TITLE:
From Normal vs Skew-Normal Portfolios: FSD and SSD Rules
AUTHORS:
Francesco Blasi, Sergio Scarlatti
KEYWORDS:
Normal Distribution; Skew-Normal Distribution; Mixture Distributions; Stochastic Ordering; Stochastic Dominance; Portfolio Selection; Derivatives; Straddles
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.2 No.1,
February
28,
2012
ABSTRACT: In this paper we study stochastic dominance rules of first and second order for univariate skew-normal random variables, the analysis being relevant in connection with the problem of portfolio choice in stock markets showing departure from the classical assumption of normality on returns. Besides that, our analysis is also relevant for markets where stocks returns are normally distributed: if standard derivatives are tradable and straddles, characterized by V-shaped pay-outs, are implementable at specific strike prices, then, portfolios including them, can exhibit exact skew-normality in their returns. We provide a set of simple conditions on the statistical parameters of the distributions which imply FSD and SSD and discuss some application of our criteria.