IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2009.08214.html
   My bibliography  Save this paper

Mean-variance portfolio selection with tracking error penalization

Author

Listed:
  • William Lefebvre

    (LPSM)

  • Gregoire Loeper

    (BNPP CIB GM Lab)

  • Huy^en Pham

    (LPSM)

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 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 & Gregoire Loeper & Huy^en Pham, 2020. "Mean-variance portfolio selection with tracking error penalization," Papers 2009.08214, arXiv.org, revised Sep 2020.
    • Handle: RePEc:arx:papers:2009.08214
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2009.08214
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Roncalli, Thierry, 2013. "Introduction to Risk Parity and Budgeting," MPRA Paper 47679, University Library of Munich, Germany.
    2. 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.
    3. 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.
    4. 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.
    5. Caihua Chen & Xindan Li & Caleb Tolman & Suyang Wang & Yinyu Ye, 2013. "Sparse Portfolio Selection via Quasi-Norm Regularization," Papers 1312.6350, arXiv.org.
    6. Ivan Guo & Nicolas Langrené & Gregoire Loeper & Wei Ning, 2020. "Robust utility maximization under model uncertainty via a penalization approach," Working Papers hal-02910261, HAL.
    7. 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.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Willliam Lefebvre & Gregoire Loeper & Huyên Pham, 2020. "Mean-variance portfolio selection with tracking error penalization," Working Papers hal-02941289, HAL.
    2. William Lefebvre & Grégoire Loeper & Huyên Pham, 2020. "Mean-Variance Portfolio Selection with Tracking Error Penalization," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
    3. Ran Ji & Miguel A. Lejeune, 2018. "Risk-budgeting multi-portfolio optimization with portfolio and marginal risk constraints," Annals of Operations Research, Springer, vol. 262(2), pages 547-578, March.
    4. Peter Nystrup & Stephen Boyd & Erik Lindström & Henrik Madsen, 2019. "Multi-period portfolio selection with drawdown control," Annals of Operations Research, Springer, vol. 282(1), pages 245-271, November.
    5. Maillet, Bertrand & Tokpavi, Sessi & Vaucher, Benoit, 2015. "Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach," European Journal of Operational Research, Elsevier, vol. 244(1), pages 289-299.
    6. 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.
    7. Ken Kobayashi & Yuichi Takano & Kazuhide Nakata, 2021. "Bilevel cutting-plane algorithm for cardinality-constrained mean-CVaR portfolio optimization," Journal of Global Optimization, Springer, vol. 81(2), pages 493-528, October.
    8. Stefania Corsaro & Valentina De Simone & Zelda Marino & Francesca Perla, 2020. "$$l_1$$ l 1 -Regularization for multi-period portfolio selection," Annals of Operations Research, Springer, vol. 294(1), pages 75-86, November.
    9. Burkhardt, Raphael & Ulrych, Urban, 2023. "Sparse and stable international portfolio optimization and currency risk management," Journal of International Money and Finance, Elsevier, vol. 139(C).
    10. Gianni Filograsso & Giacomo Tollo, 2023. "Adaptive evolutionary algorithms for portfolio selection problems," Computational Management Science, Springer, vol. 20(1), pages 1-38, December.
    11. Andrew Butler & Roy H. Kwon, 2021. "Data-driven integration of norm-penalized mean-variance portfolios," Papers 2112.07016, arXiv.org, revised Nov 2022.
    12. Nathan Lassance & Frédéric Vrins, 2021. "Minimum Rényi entropy portfolios," Annals of Operations Research, Springer, vol. 299(1), pages 23-46, April.
    13. Martin Branda & Max Bucher & Michal Červinka & Alexandra Schwartz, 2018. "Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization," Computational Optimization and Applications, Springer, vol. 70(2), pages 503-530, June.
    14. Hongxin Zhao & Lingchen Kong & Hou-Duo Qi, 2021. "Optimal portfolio selections via $$\ell _{1, 2}$$ ℓ 1 , 2 -norm regularization," Computational Optimization and Applications, Springer, vol. 80(3), pages 853-881, December.
    15. Stefania Corsaro & Valentina Simone, 2019. "Adaptive $$l_1$$ l 1 -regularization for short-selling control in portfolio selection," Computational Optimization and Applications, Springer, vol. 72(2), pages 457-478, March.
    16. Jingnan Chen & Gengling Dai & Ning Zhang, 2020. "An application of sparse-group lasso regularization to equity portfolio optimization and sector selection," Annals of Operations Research, Springer, vol. 284(1), pages 243-262, January.
    17. Zhenlong Jiang & Ran Ji & Kuo-Chu Chang, 2020. "A Machine Learning Integrated Portfolio Rebalance Framework with Risk-Aversion Adjustment," JRFM, MDPI, vol. 13(7), pages 1-20, July.
    18. Tu, Jun & Zhou, Guofu, 2010. "Incorporating Economic Objectives into Bayesian Priors: Portfolio Choice under Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(4), pages 959-986, August.
    19. Lassance, Nathan & Vrins, Frédéric, 2019. "Robust portfolio selection using sparse estimation of comoment tensors," LIDAM Discussion Papers LFIN 2019007, Université catholique de Louvain, Louvain Finance (LFIN).
    20. Meade, N. & Beasley, J.E. & Adcock, C.J., 2021. "Quantitative portfolio selection: Using density forecasting to find consistent portfolios," European Journal of Operational Research, Elsevier, vol. 288(3), pages 1053-1067.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2009.08214. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.