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Estimation of the global minimum variance portfolio in high dimensions

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  • Bodnar, Taras
  • Parolya, Nestor
  • Schmid, Wolfgang

Abstract

We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and optimal in the sense of minimizing the out-of-sample variance. Its asymptotic properties are investigated assuming that the number of assets p depends on the sample size n such that pn→c∈(0,+∞) as n tends to infinity. The results are obtained under weak assumptions imposed on the distribution of the asset returns: only the existence of the fourth moments is required. Furthermore, we make no assumption on the upper bound of the spectrum of the covariance matrix. As a result, the theoretical findings are also valid if the dependencies between the asset returns are described by a factor model which appears to be very popular in the financial literature nowadays. This is also documented in a numerical study where the small- and large-sample behavior of the derived estimator is compared with existing estimators of the GMV portfolio. The resulting estimator shows significant improvements and it turns out to be robust if the assumption of normality is violated.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:266:y:2018:i:1:p:371-390
    DOI: 10.1016/j.ejor.2017.09.028
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    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Taras Bodnar & Yarema Okhrin & Nestor Parolya, 2016. "Optimal shrinkage-based portfolio selection in high dimensions," Papers 1611.01958, arXiv.org, revised Jul 2018.
    2. Taras Bodnar & Holger Dette & Nestor Parolya & Erik Thors'en, 2019. "Sampling Distributions of Optimal Portfolio Weights and Characteristics in Low and Large Dimensions," Papers 1908.04243, arXiv.org, revised Aug 2019.
    3. repec:gam:jrisks:v:7:y:2019:i:2:p:56-:d:231435 is not listed on IDEAS
    4. 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, arXiv.org, revised Jul 2019.
    5. 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.
    6. repec:gam:jjrfmx:v:12:y:2019:i:1:p:48-:d:216804 is not listed on IDEAS
    7. repec:kap:iaecre:v:25:y:2019:i:3:d:10.1007_s11294-019-09746-3 is not listed on IDEAS
    8. Bauder, David & Bodnar, Taras & Mazur, Stepan & Okhrin, Yarema, 2018. "Bayesian inference for the tangent portfolio," Working Papers 2018:2, Örebro University, School of Business.
    9. repec:eee:jmvana:v:170:y:2019:i:c:p:63-79 is not listed on IDEAS
    10. repec:wsi:jecxxx:v:26:y:2018:i:03:n:s0219024918500541 is not listed on IDEAS
    11. Bodnar, Taras & Okhrin, Ostap & Parolya, Nestor, 2019. "Optimal shrinkage estimator for high-dimensional mean vector," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 63-79.

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