Picture of the abnormal

Source: Mandelbrot, The (mis)behaviour of markets

-
In statistics, if we have a normally distributed population (see message above), we can assume:

- 90% of the population will fall within 1.645 standard deviation

- 95% of the population will fall within 1.96 standard deviation

- 99% of the population will fall within 2.576 standard deviation

-

One of the foundation of modern theory of finance is that securities prices follow a normal distribution. Looking at the graph above, we can see some standard deviations reaching 10 and even 22 standard deviation. 22 standard deviation, according to the normal distribtuion, has a 10^-50 probability to occur. Almost impossible.