Skip to content

FRM Part I · FRM Exam Part I · External and Internal Credit Ratings

A credit analyst uses a one-year rating transition matrix in which a BBB-rated issuer has a 2.0% probability of moving to default, a 90.0% probability of staying BBB, and the remaining probability split among other non-default ratings. Assuming a time-homogeneous Markov process, which statement about the BBB issuer's two-year default probability is correct?

The two-year default probability exceeds 2.0%. Default is absorbing, so it combines year-one default with migration to another non-default rating followed by default in year two. Simply doubling the one-year figure is not exact, and the probability cannot stay at or fall below 2.0%.

  1. AIt equals exactly 4.0%, because the one-year probability is simply doubled
  2. BIt is greater than 2.0%, because default is an absorbing state and the issuer can also default after migrating to another rating in year oneCorrect
  3. CIt equals 2.0%, because the matrix only describes the first year
  4. DIt is less than 2.0%, because surviving the first year lowers the default risk

Explanation

The two-year cumulative default probability is the BBB-to-default entry of the squared matrix. It includes defaulting in year one plus migrating to a non-default rating and then defaulting in year two. Because default is absorbing, the figure exceeds 2.0%. Simple doubling ignores the survival requirement and the fact that migration changes the year-two default probability, so it is not exact.

Did you get it right without looking?

One question tells you little. A timed set on External and Internal Credit Ratings shows your real accuracy, how long you take and where you lose marks.

Practise External and Internal Credit RatingsFree diagnostic mock

More External and Internal Credit Ratings questions