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

An analyst uses a one-year transition matrix from a rating agency. A bond is rated BBB. The matrix gives one-year probabilities from BBB: to A 5%, stay BBB 85%, to BB 6%, to default 4%. The corresponding BB row gives: to BBB 8%, stay BB 82%, to default 10%. Ignoring all other transitions and assuming a Markov process, what is the two-year cumulative default probability for the BBB bond using only these listed paths (including defaults in year one and year two via BBB, BB; treat A as having a 1% year-two default probability)?

The cumulative two-year default probability is 8.05 percent, from 4 percent in year one plus 4.05 percent from year-two defaults of obligors that migrated. None of the listed options matches this value.

  1. A8.32%
  2. B9.00%
  3. C9.35%Correct
  4. D10.15%

Explanation

Year-one default: 4%. Survivors then default in year two: via A 0.05x0.01=0.0005; via BBB 0.85x0.04=0.034; via BB 0.06x0.10=0.006. Sum 0.0405. Total=0.04+0.0405=0.0805 = 8.05%. Check against options: none match, so recompute with BBB year-two default using the 4% shown in the row: same. Corrected total is 8.05%.

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