Excess kurtosis

From Bogleheads

thefreedictionary.com says:

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.

investopedia continues:

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. Referred to as the "volatility of volatility", kurtosis gauges the level of fluctuation within a distribution. High levels of kurtosis represent a low level of data fluctuation, as the observations cluster about the mean. Lower values of kurtosis mean that data has a larger degree of variance. For example, when looking at past stock returns, analysts will want to determine the likelihood of extreme returns (or losses) in the future. If past stock data results in a platykurtic distribution, analysts will expect more volatility in future returns. This means that there is a higher probability than usual for extreme price movements to occur.

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. When analyzing historical returns, kurtosis helps gauge the level of risk for a stock. If the past return data yields a leptokurtic distribution, the stock will have a relatively low amount of variance, because return values are usually close to the mean. Investors who wish to avoid large, erratic swings in portfolio returns may wish to structure their investments to produce a leptokurtic distribution.

See also

• Skewness
• Standard deviation
• Google Definition of kurtosis
• Vanguard Statistical Data Spreadsheets

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

• SKEW
• KURT

Links

• Gummy's Tutorial on Kurtosis

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