Fat Tails

Perhaps the most serious problem with the normal distribution is the fact that its tails "disappear" too fast, at least faster than what is empirically observed in financial data. We typically observe that every market experiences one or more daily moves of 4 standard deviations or more per year. Such frequency is incompatible with a normal distribution. With a normal distribution, the probability of this happening is 0.0032% for one day, which implies a frequency of once every 125 years.

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