Financial Risk Manager Part 1
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Assumed that asset prices are normally distributed. The expected value of an asset price is $80 with daily volatility of 2%. Compute the 95% confidence interval of the asset price at the end of 4 days.
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TTanishq
A
$80 \pm 2.000$
B
$80 \pm 3.200$
C
$80 \pm 6.272$
D
$80 \pm 3.136$
Explanation:
Explanation
To compute the 95% confidence interval for the asset price after 4 days, we need to:
-
Calculate the 4-day volatility:
- Daily volatility = 2%
- 4-day volatility = Daily volatility × √(time period)
- 4-day volatility = 2% × √4 = 2% × 2 = 4%
-
Convert volatility to dollar terms:
- One standard deviation move = Asset price × 4-day volatility
- One standard deviation move =
$80× 0.04 =$3.20
-
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: $80 ± 6.272$
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