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

In a one-factor Gaussian copula (Vasicek) model, each obligor has a one-year default probability of 2% and a asset correlation of 0.20 with the single systematic factor structure (pairwise asset correlation rho = 0.20). Holding the default probability fixed, what is the effect of raising rho from 0.20 to 0.40 on the portfolio loss distribution of a large homogeneous portfolio?

Expected loss stays the same because default probability and loss severity are unchanged, but higher asset correlation fattens the tail of the loss distribution. Defaults become more concentrated in bad systematic states, so credit VaR increases.

  1. AExpected loss is unchanged but the tail of the loss distribution becomes fatter, increasing the credit VaRCorrect
  2. BExpected loss rises in proportion to rho and the tail is unchanged
  3. CExpected loss falls and the tail becomes thinner
  4. DBoth expected loss and credit VaR are unchanged because default probability is fixed

Explanation

Expected loss depends on default probability and loss given default, not on correlation. Higher asset correlation increases the dependence on the systematic factor, so the conditional default rate in bad states rises and the loss distribution tail becomes fatter, raising credit VaR.

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