Skip to content

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

A scorecard assigns a 12-month PD of 2.0% to a portfolio of 5,000 accounts in one rating grade. 130 accounts default over the year. Assuming independent defaults and using a normal approximation to the binomial, what is the z-statistic for a one-sided test of whether the PD is underestimated (use sqrt(5,000 × 0.02 × 0.98) = 9.90)?

The z-statistic is about 3.03. Expected defaults are 100, observed are 130, and the binomial standard deviation is 9.90, so z equals 30 divided by 9.90. This strongly rejects the hypothesis that the 2% PD is adequate, suggesting underestimation, under the independence assumption.

  1. A3.03Correct
  2. B1.52
  3. C0.30
  4. D30.0

Explanation

Expected defaults = 5,000 × 0.02 = 100. Excess = 130 − 100 = 30. Standard deviation = 9.90. z = 30/9.90 = 3.03. Option B halves the result by mistake. Option C divides by 100 instead of the standard deviation. Option D omits the division entirely. A z of 3.03 rejects the PD at conventional levels.

Did you get it right without looking?

One question tells you little. A timed set on Credit Scoring and Retail Credit Risk Management shows your real accuracy, how long you take and where you lose marks.

Practise Credit Scoring and Retail Credit Risk ManagementFree diagnostic mock

More Credit Scoring and Retail Credit Risk Management questions