Tracking a well diversified portfolio with maximum entropy in the mean

Abstract

In this work we address the following problem: Having chosen a well diversified portfolio, we show how to improve on its return, maintaining the diversification. In order to achieve this boost on return we construct a neighborhood of the well diversified portfolio and find a portfolio that maximizes the return in that neighborhood. For that we use the method of maximum entropy in the mean to find a portfolio that yields any possible return up to the maximum return within the neighborhood. The implicit bonus of the method is that if the benchmark portfolio has acceptable risk and diversification, the portfolio of maximum return in that neighborhood will also have acceptable risk and diversification.