Design of Contingent Capital with Stock Price Trigger for Conversion

Abstract

The proposal for banks to issue contingent capital (CC) that is forced to convert into common equity when stock price falls below a certain specified low threshold (“trigger”) does not in general lead to unique equilibrium in equity and CC prices. Multiple or no equilibrium arise because both equity and CC are claims on the assets of the underlying bank that has issued these claims. For a security to be robust to price manipulation, it must have a unique equilibrium. For a unique equilibrium to exist, it is necessary that mandatory conversion must not result in any value transfers between equity and CC holders. The necessary condition for unique equilibrium is usually not satisfied by CC with fixed coupon rate. Contingent capital with floating coupon rate is shown to have a unique equilibrium if the coupon rate is set to be equal to the riskfree rate. This structure of CC anchors its value to par all the time before conversion, making it implementable in practice. Although a CC with unique equilibrium is robust to price manipulation, the no value transfer condition may preclude it from generating the desired incentives for bank managers or demand from investors.

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