Assume that the CDX-iTraxx index has 125 names in it,for a total notional of $100,000,000.If the recovery rate on default of any name is 40%,at least how many names must default for the 3-7% tranche of the CDO to be wiped out?

Question

Quizplus · Accepted Answer

The 3-7% tranche covers losses from 3% to 7% of the total notional. The total notional is $100,000,000, so the tranche covers $4,000,000 ($100,000,000 * 4%). With a recovery rate of 40%, the loss per defaulted name is 60% of $800,000 (the notional per name), which is $480,000. To wipe out the tranche, $4,000,000 / $480,000 = 8.33, so at least 9 names must default. However, since the question asks for the minimum number of defaults to wipe out the tranche, and considering the tranche starts at 3%, we need to account for the first 3% ($3,000,000) being absorbed by the equity tranche. Therefore, 15 defaults are needed to reach the 7% loss level.

Assume That the CDX-ITraxx Index Has 125 Names in It,for