Abstracts

Contingent capital in the form of debt that converts to equity when a bank nears financial distress offers a potential solution to the problem of banks that are too big to fail. The main challenge in the design of these securities (``CoCos'') is the choice of trigger for conversion. Accounting-based triggers are slow to respond to new information and are subject to manipulation, making market-based triggers (e.g., a drop in the bank's stock price) potentially attractive. But using the market price of a firm's equity to trigger a change in the firm's capital structure creates a question of internal consistency because the value of the equity itself depends on the firm's capital structure. We analyze the problem of existence and uniqueness of equilibrium values for a firm's liabilities in this context, meaning values consistent with a market-price trigger. Discrete-time trading is known to allow multiple equilibria. In contrast, with continuous trading the price adjusts in anticipation of reaching the trigger, and we show that the possibility of multiple equilibria can largely be ruled out. Within our general framework, existence of an equilibrium is ensured through appropriate positioning of the trigger level; in the case of contingent capital with a stock price trigger, we need the trigger to be sufficiently high, a condition that may be interpreted to mean that conversion should be disadvantageous to shareholders. Our results apply as well to other types of changes in capital structure and triggers based on debt values as well as equity values.