This paper analyzes competition between mutual funds in a multiple funds version of the model of Hugonnier and Kaniel (2010). 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. (C) 2010 Elsevier Ltd. All rights reserved.