From Mean Variance Space to Mean Skewness Space - Implications for Simultaneous Risk Seeking and Risk Averting Behavior

Abstract

I propose that the utility function of an economic agent will be concave for wealth below the current wealth and will be convex for wealth above the current wealth. This utility function allows the agent to display simultaneous risk averse and risk seeking behaviour. The cubic utility function and the inverse hyperbolic tangent utility function are examples of such utility functions. For an agent with such an utility function, the expected utility of wealth is independent of the second moment about the current wealth. For such agents, the mean-skewness space is relevant in understanding behaviour. In equilibrium, the efficient frontier in the mean skewness space is either concave and downward sloping or there are at best two portfolios in equilibrium.