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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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    1. Frank Fabozzi & Dashan Huang & Guofu Zhou, 2010. "Robust portfolios: contributions from operations research and finance," Annals of Operations Research, Springer, vol. 176(1), pages 191-220, April.
    2. Roncalli, Thierry, 2013. "Introduction to Risk Parity and Budgeting," MPRA Paper 47679, University Library of Munich, Germany.
    3. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    4. Ivan Guo & Nicolas Langrené & Gregoire Loeper & Wei Ning, 2020. "Robust utility maximization under model uncertainty via a penalization approach," Working Papers hal-02910261, HAL.
    5. Matteo Basei & Huyên Pham, 2019. "A Weak Martingale Approach to Linear-Quadratic McKean–Vlasov Stochastic Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 347-382, May.
    6. Michael Ho & Zheng Sun & Jack Xin, 2015. "Weighted Elastic Net Penalized Mean-Variance Portfolio Design and Computation," Papers 1502.01658, arXiv.org, revised Oct 2015.
    7. Amine Ismail & Huyên Pham, 2019. "Robust Markowitz mean‐variance portfolio selection under ambiguous covariance matrix," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 174-207, January.
    8. Caihua Chen & Xindan Li & Caleb Tolman & Suyang Wang & Yinyu Ye, 2013. "Sparse Portfolio Selection via Quasi-Norm Regularization," Papers 1312.6350, arXiv.org.
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    Cited by:

    1. 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.
    2. Ren'e Aid & Ofelia Bonesini & Giorgia Callegaro & Luciano Campi, 2021. "A McKean-Vlasov game of commodity production, consumption and trading," Papers 2111.04391, arXiv.org.
    3. Maximilien Germain & Huyên Pham & Xavier Warin, 2022. "A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection," Post-Print hal-03498263, HAL.
    4. Shuo Han & Yinan Chen & Jiacheng Liu, 2023. "Optimizing Investment Strategies with Lazy Factor and Probability Weighting: A Price Portfolio Forecasting and Mean-Variance Model with Transaction Costs Approach," Papers 2306.07928, arXiv.org.
    5. 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.
    6. 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.
    7. 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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