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

A CreditRisk+ portfolio has an expected loss of USD 12 million. In the extended model, default rates are driven by a single gamma-distributed sector factor with mean 1 and variance 0.25. Relative to a model with the same mean default rates but no sector factor (pure Poisson), what is the effect on the loss distribution?

Expected loss stays at USD 12 million because the sector factor has a mean of 1. However, its variance makes default rates random and correlated across obligors, which overdisperses defaults and fattens the loss tail, so credit VaR at high confidence levels rises relative to the pure Poisson model.

  1. AExpected loss is unchanged but the tail becomes fatter, increasing credit VaRCorrect
  2. BExpected loss rises by 25% and the tail is unchanged
  3. CExpected loss falls because default correlation is positive
  4. DBoth expected loss and the tail are unchanged because the factor has mean 1

Explanation

A mean-1 gamma factor leaves expected default rates, hence expected loss, at USD 12 million. Its variance induces positive default correlation through common random default rates, making the number of defaults overdispersed (negative-binomial-like). This fattens the tail and raises high-quantile loss and unexpected loss. Option four ignores the variance effect.

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