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Fat Tails and Trends

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Black_NITE   Saturday, 01/13/18 05:59:17 AM
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Compensated Awareness Post - View Disclaimer

Fat Tails and Trends

Historic stock returns are not normally distributed. What does this mean? If one were to measure the height of 1000 people and plot the distribution, this distribution would form the classic bell curve. The most recurring height (value) would be in the middle and the remaining heights would be equally distributed on either side. Furthermore, 68.5% of all values would fall within ±1 standard deviation of the mean, 95.4% would fall within ±2 standard deviations and 99.7% would fall within ±3 standard deviations. The solid black line shows a typical bell curve with a normal distribution.



Statisticians have found that a distribution of stock returns forms a curve with "fat tails". For example, this could be a distribution of the 1000 weekly returns for a basket of stocks. In a normal distribution, 99.7% of all these returns would be within ±3 standard deviations of the mean. This, however, is not the case for stock returns. Instead, the distribution has fat tails (black dotted lines). This means a relatively high number of returns fall outside the normal distribution. Some are lower and some are higher. These abnormal returns provide evidence of extended moves, outsized moves or trends. Note that the image above is just a hypothetical example to illustrate a point.


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