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FRM Part I · FRM Exam Part I · Measuring Credit Risk

Under the Vasicek single-factor large homogeneous portfolio model, a portfolio has a PD of 1% and an asset correlation of 0.16. Using N⁻¹(0.01) = −2.326 and N⁻¹(0.999) = 3.090, what is the 99.9% worst-case default rate (approximately)?

The worst-case default rate is about 11.7%. The numerator is −2.326 plus 0.4 times 3.090, which is −1.090. Dividing by the square root of 0.84 gives −1.189, and the normal CDF of that is roughly 0.117.

  1. A2.3%
  2. B11.7%Correct
  3. C13.8%
  4. D1.0%

Explanation

WCDR = N[(N⁻¹(PD) + √ρ·N⁻¹(0.999))/√(1−ρ)] = N[(−2.326 + 0.4×3.090)/0.9165] = N[−1.090/0.9165] = N(−1.189) ≈ 11.7%. Omitting the √(1−ρ) divisor gives N(−1.090) ≈ 13.8%. Using ρ instead of √ρ gives about 2.3%.

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