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

A portfolio manager uses a rating agency's cumulative default table where the one-year default probability for a B-rated issuer is 4.0% and the cumulative two-year default probability is 8.5%. Assuming no rating migration within the analysis, what is the conditional (marginal) probability of default in year two, given survival through year one?

The conditional year-two default probability is about 4.69%. Unconditional second-year default is 8.5% minus 4.0%, or 4.5%, and dividing by the 96% survival probability through year one gives 4.69%.

  1. A4.50%
  2. B4.69%Correct
  3. C4.25%
  4. D8.50%

Explanation

Survival through year 1 is 96.0%. Survival through year 2 is 91.5%. Unconditional year-two default is 96.0% − 91.5% = 4.5%. Conditional on surviving year one, hazard = 4.5/96.0 = 4.69%. The 4.50% option forgets to condition on survival.

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