FRM Part I · FRM Exam Part I · Measuring Credit Risk
A bank has a USD 20 million loan to a firm. A guarantor, independent of the firm, guarantees the loan fully. The firm has a one-year PD of 5% and the guarantor has a one-year PD of 1%. Assuming independence and LGD of 100% for simplicity, what is the probability that the bank suffers a loss?
With a full guarantee from an independent party, the bank loses only if both borrower and guarantor default. That probability is 5% x 1% = 0.05%. The 5.95% figure is the chance that at least one defaults, which does not cause a loss.
- A0.05%Correct
- B1.00%
- C5.00%
- D5.95%
Explanation
The bank loses only if both the borrower and guarantor default. With independence, the probability is 0.05 x 0.01 = 0.0005 = 0.05%. 5.95% is the probability that at least one defaults (0.05 + 0.01 - 0.0005 is 5.95%), which is wrong because one default alone is covered.
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