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State what types of credit risk scoring model exist, which variables they rely on and how they are used.

FRM® Part II · Credit Risk Measurement and Management · Credit Scoring and Retail Credit Risk Management · FRM2.CR.7.d

The idea

Credit scoring models are grouped by purpose. Application scores rate new applicants for accept or reject decisions. Behavioural scores use the payment history, balances and utilisation of existing accounts to manage limits, cross-selling and early collections. Collection scores rank delinquent accounts by likelihood of cure or recovery, and fraud, attrition and response scores serve other tasks. Typical inputs are demographic and employment data, income and debt ratios, and bureau history such as delinquencies, utilisation and enquiries, plus behavioural data for existing customers. Statistical methods include logistic regression, discriminant analysis, trees and neural networks, as against judgmental systems. In logistic regression the log odds are an intercept plus a sum of coefficients times variables. The logit is that log odds figure, and it converts into a probability of default as follows. PD = 1 ÷ (1 + e^−logit). A key trap is building a model only on accepted applicants, which biases it and calls for reject inference.

Formulas

PD from a logistic regression score

PD = 1 ÷ (1 + e^(−z))

z
the score, the log odds of default: the intercept plus each coefficient × its variable

Compute the score first, intercept included, then transform. A model built only on accepted applicants needs reject inference before it is trusted.

A practice question

From the question bank, with the reason each wrong option is wrong.

For what decision is an application scorecard primarily used?

  1. Setting limit increases for accounts that have performed well for several years.Why not: That is a behavioural scoring use, based on account history.
  2. Prioritising delinquent accounts for the collections team.Why not: That is collection scoring, which ranks delinquent accounts.
  3. Detecting unusual transactions on cards in real time.Why not: That is fraud scoring, which looks at transaction patterns.
  4. Deciding whether to accept or reject a new applicant and what terms to offer. - correct

Application scores are built from application and bureau data for customers with no account history, and they drive accept, reject and initial terms.

A harder one

A logistic regression scorecard has logit = -4 + 2 x utilisation + 0.7 x number of delinquencies in the last year, where PD = 1 / (1 + e^-logit). An applicant has utilisation of 0.8 and 2 delinquencies. The estimated PD is closest to:

  1. 36.8%Why not: Reports the odds e^logit as if it were a probability.
  2. 26.9% - correct
  3. 73.1%Why not: Flips the sign of the logit, giving the probability of repayment instead of default.
  4. 8.3%Why not: Leaves out the delinquency term, so only the utilisation coefficient is applied.

logit = -4 + 1.6 + 1.4 = -1.0. PD = 1 / (1 + e^1.0) = 26.9%. The log odds are linear in the characteristics; PD is the logistic transform.

The hardest tier

In scorecard development, weight of evidence for a bin is ln(% of goods / % of bads) and information value is the sum over bins of (% goods - % bads) x WoE. A variable has three bins with goods of 50%, 30%, 20% and bads of 20%, 30%, 50%. The information value is closest to:

  1. 0.55 - correct
  2. 0.24Why not: Uses a base-10 logarithm instead of the natural logarithm.
  3. 1.83Why not: Sums the absolute weights of evidence and omits the (% goods - % bads) weighting.
  4. 0.27Why not: Counts only the first bin and ignores the contribution of the third bin.

WoE = ln(2.5) = 0.916, 0, and ln(0.4) = -0.916. IV = 0.3 x 0.916 + 0 + (-0.3) x (-0.916) = 0.55. A higher IV means the variable separates goods from bads better.

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