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

Zinoviy Landsman, Udi Makov, Tomer Shushi

Research output: Contribution to journalArticlepeer-review


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.

Original languageAmerican English
Pages (from-to)165-178
Number of pages14
JournalEuropean Journal of Finance
Issue number2-3
StatePublished - 11 Feb 2020


  • Allocation rules
  • optimal portfolio selection
  • skew-elliptical distributions
  • skew-normal distributions

All Science Journal Classification (ASJC) codes

  • Economics, Econometrics and Finance (miscellaneous)


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