Risk and Potential: An Asset Allocation Framework with Applications to Robo-Advising

We propose a novel dynamic asset allocation framework based on a family of mean-variance-induced utility functions that alleviate 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. This naturally leads to a different characterization of possible investment outcomes below and above a target wealth as risk and potential. 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.