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Excess kurtosis

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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.

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As Table 3 shows, the SP500 distribution exhibits excess kurtosis, which is a common characteristic of stock return distributions.
In all cases the Jarque-Bera test for normality are highly significant with excess kurtosis and negatively skewed.
The high value of excess kurtosis reported in table 3 implies that the market is likely to be affected by big surprises, conditional on the information available at any point in time.
 
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