FRM Part II · FRM Exam Part II · Credit Value at Risk
A bank's retail book has a one-year PD of 1% for each obligor and a uniform asset correlation of 0.20 with the single systematic factor. Using the Vasicek large-portfolio formula, what is the 99.9% worst-case default rate? (N^-1(0.01) = -2.3263; N^-1(0.999) = 3.0902)
The 99.9% worst-case default rate is about 14.6%. Combine the PD quantile of -2.3263 with 0.4472 times 3.0902, divide by the square root of 0.8 to get -1.056, and apply the normal CDF. Skipping the division by the square root of one minus correlation overstates the rate.
- A14.6%Correct
- B17.3%
- C2.8%
- D0.002%
Explanation
WCDR = N[(N^-1(PD) + sqrt(ρ)·N^-1(0.999))/sqrt(1-ρ)] = N[(-2.3263 + 0.4472×3.0902)/0.8944] = N[-0.9443/0.8944] = N(-1.056) ≈ 14.6%. Omitting the division by sqrt(1-ρ) gives N(-0.944) ≈ 17.3%, which is wrong.
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