Explanation

When returns are independently and identically distributed (i.i.d.), the VaR scales with the square root of time. The formula for converting VaR from one time horizon to another is:

$\text{VaR}_{T} = \text{VaR}_{1} \times \sqrt{T}$

Where:

• $\text{VaR}_{1}$ = 1-day VaR = USD 100 million
• $T$ = 10 days

Calculation: $\text{VaR}_{10} = 100 \times \sqrt{10} = 100 \times 3.162 \approx \text{USD 316 million}$

Key Points:

• This scaling relationship only holds when returns are i.i.d.
• If returns are not i.i.d. (Option A), the square root of time rule does not apply
• VaR does depend on the time horizon (Option C is incorrect)
• Option D is incorrect because it shows a decrease in VaR with longer horizon, which contradicts risk theory

Therefore, the correct answer is B - USD 316 million if returns are independently and identically distributed.