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

The proposal for banks to issue contingent capital that must convert into common equity when the banks' stock price falls below a specified threshold, or "trigger," does not in general lead to a unique equilibrium in equity and contingent capital prices. Multiple or no equilibrium arises because both equity and contingent capital are claims on the assets of the issuing bank. For a security to be robust to price manipulation, it must have a unique equilibrium. For a unique equilibrium to exist, mandatory conversion cannot result in any value transfers between equity holders and contingent capital investors. The necessary condition for unique equilibrium is usually not satisfied by contingent capital with a fixed coupon rate; however, contingent capital with a floating coupon rate is shown to have a unique equilibrium if the coupon rate is set equal to the risk-free rate. This structure of contingent capital anchors its value to par throughout the time before conversion, making it implementable in practice. Although contingent capital with a unique equilibrium is robust to price manipulation, the no-value-transfer condition may preclude it from generating the desired incentives for bank managers and demand from investors.