The risk contribution of an asset to the portfolio unexpected loss (ULP) is calculated using the formula:

$$RC_i = UL_i \times \frac{UL_i + (\rho_{ij} \times UL_j)}{UL_P}$$

Here,

• $UL_i$ is the unexpected loss of Asset X
• $UL_j$ is the unexpected loss of Asset Y,
• $\rho_{ij}$ is the correlation between the two assets.

$$\begin{aligned} UL_P &= \sqrt{UL_X^2 + UL_Y^2 + 2 \cdot \rho_{XY} \cdot UL_X \cdot UL_Y} \\ &= \sqrt{556417^2 + 387732^2 + 2 \cdot 0.4 \cdot 556417 \cdot 387732} \\ &= \sqrt{309598595089 + 150343756624 + 172895132564} \\ &= \sqrt{632837484277} \\ &\approx 795,317 \end{aligned}$$

The risk contribution of Asset X can be calculated as follows:

RC_X = 556417 \times \frac{556417 + (0.4 \times 387732)}{795317} = \`$497`,784

Things to Remember

• The risk contribution (RC) of an asset considers the asset’s unexpected loss and its correlation with other assets in the portfolio.
• In a two-asset portfolio, the risk contribution of one asset can be calculated while taking into account the correlation with the other asset.