Initial proposals for contingent convertibles (CoCos) envisioned that these bonds would convert to equity when the issuing bank’s stock price declined to a prespecified trigger. Subsequent research has claimed that doing so causes the stock price to have multiple equilibria or no equilibrium. We show that when CoCos are perpetuities, which characterizes most actual CoCos, a unique stock price equilibrium exists, except under unrealistic conditions. Unique equilibria occur when conversion favors or disfavors CoCo investors, when CoCos convert to equity or are written down, and when CoCos are callable. We also analyze a bank’s risk choices before and after conversion. Received November 29, 2016; editorial decision July 15, 2018 by Editor Itay Goldstein.

Our model shows that when regulation is based on credit ratings, banks with low charter value maximize shareholder value by minimizing capital and selecting identically rated loans and bonds with the highest systematic risk. This regulatory arbitrage is possible if the credit spreads on same-rated loans and bonds are greater when their systematic risk (debt beta) is higher. We empirically confirm this relationship between credit spreads, ratings, and debt betas. We also show that banks with lower capital select syndicated loans with higher debt betas and credit spreads. Banks with lower charter value choose overall assets with higher systematic risk. Received July 27, 2016; editorial decision May 29, 2018 by Editor Itay Goldstein.