Explanation:

To determine which loan has the highest dollar expected loss, we need to calculate the probability of default (PD) for each loan using the default intensity model:

PD = 1 - e^(-λ × t)

Where:

• λ = default intensity
• t = time in years

Calculations:

• Loan (a): λ = 4.0%, t = 3/12 = 0.25 years PD = 1 - e^(-0.04 × 0.25) = 1 - e^(-0.01) = 1 - 0.9900 = 1.00%

• Loan (b): λ = 3.0%, t = 6/12 = 0.5 years PD = 1 - e^(-0.03 × 0.5) = 1 - e^(-0.015) = 1 - 0.9851 = 1.49%

• Loan (c): λ = 2.0%, t = 9/12 = 0.75 years PD = 1 - e^(-0.02 × 0.75) = 1 - e^(-0.015) = 1 - 0.9851 = 1.49%

• Loan (d): λ = 1.0%, t = 12/12 = 1.0 years PD = 1 - e^(-0.01 × 1.0) = 1 - e^(-0.01) = 1 - 0.9900 = 1.00%

Expected Loss Calculation: EL = Exposure × PD × LGD

Since all loans have the same LGD (60.0%), the loan with the highest PD will have the highest expected loss. However, loans (b) and (c) both have PD = 1.49%, but loan (c) has a longer remaining term (9 months vs 6 months), which typically means higher exposure and therefore higher dollar EL.

Loan (c) has the highest dollar EL = $150 million × (1 - e^(-2% × 9/12)) × 60.0% = $1.34 million

Therefore, loan (c) has the highest dollar expected loss.