Excess kurtosis

[Asuka]

Why the calculated Excess Kurtosis (0.05) on P.402 of CFA text Vol 1 P.402 is not 4.39-0 = 1.39 (leptokurtic) as stated on P.400 ?

[busprof]

The difference is becasue you’re using sample excess kurtosis - see the formula 18 pn pg 400. Excess kurtosis for a SAMPLE is calculated as sample kurtosis less the “adjustment”.

In the adjustment, you’re subtracting 3 x (n-1)^2/(n-2)(n-3) ==> the second term goes to one in the limit (and in this case you’re subtracting 3. But the adjustment can significantly inflate the adjustment in small samples. As examples - for a samle of size 10 (like in the problem), the “factor” is almost 1.5, so you’re calculating excess kurtosis as sample kurtosis - 4.34; at n=30, excess kurtosis is sample kurtosis minus 3.34, and at n=60, it’s minus 3.16

[Asuka]

@busprof

The difference is becasue you’re using sample excess kurtosis - see the formula 18 pn pg 400. Excess kurtosis for a SAMPLE is calculated as sample kurtosis less the “adjustment”.

In the adjustment, you’re subtracting 3 x (n-1)^2/(n-2)(n-3) ==> the second term goes to one in the limit (and in this case you’re subtracting 3. But the adjustment can significantly inflate the adjustment in small samples. As examples - for a samle of size 10 (like in the problem), the “factor” is almost 1.5, so you’re calculating excess kurtosis as sample kurtosis - 4.34; at n=30, excess kurtosis is sample kurtosis minus 3.34, and at n=60, it’s minus 3.16

Thank you so much !