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

A portfolio of 100 equally weighted names has identical 5-year default probability of 10% and a one-factor Gaussian copula. A risk manager compares two correlation assumptions, 0.10 and 0.50. Which conclusion is correct for the distribution of the portfolio default count?

Expected defaults stay at 10 because marginal default probabilities do not change, but the variance of the default count is higher at correlation 0.50. Greater correlation raises pairwise covariance, fattening both tails of the loss distribution and increasing the chance of many simultaneous defaults.

  1. AThe expected number of defaults is higher at correlation 0.50
  2. BThe expected number of defaults is unchanged at 10, but the variance of the default count is higher at correlation 0.50Correct
  3. CThe expected number of defaults is unchanged at 10 and the variance is also unchanged
  4. DThe expected number of defaults is lower at 0.50 because of diversification

Explanation

Expected defaults equal 100 x 10% = 10 regardless of correlation, since marginal probabilities are unchanged. Variance of the count equals n*p(1-p)+n(n-1)*Cov, and covariance rises with default correlation, so variance and tail risk increase. Claiming the mean changes confuses marginal and joint effects.

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