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Tail Risk
In a normal distribution, the largest number of observations centers around the mean and declines to the right and left as there are typically fewer observations of extreme returns (for instance 30%) thus giving it a bell shape. Units of standard deviation (‘Sigma’ noted by the symbol δ in the diagram) provide a measurement of the expected frequency of the returns. In a normal distribution, returns that are generated within one sigma of the mean are predicted to happen 68.5% of the time. Fat tails exist because extreme events are far more prevalent than is explained by the normal distribution."
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