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FRM Part I · FRM Exam Part I · External and Internal Credit Ratings

A bank's internal scale has grades A, B and C. Over one year, 500 borrowers began in grade B. Of these, 40 were upgraded to A, 60 were downgraded to C, 20 defaulted, and the rest stayed in B. What is the one-year probability that a grade B borrower remains in grade B?

The probability is 76%. Of 500 grade B borrowers, 40 were upgraded, 60 were downgraded and 20 defaulted, so 120 left the grade. That leaves 380 who stayed, and 380 divided by 500 equals 0.76. Defaults must be counted as exits from the grade.

  1. A76%Correct
  2. B80%
  3. C84%
  4. D72%

Explanation

Borrowers leaving B: 40 + 60 + 20 = 120. Remaining: 500 − 120 = 380. 380/500 = 76%. The 80% option ignores defaults (excludes the 20 defaulters from the exit count, giving 400/500... i.e., counts only 100 leaving). The 84% option ignores downgrades beyond a partial count; 72% double-counts defaults.

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