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FRM Part II · FRM Exam Part II · Fundamentals of Credit Risk

A bank has an exposure of USD 20 million to a borrower with a one-year default probability of 4% and a guarantor's independent default probability of 2%. LGD is 100% for both if default occurs, and the guarantee covers the full exposure. Assuming default independence, what is the bank's expected loss with the guarantee, and by how much does it fall relative to unguaranteed?

With full guarantee and independence, the bank loses only if borrower and guarantor both default, probability 0.08%. Expected loss is USD 20 million times 0.0008, or USD 16,000, versus USD 800,000 unguaranteed, a fall of USD 784,000.

  1. AUSD 16,000 expected loss; falls by USD 784,000Correct
  2. BUSD 400,000 expected loss; falls by USD 400,000
  3. CUSD 800,000 expected loss; falls by zero
  4. DUSD 320,000 expected loss; falls by USD 480,000

Explanation

Unguaranteed EL = 20m x 4% = 800,000. With a full guarantee, loss occurs only if both default: 4% x 2% = 0.08%. EL = 20m x 0.0008 = 16,000. Reduction = 800,000 - 16,000 = 784,000. Using 2% alone ignores that joint default is needed.

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