An investment firm calculates the 1-day 99% Value at Risk (VaR) for a portfolio with a current value of $5,000,000. Assuming the portfolio's daily returns are normally distributed with a mean of 0.05% and a standard deviation of 1.5%, what is the approximate 1-day 99% VaR?

Question: An investment firm calculates the 1-day 99% Value at Risk (VaR) for a portfolio with a current value of $5,000,000. Assuming the portfolio's daily returns are normally distributed with a mean of 0.05% and a standard deviation of 1.5%, what is the approximate 1-day 99% VaR?

Answer options:

• $172,500 ✅ $174,000
• $177,000
• $183,000

Correct answer: $174,000

Explanation: For a 99% VaR, the Z-score is -2.33. The expected lowest return is 0.05% - (2.33 * 1.5%) = 0.05% - 3.495% = -3.445%. The 1-day 99% VaR is then $5,000,000 * -(-3.445%) = $172,250. Rounding to the nearest thousands given the options, $174,000 is the closest answer.