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

In the Vasicek single-factor model for a large homogeneous loan portfolio, the worst-case default rate at a given confidence level is computed from the obligor's PD and the asset correlation. Holding PD and the confidence level constant, what happens to the worst-case default rate as the asset correlation approaches zero?

The worst-case default rate approaches the PD. With zero asset correlation the systematic factor has no effect, so the conditional default rate equals the unconditional PD at every confidence level, and a large portfolio has no unexpected loss from systematic risk.

  1. AIt approaches 100%
  2. BIt approaches the PD itselfCorrect
  3. CIt approaches zero
  4. DIt approaches 50%

Explanation

With zero correlation the systematic factor has no influence, so the conditional default rate equals N[N^-1(PD)] = PD at any confidence level. Defaults are then fully diversifiable in a large portfolio. Credit VaR beyond expected loss therefore falls to zero.

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