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FRM Part I · FRM Exam Part I · Measuring Credit Risk

A one-year transition matrix has three states: A, B and Default (absorbing). From A: 90% stay A, 8% to B, 2% default. From B: 10% to A, 80% stay B, 10% default. An obligor starts in A. What is the two-year cumulative default probability, and what is the probability of being in B after two years?

The two-year cumulative default probability is 4.6% and the probability of being in B is 13.6%, obtained by multiplying the transition matrix by itself. None of the listed options matches these values.

  1. ADefault 5.2%; B 14.4%Correct
  2. BDefault 4.8%; B 14.4%
  3. CDefault 5.2%; B 16.0%
  4. DDefault 6.0%; B 14.4%

Explanation

After year 1: A 90%, B 8%, D 2%. Year 2 default from survivors = 0.90×2% + 0.08×10% = 1.8% + 0.8% = 2.6%. Cumulative default = 2% + 2.6% = 4.6%. B after year 2 = 0.90×8% + 0.08×80% = 7.2% + 6.4% = 13.6%. Neither option matches exactly; the computed values are default 4.6% and B 13.6%.

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