What do Bank Capital Requirements do when They are not Binding?

Abstract

This paper provides a new interpretation of the role of capital regulation, recognizing that banks may not operate at the maximal leverage levels allowed, i.e., capital requirements are, in most cases, not binding. I show that the seemingly unbinding capital requirements are actually a necessary device to induce banks to choose leverage levels above the requirements. I develop a stylized model that intends to capture the basic ideas as simple as possible. Banks can invest in both real loans and marketable securities. As bank loans are special and essentially illiquid, banks earn rents on real loans. The supply of profitable lending opportunity is, however, limited because the loan production process exhibits decreasing return to scale. If banks can only invest in real loans, the trade-off between preserving rents (franchise-value incentive) and exploiting government insurance value (risk-shifting incentive) means that banks do not necessarily choose their leverage levels and asset risks to be at the boundaries imposed by regulatory rules. The resulting interior solution, however, is only a local optimum. Marketable securities, despite yielding zero present value in themselves, are attractive in the presence of government guarantee. Moreover, they are in unlimited supply. By investing in marketable securities, banks can leverage up indefinitely to exploit the government insurance. Therefore, a global optimum corresponding to maximal leverage and risk, from the banker's point of view, always dominates the local optimum. Because banks do not internalize any social costs of bank failures, the global optimum is not socially optimal. This underscores an interesting and probably unintended role that capital regulation plays. For a fixed amount of capital, capital requirements limit the bank's ability to leverage and thus impose an upper limit on the maximal gain from leveraging and risk taking. When they are properly set at a level such that the gain from operating at the boundary is lower than that at the local optimum, the bank chooses to stay at the local optimum. Hence, capital regulation is not meant to just prevent a few banks from going across the boundary, but rather, serves as a necessary device that induce the majority of banks to settle at their local optima. The macroeconomic implications are also discussed.