Efficient Goal Probabilities: A New Frontier

In goals-based wealth management (GBWM), an investor looks to maximize the probabilities of attaining each of n goals over time. Because the goals are in competition for potentially limited financial resources, their relative importance must be specified, which we do by assigning utility weights to each goal. Given these weights, dynamic programming can determine both the optimal investment strategy and the optimal strategy for when to fulfill versus forgo each goal. This yields the optimal goal probabilities for fulfilling each goal. By altering the utility weights, we show how to generate the efficient goal probability frontier (EGPF), an (n - 1)-dimensional hypersurface of the optimized goal probability combinations. Just as the classic efficient frontier in mean-variance portfolio optimization allows investors to understand the trade-offs under the best circumstances between their portfolio's mean and variance, the EGPF allows the investor to understand the trade-offs under the best circumstances between the probabilities of attaining each of their goals-without needing to see or understand the goals'underlying utility weights. We extend our EGPF framework to determine either the minimum initial wealth or the minimum of a one-parameter family of infusions over time that are needed to attain specified probabilities for each completely or partially fulfilled goal.