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FRM Part II · FRM Exam Part II · Estimating Default Probabilities

A credit analyst uses a historical table in which the cumulative five-year default probability for B-rated issuers is 20% and the cumulative four-year probability is 16%. Which is the conditional probability of default in year 5, given survival through year 4?

The conditional year-5 default probability is the incremental default probability of 4% divided by the 84% survival probability to year 4, about 4.8%, so roughly 5%. Using 4% alone gives the unconditional probability and ignores that only survivors can default in year 5.

  1. A5.0%Correct
  2. B4.0%
  3. C20.0%
  4. D25.0%

Explanation

Unconditional year-5 default probability is 20% - 16% = 4%. Survival to year 4 is 1 - 16% = 84%. The conditional probability is 4%/84% = 4.76%, which is closest to 5.0% only approximately, so recompute with clean data: this gives about 4.8%, and the nearest listed value is 5.0%. The 4.0% option ignores conditioning on survival.

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