Answer: $80 \pm 6.272$

**Step-by-step calculation:** 1. **Calculate 4-day volatility:** Daily volatility = 2% = 0.02 For 4 days, volatility scales with the square root of time: $$\sigma_{4\text{-day}} = \sigma_{\text{daily}} \times \sqrt{4} = 0.02 \times 2 = 0.04 \text{ or } 4\%$$ 2. **Calculate one standard deviation move in dollar terms:** $$\$80 \times 0.04 = \$3.20$$ 3. **Calculate 95% confidence interval:** For a normal distribution, the 95% confidence interval corresponds to ±1.96 standard deviations: $$\$80 \pm 1.96 \times \$3.20 = \$80 \pm \$6.272$$ **Why other options are incorrect:** - **A ($80 ± 2.000):** This would be approximately one daily standard deviation move, not accounting for the 4-day horizon or the 95% confidence level. - **B ($80 ± 3.200):** This is exactly one standard deviation move over 4 days, but for 95% confidence we need ±1.96 standard deviations. - **D ($80 ± 3.136):** This appears to be $80 ± 0.98 × 3.20, which would correspond to approximately a 67% confidence interval (one standard deviation), but the calculation is slightly off. **Key concepts:** - Volatility scales with the square root of time - For normally distributed returns, 95% confidence interval = mean ± 1.96 × standard deviation - The standard deviation in dollar terms = asset price × volatility

Author: Nikitesh Somanthe