Answer: 1-day normal 95% VaR = 3.06% and 1-day lognormal 95% VaR = 4.12%

The question is asking to determine the correct Value at Risk (VaR) for a portfolio using two different statistical distributions: normal and lognormal. The risk manager has provided data on the portfolio's arithmetic and geometric returns, along with their respective standard deviations and the current portfolio value. The Value at Risk (VaR) is a statistical technique used to measure and quantify the level of financial risk within a firm or investment portfolio over a specific time frame. It represents the maximum potential loss over a given time period at a given confidence level. For the normal distribution, the 1-day 95% VaR is calculated using the formula: \[ 1-day \text{ normal } 95\% \text{ VaR} = -\left[\left(\frac{\text{Annualized average of arithmetic returns}}{252}\right) - 1.645 \times \left(\frac{\text{Annualized standard deviation of arithmetic returns}}{\sqrt{252}}\right)\right] \] For the lognormal distribution, the 1-day 95% VaR is calculated using the formula: \[ 1-day \text{ lognormal } 95\% \text{ VaR} = 1 - \exp\left[\left(\frac{\text{Annualized average of geometric returns}}{252}\right) - 1.645 \times \left(\frac{\text{Annualized standard deviation of geometric returns}}{\sqrt{252}}\right)\right] \] Plugging in the provided values: - For the normal distribution: \[ 1-day \text{ normal } 95\% \text{ VaR} = -\left[\left(\frac{0.12}{252}\right) - 1.645 \times \left(\frac{0.30}{\sqrt{252}}\right)\right] = 3.06\% \] - For the lognormal distribution: \[ 1-day \text{ lognormal } 95\% \text{ VaR} = 1 - \exp\left[\left(\frac{0.11}{252}\right) - 1.645 \times \left(\frac{0.41}{\sqrt{252}}\right)\right] = 4.12\% \] Thus, the correct answer is A. 1-day normal 95% VaR = 3.06% and 1-day lognormal 95% VaR = 4.12%. This is because the calculations match the values provided in the explanation.

Author: LeetQuiz Editorial Team