The Unexpected Loss (UL) for a loan is calculated using the formula: $UL = EAD \times \sqrt{PD \times \sigma_{LGD}^2 + LGD^2 \times \sigma_{PD}^2}$

Here, Exposure at Default (EAD) is the outstanding balance of USD 80 million (assuming no further drawdowns since no Credit Conversion Factor is provided for the undrawn amount).

Given:

• $PD = 1\% = 0.01$
• $LGD = 25\% = 0.25$
• $\sigma_{PD} = 4\% = 0.04$
• $\sigma_{LGD} = 15\% = 0.15$

Calculating the terms under the square root: $PD \times \sigma_{LGD}^2 = 0.01 \times (0.15)^2 = 0.01 \times 0.0225 = 0.000225$ $LGD^2 \times \sigma_{PD}^2 = (0.25)^2 \times (0.04)^2 = 0.0625 \times 0.0016 = 0.000100$

Sum of the terms: $`$0.00`0225 + 0.000100 = 0.000325 $$

Taking the square root: $\sqrt{0.000325} \approx 0.0180277$

Multiply by EAD: $UL = 80 \text{ million} \times 0.0180277 \approx 1.4422 \text{ million}$

Therefore, the unexpected loss is USD 1.442 million.