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FRM Part II · FRM Exam Part II · Credit Value at Risk

A portfolio has 200 independent obligors, each with a one-year default probability of 1.5%. Under the CreditRisk+ Poisson approximation, what is the probability of exactly zero defaults in one year (use e^-3 = 0.0498)?

The expected number of defaults is 200 times 1.5%, which is 3. Under the Poisson distribution, the probability of zero defaults is e to the power minus 3, about 4.98%. This differs from the single-name default probability because it concerns the whole portfolio.

  1. A4.98%Correct
  2. B1.50%
  3. C22.4%
  4. D95.0%

Explanation

The mean number of defaults is 200 x 0.015 = 3. Poisson P(N=0) = e^-3 = 0.0498, or about 4.98%. The 22.4% figure is the probability of exactly one default (3 x e^-3 = 0.149 is actually 14.9%), and 22.4% corresponds to exactly three defaults, so it is wrong here. Using 1.5% confuses the single-name PD with the portfolio event.

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