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

In a one-factor Gaussian copula model of a large homogeneous loan portfolio, each obligor's latent variable is Mi = sqrt(rho)*M + sqrt(1-rho)*Zi. Holding each loan's unconditional default probability fixed, what is the effect of increasing the copula correlation rho?

Expected portfolio loss stays the same because marginal default probabilities are fixed, but higher copula correlation makes defaults cluster, so the loss distribution becomes more skewed with a fatter right tail and higher probability of extreme losses.

  1. AExpected portfolio loss rises, and the tails of the loss distribution become thinner
  2. BExpected portfolio loss is unchanged, but the loss distribution becomes more skewed with a fatter right tailCorrect
  3. CExpected portfolio loss falls, and the loss distribution becomes more symmetric
  4. DExpected portfolio loss is unchanged and the loss distribution is unchanged

Explanation

Marginal default probabilities fix expected loss, so it does not change with rho. Higher rho increases dependence on the common factor, raising the probability of many simultaneous defaults and fattening the right tail while making more scenarios with very few defaults.

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