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Mean-Variance Portfolio Selection with Tracking Error Penalization

Author

Listed:
  • William Lefebvre

    (BNP Paribas Global Markets, 20 Boulevard des Italiens, 75009 Paris, France
    Building Sophie Germain, Statistique et Modélisation (LPSM, UMR CNRS 8001), Laboratoire de Probabilités, Université de Paris and Sorbonne Université, Avenue de France, 75013 Paris, France)

  • Grégoire Loeper

    (BNP Paribas Global Markets, 20 Boulevard des Italiens, 75009 Paris, France
    School of Mathematics, Monash University, Clayton, Victoria 3800, Australia)

  • Huyên Pham

    (Building Sophie Germain, Statistique et Modélisation (LPSM, UMR CNRS 8001), Laboratoire de Probabilités, Université de Paris and Sorbonne Université, Avenue de France, 75013 Paris, France)

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 reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in the 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

  • William Lefebvre & Grégoire Loeper & Huyên Pham, 2020. "Mean-Variance Portfolio Selection with Tracking Error Penalization," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1915-:d:438593
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    References listed on IDEAS

    as
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    Cited by:

    1. Apichat Chaweewanchon & Rujira Chaysiri, 2022. "Markowitz Mean-Variance Portfolio Optimization with Predictive Stock Selection Using Machine Learning," IJFS, MDPI, vol. 10(3), pages 1-19, August.
    2. Maximilien Germain & Huy^en 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," Papers 2112.11059, arXiv.org, revised Nov 2022.
    3. 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.

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