FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility
Five daily returns are observed: +1%, -2%, +3%, 0%, -2%. The mean is estimated from these data. What is the sample standard deviation, using the unbiased estimator?
The mean is zero and the squared deviations sum to 18. With the unbiased estimator dividing by n-1 = 4, the variance is 4.5 and the standard deviation is about 2.12%. Dividing by n gives 1.90%, and 4.5 or 3.6 are variances rather than volatilities.
- A1.90%
- B2.12%Correct
- C3.60%
- D4.50%
Explanation
The mean is 0. The sum of squared deviations is 1+4+9+0+4 = 18. Dividing by n-1 = 4 gives a variance of 4.5, so the standard deviation is √4.5 = 2.12%. Dividing by n gives 3.6, whose root is 1.90%, which is the biased estimator. The options 3.60 and 4.50 are variances, not standard deviations.
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