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

A large homogeneous portfolio has a one-year PD of 1% and an asset correlation of 0.20. Using the Vasicek large-portfolio formula, the 99.9% worst-case default rate is closest to (use N^-1(0.01) = -2.3263 and N^-1(0.999) = 3.0902):

The worst-case default rate is about 14.6%. The numerator is -2.3263 plus 0.4472 times 3.0902, which is -0.9443. Dividing by the square root of 0.8 gives -1.056, and the normal CDF of that value is roughly 14.6%.

  1. A14.6%Correct
  2. B1.6%
  3. C7.5%
  4. D28.5%

Explanation

WCDR = N[(N^-1(PD) + sqrt(ρ)·N^-1(0.999))/sqrt(1-ρ)]. sqrt(0.2) = 0.4472, so the numerator is -2.3263 + 1.3820 = -0.9443. Dividing by sqrt(0.8) = 0.8944 gives -1.0558, and N(-1.0558) ≈ 0.1456. Using ρ instead of sqrt(ρ) gives 1.6%, and using 99% confidence gives 7.5%.

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