How skewness influences optimal allocation in a risky asset?

Abstract

This article extends the classic Samuelson (1970) and Merton (1973) model of optimal portfolio allocation with one risky asset and a riskless one to include the effect of the skewness. Using an extended version of Stein's Lemma, we provide the explicit solution for optimal demand that holds for all expected utility maximizing investors when the risky asset is skew-normally and normally distributed. A closed expression is achieved for investors with constant absolute risk aversion.

Keywords:

• Stein's Lemma
• optimal asset allocation
• skew-normal distribution
• skewness

JEL Classification:

• D81
• C10

Notes

¹ It is worthwhile noting that is positive. If , the proof is trivial. If , that follows from the Theorem of the Mean . The fact that is not surprising, since the support of is non-negative.

² Note that , if , and , if .