Excess kurtosis

Kurtosis measures the "fatness" of the tails of a distribution. Positive excess kurtosis means that distribution has fatter tails than a normal distribution. Fat tails means there is a higher than normal probability of big positive and negative returns realizations. When calculating kurtosis, a result of +3.00 indicates the absence of kurtosis (distribution is mesokurtic). For simplicity in its interpretation, some statisticians adjust this result to zero (i.e. kurtosis minus 3 equals zero), and then any reading other than zero is referred to as excess kurtosis. Negative numbers indicate a platykurtic distribution; positive numbers indicate a leptokurtic distribution.

What does "Platykurtic" mean?
A description of the kurtosis in a distribution in which the statistical value is negative. When compared to a normal distribution, a platykurtic data set has a flatter peak around its mean, which causes thin tails within the distribution. The flatness results from the data being less concentrated around its mean, due to large variations within observations. Returns following this distribution will have fewer large fluctuations than assets displaying normal or leptokurtic distributions. Equity returns are generally considered to be closer to a leptokurtic distribution than to a normal or platykurtic distribution. If market returns were more platykurtic, events such as black swans would be less likely to occur, since that type of outlier is less likely to fall within a platykurtic distribution’s short tails. Conservative investors will be more comfortable dealing with investments with a platykurtic return distribution.

What does "Leptokurtic" mean?
A description of the kurtosis in a distribution in which the statistical value is positive. Leptokurtic distributions have higher peaks around the mean compared to normal distributions, which leads to thick tails on both sides. These peaks result from the data being highly concentrated around the mean, due to lower variations within observations. The fat tail means risk is coming from outlier events and extreme observations are much more likely to occur. Therefore, conservative investors would probably avoid this type of return distribution.


 * [[image:Kurtosis.gif]]

The mathematical formulas used in google/excel spreadsheet statistical functions that are used in wiki statistical spreadsheets:
 * SKEW
 * KURT