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

A portfolio manager uses a one-factor Gaussian copula (Vasicek-type) model, as underlies the Basel IRB formula, for a large homogeneous portfolio with PD of 2% and asset correlation 0.20. Using N^-1(0.02) = -2.054 and N^-1(0.999) = 3.090, what is the approximate 99.9% worst-case default rate? Use N(-0.8) ≈ 0.2119 and note: conditional PD = N[(N^-1(PD) + sqrt(rho)*N^-1(0.999))/sqrt(1-rho)], sqrt(0.2)=0.4472, sqrt(0.8)=0.8944.

The worst-case default rate is about 21%. Stressing the systematic factor gives (-2.054 + 0.4472×3.090)/0.8944 ≈ -0.75, and the normal CDF of that is roughly 0.22. The unconditional 2% PD ignores the 99.9% systematic stress.

  1. AAbout 21.2%Correct
  2. BAbout 2.0%
  3. CAbout 8.5%
  4. DAbout 47.2%

Explanation

Numerator: -2.054 + 0.4472*3.090 = -2.054 + 1.382 = -0.672. Divide by 0.8944 = -0.751. N(-0.751) ≈ 0.226, so approximately 21-23%, closest to 21.2%. The 2.0% option is just the unconditional PD, ignoring the systematic stress.

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