FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility
An asset has a daily return volatility of 1.5%. Assuming independent, identically distributed daily returns and 252 trading days per year, what is the annualized volatility?
Under i.i.d. returns, volatility grows with the square root of time, so annualized volatility is 1.5% times the square root of 252, about 23.81%. Scaling linearly by 252 or using 365 calendar days gives wrong results, and the square root of 21 gives a monthly figure.
- A6.87%
- B23.81%Correct
- C28.66%
- D378.00%
Explanation
Volatility scales with the square root of time: 1.5% × √252 = 1.5% × 15.875 = 23.81%. Multiplying by 252 (378%) wrongly scales volatility linearly. Using √365 gives 28.66%, which uses calendar days instead of the stated trading days. Using √21 gives 6.87%, which is a monthly figure.
Did you get it right without looking?
One question tells you little. A timed set on Measuring and Monitoring Volatility shows your real accuracy, how long you take and where you lose marks.
More Measuring and Monitoring Volatility questions
- A risk manager builds an EWMA covariance matrix for many risk factors. Which design choice ensures the resulting matrix is positive semi-def…
- A risk manager estimates a two-asset portfolio's variance from volatilities and correlation. Weights are 50% each, volatilities are 10% and …
- Over the past year, equity index options with a strike 10% below spot have had implied volatilities of 28%, while at-the-money options have …
- Daily returns have a standard deviation of 1.00% and a first-order autocorrelation of +0.25, with no higher-order autocorrelation. What is t…
- An analyst estimates daily volatility from five observed daily log returns: +1%, -2%, +3%, 0%, -2%. Assuming the true mean is zero, the anal…
- The daily log returns of a portfolio are assumed i.i.d. with a standard deviation of 1.2% per day. Using the square-root-of-time rule with 2…