The economic value of score-splitting accept–reject policies

Individuals apply to a company (banking, insurance, mortgage) for credit. Based on an assessment of applicant risk and predictions of likely profitability of accepting that risk, the company decides whether or not to issue credit (an insurance policy, a loan) to the applicant. The company assesses the risk as a function of different characteristics (e.g. income, ownership of assets, residential location, employment, historical use of credit, payment patterns) and develops an imperfect conditional predictor of that risk in the form of a score for each applicant. The score is available prior to the accept–reject decision and is derived from the composition of the credit-seeking population and a likelihood, theoretically derived, or estimated from data, which maps the distribution of profits and losses of accepted applicants into non-overlapping score intervals that uniquely identify many risk classes. Thus, it is possible to predict, on the basis of each risk class, the conditional profitability of each scored applicant. In the paper, it is assumed that the objective of the company is to maximize expected profit by accepting the best subset of risk classes. The author examines the economic value and sensitivity of optimal acceptance policies as a function of the conditional expectation of profit–loss ratios and the conditional probability distribution of losses. The boundaries of the optimal decision regions are determined by the solution of a system of equations whose coefficients are conditional probabilities obtained from Bayes' rule. It is shown that, under certain conditions, it may be optimal to reject a low-risk applicant but accept a high-risk one. The results also suggest that it will be less profitable to accept an individual in one risk class determined by a single score cut-off than to use optimal policies with multiple risk classes.