This paper theoretically analyzes the proposal that the issuance of subordinated notes and debentures (SND) by banks will improve market discipline, and makes up for regulatory supervision. It mainly focuses on the changes in the incentive structures of the stakeholders. Bank SND reduces portfolio risks under symmetric information for the following reasons. First, the manager-shareholder chooses a safer portfolio to lower the interest rate on the risky financial instrument. Second, the deposit insurance (DI) corporation adopts a tighter liquidation policy and, by which the manager-shareholder refrains from taking risks. As the SND investor provides a part of the bank's fund, the DI corporation's portion becomes smaller. As a result, the bank is no longer '' too big to fail.'' Instead, the DI corporation is better off to liquidate the bank to collect the liquidation value in case the bank's prospect is not promising. Under information asymmetry the DI corporation needs to be good at processing information for the bank SND in order to contribute to efficiency. Also, the manager-shareholder maintains his incentive to lower the bank portfolio risk. However, his incentive may be adversely affected by the DI corporation's liquidation policy if the sign is not sufficiently accurate (or if the DI corporation is not sufficiently good at processing information). The DI corporation may adopt loose liquidation policy if its liability is relatively large compared with the liquidation value. This will induce the bank towards riskier portfolio. On the other hand, the DI corporation may choose a tighter liquidation policy if its liability is relatively small. In this case, banks will give up choosing a safer portfolio.