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How do you define Kurtosis
Kurtosis can be defined as the statistical term that is used for describing a probability or return distribution that has a kurtosis coefficient that is larger than the coefficient which is associated with a normal distribution.
For this type, the value will be around 3 and this is mainly used to signal that the probability of obtaining an extreme value in the future is higher than a lower level of kurtosis. It is usually a measure of the likelihood that an event occurring is extreme in relation to a given distribution.
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It is an important consideration that has to be taken when examining historical returns from stock or portfolio. If the kurtosis coefficient is higher than the "normal level", then the future returns will be either extremely large or extremely small and so the kurtosis is often referred to as the "volatility of volatility" and this is denoted by or. This is represented as follows
It is commonly used because a normal distribution is equal to 0 and the kurtosis proper will be equal to 3. They usually have higher peaks around the mean when compared to normal distributions.
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Since they have higher peaks this may lead to thick tails on both sides. These peaks are produced from the data that is highly concentrated around the mean and this is due to lower variations within observations when analyzing the historical returns, the kurtosis helps gauge the level of risk for a stock. If the past return data gives a leptokurtic distribution, the stock will have a moderately low amount of variance.
This is because return values are usually close to the mean and the investors who wish to avoid large erratic swings in portfolio returns may wish to structure their investments to produce a leptokurtic distribution.
When compared to a normal distribution, a platykurtic data set has a peak that is flat around its mean, which produces thin tails within the distribution, and the flatness results from the data being less concentrated around its mean.
This is due to large variations within observations and so it is referred to as the "volatility of volatility" where the kurtosis gauges the level of fluctuation within a distribution and high levels of kurtosis represent a low level of data fluctuation. This is because the observations cluster about the mean.
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