In this paper, we analyze the effect of the conversion price of CoCo bonds on equity holders' incentives. First, we use an option-pricing context to show that CoCo bonds can magnify equity holders' incentives to increase the riskiness of assets and decrease incentives to raise new equity in a crisis in cases in which conversion transfers wealth from CoCo bond holders to equity holders. Second, we present a clinical study of the CoCo bonds issued so far. We show that i) almost all existing CoCo bonds are designed in a way that implies a wealth transfer from CoCo bond holders to equity holders at conversion and ii) this contractual design is reflected in traded prices of CoCo bonds. In particular, CoCo bonds are short volatility with a magnitude five times greater than that which can be observed for straight bonds. These results are robust and economically significant. We conclude that the CoCo bonds issued so far can create perverse incentives for banks' equity holders.