Co Kurtosis. The relevance of 3 is that it is the value of the kurtosis for any G aussian random variable ie the excess kurtosis of a G aussian random variable is zero. If its a sample in needs to divide the sum by n.
Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. If the coefficient of kurtosis is larger than 3 then it means that the return distribution is inconsistent with the assumption of normality in other words large magnitude returns occur more frequently than a normal distribution. This type of distribution has a coeffecient of kurtosis of 3 which is the same as that of a normal distribution.
Volatility but also the risk of assymetry skewness and extreme events kurtosis.
15 Descriptive statistics are reported in table 1 for the two measures of co-skewness and co- kurtosis the standardised measures as used by Harvey and Siddique HS and the traditional measure as used by Kraus and Litzenberger KL Harvey and Siddique 2000. Skewness tells you the amount and direction of skewdeparture from horizontal symmetry and kurtosis tells you how tall and sharp the central peak is. If the coefficient of kurtosis is larger than 3 then it means that the return distribution is inconsistent with the assumption of normality in other words large magnitude returns occur more frequently than a normal distribution. Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution.
