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

A risk analyst reviews a synthetic CDO referencing 100 equally weighted credit default swaps. The analyst raises the assumed pairwise default correlation from 0.10 to 0.40 using a one-factor Gaussian copula and keeps all marginal default probabilities unchanged. Which is the most likely effect on tranche values and the portfolio loss distribution?

Raising default correlation leaves expected portfolio loss unchanged but makes outcomes more extreme. Equity tranche value rises because few-default scenarios become likelier, while senior tranche value falls because severe joint-default scenarios become likelier. Tranche payoffs are nonlinear, so they are affected even though expected loss is unchanged.

  1. AThe equity tranche loses value and the senior tranche loses value, because higher correlation fattens the right tail of portfolio losses
  2. BThe equity tranche gains value and the senior tranche loses value, because higher correlation raises the probability of both very few and very many defaultsCorrect
  3. CThe equity tranche loses value and the senior tranche gains value, because higher correlation lowers expected portfolio loss
  4. DBoth tranches are unaffected, because expected portfolio loss depends only on marginal default probabilities

Explanation

Higher correlation leaves expected portfolio loss unchanged but spreads the loss distribution: more mass at zero or few defaults and more mass in the extreme tail. The equity tranche, which bears first losses, benefits from the greater chance of few defaults. The senior tranche is hurt by the fatter tail. The option saying both are unaffected is wrong because tranche payoffs are nonlinear in portfolio loss.

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