[yummyfajitas]

Consider a plain vanilla housing package. Payoff = homeowner_payments.sum().

Now consider the least risky tranch of a CDO. Payoff = min(homeowner_payments.sum(), 0.7 x MAX_HOMEOWNER_PAYMENT).

Is it unclear that if homeowner_payments.sum() goes way down, you lose money? Of course not. For every derivative on the market, computing your gains/losses given a specific scenario is straightforward.

The only difficulty is computing the probability of each scenario, but derivatives don't change that calculation at all.