Optimal Design of Contingent Capital

This paper proposes a parsimonious framework for designing contingent capital contracts (CoCos). CoCos designed this way (i) are either optimal or incentive compatible for equity holders, (ii) implement a unique equilibrium, and (iii) result in an optimal capital structure for the firm. We consider CoCos with equity conversion and write-down modalities. Equity conversion CoCos are optimal; write-down CoCos are incentive-compatible. Both types of CoCos can be implemented by exogenously specifying a capital ratio rule that triggers conversion and, hence, qualify as additional tier 1 (AT1) capital. A policymaker can use a normative criterion, e.g., capital ratio after conversion, to determine the desired capital ratio rule ex-ante. Given the policymaker's choice of the capital ratio rule, our model pins down the CoCo that respects (i), (ii), and (iii). We show that including such a CoCo in the firm's capital structure increases its optimal levered value while making it more resilient to bankruptcy. Lastly, CoCos in this framework are time-consistent. This characteristic alleviates the risk of renegotiation by stakeholders and removes the uncertainty of a discretionary trigger: precisely what spooked markets during the run on Credit Suisse in March 2023.