Explanation

The time scaling of VaR follows the square root of time rule when returns are independently and identically distributed (IID):

$\text{VaR}_{10\text{-day}} = \text{VaR}_{1\text{-day}} \times \sqrt{10}$

Calculation: $\text{VaR}_{10\text{-day}} = 100 \times \sqrt{10} = 100 \times 3.162 ≈ 316\text{ million}$

Key Points:

• The square root of time rule only applies when returns are IID
• If returns are not IID (autocorrelated, trending, etc.), this scaling doesn't hold
• Option A is incorrect because it states the opposite condition
• Option C is wrong - VaR absolutely depends on the time horizon
• Option D is incorrect - it uses division instead of multiplication

Correct Answer: B - The 10-day VaR is USD 316 million only if returns are independently and identically distributed.