hard · FRM Part 2 Credit Risk

A credit portfolio of 100 identical names is modeled with a one-factor Gaussian copula, asset correlation ρ, and common marginal default probability p. An analyst recalibrates by doubling ρ while holding p fixed, then is surprised that the expected number of defaults is unchanged but the equity-tranche (first-loss) value rises. The most accurate explanation is:

1. Raising ρ leaves the marginal p and hence expected defaults unchanged, but fattens both tails of the loss distribution, shifting mass toward zero and many defaults — sparing the equity tranche while hurting senior tranches.
2. Raising ρ lowers each name's marginal default probability, so expected defaults fall and the equity tranche gains from the lower loss mean.
3. Raising ρ increases expected defaults but compresses the loss variance, so the equity tranche gains purely from reduced dispersion.
4. Raising ρ leaves the entire loss distribution unchanged because the Gaussian copula is exchangeable, so the tranche-value change must stem from a recovery-rate misspecification.

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