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Mean-variance portfolio selection with tracking error penalization

Author

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  • Willliam Lefebvre

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique)

  • Gregoire Loeper

    (Monash University [Melbourne], BNPP CIB GM Lab - BNP Paribas CIB Global Markets Data & AI Lab)

  • Huyên Pham

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique, ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique)

Abstract

This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a refe\-rence portfolio with same wealth and fixed weights. Such consideration is motivated as fo\-llows: (i) On the one hand, it is a way to robustify the mean-variance allocation in case of misspecified parameters, by ``fitting" it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean-Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.

Suggested Citation

  • Willliam Lefebvre & Gregoire Loeper & Huyên Pham, 2020. "Mean-variance portfolio selection with tracking error penalization," Working Papers hal-02941289, HAL.
    • Handle: RePEc:hal:wpaper:hal-02941289
    Note: View the original document on HAL open archive server: https://hal.science/hal-02941289v2
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    References listed on IDEAS

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    6. Maximilien Germain & Huyên Pham & Xavier Warin, 2021. "A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection," Working Papers hal-03498263, HAL.
    7. Weng Hoe Lam & Weng Siew Lam & Kah Fai Liew & Pei Fun Lee, 2023. "Decision Analysis on the Financial Performance of Companies Using Integrated Entropy-Fuzzy TOPSIS Model," Mathematics, MDPI, vol. 11(2), pages 1-18, January.

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