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Minimum Variance Portfolio Optimisation under Parameter Uncertainty: A Robust Control Approach

Author

Listed:
  • Bertrand Maillet
  • Sessi Tokpavi
  • Benoit Vaucher

Abstract

The global minimum variance portfolio computed using the sample covariance matrix is known to be negatively affected by parameter uncertainty. Using a robust control 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 theoretically corresponds 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, 2013. "Minimum Variance Portfolio Optimisation under Parameter Uncertainty: A Robust Control Approach," EconomiX Working Papers 2013-28, University of Paris Nanterre, EconomiX.
  • Handle: RePEc:drm:wpaper:2013-28
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    References listed on IDEAS

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    More about this item

    Keywords

    Global minimum variance portfolio; Parameter uncertainty; Robust control approach; Robust portfolio.;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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