Contingent capital (CC), which intends to internalize the costs of too-big-to-fail in the capital structure of large banks, has been under intense debate by policy makers and academics. We show that CC with a market trigger, in which direct stake-holders are unable to choose optimal conversion policies, does not lead to a unique competitive equilibrium, unless value transfer at conversion is not expected ex-ante. The "no value transfer" restriction precludes penalizing bank managers for taking excessive risk. Multiplicity or absence of an equilibrium introduces the potential for price uncertainty, market manipulation, inefficient capital allocation, and frequent conversion errors. These results point to the need to explore alternative designs of a prudential capital structure for banks.