Business Analytics

Portfolio Selection with Skew Normal Asset Returns

Dr. Quan Gan, Discipline of Finance; The University of Sydney

9th Aug 2013  11:00 am - Room 498, Merewether Bldg H04

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 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.

Keywords: Portfolio selection, Skew normal, Certainty equivalent, Skewness premium