Answer: USD 2,737,737

The question is asking for the estimate of the annual Value at Risk (VaR) at the 95% confidence level for a portfolio of investment securities. The portfolio's current market value is USD 7,444,000 and has a daily variance of 0.0002. It is given that there are 250 trading days in a year and that the portfolio returns follow a normal distribution. The correct answer is C, which is USD 2,737,737. Here's the step-by-step explanation: 1. **Calculate the Daily Standard Deviation**: The daily variance is given as 0.0002. The standard deviation is the square root of the variance, so it is \( \sqrt{0.0002} = 0.01414 \). 2. **Convert Daily VaR to Annual VaR**: The formula for VaR is: \[ \text{VaR} = \text{Portfolio Value} \times \sqrt{\text{Number of Trading Days}} \times \text{Daily Standard Deviation} \times \text{Z-Score} \] where the Z-Score for a 95% confidence level is approximately 1.645. 3. **Apply the Formula**: Plugging in the values: \[ \text{Annual VaR} = 7,444,000 \times \sqrt{250} \times 0.01414 \times 1.645 = 2,737,737 \] The incorrect options are explained as follows: - Option A (USD 38,723) is incorrect because it uses the variance instead of the standard deviation in the VaR formula. - Option B (USD 173,150) is incorrect because it represents the 1-day VaR at the 95% confidence level, not the annual VaR. - Option D (USD 3,871,110) is incorrect because it represents the 1-year VaR at the 99% confidence level, not the 95% level. This question tests the understanding of calculating VaR and the importance of using the correct confidence level and standard deviation in the formula.

Author: LeetQuiz Editorial Team