A bank has a Var estimate of $100 million.

Current VaR: The bank has an existing VaR estimate of $100 million.

Standalone VaR for New Transaction: The standalone VaR of the new transaction is $5 million.

Correlation with Current Portfolio: The correlation of the new transaction with the current portfolio is 0.35.

Formula for Combined VaR:

New VaR=(Current VaR2)+(Standalone VaR2)+2×Correlation×Current VaR×Standalone VaR\text{New VaR} = \sqrt{(\text{Current VaR}^2) + (\text{Standalone VaR}^2) + 2 \times \text{Correlation} \times \text{Current VaR} \times \text{Standalone VaR}}New VaR=(Current VaR2)+(Standalone VaR2)+2×Correlation×Current VaR×Standalone VaR​

Plugging in the values:

New VaR=(1002)+(52)+2×0.35×100×5=10000+25+350=10375≈101.86\text{New VaR} = \sqrt{(100^2) + (5^2) + 2 \times 0.35 \times 100 \times 5} = \sqrt{10000 + 25 + 350} = \sqrt{10375} \approx 101.86New VaR=(1002)+(52)+2×0.35×100×5​=10000+25+350​=10375​≈101.86

References

Source: How Finance Works​