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

Historical data show a BBB issuer's marginal (conditional) annual default probabilities of 1% in year one and 2% in year two. What is the cumulative two-year default probability, and what does this imply?

The cumulative two-year default probability is 2.98%. Survival is 0.99 times 0.98, which equals 0.9702, so default is 1 minus that. The second-year 2% is conditional on surviving year one, so adding the two rates to get 3% overstates it.

  1. A3.00%, the sum of the marginal probabilities
  2. B2.98%, because survival through year one is 99% and year-two default is conditional on survivalCorrect
  3. C2.00%, because only the latest year matters
  4. D1.98%, the product of the two marginal probabilities

Explanation

Survival = 0.99 × 0.98 = 0.9702, so cumulative PD = 1 − 0.9702 = 0.0298. Summing conditional probabilities (3%) overstates because year-two default applies only to survivors. The product 0.01×0.02 is the joint chance of ... not appropriate, and 1.98% equals 0.99×0.02, an unconditional year-two probability only.

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