Abstract This paper studies bank runs in an extended Diamond and Dybvig model. The model is extended in two ways. One, agents have heterogeneous wealth and two, banks can invest in both liquid and illiquid assets. We argue that the underlying reason for bank runs is ambiguous property rights. Sequential conversion is an example of such ambiguity. Demand deposit insurance eliminates this ambiguity. In this regard, we characterize conditions on the economy where banks can preclude bank runs as an equilibrium by self-insuring their deposits with an FDIC deposit insurance like contract.