A Reexamination of Contingent Convertibles with Stock Price Triggers

Abstract

Initial proposals for bank contingent convertibles (CoCos) envisioned that these bonds would convert to new equity when the bank's stock price declined to a pre-specified trigger, thereby automatically re-capitalizing the bank and enhancing financial stability. However, subsequent research argued that doing so causes the bank's stock price to have multiple equilibria or no equilibrium. This paper shows that when CoCos have a perpetual maturity, which characterizes the majority of actual CoCos, a unique stock price equilibrium exists except under unrealistic conditions. A unique equilibrium can occur when conversion terms are advantageous or disadvantageous to CoCo investors and when CoCos convert to new equity shares or are written down. Moreover, the existence of a unique equilibrium stock price is more likely when the bank's asset risk is higher, when there are direct costs of bankruptcy, and when CoCos are callable by the bank. We illustrate these results by developing models of CoCos with either perpetual or finite maturities that lead to closed-form solutions for stock and CoCo values.