Do asset managers reach for yield because of competitive pressures in a low interest rate environment? I propose a tournament model of money market funds (MMFs) to study this issue. When funds care about relative performance, an increase in the risk premium leads funds with lower default costs to increase risk taking, while funds with higher default costs decrease risk taking. Without changes in the premium, lower risk-free rates reduce the risk taking of all funds. I show that these predictions are consistent with MMF risk taking during the 2002-08 period and that rank-based performance is indeed a key determinant of money flows to MMFs.