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Explanation:
To find the expected loss (EL) in dollar terms, we use the formula:
Given that the one-year probability of default (PD) acts as an annualized rate (hazard rate), we must adjust it for the remaining term of the loan. Assuming a discrete approximation as stated in the question:
Calculating the EL for each loan:
Loan (a):
EL = \`100.00 \times 1.00\% \times 90.0\% = \
Loan (b):
EL = \`120.00 \times 1.50\% \times 60.0\% = \
Loan (c):
EL = \`150.00 \times 1.50\% \times 60.0\% = \
Loan (d):
EL = \`200.00 \times 1.00\% \times 50.0\% = \
Loan (c) has the highest expected loss in dollar terms at $1.35 million. Thus, the correct option is C.
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506.1. Consider the following four short-term loans held by a bank:
| Loan | Remaining Term (in months) | Exposure at default (millions) | One-year Probability of Default (*) | Loss Given Default |
|---|---|---|---|---|
| a. | 3 | $100.00 | 4.00% | 90.0% |
| b. | 6 | $120.00 | 3.00% | 60.0% |
| c. | 9 | $150.00 | 2.00% | 60.0% |
| d. | 12 | $200.00 | 1.00% | 50.0% |
(*) Hazard rate (aka, default intensity) which is by definition continuous, but it is okay to assume discrete as difference is not here material
Which loan has the highest expected loss in dollar terms? (this question is a variation on FRM Handbook Example 24.3)
A
Loan (a)
B
Loan (b)
C
Loan (c)
D
Loan (d)