FRM Part I · FRM Exam Part I · Sample Moments
An analyst estimates the standard deviation of daily returns from a sample as 1.20% using n-1 in the denominator, with n = 25 observations. What is the biased estimate of the standard deviation that uses n in the denominator?
The biased standard deviation is about 1.18 percent. Multiply the unbiased variance 1.44 by 24 to get 34.56, divide by 25 to get 1.3824, and take the square root. The n-denominator estimate is always smaller than the n-1 estimate.
- A1.18%Correct
- B1.15%
- C1.25%
- D1.20%
Explanation
Unbiased variance = 1.44. Sum of squared deviations = 1.44 x 24 = 34.56. Dividing by 25 gives 1.3824, and its square root is 1.1757, about 1.18%. Equivalent: 1.20 x sqrt(24/25) = 1.1758. The biased estimate is smaller than the unbiased one, so 1.25% is wrong.
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