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On time consistency for mean-variance portfolio selection

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  • Elena Vigna

Abstract

This paper addresses a comparison between different approaches to time inconsistency for the mean-variance portfolio selection problem. We define a suitable intertemporal preferences-driven reward and use it to compare the three possible approaches to time inconsistency for the mean-variance portfolio selection problem over [t0, T]: precommitment approach (Zhou & Li (2000)), game theoretical approach (Basak & Chabakauri (2010), Bj¨ork & Murgoci (2010)), and dynamic approach (Pedersen & Peskir (2016)). We find that the precommitment strategy beats the other strategies if the investor only cares at the view point at time t0 and is not concerned to be time inconsistent in (t0, T); the Nash-equilibrium strategy dominates the dynamic strategy until a time point t∗ ∈ (t0, T) and is dominated by the dynamic strategy from t∗ on wards.

Suggested Citation

  • Elena Vigna, 2016. "On time consistency for mean-variance portfolio selection," Carlo Alberto Notebooks 476, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:476
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    References listed on IDEAS

    as
    1. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    2. repec:dau:papers:123456789/11473 is not listed on IDEAS
    3. Christoph Czichowsky, 2013. "Time-consistent mean-variance portfolio selection in discrete and continuous time," Finance and Stochastics, Springer, vol. 17(2), pages 227-271, April.
    4. Tomas Björk & Agatha Murgoci & Xun Yu Zhou, 2014. "Mean–Variance Portfolio Optimization With State-Dependent Risk Aversion," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 1-24, January.
    5. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    6. Elena Vigna, 2014. "On efficiency of mean--variance based portfolio selection in defined contribution pension schemes," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 237-258, February.
    7. Isabelle Bajeux-Besnainou & Roland Portait, 1998. "Dynamic Asset Allocation in a Mean-Variance Framework," Management Science, INFORMS, vol. 44(11-Part-2), pages 79-95, November.
    8. Henry R. Richardson, 1989. "A Minimum Variance Result in Continuous Trading Portfolio Optimization," Management Science, INFORMS, vol. 35(9), pages 1045-1055, September.
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    Citations

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    Cited by:

    1. Elena Vigna, 2017. "Tail optimality and preferences consistency for intertemporal optimization problems," Carlo Alberto Notebooks 502, Collegio Carlo Alberto, revised 2021.
    2. Marcos Escobar-Anel, 2022. "A dynamic programming approach to path-dependent constrained portfolios," Annals of Operations Research, Springer, vol. 315(1), pages 141-157, August.
    3. Van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2018. "Time-consistent mean–variance portfolio optimization: A numerical impulse control approach," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 9-28.
    4. Felix Fie{ss}inger & Mitja Stadje, 2023. "Time-Consistent Asset Allocation for Risk Measures in a L\'evy Market," Papers 2305.09471, arXiv.org, revised Jun 2023.
    5. Guohui Guan & Zongxia Liang & Yilun Song, 2022. "The continuous-time pre-commitment KMM problem in incomplete markets," Papers 2210.13833, arXiv.org, revised Feb 2023.
    6. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.

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    More about this item

    Keywords

    time inconsistency; dynamic programming; Bellman's optimality principle; precommitment approach; Nash perfect equilibrium; mean-variance portfolio selection.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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