Optimal score cutoffs and pricing in regulatory capital in retail credit portfolios

Abstract

This paper addresses the risk cutoff policies of a retail bank whose objectives are to maximize return on equity for shareholders and live within regulatory capital requirements, such as those of the Basel Capital Accord, to meet unexpected default losses. It investigates the changes that have to be made in the operating decision of which applicants for loans to accept and which to reject because of the changes in the financial regulations imposed on the bank. It is assumed that portfolios consist entirely of consumer credit accounts (mortgages, auto loans, revolving credit etc) for which acquisition risk scores are available to the lender and regulator. The solutions that we obtain not only yield an optimal cutoff score for default risk but also optimal pricing conditions for additional equity capital in the event that the existing level can not satisfy the regulatory requirements. The paper concludes with several numerical examples illustrating the effects of current and proposed Basel regulations. We believe that some important insights are derived from this formulation linking the financial variables such as the lending and borrowing rates, and the debt and equity structure of the lender and the operational decisions of which level of risk to set as the cutoff in the consumer credit portfolios.

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