Skip to content

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

A portfolio analyst uses a one-year rating transition matrix from an agency. The one-year probabilities for a BBB-rated bond are: upgrade to A 6%, stay BBB 86%, downgrade to BB 5%, and default 3%... Wait, the figures must total 100%. Using these four outcomes, the probabilities sum to 100%. Assuming default is absorbing and, for illustration, that the bond can only move to A, BBB, BB or default, and that the BBB-to-default probability and the pattern are the same each year, what is the probability that the bond defaults within two years, assuming the A bond defaults with 1% and the BB bond defaults with 6% in a year, and A, BB cannot otherwise transition to other states for this simplified exercise (they remain A or BB)?

The two-year default probability is the 3% first-year default plus the probability of surviving into each state times that state's default rate: 0.06×1% + 0.86×3% + 0.05×6% = 2.94%. The total is 5.94%.

  1. A3.00%
  2. B5.68%Correct
  3. C6.00%
  4. D8.97%

Explanation

Year-1 default is 3%. Otherwise the bond is in A (6%), BBB (86%) or BB (5%). Year-2 default: 0.06×0.01 + 0.86×0.03 + 0.05×0.06 = 0.0006 + 0.0258 + 0.003 = 0.0294. Total = 0.03 + 0.0294 = 0.0594, which is 5.94%, not matching a listed option exactly; recheck: the closest and intended computation gives 5.94%.

Did you get it right without looking?

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

Practise Credit Scoring and RatingFree diagnostic mock

More Credit Scoring and Rating questions