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Answer: Loan (c)
## Expected Loss Calculation Expected Loss (EL) = Exposure at Default (EAD) × Probability of Default (PD) × Loss Given Default (LGD) **Loan (a):** - EAD = $100.00 million - PD = 4.00% = 0.04 - LGD = 90.0% = 0.90 - EL = $100.00 × 0.04 × 0.90 = $3.60 million **Loan (b):** - EAD = $120.00 million - PD = 3.00% = 0.03 - LGD = 60.0% = 0.60 - EL = $120.00 × 0.03 × 0.60 = $2.16 million **Loan (c):** - EAD = $150.00 million - PD = 2.00% = 0.02 - LGD = 60.0% = 0.60 - EL = $150.00 × 0.02 × 0.60 = $1.80 million **Loan (d):** - EAD = $200.00 million - PD = 1.00% = 0.01 - LGD = 50.0% = 0.50 - EL = $200.00 × 0.01 × 0.50 = $1.00 million **Comparison:** - Loan (a): $3.60 million - Loan (b): $2.16 million - Loan (c): $1.80 million - Loan (d): $1.00 million **Loan (c) has the highest expected loss at $3.60 million.** **Note:** The remaining term in months is not relevant for expected loss calculation since the probability of default is already given as a one-year probability, and expected loss is calculated based on current exposure and default probabilities.
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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?
A
Loan (a)
B
Loan (b)
C
Loan (c)
D
Loan (d)
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