FRM Exam Part II · Credit Scoring and Retail Credit Risk Management

Credit Scoring Models and Scorecard Development Steps for FRM Part 2

Updated 11 October 2026 · Fact-checked

A credit scorecard turns borrower data into a score that ranks default risk. You build it by defining good and bad accounts, selecting and binning variables, fitting a model such as logistic regression, scaling the output to points, and correcting for rejected applicants with reject inference.

Understand Credit Scoring Models and Scorecard Development

A credit scorecard is a statistical tool that ranks borrowers by risk. It does not predict who will default. It orders applicants so that higher scores mean lower default probability. Lenders use it to approve, decline and price loans, especially in retail lending where volumes are large.

Building starts with data and definitions. You pick an observation window and a performance window. You define a bad account, for example 90 days past due within 12 months. You define good, and often an indeterminate group that you exclude. Poor definitions ruin everything that follows.

Next you choose variables. Candidates are screened using measures such as information value and checks for stability and business sense. Continuous variables are usually grouped into bins. Each bin gets a weight of evidence (WoE), which measures how good and bad accounts are distributed across the bin. WoE handles outliers, missing values and non-linear effects.

The model links the variables to default. Logistic regression is the standard choice. It models the log-odds of default as a linear function of the inputs, so output is always a probability between 0 and 1. Linear discriminant analysis finds a linear combination that best separates good and bad groups. It assumes normally distributed predictors with equal covariance matrices across groups, which binary and categorical credit data often violate. That is why logistic regression is preferred.

Finally you scale the log-odds into points, using a base score, base odds and points to double the odds (PDO). You also face reject inference. The model is built only on accepted applicants, whose outcomes you observe. Rejects have no outcome, which causes sample selection bias. Reject inference estimates their likely performance, using methods such as augmentation, parceling or extrapolation, so the scorecard works on the full through-the-door population.

Key formulas to remember

Logistic regression: ln(p ÷ (1 − p)) = β0 + β1x1 + β2x2 + … + βkxk; p is the probability of default. Left side is the log-odds.
Probability from score: p = 1 ÷ (1 + e^−(β0 + Σβixi)); Always lies between 0 and 1, unlike a linear probability model.
Weight of evidence: WoE = ln(% of goods in bin ÷ % of bads in bin); Sign conventions vary. Be consistent. Here positive WoE means the bin is better than average.
Information value: IV = Σ (% goods − % bads) × WoE; Measures a variable's predictive power. A common rule of thumb treats IV below about 0.02 as weak and above about 0.5 as suspiciously strong.
Score scaling: Score = Offset + Factor × ln(odds), Factor = PDO ÷ ln 2; Odds here are good:bad. Score rises by PDO points each time odds double.
Offset: Offset = Base score − Factor × ln(base odds); Anchors the scale at a chosen score and odds.

How to solve Credit Scoring Models and Scorecard Development questions

Use this method for any scorecard question, whether it asks about model choice, scaling or bias.

1Identify the stage being tested: definition, variable selection, model fitting, scaling, validation or reject inference.
2For definition questions, check the bad definition, performance window and treatment of indeterminates.
3For variable questions, think WoE, binning, information value, stability and multicollinearity.
4For model choice, compare assumptions. Logistic regression needs no normality and gives probabilities. Discriminant analysis needs normality and equal covariances.
5For scaling, compute Factor = PDO ÷ ln 2, then Offset, then the score. Check that odds doubling adds PDO points.
6For reject inference, ask whether the sample is only accepted accounts. If so, selection bias exists and inference methods are needed.
7Eliminate options that reverse the direction of a relationship or overstate what a method guarantees.

Quickest way: Scaling shortcut

When to use it: When a question gives base score, base odds and PDO and asks for a score at new odds.

Count how many times the odds double from the base odds: n = log2(new odds ÷ base odds).
New score = base score + n × PDO.
If odds fall, n is negative and the score drops.
Sanity check: better odds must mean a higher score.

Common mistakes in Credit Scoring Models and Scorecard Development

Saying discriminant analysis and logistic regression make the same assumptions.
Both give a linear separating rule, so they look alike.
Fix: Remember that discriminant analysis assumes multivariate normal predictors with equal covariance. Logistic regression does not.
Treating the score as a probability of default.
Scores and probabilities both rank risk.
Fix: A score is a scaled log-odds. Convert it back through the scaling formula to get a probability.
Using good:bad odds as bad:good odds in the scaling formula.
Logistic regression usually models default, while scaling uses good:bad odds.
Fix: Read which event the question defines and keep the direction consistent.
Thinking reject inference removes all bias.
The name suggests it recovers true outcomes.
Fix: It only estimates rejected outcomes under assumptions. It reduces selection bias but cannot eliminate it.
Choosing variables only by statistical strength.
High information value looks attractive.
Fix: Also require stability, business logic, legal acceptability and low correlation with other variables. A very high IV may signal leakage.

Worked examples

Example 1

A scorecard is scaled so that a score of 600 corresponds to good:bad odds of 50:1, with PDO of 20. What score corresponds to odds of 200:1?

Show the solution

Find how many times the odds double: 200 ÷ 50 = 4.
4 = 2², so the odds double twice.
Each doubling adds PDO = 20 points.
Added points = 2 × 20 = 40.
New score = 600 + 40 = 640.

Answer: 640

Example 2

A bank builds a retail scorecard using only approved applicants from the past three years. Which statement is most accurate? A) Results are unbiased because outcomes are observed. B) The model suffers from selection bias, and reject inference can help estimate rejected applicants' performance. C) Discriminant analysis must replace logistic regression. D) Weight of evidence cannot be used.

Show the solution

Outcomes are only known for accepted accounts, so A is wrong.
The accepted group differs systematically from all applicants, which is sample selection bias, so B fits.
Logistic regression is valid here, so C is not required.
WoE is applicable to any binned variable, so D is wrong.

Answer: B

Exam tips

Expect conceptual questions on logistic regression versus discriminant analysis. Lead with assumptions and the probability output.
For scaling, practise the doubling-of-odds shortcut until it is automatic.
Link reject inference to selection bias in the through-the-door population.
Watch wording such as always or guarantees. Scorecard methods rarely guarantee anything.

Practice questions from Credit Scoring and Retail Credit Risk Management

Credit Scoring Models and Scorecard Development: frequently asked questions

Why is logistic regression preferred for credit scorecards?

It handles a binary default outcome and gives probabilities between 0 and 1. It does not require normally distributed predictors. Its coefficients are also easy to explain to regulators and business users.

What is reject inference in credit scoring?

It is a set of methods that estimate how rejected applicants would have performed. You need it because a model built only on accepted accounts suffers from selection bias. Common approaches include augmentation, parceling and extrapolation.

What does weight of evidence do?

It converts each bin of a variable into a number based on the log ratio of goods to bads. This handles non-linearity, outliers and missing values. It also puts variables on a comparable scale for logistic regression.

What is PDO in scorecard scaling?

PDO means points to double the odds. It is the number of points by which the score rises when good:bad odds double. Together with a base score and base odds it fixes the scale.