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FRM Part II · FRM Exam Part II · Financial Correlation Modeling - Bottom-Up Approaches

In a one-factor Gaussian copula model for a large homogeneous portfolio of loans, the pairwise correlation parameter is increased while every loan's marginal default probability is held constant. What is the expected effect?

The expected default rate stays the same because it depends only on the marginal default probabilities. Higher correlation raises the likelihood of many simultaneous defaults, spreading the distribution and fattening the right tail, which increases unexpected loss and tail risk measures.

  1. AExpected portfolio default rate rises and its distribution becomes narrower
  2. BExpected portfolio default rate is unchanged and the loss distribution has a fatter right tailCorrect
  3. CExpected portfolio default rate falls and the loss distribution is more symmetric
  4. DExpected portfolio default rate is unchanged and the loss distribution becomes more concentrated around the mean

Explanation

Expected default rate depends only on the marginal probabilities, so it is unchanged. Higher correlation increases the chance of many simultaneous defaults, raising variance and the right-tail loss, while also increasing the chance of very few defaults.

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