The Behavior of Banks under the Deposit Insurance and Capital Requirements

Deposit insurance and capital requirements are two focuses in banking literature. Many researchers criticize these two important schemes using moral hazard theory: Under the protection of the deposit insurance, banks have incentive to take deposits as much as they can for some debt-favor reasons such as tax deduction on interest payment, and let the FDIC pay for the deposits if it turns out banks do not have enough capital to pay the deposits back. One the other hand, banks also have incentive to take riskier investment in hope of having higher returns. When capital requirements are imposed, insured banks may shift priced risks to unpriced risks. Therefore, capital requirements actually will lead banks to take more risks, and hence lead to higher probability of bank failure. However, this criticism does not consider the implicit costs of bankruptcy. If a bank is bankrupt, it will lose the benefit of deposit insurance. Moreover, it will lose the possible future earnings. In this paper, I take into account the implicit costs of bankruptcy, and investigate how banks react to the fixed and risk-based capital requirements under deposit insurance. In my basic model, I adopt one factor option pricing model and find a closed-form solution for bank equity in terms of asset-to-debt ratio. In my extension model, I relax the assumption of constant interest rate in the basic model. Thus, the uncertainty of bank equity comes from two sources: capital ratio and interest rate. I adopt a general form of term structure and find the numerical solution for the bank equity value as a function of both asset-to-debt ratio and interest rate. Through the stochastic term structure, interest rate risk is also involved. The results show that banks actually prefer to use more capital even there are no capital requirements. Moreover, banks tend to take lower risk instead of high risk no matter there are capital requirements or not, if they are solvent. However, for insolvent banks, they may take riskier investment. Under the risk-based capital requirements, banks would prefer lower capital requirements by taking lower risk. Lastly, capital requirements only have impact on banks with low capital. For those well capitalized banks, capital requirements will not affect their behavior too much.