinkage in portfolio selection," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 317-328, February.
    19. Frahm, Gabriel & Memmel, Christoph, 2010. "Dominating estimators for minimum-variance portfolios," Journal of Econometrics, Elsevier, vol. 159(2), pages 289-302, December.
    20. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679,
    21. Golosnoy, Vasyl & Okhrin, Yarema, 2008. "General uncertainty in portfolio selection: A case-based decision approach," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 718-734, September.
    22. Varga-Haszonits, Istvan & Caccioli, Fabio & Kondor, Imre, 2016. "Replica approach to mean-variance portfolio optimization," LSE Research Online Documents on Economics 68955, London School of Economics and Political Science, LSE Library.
    23. G'abor Papp & Fabio Caccioli & Imre Kondor, 2016. "Fluctuation-bias trade-off in portfolio optimization under Expected Shortfall with $\ell_2$ regularization," Papers 1602.08297,
    24. Imre Kondor & G'abor Papp & Fabio Caccioli, 2016. "Analytic solution to variance optimization with no short-selling," Papers 1612.07067,, revised Jan 2017.


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