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

A lender's mortgage scorecard assigns a 12-month PD of 2.0% to a score band. Over the past year 2,000 loans were in that band and 60 defaulted. Using a one-sided binomial test at about 95% confidence (z = 1.645) with the normal approximation, which conclusion is correct?

The observed default rate of 3.0% is significantly higher than the predicted 2.0%. Expected defaults are 40 with a standard deviation of about 6.26, giving z of roughly 3.19, above 1.645. The binomial test rejects the calibration, so the model underestimates PD.

  1. AThe observed rate of 3.0% is not significantly above 2.0%; the PD is acceptable
  2. BThe observed rate of 3.0% is significantly above 2.0% since the test statistic is about 3.2, so PD is underestimatedCorrect
  3. CThe observed rate of 3.0% is significantly below 2.0%, so PD is overestimated
  4. DThe test statistic is about 1.6, which is just below the critical value, so no conclusion can be drawn

Explanation

Expected defaults = 2,000 × 2% = 40. Standard deviation = sqrt(2000 × 0.02 × 0.98) = sqrt(39.2) = 6.26. z = (60 − 40)/6.26 = 3.19, well above 1.645. The calibration is rejected, indicating PD underestimation. The 1.6 option wrongly uses the standard deviation of 12.5 or mishandles the variance.

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