Standard Deviation

Standard deviation is a statistical term that provides a fair and good indication of volatility. It measures how widely values (closing prices of a security for instance) are dispersed from the average. Dispersion means the difference between the actual value (closing price) and the average value (mean closing price). The larger the difference between the closing prices and the average price, the higher the standard deviation will be and indicates that higher is the volatility. The closer the closing prices are to the average price, the lower the standard deviation and indicates that lower is the volatility.

How to calculate Standard Deviation

The steps for calculating a 20-period standard deviation would be :
First, Calculate the simple average (mean) of the closing price. i.e., Sum the last 20 closing prices and divide by 20.
Second, for each period, subtract the average closing price from the actual closing price. This gives the deviation for each period.
Third, Square each period’s deviation.
Fourth, Sum the squared deviations.
Fifth, Divide the sum of the squared deviations by the number of periods (the number of periods in above example is 20).

The standard deviation is then equal to the square root of that number.

Standard Deviation is basically used to determine the spread between upper and lower Bollinger Bands and the Bollinger Band Width Indicator can be used as a better substitute for the Standard Deviation indicator. Since the standard deviation is doubled when plotting Bollinger Bands, the Bollinger Band Width must be divided by two in order to get the actual Standard Deviation value.
When used in stock market, standard deviation bands are plotted above and below the simple moving average of the same period as the standard deviation period.
Classic example of usage of standard deviation in stock market would be for a low risk stock it would be apt to invest in a stock which over a long period of time is giving consistently small bandwidth (this is the difference between the top and bottom std deviation bands). For high risk/reward ratio players stocks falling under a consistently wide bandwidth would be the choice of investment.

Analysts believe that Standard Deviations should be used as secondary signals rather than primary identifiers of whether to make a purchase or sale. It should be used in conjunction with other indicators like RSI or MACD before making a buy or sell decision.