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On Time Consistency For Mean-Variance Portfolio Selection

Author

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  • ELENA VIGNA

    (University of Torino and Collegio Carlo Alberto, Italy2Corso Unione Sovietica 218 bis, 10134, Torino, Italy)

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 three common approaches to time inconsistency for the mean-variance portfolio selection problem over [t0,T]: precommitment approach, consistent planning or game theoretical approach, and dynamically optimal approach. We prove that, while the precommitment strategy beats the other two strategies (that is a well-known obvious result), the consistent planning strategy dominates the dynamically optimal strategy until a time point t∗∈ (t 0,T) and is dominated by the dynamically optimal strategy from t∗ onwards. Existence and uniqueness of the break even point t∗ is proven.

Suggested Citation

  • Elena Vigna, 2020. "On Time Consistency For Mean-Variance Portfolio Selection," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(06), pages 1-22, September.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:06:n:s0219024920500429
    DOI: 10.1142/S0219024920500429
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    Citations

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    Cited by:

    1. Zhang, Hanwen & Dang, Duy-Minh, 2024. "A monotone numerical integration method for mean–variance portfolio optimization under jump-diffusion models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 112-140.
    2. Forsyth, Peter A., 2022. "Short term decumulation strategies for underspending retirees," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 56-74.
    3. Balter, Anne G. & Mahayni, Antje & Schweizer, Nikolaus, 2021. "Time-consistency of optimal investment under smooth ambiguity," European Journal of Operational Research, Elsevier, vol. 293(2), pages 643-657.
    4. Hanwen Zhang & Duy-Minh Dang, 2023. "A monotone numerical integration method for mean-variance portfolio optimization under jump-diffusion models," Papers 2309.05977, arXiv.org.
    5. Pieter van Staden & Peter Forsyth & Yuying Li, 2024. "Smart leverage? Rethinking the role of Leveraged Exchange Traded Funds in constructing portfolios to beat a benchmark," Papers 2412.05431, arXiv.org.
    6. Keffert, Henk, 2024. "Robo-advising: Optimal investment with mismeasured and unstable risk preferences," European Journal of Operational Research, Elsevier, vol. 315(1), pages 378-392.
    7. Kristoffer Andersson & Cornelis W. Oosterlee, 2023. "D-TIPO: Deep time-inconsistent portfolio optimization with stocks and options," Papers 2308.10556, arXiv.org, revised Sep 2023.
    8. Pieter M. van Staden & Peter A. Forsyth & Yuying Li, 2023. "A parsimonious neural network approach to solve portfolio optimization problems without using dynamic programming," Papers 2303.08968, arXiv.org.

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