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FRM Part II · FRM Exam Part II · Credit Derivatives

A CDS index has 100 equally weighted reference entities with a notional of USD 200 million. One entity defaults with a recovery rate of 40%. Ignoring accrued premium, what is the protection buyer's payout, and what is the remaining index notional?

The payout is USD 1.2 million and the remaining notional is USD 198 million. Each name is USD 2 million of the index, loss is 60% after 40% recovery, and the defaulted name is removed while the contract continues on the surviving names.

  1. APayout USD 1.2 million; remaining notional USD 198 millionCorrect
  2. BPayout USD 2.0 million; remaining notional USD 198 million
  3. CPayout USD 1.2 million; remaining notional USD 200 million
  4. DPayout USD 0.8 million; remaining notional USD 198 million

Explanation

Each name carries USD 2 million of notional (200/100). Loss given default is 60%, so payout is 2 x 0.6 = USD 1.2 million. The index continues with the defaulted name removed, so notional falls to USD 198 million. Using the 40% recovery as the loss gives 0.8, which is wrong.

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