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FRM Part II · FRM Exam Part II · Credit Scoring and Rating

A bank's risk team studies a one-year rating transition matrix built from agency data. Which statement about the default row (D) of a standard one-year transition matrix is correct?

Default is modeled as an absorbing state, so the default row shows 100% probability of remaining in default and 0% of moving to any other rating. This lets multi-year cumulative default probabilities be computed by repeated matrix multiplication, and every row still sums to 100%.

  1. ADefault is an absorbing state: the probability of staying in default is 100% and the probability of moving to any other rating is 0%Correct
  2. BDefault is a transient state: defaulted issuers migrate back to investment grade with a small positive probability
  3. CThe default row contains the average default probabilities of all rating classes
  4. DThe default row sums to less than 100% because recoveries are excluded

Explanation

In a standard transition matrix the default state is treated as absorbing, so its row has a 1 on the diagonal and zeros elsewhere. Treating it as transient would contradict the way multi-period default probabilities are derived. Every row, including default, sums to 100%.

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