FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
An analyst observes five daily log returns for a stock: 1%, -2%, 3%, 0%, and 3%. Using the unbiased sample variance estimator (dividing by n-1), what is the sample daily volatility?
The sample daily volatility is 2.12%. The mean return is 1%, the squared deviations sum to 18, dividing by n-1 equals 4 gives a variance of 4.5, and its square root is about 2.12%.
- A2.00%
- B1.79%
- C2.12%Correct
- D4.00%
Explanation
Mean = (1-2+3+0+3)/5 = 1%. Deviations: 0, -3, 2, -1, 2; squares: 0, 9, 4, 1, 4 = 18. Dividing by n-1=4 gives 4.5, so volatility = sqrt(4.5) = 2.12%. Dividing by n gives 3.6, i.e. 1.90%, not an option; 2.00% would come from using 16 as the sum; 4.00% is a variance-style value.
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