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# Bollinger Bands®

Bollinger Bands® is a technical trading tool that was created by John Bollinger, based on Standard Deviation. The purpose of Bollinger Bands® is to provide a definition of high and low price ranges, relative to price volatility. By definition if the price rises above the upper Bollinger Band® line then the price is considered to be at a high, and if the price falls below the lower Bollinger Band®, the price is consider to be at a low.

In times of high price volatility the distance between the upper and the lower Bollinger Bands® increases and in times of low volatility the distance between the Bollinger Bands® decreases. The distance between the upper and lower bands is determined by the standard deviation of the same data that is used for the moving average. The default parameters are 20 interval periods and 2 standard deviations, which can be adjusted to suit your purposes.

The Bollinger Bands® are based on the range of price movement relative to the Moving Average. The number of periods associated with the Bollinger Band®, are used to calculate the moving average, and the number of deviations is used to calculate the upper and lower band relative to the moving average. For example if the interval is set to 2 hours and the number of periods associated with the Bollinger Band® is set to 20, then the Bollinger Band® is based on the moving average of the price at 2 hour intervals, over 20 interval periods i.e. 40 hours.

The prices at each interval for the defined number of periods are used to determine the deviation values. One standard deviation represents 68.2% of the range of price movement relative to the moving average; two standard deviations represent 95.4% of the price movement relative to the moving average and therefore only excludes the extreme highs and lows during the period; three standard deviations represents 99.6% of the price movement. Typically the Bollinger Band® is based on two standard deviations.

## Bollinger Bands® Formula

The Bollinger Bands® default chart is calculated as follows:

• Upper Bollinger Band = Simple Moving Average over 20 periods + 2 Standard Deviations
• Lower Bollinger Band = Simple Moving Average over 20 periods - 2 Standard Deviations

The expectation is that the price distribution around the Simple Moving Average forms a bell curve and that Standard Deviations can be used to establish if the price movement is within normal trading ranges. The following chart provides a visual representation of a classic bell curve with the Standard Deviations representing the range of price movement captured within each deviation:

where:

• 1 Standard Deviation (1σ) = 68.2%
• 2 Standard Deviation (2σ) = 95.4%
• 3 Standard Deviation (3σ) = 99.6%

By increasing the default periods used to calculate the Bollinger Bands, it makes the trading range less sensitive to short term price fluctuations.

To calculate the Bollinger Bands® start by calculating the Simple Moving Average, where $\displaystyle n$ is typically 20 periods:

$\displaystyle \text{Simple Moving Average} = \displaystyle \frac { \displaystyle \sum_{j=1}^n \text{CLOSE}j } { n }$

To calculate the Upper Bollinger Band add the Standard Deviation $\displaystyle SD$ to the Simple Moving Average, where the Standard Deviation $\displaystyle SD$ is typically 2 deviations and $\displaystyle n$ is typically 20 periods:

$\displaystyle \text{Upper Bollinger Band} = \displaystyle \text{Simple Moving Average} + \left ( SD * \sqrt { \frac { \displaystyle \sum_{j=1}^n (\text{CLOSE}j - \text{Simple Moving Average})^2 } { n } } \right )$

To calculate the Lower Bollinger Band, subtract the Standard Deviation $\displaystyle SD$ to the Simple Moving Average, where as before the Standard Deviation $\displaystyle SD$ is typically 2 deviations and $\displaystyle n$ is typically 20 periods:

$\displaystyle \text{Lower Bollinger Band} = \displaystyle \text{Simple Moving Average} - \left ( SD * \sqrt { \frac { \displaystyle \sum_{j=1}^n (\text{CLOSE}j - \text{Simple Moving Average})^2 } { n } } \right )$

## Bollinger Band Indicator

The Bollinger Band indicator can be displayed on the TimeToTrade charts. To add the Bollinger Band indicator to the TimeToTrade charts, go to the chart settings and click on the 'Add Indicator' button. Click on the search box and type the name of the indicator that you are looking for, or for example type Bollinger Band and scroll through the results:

After adding the Bollinger Band indicator, within the chart settings, click on it to set the parameters and change colours.

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