Financial Risk Manager Part 1

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: $80 ± 6.272$