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Answer: $22.36 million
## Explanation When two positions are **not correlated** (correlation = 0), the portfolio VaR is calculated using the **square root of the sum of squares** formula: \[\text{Portfolio VaR} = \sqrt{(\text{VaR}_1)^2 + (\text{VaR}_2)^2}\] Given: - VaR₁ = $10 million - VaR₂ = $20 million Calculation: \[\text{Portfolio VaR} = \sqrt{(10)^2 + (20)^2} = \sqrt{100 + 400} = \sqrt{500} = 22.36\] Therefore, the portfolio VaR is **$22.36 million**. **Key Points:** - When correlation = 0, diversification benefit occurs - Simple sum ($30 million) would overestimate risk - Square root formula captures diversification effect - Answer C ($22.36 million) is correct
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A portfolio consists of two positions. The VaR of the two positions are $10 million and $20 million. If the returns of the two positions are not correlated. The VaR of the portfolio would be closest to:
A
$5.48 million
B
$15.00 million
C
$22.36 million
D
$25.00 million
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