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Answer: USD 1,924,720
## 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.
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A market risk analyst at a regional bank is calculating the annual VaR of portfolio of investment securities. The portfolio has a current market value of USD 3,700,000 with a daily variance of 0.0004. Assuming there are 250 trading days in a year and the daily portfolio returns are independent and follow the same normal distribution with a mean of zero, what is the estimate of the 1-year VaR at the 95% confidence level?
A
USD 38,494
B
USD 121,730
C
USD 1,924,720
D
USD 2,721,519
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