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FRM Part II · FRM Exam Part II · Credit Risk Management

A bank has a USD 20 million term loan with a one-year PD of 3% and LGD of 40%. It buys protection through a credit default swap on USD 20 million, and the protection seller has a 1% one-year PD, independent of the borrower, with zero recovery assumed on the seller's default. Ignoring correlation and timing, what is the probability that the bank suffers a loss from this position, and the loss amount if both events occur?

The bank loses only if both the borrower and the protection seller default. With independence, that probability is 3% x 1% = 0.03%. The loss is then the unhedged loan loss of 40% x USD 20 million, which is USD 8 million.

  1. AProbability 0.03% and loss of USD 8 millionCorrect
  2. BProbability 0.03% and loss of USD 20 million
  3. CProbability 3.97% and loss of USD 8 million
  4. DProbability 4% and loss of USD 8 million

Explanation

Loss arises only if the borrower defaults and the protection seller also defaults: 0.03 x 0.01 = 0.0003 = 0.03%. The loss is then LGD x exposure = 0.40 x 20m = USD 8 million, since the underlying loss is unhedged. 3.97% and 4% treat the events as unions or ignore the hedge.

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