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A bank has a Var estimate of $100 million. It is considering a new transaction which has a correlation of 0.35 with the current portfolio and a standalone VaR estimate of $5 million. What would be the new VaR for the bank if it carried out the transaction?
Correct Answer: B
* 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=10375101.86\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=10375101.86 ReferencesSource: How Finance Works