Explanation

This question involves calculating Value at Risk (VaR) using the square root of time rule, which allows us to scale daily risk measures to annual measures.

Step-by-Step Calculation:

1. Calculate Daily Standard Deviation:

   • Given daily variance = 0.0004
   • Daily standard deviation = √0.0004 = 0.02 = 2%

2. Calculate Annual Standard Deviation:

   • Using square root rule: σ_annual = σ_daily × √T
   • Where T = 250 trading days
   • σ_annual = 0.02 × √250 = 0.02 × 15.8114 = 0.316228

3. Calculate 1-Year VaR at 95% Confidence:

   • VaR = Portfolio Value × Z-score × σ_annual
   • Z-score for 95% confidence level = 1.645
   • VaR = 3,700,000 × 1.645 × 0.316228
   • VaR = 3,700,000 × 0.5202 = USD 1,924,720

Why Other Options Are Incorrect:

• A (USD 38,494): Uses variance instead of standard deviation in the VaR formula
• B (USD 121,730): This is the 1-day VaR at 95% confidence level
• D (USD 2,721,519): This is the 1-year VaR at 99% confidence level (Z-score = 2.326)

The square root rule is valid here because the daily returns are independent and identically distributed with mean zero, which satisfies the conditions for time scaling in VaR calculations.