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

A bank portfolio has 400 independent obligors, each with a one-year default probability of 0.5%. Using the Poisson approximation as in CreditRisk+, what is the approximate probability of exactly two defaults in one year? (Use e^-2 = 0.1353.)

The probability is about 27.07%. Expected defaults are 400 times 0.5%, which is 2, and the Poisson probability of exactly two defaults is e^-2 times 2 squared divided by 2 factorial, giving 0.1353 times 2, or 0.2707.

  1. A13.53%
  2. B27.07%Correct
  3. C18.04%
  4. D5.41%

Explanation

Expected defaults μ = 400 × 0.005 = 2. P(n=2) = e^-μ μ^2/2! = 0.1353 × 4 / 2 = 0.2707. The 13.53% option is P(0 defaults), 18.04% is P(3) = 0.1353×8/6, and 5.41% is P(4).

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