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Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach

Author

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  • Bertrand Maillet

    () (A.A.Advisors-QCG - ABN AMRO, LEDa - Laboratoire d'Economie de Dauphine - Université Paris-Dauphine)

  • Sessi Tokpavi

    () (EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • Benoit Vaucher

Abstract

The global minimum variance portfolio computed using the sample covariance matrix is known to be negatively affected by parameter uncertainty, an important component of model risk. Using a robust approach, we introduce a portfolio rule for investors who wish to invest in the global minimum variance portfolio due to its strong historical track record, but seek a rule that is robust to parameter uncertainty. Our robust portfolio corresponds theoretically to the global minimum variance portfolio in the worst-case scenario, with respect to a set of plausible alternative estimators of the covariance matrix, in the neighbourhood of the sample covariance matrix. Hence, it provides protection against errors in the reference sample covariance matrix. Monte Carlo simulations illustrate the dominance of the robust portfolio over its non-robust counterpart, in terms of portfolio stability, variance and risk-adjusted returns. Empirically, we compare the out-of-sample performance of the robust portfolio to various competing minimum variance portfolio rules in the literature. We observe that the robust portfolio often has lower turnover and variance and higher Sharpe ratios than the competing minimum variance portfolios.

Suggested Citation

  • Bertrand Maillet & Sessi Tokpavi & Benoit Vaucher, 2015. "Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach," Post-Print hal-01243408, HAL.
  • Handle: RePEc:hal:journl:hal-01243408
    DOI: 10.1016/j.ejor.2015.01.010
    Note: View the original document on HAL open archive server: http://hal.univ-reunion.fr/hal-01243408
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    1. repec:eee:ejores:v:266:y:2018:i:1:p:371-390 is not listed on IDEAS
    2. 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.
    3. Emmanouil Platanakis & Athanasios Sakkas & Charles Sutcliffe, 2017. "Harmful Diversification: Evidence from Alternative Investments," ICMA Centre Discussion Papers in Finance icma-dp2017-09, Henley Business School, Reading University.
    4. Chiu, Wan-Yi & Jiang, Ching-Hai, 2016. "On the weight sign of the global minimum variance portfolio," Finance Research Letters, Elsevier, vol. 19(C), pages 241-246.
    5. Al Janabi, Mazin A.M. & Arreola Hernandez, Jose & Berger, Theo & Nguyen, Duc Khuong, 2017. "Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1121-1131.
    6. repec:spr:annopr:v:262:y:2018:i:2:d:10.1007_s10479-015-2081-4 is not listed on IDEAS
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    9. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2016. "Good deals and benchmarks in robust portfolio selection," European Journal of Operational Research, Elsevier, vol. 250(2), pages 666-678.
    10. repec:eee:ejores:v:262:y:2017:i:1:p:299-305 is not listed on IDEAS
    11. Philippe Bertrand & Vincent Lapointe, 2018. "Risk-based strategies: the social responsibility of investment universes does matter," Annals of Operations Research, Springer, vol. 262(2), pages 413-429, March.
    12. repec:eee:ecmode:v:64:y:2017:i:c:p:60-71 is not listed on IDEAS

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