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

A lender is deciding the cutoff for a credit score. Approving an applicant who later defaults costs 800 in loss, while a good applicant who is approved earns a profit of 100. Ignoring other costs, at what minimum probability of being good should the lender be indifferent about approving?

The breakeven probability of being good is 88.9%. Setting expected profit 100p minus 800(1-p) to zero gives p equal to 800 divided by 900, so the lender should approve only applicants whose good probability exceeds that level.

  1. A88.9%Correct
  2. B80.0%
  3. C12.5%
  4. D50.0%

Explanation

Let p be the probability of good. Expected profit = 100p - 800(1-p) = 0, so 900p = 800 and p = 0.8889. Approve above 88.9%. The 80% choice wrongly uses 800/1000; 12.5% is the default probability at breakeven, not the good probability.

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