Recalibrating scorecards
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Recalibrating scorecards LC Thomas1*, J Banasik2 and JN Crook2 1
University of Southampton, Southampton, UK; and 2University of Edinburgh, Edinburgh, UK
Many credit scoring systems depend on scorecards which order applicants by credit risk. However the scorecards may also have other properties with certain scores reflecting certain good:bad odds or differences in scores having the same property throughout the score range. Other properties like positivity of attribute points may be required for palatability or internal marketing reasons. The paper outlines the results of a small survey of what properties scorecard builders require of their scorecards. It then discusses how these properties can be obtained and describes a linear programming formulation which recalibrates scorecards so as to produce the best approximate scorecard with the properties required. Keywords: credit scoring; linear programming; credit scorecards
Introduction 1
Most of the approaches to credit and behaviour scoring result in a system which gives a score to applicants (credit scoring) or to customers (behaviour scoring) which reflects their credit worthiness. The credit worthiness measure is decided upon by the lender. The industry’s Guide to Credit Scoring2 defines a good or creditworthy account as one where the performance is such that the credit grantor would choose to accept that applicant again. For credit scoring, the lender decides on a cut-off score so those with scores above the cut-off are classified as desirable and those with scores below the cut-off are classified as undesirable. The system can then be used on new customers by accepting those with scores above the threshold and rejecting those with scores below it. For such binary accept=reject decisions, scorecards appear to be ordinal rather than cardinal measures in that it is the order of the applicants on the scale that is important. There are other credit decisions where the score value is important, as it gives an estimate of the credit risk involved. Thus the values may be useful in deciding what percentage of applicants to accept or what the price of the product should be. However, for the accept=reject decisions all that matters is the relative ranking of the applicant scores and where the cut-off point occurs. The exact difference between two scores is unimportant. However, logistic regression3 builds scorecards where the score is supposed to represent the log of the odds of goods to bads at that score. Thus if the scores for two different applicants differ by 20 points then the odds of goods to bads for the two different applicants should differ by the same multiplicative factor, no matter what the
*Correspondence: LC Thomas, Department of Management, University of Southampton, Highfield, Southampton SO17 1BJ, UK. E-mail: [email protected]
original scores are. Similarly, if the scorecard is based on a discriminant analysis approach which is essentiall
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