The unexpected loss (UL) is calculated using the formula: $UL = EAD \times \sqrt{PD \times \sigma_{LR}^2 + LR^2 \times \sigma_{PD}^2}$

Where:

• $EAD = 80$ million (outstanding balance)
• $PD = 0.01$
• $\sigma_{PD} = 0.04$
• $LR = 0.25$
• $\sigma_{LR} = 0.15$

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

Variance $= 0.000225 + 0.000100 = 0.000325$ Standard Deviation $= \sqrt{0.000325} \approx 0.0180277$

$UL = 80 \times 0.0180277 = 1.4422$ million USD.