FRM Part I · FRM Exam Part I · Sample Moments
A sample of five returns (in %) is -2, -1, 0, 1, 2. Using moments computed by dividing by n, what is the excess kurtosis?
Excess kurtosis is -1.30. The variance is 2, so the squared variance is 4, and the average fourth power of deviations is 6.8. Kurtosis is 6.8/4 = 1.7, and subtracting the normal benchmark of 3 gives -1.30, a platykurtic sample with thin tails.
- A-1.30Correct
- B1.70
- C3.80
- D-1.91
Explanation
Mean = 0 and variance = 10/5 = 2, so sigma^4 = 4. The fourth moment = (16+1+0+1+16)/5 = 6.8. Kurtosis = 6.8/4 = 1.7, so excess kurtosis = 1.7 - 3 = -1.30. Option 1.70 forgets to subtract 3; -1.91 uses an n-1 variance.
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