Risk and Potential: A Perspective from Mean-Variance Induced Utility Functions

Abstract

We propose a novel dynamic asset allocation framework based on a family of mean-variance induced utility functions that overcome the non-monotonicity and time-inconsistency problems of mean-variance optimization. The utility functions are motivated by the equivalence between the mean-variance objective and a quadratic utility function. Crucially, our framework differs from mean-variance analysis in that we allow different treatment of upside and downside deviations from a target wealth level, which naturally leads to a different characterization of investment outcomes. Risk can be viewed as the possible outcomes below the target wealth, whereas potential can be used to describe the possible outcomes exceeding the target wealth. Our proposed asset allocation framework retains two attractive features of mean-variance optimization: an intuitive explanation of the investment objective and an easily-computed optimal strategy. We establish a semi-analytical solution for the optimal trading strategy in our framework and provide numerical examples to illustrate its behavior. Finally, we discuss applications of this framework to robo-advisors.