Financial Risk Manager Part 1

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Explanation:

The following formula gives the expected loss:

\text{EL} = \text{EA} \times \text{PD} \times \text{LR}

Exposure at default, EA, is given by:

\begin{aligned} \text{EA} &= \text{drawn amount} + \text{drawdown on default} \\ &= 80\% \times 100,000 + 70\% \times (100,000 - 80\% \times 100,000) \\ &= 80,000 + 14,000 = 94,000 \end{aligned}

Note: Drawdown on default measures the amount of the committed funds likely to be drawn further if a default occurs.

The expected loss, EL, is therefore USD 752:

\text{EL} = 94,000 \times 0.02 \times 0.4 = \text{USD } 752

The following formula gives the unexpected loss, UL:

\text{UL} = \text{EA} \times \sqrt{\text{PD} \times \sigma_{\text{LR}}^2 + \text{LR}^2 \times \sigma_{\text{PD}}^2}

\sigma_{\text{LR}}^2 = 0.3^2, \; \sigma_{\text{PD}}^2 = p(1-p) = 0.02 \times 0.98 = 0.0196

Thus,

\begin{aligned} \text{UL} &= 94,000 \times \sqrt{0.02 \times 0.3^2 + 0.4^2 \times 0.0196} \\ &= \text{USD } 6,604 \end{aligned}

Explanation:

The following formula gives the expected loss:

\text{EL} = \text{EA} \times \text{PD} \times \text{LR}

Exposure at default, EA, is given by:

\begin{aligned} \text{EA} &= \text{drawn amount} + \text{drawdown on default} \\ &= 80\% \times 100,000 + 70\% \times (100,000 - 80\% \times 100,000) \\ &= 80,000 + 14,000 = 94,000 \end{aligned}

Note: Drawdown on default measures the amount of the committed funds likely to be drawn further if a default occurs.

The expected loss, EL, is therefore USD 752:

\text{EL} = 94,000 \times 0.02 \times 0.4 = \text{USD } 752

The following formula gives the unexpected loss, UL:

\text{UL} = \text{EA} \times \sqrt{\text{PD} \times \sigma_{\text{LR}}^2 + \text{LR}^2 \times \sigma_{\text{PD}}^2}

\sigma_{\text{LR}}^2 = 0.3^2, \; \sigma_{\text{PD}}^2 = p(1-p) = 0.02 \times 0.98 = 0.0196

Thus,

\begin{aligned} \text{UL} &= 94,000 \times \sqrt{0.02 \times 0.3^2 + 0.4^2 \times 0.0196} \\ &= \text{USD } 6,604 \end{aligned}

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RRohit

Last updated: June 22, 2026 at 14:25

Expected loss = USD 640; unexpected loss = USD 5,621.

Expected loss = USD 640; unexpected loss = USD 6,604.

Expected loss = USD 752; unexpected loss = USD 6,604.

Expected loss = USD 752; unexpected loss = USD 5,621.