Title: Analytic solution of a portfolio optimization problem in a mean-variance-skewness model
Authors: Zinoviy Landsman - University of Haifa (Israel) [presenting]
Udi Makov - University of Haifa (Israel)
Tomer Shushi - University of Haifa (Israel)
Abstract: In portfolio theory, it is well-known that in most of the cases stocks follows a non-symmetric and unimodal distributions. Therefore, many researches have suggested considering the skew-normal distribution an accurate model in quantitative finance. From the fact that the portfolio of stocks is non-symmetric, the celebrated mean-variance theory fails to provide an optimal portfolio selection rule, which comes from the fact that the mean-variance model does not take into account the skewness of the stocks. We provide a novel approach that solves such a problem of optimal portfolio selection with non-symmetric stocks, by putting it into a framework of mean-variance-skewness measure. For example, we show an analytical portfolio optimization solution to the exponential utility of the well-known skew-normal distribution or, even more general, scale mixtures of skew-normal distribution. Moreover, our optimal solutions are explicit and has closed-forms, and therefore they can be investigated in comparison to other portfolio selection rules, such as the standard mean-variance model. The results are then illustrated numerically.