Hull RM&FI volatility EOC Question 10.2 and 10.17

[FRM candidate]

Hello,

How was the confidence interval in question 10.2 calculated?

 

[David Harper CFA FRM]

Hi @FRM candidate To recap Hull's EOC Question 10.2, he asks:

"The volatility of an asset is 25% per annum. What is the standard deviation of the percentage price change in one trading day? Assuming a normal distribution with zero mean, estimate 95% confidence limits for the percentage price change in one day." -- Hull, John C.. Risk Management and Financial Institutions (Wiley Finance) (Kindle Locations 8268-8270). Wiley. Kindle Edition.

If he were seeking a 95.0% VaR, then he'd use 25.0%*1/sqrt(250)*1.645 because VaR is always one-tailed. But here he's looking for a two-sided confidence interval, where the 95.0% two-sided deviate is 1.96. So he's solving for 25%/sqrt(250)*1.96 ~= 3.09%. I hope that's helpful!