### Technical Analysis, Studies, Indicators:

## Standard Deviation

The Standard Deviation is used in statistics to measure the variability or dispersion of a data set. If the data are very close to the average value (mean), we have a small standard deviation. In cases in which the data are dispersed over a wide range of values we have a large standard deviation.

In statistics the Standard Deviation provides a good indication of volatility and is often called a volatility indicator. In technical analysis this indicator is applied to the closing price of the bar to measure the dispersion of values about the average closing price. The difference between the actual closing security (stock, index, etc.) price and the average closing security price is called the dispersion. The greater the dispersion (the difference between the closing and the average prices), the higher will be the standard deviation and the volatility. The smaller the dispersion (the closer the closing prices are to the average price), the smaller will be the standard deviation and the lower the security's price volatility.

The calculation of the Standard Deviation can be accomplished in six steps. For example, to calculate a 10-period standard deviation, you must:

- Calculate the simple average (mean) of the closing price (i.e., add the last 10 closing prices and divide the total by 10).
- For each period, subtract the average closing price from the actual closing price. This will gives the deviation for each period.
- Square each period's deviation that was obtained in step #2.
- Sum the squared deviations that were obtained in step #3.
- Divide the sum of the squared deviations by the number of periods (10 in our example).
- The standard deviation is equal to the square root of that number.

As we mentioned before, the Standard Deviation is used in technical analysis and trading systems to statistically measure a stock's volatility by showing the difference between the price and the average price. Normally, this indicator is used as a component of other indicators. Thus, the Standard Deviation is used to determine the spread between upper and lower Bollinger Bands® and, as a result, the Bollinger Band Width indicator can be used as a substitute for the Standard Deviation indicator.

Another use of the Standard deviation is to confirm a down-trend or up-trend. As a rule, the market is less volatile during an up-trend, while during a downtrend or market crash, we may witness high volatility due to panic selling.

In trading systems the Standard Deviation (like other volatility indicators) is used to define periods of volatility and to adjust the settings of technical indicators used to it. It is well known that, in a highly volatile market, the price trend changes more quickly. Therefore, a trading system should react to the signals more quickly or one might be too late to open or close a trade. At the same time, in a market of low volatility, a trader may set the trading system to delay the generation of signals to avoid prematurely opening or closing trades.**Chart 1:** S&P 500 index - Standard Deviation.

Victor Kalitowski

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