Optimal Bank Liability Structure

We develop a model of capital and liability structure of banks that optimally respond to changes of regulatory environment. The model produces the following results. In the absence of regulation, banks in our model take high leverage, both in the form of deposits and subordinated debt. We find that subordinated debt is important in banks’ liability structure—holding zero subordinated debt is never optimal for a bank. However, a bank optimizes its liability structure should not have too much subordinated debt; the optimal level is to set the endogenous default of debt to coincide with the point at which the depositors will choose to run. In this optimal choice of liability structure, the subordinated debt does not protect deposits from default. The introduction of FDIC regulation and insurance raises the market value of banks, even when banks are charged for fair insurance premium. With deposit insurance, banks issue more deposits but reduce their subordinated debt to ensure that endogenous default still coincides with bank closure. In this optimal liability structure, subordinated debt does not protect FDIC from losses in covering deposits when the bank is closed. This particular response by banks dampens the reduction of expected bankruptcy loss potential that could be brought by the FDIC insurance program: if banks were not able to adjust their liability structure in response to the introduction of FDIC insurance, the reduction in expected losses would have been higher. Another important finding is that charging a fair insurance premium takes away the incentive of risk shifting. The optimal response of banks to equity requirement are more complicated to analyze. Obviously, there should be no response if a bank’s optimal liability structure automatically satisfies the equity requirement imposed by the regulators. For a set of reasonable parameters for typical banks, we find Basel’s 7-percent equity requirement is mostly binding. Subject to binding capital requirement, banks need to trim both deposits and subordinated debt, as expected. However, in some cases it is optimal for banks to trim more subordinated debt than deposits so that the endogenous default is shielded by bank run/closure. In other cases, it is optimal for banks to set endogenous default exactly at the point of bank run/closure. Again, banks with optimal liability structure issue some subordinated debt, but not so much that it protects deposits. ∗Columbia University, Graduate School of Business †Indiana University, Kelley School of Business; China Academy of Financial Research ‡The current version of the paper is preliminary and incomplete. Comments are welcome. We are grateful for helpful discussions with Mark Flannery and comments by participants of seminars at the NY Fed and UNC at Charlotte.