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FRM Part II · FRM Exam Part II · Credit Value at Risk

In a one-factor Gaussian copula model (Vasicek) for a large homogeneous loan portfolio, the asset correlation is 0.20 and the PD is 2%. Which effect results from raising the asset correlation to 0.40, holding PD and LGD fixed?

Raising asset correlation leaves the mean default rate, equal to PD, and hence expected loss unchanged. However the worst-case default rate at a high confidence level increases, because common-factor shocks drive more defaults together, so credit VaR rises and the distribution becomes more skewed.

  1. AExpected loss rises and the loss distribution becomes more symmetric
  2. BExpected loss is unchanged but the worst-case default rate at a high confidence level risesCorrect
  3. CExpected loss falls because defaults become more predictable
  4. DBoth expected loss and the worst-case default rate stay unchanged

Explanation

In the Vasicek model, the mean default rate equals PD, so expected loss is unchanged. The conditional default rate at a high confidence level, N[(N^-1(PD)+sqrt(rho)N^-1(q))/sqrt(1-rho)], increases with rho, so tail loss rises.

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