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I have set of log-return values. For this set need to calculate Coefficient of Variation with outlier values penalization.

I'm just squaring all values to penalize outliers and there are different variants how we can calculate CoV:

CoV = $\frac{StDev(X^2)}{Average(X^2)}$

CoV = $\frac{\sqrt{StDev(X^2)}}{Average(X)}$

CoV = $\frac{\sqrt{StDev(X^2)}}{\sqrt{Average(X^2)}}$

Which method is more useful and correct?

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