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

A CreditRisk+ portfolio has a mean default count of 10 in one year. The analyst first assumes defaults are Poisson, then allows the default rate to be random with a gamma distribution, keeping the same mean. How does the number-of-defaults distribution change?

Variance rises above 10 and the tail becomes fatter. Making the default rate random with a gamma distribution creates overdispersion relative to the Poisson, whose variance equals its mean, and this captures default correlation through a common systematic factor.

  1. AVariance falls below 10 and the tail becomes thinner
  2. BVariance remains 10 because the mean is unchanged
  3. CVariance rises above 10 and the tail becomes fatter, reflecting default correlation through a common factorCorrect
  4. DThe distribution becomes normal with variance equal to 10 squared

Explanation

A Poisson has variance equal to its mean (10). Mixing it with a gamma-distributed rate produces a negative-binomial-type distribution with variance greater than the mean (overdispersion). This induces default correlation through the common background factor and fattens the tail, raising credit VaR.

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