© 1992 by Institute of Mathematics and its Applications
The assignment of credit limits with a behaviour-scoring system
Freemans plc
Received on 1 July 1991. Behaviour-scoring systems for authorizations enable the risk of a customer defaulting to be quantified. These risks must be incorporated into a credit strategy which assigns credit limits and makes authorization decisions in the most effective manner. This paper introduces the concept of marginal risk which has proved a useful tool in defining credit limit strategies for a mail-order company.
Behaviour scores for authorizations are similar to credit application scores in that they predict the overall risk of a customer defaulting. If a cut-off risk can be established, then the optimal strategy would appear to be to withhold credit for customers exceeding this risk and to grant unlimited credit for the remainder (this is analogous to application strategies). The notion of granting unlimited credit is often commercially unacceptable (particularly if customers are to be informed of their credit limits!) and so strategies which give all or nothing are of limited value and need further refinement.
In order to overcome this problem, the concept of marginal risk has been devised. The marginal risk is the risk of the ‘last £’ of an account being defaulted. This reflects the fact that small-balance customers may well pay off their current balance only to default on larger subsequent purchases. Although the overall risk of customers with a given behaviour score defaulting is relatively constant, their marginal risk will vary according to their outstanding balance. This paper explores the relationships between marginal risk and overall risk and between marginal risk and outstanding balance. A model which summarizes these relationships is proposed, and contours of equal marginal risk are built on the basis of this model. These contours provide strategies for allocating credit limits which are both practical and optimal for a well formulated cut-off risk and which suggest that the probability of defaulting is not the best criterion for allocating credit limits.
The results of the application of this approach will be demonstrated. Some of the problems that have been overcome are discussed, as are some of the outstanding problems.