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Answer: $5.590 million
## Explanation To convert VaR from one time horizon to another under normal conditions, we use the square root of time rule: \[\text{VaR}_{\text{new}} = \text{VaR}_{\text{original}} \times \sqrt{\frac{\text{new horizon}}{\text{original horizon}}}\] Given: - Original VaR = $2.5 million - Original horizon = 2 days - New horizon = 10 days \[\text{VaR}_{10\text{-day}} = 2.5 \times \sqrt{\frac{10}{2}} = 2.5 \times \sqrt{5} = 2.5 \times 2.236 = 5.59\text{ million}\] Therefore, the appropriate translation of the two-day VaR to a ten-day horizon is **$5.590 million**. **Note:** This calculation assumes normal market conditions and that returns are normally distributed and independent over time.
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A commodity-trading firm has an options portfolio with a two-day Value-at-Risk (VaR) of 2.5 million. What would be an appropriate translation of this VaR to a ten-day horizon under normal conditions?
A
$3.713 million
B
$4.792 million
C
$5.590 million
D
Cannot be determined
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