A uniformly distributed random portfolio

Abstract

In this study, we propose a uniformly distributed random portfolio as an alternative benchmark for portfolio performance evaluation. The uniformly distributed random portfolio is analogous to an 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 a closed-form expression for the probability distribution of the Sharpe ratio of a uniformly distributed random portfolio, and conduct comparative analysis with US equity mutual funds. We find that the uniformly distributed random portfolio properly captures the historical performance distribution of equity mutual funds. In addition, we evaluate performance of cap-weighted equity portfolios via uniformly distributed random portfolios.