This paper presents a theoretical model based on risk diversification to rationalize the observed dichotomy in the federal funds market by which small banks are net providers of funds while large banks become net purchasers. As larger banks are more diversified they can raise a larger proportion of funds as equity and provide more loans. To finance these loans, they will need to obtain funds in the wholesale money market. In contrast, smaller banks will be less diversified and will find it harder to raise equity which means producing a lower amount of loans and supplying the extra funds in the wholesale money market. The model also produces a set of testable predictions about the performance of large and small banks that are in line with data for the US.