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FRM Part II · FRM Exam Part II · Portfolio Credit Risk

A credit portfolio manager moves from a Gaussian copula to a Student t copula with low degrees of freedom, keeping the same marginal default probabilities and the same correlation matrix. What is the most likely effect on the portfolio loss distribution?

Switching to a Student t copula with low degrees of freedom adds tail dependence, so defaults cluster more in stress. Marginals and correlations are unchanged, but joint extreme defaults become more likely and the right tail of the loss distribution becomes fatter than under the Gaussian copula.

  1. ALower tail dependence and a thinner right tail of losses
  2. BNo change, because the marginals and correlations are identical
  3. CHigher tail dependence, so joint extreme defaults become more likely and the right tail of losses fattensCorrect
  4. DHigher expected loss but unchanged joint default behavior in stress

Explanation

The Student t copula exhibits positive tail dependence, while the Gaussian copula has zero asymptotic tail dependence. With the same marginals and correlations, the t copula therefore produces more joint extreme events, raising high-quantile losses. It does not change expected loss, which depends on marginals.

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