FRM Part I · FRM Exam Part I · Sample Moments
A small data set of excess returns is -2, -1, 0, 1, 2 (percent). Using 1/n moments, which statement about its kurtosis is correct?
Kurtosis is 1.70. The variance is 2 and the fourth central moment is 6.8, so kurtosis is 6.8 divided by 4. Since this is below the normal value of 3, excess kurtosis is -1.3 and the distribution is platykurtic with thin tails.
- AKurtosis is 1.70, so excess kurtosis is negative and the distribution is platykurticCorrect
- BKurtosis is 1.70, so the distribution is leptokurtic
- CKurtosis is 6.80, so the distribution is leptokurtic
- DKurtosis is 4.70, so the distribution is leptokurtic
Explanation
Mean is 0. Variance = (4+1+0+1+4)/5 = 2. Fourth moment = (16+1+0+1+16)/5 = 6.8. Kurtosis = 6.8/2^2 = 1.7, which is below 3, so excess kurtosis is -1.3 and the distribution is platykurtic. Using 6.8 skips division by variance squared; 4.7 wrongly adds 3.
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