Optimal Bank Capital and Securitization: The Case of Corporate Loans for U.S. Commercial Banks

Abstract

This paper derives a bank capital allocation model and applies it in the determinants of securitization. According to Bank for International Settlements (BIS), banks are required to prepare regulatory capital for investment and loans, based on the quality and quantity of assets. Hence, the required regulatory capital should be larger when holding riskier assets. In order to allocate banks capital efficiently, banks will consider between return and risk. For example, banks could increase riskier loans to raise capital return, or to decrease loans to alleviate risk.Securitization is one way to alleviate risk. By allowing banks to convert illiquid loans into marketable securities, required capital is released. However, risky loans would yield higher rate of returns if not default. Therefore, banks would reduce their yields when their assets are securitized to cash. Obviously, there is a trade-off between risk and return so that a bank could choose an optimal ratio of securitization to maximize utility. To derive a bank capital allocation model, HJB equation in control theory and a specific utility function is used. Besides, stochastic features of interest rates are considered. To verify this model, we use corporate loans for U.S. commercial banks. Using this model, the optimal capitals used in low risk loan, high risk loan, surplus, and securitization ratio are determined. The main contribution of the paper is to provide a theoretical framework in which to identify factors affecting optimal capital allocation for banks.