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