Equilibrium Relationship between Expected Return and Skewness

Abstract

Traditional finance theories assume that investors are risk averse whereas in reality investors exhibit both risk averse and risk seeking behaviors. For example the same individual could be purchasing insurance (risk averse) and lottery ticket (risk seeking) simultaneously. We propose that the utility function of an economic agent is concave (risk averse) for wealth below his/her current wealth and is convex (risk seeking) for wealth above his/her current wealth. This type of utility function allows the agent to display simultaneous risk averse and risk seeking behavior. We show that for an agent with such a utility function, the mean-skewness space is relevant in understanding his/her behavior. More specifically, we prove that in equilibrium, the efficient frontier in the mean-skewness space is concave and downward sloping. We test our equilibrium relationship empirically with stocks listed on the NYSE from 2002 to 2007 and find that our results support our theory.