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FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation

A sample of 5 returns is: -4%, -2%, 0%, 2%, 4%. Using the population-style moment formulas (dividing by n), what are the sample skewness and kurtosis?

The data are symmetric around zero, so skewness is 0. Variance is 8 and the average fourth power is 108.8, giving kurtosis of 108.8/64 = 1.70, well below the normal value of 3.

  1. ASkewness 0; kurtosis 1.70Correct
  2. BSkewness 0; kurtosis 3.00
  3. CSkewness 0; kurtosis 1.25
  4. DSkewness 0.5; kurtosis 1.70

Explanation

Mean = 0. Deviations squared: 16,4,0,4,16 sum 40; variance = 8. Fourth powers: 256,16,0,16,256 sum 544; fourth moment = 108.8. Kurtosis = 108.8/64 = 1.70. Odd moments cancel by symmetry, so skewness is 0. Kurtosis of 3.00 would wrongly assume normality.

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