Portfolio Selection: A Target-Distribution Approach

We introduce a general framework to the portfolio-selection problem in which investors aim at targeting a distribution of returns, which can accommodate a wide range of preferences. The resulting optimal portfolio has a return density that is as close as possible to the target-return density. We study the theoretical properties of this approach for two classes of target distribution that allow for different first four moments. Three results that stand out are, first, that the fit to higher moments is controlled by the entropy of standardized portfolio returns when targeting a Gaussian distribution. Second, when targeting a specific Dirac-delta distribution, no norm-constrained portfolio can stochastically dominate the proposed optimal portfolio. Third, if the target-return mean and variance are located on or above the efficient frontier, the optimal portfolio is mean-variance efficient when asset returns are Gaussian. For non-Gaussian returns, the optimal portfolio may move away from the frontier to better fit the higher moments of the target distribution. The empirical analysis illustrates that the proposed framework helps the investor obtain portfolio returns in line with her preferences.