Design of contingent capital with a stock price trigger for mandatory conversion

Contingent capital (CC), a regulatory debt that must convert into common equity when a bank?s equity value falls below a specified threshold (a trigger), does not in general lead to a unique equilibrium in the prices of the bank?s equity and CC. Multiplicity or absence of equilibrium arises because economic agents are not allowed to choose a conversion policy in their best interests. The lack of unique equilibrium introduces the potential for price manipulation, market uncertainty, inefficient capital allocation, and unreliability of conversion. Because CC may not convert to equity in a timely and reliable manner, it is not a substitute for common equity as capital buffer. The problem exists even if banks can issue new equity to avoid conversion. The problem is more pronounced when bank asset value has jumps and when bankruptcy is costly. For a unique equilibrium to exist, allowing for jumps and bankruptcy costs, we prove that, at trigger price, mandatory conversion must not transfer value between equity holders and CC investors. Besides the challenge of practically designing such a CC, absence of value transfer prevents punishment of bank managers at conversion. This is problematic because punitive conversion is desirable to generate the desired incentives for bank managers to avoid excessive risk taking.