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Analytic solution to the portfolio optimization problem in a mean-variance-skewness model

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  • Zinoviy Landsman
  • Udi Makov
  • Tomer Shushi

Abstract

In portfolio theory, it is well-known that the distributions of stock returns are often unimodal asymmetric distributions. Therefore, many researches have suggested considering the skew-normal distribution as an adequate model in quantitative finance. Such asymmetry explains why the celebrated mean-variance theory, which does not account to the skewness of distribution of returns, frequently fails to provide an optimal portfolio selection rule. In this paper, we provide a novel approach for solving the problem of optimal portfolio selection for asymmetric distributions of the stock returns, by putting it into a framework of a mean-variance-skewness measure. Moreover, our optimal solutions are explicit and are closed-form. In particular, we provide an analytical portfolio optimization solution to the exponential utility of the well-known skew-normal distribution. Our analytical solution can be investigated in comparison to other portfolio selection rules, such as the standard mean-variance model. The new methodology is illustrated numerically.

Suggested Citation

  • Zinoviy Landsman & Udi Makov & Tomer Shushi, 2020. "Analytic solution to the portfolio optimization problem in a mean-variance-skewness model," The European Journal of Finance, Taylor & Francis Journals, vol. 26(2-3), pages 165-178, February.
    • Handle: RePEc:taf:eurjfi:v:26:y:2020:i:2-3:p:165-178
    DOI: 10.1080/1351847X.2019.1618363
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    Cited by:

    1. Ashfaq, Saira & Ayub, Usman & Mujtaba, Ghulam & Raza, Naveed & Gulzar, Saqib, 2021. "Gainers and losers with higher order portfolio risk optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    2. Nicola Loperfido & Tomer Shushi, 2023. "Optimal Portfolio Projections for Skew-Elliptically Distributed Portfolio Returns," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 143-166, October.
    3. Khashanah, Khaldoun & Simaan, Majeed & Simaan, Yusif, 2022. "Do we need higher-order comoments to enhance mean-variance portfolios? Evidence from a simplified jump process," International Review of Financial Analysis, Elsevier, vol. 81(C).

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