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

In a Vasicek single-factor model, an obligor has PD of 2% and asset correlation of 0.25. The systematic factor M is standard normal, and in a severe downturn it takes the value -2. Using N^-1(0.02) = -2.0537, the default probability conditional on M = -2 is closest to:

The conditional default probability is about 11.2%. Subtracting 0.5 times -2 from -2.0537 gives -1.0537. Dividing by the square root of 0.75 gives -1.2167, and the normal CDF of that value is roughly 11.2%, well above the 2% unconditional PD.

  1. A11.2%Correct
  2. B0.02%
  3. C47.5%
  4. D2.0%

Explanation

Conditional PD = N[(N^-1(PD) − sqrt(ρ)·M)/sqrt(1−ρ)]. With sqrt(0.25) = 0.5 and M = -2, the numerator is -2.0537 + 1 = -1.0537. Dividing by sqrt(0.75) = 0.8660 gives -1.2167, and N(-1.2167) ≈ 11.2%. Adding sqrt(ρ)·M instead of subtracting it gives the 0.02% distractor.

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