Skip to content

FRM Part II · FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment

A bank validates a scorecard on a holdout sample of 10,000 loans, of which 500 defaulted. At a cutoff score, the scorecard flags 600 loans as high risk, and 350 of these actually defaulted. What is the scorecard's true positive rate (sensitivity) and false positive rate at this cutoff?

Sensitivity is 70% because 350 of the 500 defaulters were flagged. The false positive rate is about 2.6% because 250 of the 9,500 non-defaulters were flagged. Using the number of flagged loans as the denominator would instead give precision, not sensitivity.

  1. ASensitivity 70.0%; false positive rate 2.6%Correct
  2. BSensitivity 58.3%; false positive rate 2.6%
  3. CSensitivity 70.0%; false positive rate 4.2%
  4. DSensitivity 58.3%; false positive rate 4.2%

Explanation

Sensitivity = defaulters flagged / all defaulters = 350/500 = 70%. Non-defaulters = 9,500; flagged non-defaulters = 600-350 = 250; FPR = 250/9,500 = 2.63%. The 58.3% figure is precision (350/600), and 4.2% is 250/600, both wrong bases.

Did you get it right without looking?

One question tells you little. A timed set on Introduction to Credit Risk Modeling and Assessment shows your real accuracy, how long you take and where you lose marks.

Practise Introduction to Credit Risk Modeling and AssessmentFree diagnostic mock

More Introduction to Credit Risk Modeling and Assessment questions