We study the optimal design of financial aid policies for college students. The model incorporates multidimensional heterogeneity, idiosyncratic risk and borrowing constraints. It matches key empirical results on college enrollment patterns, returns to education and enrollment elasticities. We find that a marginal increase in college subsidies in the US is at least 70 percent self-financing through the net-present value increase in future tax revenue. When targeting this increase to children in the lowest parental income tercile, it is more than self-financing with a fiscal return of 165 percent. Optimal financial aid policies are decreasing in parental income.