FRM Part I · FRM Exam Part I · Measuring Credit Risk
A bank holds a USD 20 million exposure to a counterparty and has a legally enforceable guarantee from a third party covering 60% of the exposure. The counterparty's PD is 4% and the guarantor's PD is 1%. Assuming defaults are independent and LGD is 100% for both, what is the probability the bank suffers a loss on the guaranteed portion?
The guaranteed portion is lost only if both the borrower and the guarantor default. With independent defaults, the joint probability is 4% x 1%, which is 0.04%. Adding the two PDs would wrongly assume that either default alone causes a loss.
- A0.04%Correct
- B1.00%
- C4.00%
- D5.00%
Explanation
The bank loses on the guaranteed portion only if both the counterparty and the guarantor default. With independence, joint probability = 0.04 x 0.01 = 0.0004 = 0.04%. Adding the probabilities (5%) wrongly treats either default as causing loss.
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