The question involves calculating the Value at Risk (VaR) for a portfolio using both normal and lognormal distribution assumptions. The manager has provided annualized averages and standard deviations for arithmetic and geometric returns, respectively, along with the current portfolio value and the number of trading days in a year.

For the normal distribution (arithmetic returns):

1. The annualized average return is 12%.
2. The annualized standard deviation of returns is 30%.
3. The 95% VaR is calculated using the Z-score for a 95% confidence level, which is 1.645.
4. The daily return is calculated by dividing the annualized average return by the number of trading days (12% / 252).
5. The daily standard deviation is calculated by dividing the annualized standard deviation by the square root of the number of trading days (30% / sqrt(252)).
6. The 1-day 95% VaR is then calculated as -[(0.12/252) - 1.645 * (0.30/sqrt(252))], which equals 3.06%.

For the lognormal distribution (geometric returns):

1. The annualized average return is 11%.
2. The annualized standard deviation of returns is 41%.
3. The 95% VaR is calculated using the same Z-score of 1.645.
4. The daily return and daily standard deviation are calculated similarly to the normal distribution.
5. The 1-day 95% VaR for the lognormal distribution is calculated using the exponential function: 1 - exp[(0.11/252) - 0.41 * 1.645 / sqrt(252)], which equals 4.12%.

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 for both the normal and lognormal VaRs are based on the provided data and the appropriate statistical formulas for each distribution.