A simple model of a money-management market with rational and extrapolative investors

I analyze a simple model of competition in fees among mutual funds. The funds are vertically differentiated in terms of the expected return they can generate for investors. Following Berk and Green (2004), I assume that a fund's net return is decreasing in the amount of capital it manages, and that there is an infinite supply of capital by rational investors. Unlike the Berk-Green model, I assume there is also a finite supply of capital by non-rational investors who naively chase recent net returns. Investor behavior and the funds’ fee profile induce a long-run average amount of managed capital for each fund. I analyze Nash equilibrium in the game played by the funds, focusing on the implications of fund skill on fees, capital flows and net performance.