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. A gain, because higher assumed correlation always raises the probability of joint defaults occurring across the entire reference pool, and this uniformly increases the expected loss borne by every tranche, including equity
3. Stay the same, because each underlying reference name's own individual marginal default probability is unchanged and total portfolio expected loss is invariant to the correlation parameter assumed
4. Decrease, but only for the senior tranche; the equity tranche's fair spread instead rises, since it absorbs the very first losses in the capital structure regardless of the correlation assumption used

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