Normal Distribution and Standard Deviation of Stock Prices

Stock and share prices do not always form an exact "Normal Distribution". A graph of price data over a period would look similar to the classic bell-curve but there would probably be some slight difference - the extreme left and right of the curves for stock prices are often slightly higher than would normally be expected. This is a phenomenon known as "fat tails". As a result, stock and share prices which are more than two multiples of the standard deviation away from the average may be slightly more common than the statistical 95.4% which would be expected for a "Normal Distribution". Similarly, prices whch are over three multiples of the standard deviation away from the average can be more common than the 99.73% predicted by normal statistical analysis.

There are a number of theories regarding the possible reasons for stocks and shares not following exactly the normal bell-shaped curve of Normal Distribution. One possibility is the "Herd Mentality" of some investors. If a stock price is rising of falling considerably, investors may follow the trend and buy (or sell), thus increasing the extremity of the rise (or fall). Alternatively, a similar effect is caused by market followers who see a stock break outside of its normal trading range and buy (or sell) in the theory that the breakthrough indicates the stock may be moving permanently to a new higher (or lower) trading range.