In this paper, I theoretically examine the ability of Contingent Convertible bonds (CoCos), a source of bank capital under Basel III, to reduce the bank's default risk. Although issuing CoCos adds a buffer to the bank's balance sheet, it may induce wrong incentives in the form of debt overhang and risk shifting. My results indicate that the most popular type of CoCos, temporary write-down (TWD), is least effective at mitigating default risk. Unlike other types of CoCos, TWDs continue affecting shareholders' incentives even after the trigger event, thereby, inducing an earlier endogenous default.