Standard Deviation

What

Standard deviation is the measure of tightness of a probability distribution.  It is a statistical measure of volatility that can be used for a number of different purposes in investment decision making.  Standard deviation can be used to make important extrapolations from past data.  As a measure of volatility, standard deviation measures the tendency of data to be spread out.  When looking at the historic returns of a mutual fund, standard deviation can be used to measure the variation of expected return that has taken place in the past giving a sense of range of performance that can be expected given different probabilities of return for the future.  It is also used to measure the risk of a security.  The smaller the standard deviation, the tighter the probability distribution, and the lower the risk associated with the security

How

The steps for calculating a n-period standard deviation are as follows:

Calculate the simple average (mean) of the closing price. i.e., Sum the last n closing prices and divide by n.

For each period, subtract the average closing price from the actual closing price. This gives us the deviation for each period.

Square each period's deviation.

Sum the squared deviations.

Divide the sum of the squared deviations by the number of periods.

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

When

Standard deviation is used in technical analysis as a measure of volatility. The standard Deviation can be viewed as an oscillator below the chart. At times of high volatility a high reading will be recorded and at times of low volatility a low reading will be recorded. Options premiums will be lower at times of low volatility and higher at times of high volatility (all else remaining the same). Many traders use the standard deviation to gauge when to buy and sell options. Standard deviation is also used in the construction of Bollinger bands as an upper and lower band that are a certain standard deviation level away from a central moving average.  In this way, during times of lower volatility, Bollinger bands contract as the range of prices during the period being used for data points gets smaller, reflecting the lower volatility.  When volatility increases for a security, the standard deviation lines widen. (Refer Bollinger Bands page for further info)