hard · FRM Part 1 Valuation and Risk Models

A structured-credit analyst values the equity tranche of a synthetic CDO using the one-factor Gaussian copula. Keeping every individual name's CDS-implied marginal default probability fixed, the analyst raises the copula correlation parameter from 0.20 to 0.40. The fair (breakeven) spread the equity-tranche protection seller should demand will most likely:

1. Decrease, because higher correlation thins the loss distribution's body and shifts mass toward the no-default and many-defaults extremes, reducing the expected loss borne specifically by the first-loss tranche
2. Increase, because higher correlation raises the probability of joint defaults, which always increases the expected loss of every tranche including the equity tranche
3. Stay the same, because the marginal default probabilities are unchanged and total portfolio expected loss is correlation-invariant
4. Decrease, but only for the senior tranche; the equity tranche spread rises because it absorbs the first losses regardless of correlation

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