We derive an equivalence result that shows that absent a banking panic, the set of allocations achieved with private financial intermediation will also be achieved with a CBDC. During a panic, however, we show that the rigidity of the central bank's contract with the investment banks has the capacity to deter runs. Thus, the central bank is more stable than the commercial banking sector. Depositors internalize this feature ex-ante, and the central bank arises as a deposit monopolist, attracting all deposits away from the commercial banking sector. This monopoly might endanger maturity transformation.