The assignment of credit limits with a behaviour-scoring system

Received on 1 July 1991. Behaviour-scoring systems for authorizations enable the riskof a customer defaulting to be quantified. These risks mustbe incorporated into a credit strategy which assigns creditlimits and makes authorization decisions in the most effectivemanner. This paper introduces the concept of marginal risk whichhas proved a useful tool in defining credit limit strategiesfor a mail-order company. Behaviour scores for authorizations are similar to credit applicationscores in that they predict the overall risk of a customer defaulting.If a cut-off risk can be established, then the optimal strategywould appear to be to withhold credit for customers exceedingthis risk and to grant unlimited credit for the remainder (thisis analogous to application strategies). The notion of grantingunlimited credit is often commercially unacceptable (particularlyif customers are to be informed of their credit limits!) andso strategies which give all or nothing are of limited valueand need further refinement. In order to overcome this problem, the concept of marginal riskhas been devised. The marginal risk is the risk of the ‘last£’ of an account being defaulted. This reflectsthe fact that small-balance customers may well pay off theircurrent balance only to default on larger subsequent purchases.Although the overall risk of customers with a given behaviourscore defaulting is relatively constant, their marginal riskwill vary according to their outstanding balance. This paperexplores the relationships between marginal risk and overallrisk and between marginal risk and outstanding balance. A modelwhich summarizes these relationships is proposed, and contoursof equal marginal risk are built on the basis of this model.These contours provide strategies for allocating credit limitswhich are both practical and optimal for a well formulated cut-offrisk and which suggest that the probability of defaulting isnot 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.