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

A one-year transition matrix gives a B-rated issuer a 10% chance of default, 60% chance of remaining B, and 30% chance of upgrade to BB. A BB-rated issuer has a 2% chance of default, 78% chance of remaining BB, and 20% chance of moving to B. Assuming time-homogeneity and default is absorbing, what is the two-year cumulative default probability for a B-rated issuer?

The two-year cumulative default probability is 16.6%. It is the 10% first-year default plus second-year defaults from survivors: 60% × 10% from staying B and 30% × 2% from upgrading to BB, giving 6.0% and 0.6%.

  1. A10.0%
  2. B12.0%
  3. C16.6%Correct
  4. D20.0%

Explanation

Year 1 default is 10%. Year 2 default: stay B (60%) then default 10% = 6.0%; upgrade to BB (30%) then default 2% = 0.6%. Total = 10% + 6.0% + 0.6% = 16.6%. Simply doubling 10% to 20% ignores that defaulted issuers cannot default again and survivors migrate.

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