A Uniformly Distributed Random Portfolio

Abstract

In this study, we propose a uniformly distributed random portfolio as an alternative benchmark for the portfolio performance evaluation. The uniformly distributed random portfolio is analogous to the enumeration of all feasible portfolios without any prior on the market. Therefore, the relative ranking of a portfolio can be evaluated without peer group information. We derive the closed form expression of the probability distribution of the Sharpe ratio of a uniformly distributed random portfolio, and conduct comparisons analysis with the U.S. equity mutual funds. We find that the uniformly distributed random portfolio properly captures the historical performance distribution of the equity mutual funds.