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

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.