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Bollinger Bands Standard Deviation

John Bollinger developed the technique of using a moving average with two bands calculated through the standard deviation above and below it.

The Bollinger bands are composed as follows:

a Mobile Linear average at N days, which draws the central line;

the upper band is obtained by a linear moving average to which the standard deviation is added twice;

The lower band is obtained from a linear moving average from which the standard deviation is subtracted twice.

Bollinger only adds and subtracts the standard deviation from the moving average without performing calculations in percentage terms.

The Bollinger Bands Standard Deviation Calculation

To calculate the standard deviation, it is necessary to add the square root of the difference between the examined value and its moving average for each of the previous x periods taken into consideration, then divide this sum by the number of x periods evaluated and finally calculate the square root the result obtained from this report.

But what does the standard deviation represent? The standard deviation measures volatility.

By measuring price volatility, the Bollinger Bands indicator adapts to market conditions, and this is precisely what makes this indicator so valid.

Different ways are used to determine volatility, which in turn produce different results. The most commonly used method is the Standard Deviation, which expresses the distance of a value from its average; this difference will be the more extensive, the higher the volatility.

This result was achieved thanks to the use of the Standard Deviation, which exhibits two advantages.

The value of the Standard Deviation detects the degree of volatility. In statistical terms, the Standard Deviation indicates the probability of a data set is distributed.

bollinger bands standard deviation

How to draw the indicator

The first step in creating the Bollinger bands is to draw the midline:

Midline = Sma20(P)

The midline is essentially the 20-period moving average of prices, from which the other two bands can be drawn:

Upper band = midline + 2 Std Dev.

Lower band = midline – 2 Std. Dev.

John Bollinger decided to use two Standard Deviations as the basis for counting variable-width bands, so as not to widen the dynamic channel too much and limit cases where prices may fall outside the bands.

Usually, most of the time, all prices are between the two bands.

According to his studies, the approaches chosen should contain almost 90% of prices in most markets.

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