The standard methods of estimating the financial risk are based explicitly or implicitly on the assumption that the returns follow the normal distribution.

The image from the right displaying the empirical Probability of Density Function (PDF) for Microsoft (MSFT), Cisco Systems (CSCO), Yahoo (YHOO), IBM (IBM), and Nasdaq (QQQQ) over the last decade confirming that none is even close to a normal distribution.

The image below displays for the daily return of Microsoft (MSFT) during the last decade the PDF of the empirical distribution, equivalent normal, best fit, and optimum approximation. It makes obvious the fact that formulas for the average and standard deviation based on the samples produce a standard distribution (depicted in red) far from the empirical representation.

There are now better methods to estimate the financial risk.