This paper deals with the question of the optimal capital structure for a banking firm. It considers a competitive bank as an insurer of unpredictable liquidity demanded by depositors in the sense described by Diamond and Dybvig. The model developed in this paper is able to explain the stylized facts. It considers three key features of a bank: first, the demand deposit contract allows the depositor to run the bank if he believes that the banks solvency is insufficient. Secondly, four financial states of the shareholders wealth are considered explicitly. Thirdly, the maximization of the shareholders expected utility of pay-offs is constrained by the (weakest) condition that the expected yield on equity exceeds the risk-free rate of interest (the yield-on-equity constraint).