FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility
An analyst estimates daily volatility using an equally weighted moving average of the last 5 daily returns, assuming a zero mean. The returns are +1%, -2%, +3%, -1% and +1%. What is the estimated daily volatility (to two decimals)?
With a zero-mean assumption, variance is the average of squared returns: (1+4+9+1+1)/5 = 3.2, so volatility is the square root, about 1.79% per day. Dividing by n-1 instead would wrongly give 2.00%, since no sample mean is estimated.
- A1.41%
- B1.55%
- C1.79%Correct
- D2.00%
Explanation
Squared returns: 1, 4, 9, 1, 1 sum to 16. Divide by 5 to get 3.2, and the square root is 1.789%, about 1.79%. Dividing by 4 would give variance 4 and volatility 2.00%, which wrongly applies the sample-mean degrees-of-freedom correction to a zero-mean estimate.
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