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FRM Part II · FRM Exam Part II · Structured Credit Risk

A risk analyst at a bank is pricing tranches of a synthetic CDO using a one-factor Gaussian copula in which every reference entity has the same pairwise asset correlation. The analyst raises the asset correlation from 0.20 to 0.50, holding each entity's individual default probability constant. Which is the most likely effect on the portfolio loss distribution and tranche risk?

Raising correlation leaves expected portfolio loss unchanged because marginal default probabilities are fixed, but it fattens both tails of the loss distribution. The equity tranche becomes less risky and the senior tranche becomes riskier, since senior losses occur only in extreme clustered-default scenarios.

  1. AThe expected portfolio loss falls and the senior tranche becomes safer
  2. BThe expected portfolio loss is unchanged, but the likelihood of very low and very high losses both increases, so the equity tranche becomes less risky and the senior tranche becomes more riskyCorrect
  3. CThe expected portfolio loss rises and all tranches lose value equally
  4. DThe portfolio loss distribution becomes more symmetric and tranche spreads converge

Explanation

Expected loss depends only on marginal default probabilities and recovery, so it is unchanged. Higher correlation fattens both tails: more scenarios with few defaults and more with many. The equity tranche benefits from the higher chance of few defaults (lower expected loss, since its loss is concave in portfolio loss), while the senior tranche is hit more often in extreme scenarios.

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