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FRM Part II · FRM Exam Part II · Portfolio Credit Risk

In the CreditRisk+ model, a portfolio of many obligors has an expected number of defaults of 4 over the horizon. Assuming defaults are independent and the number of defaults follows a Poisson distribution, what is the probability of exactly 2 defaults (to three decimals)?

The probability is about 0.147. With a Poisson mean of 4, P(2) equals e to the power minus 4 times 4 squared divided by 2 factorial, which is 0.018316 times 8, or roughly 0.1465.

  1. A0.092
  2. B0.147Correct
  3. C0.238
  4. D0.073

Explanation

P(2)=e^-4 × 4^2/2! = 0.018316 × 16/2 = 0.018316 × 8 = 0.1465, which rounds to 0.147. Option 0.092 is roughly P(n=2) using mean 3 miscalculated, and 0.073 is P(2)/2 without dividing correctly, i.e., omitting the factorial adjustment.

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