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

A risk analyst uses the Vasicek single-factor model to estimate the worst-case default rate (WCDR) of a large homogeneous loan portfolio at the 99.9% confidence level. The PD is held constant. If the asset correlation parameter is raised from 0.10 to 0.25, what is the effect on the WCDR?

The WCDR rises. A higher asset correlation gives the common systematic factor more weight, so diversification removes less risk and the default rate in a bad tail scenario moves further above the PD at a 99.9% confidence level.

  1. AIt falls, because higher correlation makes borrowers more similar and so less likely to default
  2. BIt rises, because more of each borrower's default risk comes from the common factor and less can be diversified awayCorrect
  3. CIt is unchanged, because the WCDR depends only on PD and the confidence level
  4. DIt rises only if the PD is above 50%

Explanation

In the Vasicek formula WCDR = N[(N^-1(PD) + sqrt(rho)·N^-1(X))/sqrt(1-rho)], a higher rho increases the weight on the confidence-level quantile, which is positive for X above 50%. The tail default rate therefore moves further above the PD. Correlation does not leave the WCDR unchanged, and the effect does not depend on PD exceeding 50%.

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