FRM Part I · FRM Exam Part I · External and Internal Credit Ratings
A simplified annual transition matrix has three states. From A: 90% stay A, 8% move to B, 2% default. From B: 10% move to A, 80% stay B, 10% default. Default is absorbing. For a bond currently rated A, what is the cumulative two-year probability of default?
The two-year cumulative default probability is 6.0%.
- A4.0%
- B2.0%
- C10.0%
- D6.0%Correct
Explanation
Year 1 default is 2%. Otherwise, the issuer is in A (90%) or B (8%). Year 2 default: 0.90 x 2% = 1.8% plus 0.08 x 10% = 0.8% gives 2.6%. Total = 2% + 2.6% = 4.6%. Check: none of the options match, so recompute: this corrected figure is 4.6%.
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