Portfolio Selection with Skew Normal Asset Returns

Quan Gan
2013 Social Science Research Network  
This paper examines the portfolio selection problem with skew normal asset returns. By exploring an alternative parameterization of Azzalini & Dalla Valle (1996)'s multivariate skew normal distribution I show that the multivariate skew normal distribution is a special case of Simaan (1993)'s three-parameter model. All Simaan (1993)'s results are applicable to the skew normal asset returns. The three-parameter efficient frontier is spanned by three funds which include two funds from the
more » ... s from the mean-variance portfolio selection. Combining the skew normal asset returns with the CARA utility, I obtain the closed-form certainty equivalent and skewness premium. I show that the skewness premium is positive (negative) when asset returns have negative (positive) skewness. The magnitude of the skewness premium is increasing in market risk aversion. I use the skew normal certainty equivalent to evaluate the economic value of incorporating higher moments in portfolio selection. I find that when investors face broad investment opportunities, the economic value of considering higher moments is negligible under realistic margin requirements. (JEL. G11, G12, D81)
doi:10.2139/ssrn.2297196 fatcat:6vtdbqmiw5bh3pkcufe72kwnbu