This paper analyzes competition between mutual funds in a multiple funds version of the model of Hugonnier and Kaniel [17]. We characterize the set of equilibria for this portfolio management game and show that there exists a unique Pareto optimal equilibrium. The main result of this paper shows that the funds cannot differentiate themselves through portfolio choice in the sense that they should offer the same risk/return tradeoff in equilibrium. This result brings theoretical support to the findings of recent empirical studies on the importance of media coverage and marketing in the mutual funds industry.