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Mean-variance-time: An extension of Markowitz's mean-variance portfolio theory

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  • Fahmy, Hany

Abstract

In finance, investment decisions are commonly based on Markowitz's ex-ante mean-variance (MV) portfolio problem. The static ex-post trading problem, however, is completely absent. In this paper, we propose a theoretical extension of the MV framework by adding a time dimension so that the construction of a portfolio is thought of as an activity that consists of n monetary outcomes, i.e., rates of return on n risk assets, and the portfolio duration time t, which is the investor's optimal trading strategy time. Under a set of axioms, we show the existence and uniqueness of a utility function that represents investors’ preference over different time horizons. The analytical solution over the extended field yields an expression where optimal portfolio duration time depends explicitly on various sources of uncertainty; a key result that distinguishes this paper from the existing literature. We demonstrate empirically that our proposed model can explain many of the observed time-related anomalies of stock returns. Finally, we show that long-term trading strategies are more profitable for rational investors under perfect information.

Suggested Citation

  • Fahmy, Hany, 2020. "Mean-variance-time: An extension of Markowitz's mean-variance portfolio theory," Journal of Economics and Business, Elsevier, vol. 109(C).
    • Handle: RePEc:eee:jebusi:v:109:y:2020:i:c:s0148619519302097
    DOI: 10.1016/j.jeconbus.2019.105888
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    Cited by:

    1. Oleg S. Sukharev, 2020. "Portfolio Theory in Solving the Problem Structural Choice," JRFM, MDPI, vol. 13(9), pages 1-21, September.
    2. Fahmy, Hany, 2022. "Clean energy deserves to be an asset class: A volatility-reward analysis," Economic Modelling, Elsevier, vol. 106(C).
    3. Vukovic, Darko B. & Maiti, Moinak & Frömmel, Michael, 2022. "Inflation and portfolio selection," Finance Research Letters, Elsevier, vol. 50(C).
    4. Fahmy, Hany, 2023. "Satiation, habit formation, and other temporal anomalies: Extending the choice theory to multiple neighborhoods of time," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 163-173.
    5. Spyridon D. Mourtas & Vasilios N. Katsikis, 2022. "V-Shaped BAS: Applications on Large Portfolios Selection Problem," Computational Economics, Springer;Society for Computational Economics, vol. 60(4), pages 1353-1373, December.
    6. Ossa González, Genjis A., 2023. "Comparación de los modelos de Black-Litterman, Markowitz y CAPM en la estimación de los rendimientos esperados en el mercado de renta variable en Colombia," Revista Estrategia Organizacional, Universidad Nacional Abierta y a Distancia, vol. 12(2), pages 29-53, October.

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    More about this item

    Keywords

    Portfolio selection; Mean-variance portfolio theory; Uncertain time horizon; Overreaction; Portfolio duration;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G41 - Financial Economics - - Behavioral Finance - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making in Financial Markets

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