Answer: $80 \pm 6.272$

## Explanation To compute the 95% confidence interval for the asset price after 4 days, we need to: 1. **Calculate the 4-day volatility**: - Daily volatility = 2% - 4-day volatility = Daily volatility × √(time period) - 4-day volatility = 2% × √4 = 2% × 2 = 4% 2. **Convert volatility to dollar terms**: - One standard deviation move = Asset price × 4-day volatility - One standard deviation move = $80 × 0.04 = $3.20 3. **Calculate the 95% confidence interval**: - For a normal distribution, the 95% confidence interval corresponds to ±1.96 standard deviations - 95% CI = Expected value ± (1.96 × standard deviation move) - 95% CI = $80 ± (1.96 × $3.20) = $80 ± $6.272 **Key Points**: - Volatility scales with the square root of time - The 95% confidence interval uses the z-score of 1.96 for a normal distribution - The calculation correctly accounts for the compounding effect of volatility over multiple days Therefore, the correct answer is **C: $80 ± 6.272$**

Author: Tanishq Prabhu