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

A risk manager explains why the Vasicek model can express portfolio credit VaR through a single conditional default rate. Which assumption makes this possible?

The model relies on a large homogeneous portfolio. Idiosyncratic risk diversifies away, so the portfolio default rate equals the PD conditional on the systematic factor, which lets the tail loss be read from a single quantile of that factor.

  1. AThe portfolio is large and homogeneous, so idiosyncratic risk diversifies away and the realized default rate equals the conditional PD given the systematic factorCorrect
  2. BAll borrowers have the same recovery rate, so losses are independent of the economy
  3. CAsset correlations between all pairs of borrowers are zero
  4. DDefault probabilities are constant across all states of the economy

Explanation

With many equally sized, identical exposures, borrower-specific shocks average out, so the portfolio default rate is determined entirely by the systematic factor. This is what allows a closed-form worst-case default rate. Zero correlation would remove the systematic factor, and PDs in the model are conditional on the factor, so they are not constant across states.

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