Bollinger bands mathematical formula

Information on both was hard to obtain in those days but I persisted; with the help of an early microcomputer I was able to make some progress. A touch of the upper band by price that was not confirmed by strength in the oscillator was a sell setup and a similarly unconfirmed tag of the lower band was a buy setup.

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The problem with that approach was that percentage bands needed to be adjusted over time to keep them germane to the price structure and the adjustment process let emotions into the analytical process. If you were bullish, you had a natural tendency to draw the bands so they presented a bullish picture, if you were bearish the natural result was a picture with a bearish bias.

This was clearly a problem. We tried reset rules like lookbacks with some success, but what we really needed was an adaptive mechanism.

I was trading options at the time and had built some volatility models in an early spreadsheet program called SuperCalc. One day I copied a volatility formula down a column of data and noticed that volatility was changing over time. Seeing that, I wondered if volatility couldn't be used to set the width of trading bands.

That idea may seem obvious now, but at the time it was a leap of faith. At that time volatility was thought to be a static quantity, a property of a security, and that if it changed at all, it did so only in a very long-term sense, over the life of a company for example. Today we know the volatility is a dynamic quantity, indeed very dynamic.

After some experimentation I settled on the formulation we know today, an n period moving average with bands drawn above and below at intervals determined by a multiple of standard deviation We use the population calculation for standard deviation. The defaults today are the same as they were 35 years ago, 20 periods for the moving average with the bands set at plus and minus two standard deviations of the same data used for the average.

I had presented a chart showing an unconfirmed tag of my upper band and explained that the first down day would generate a sell signal. They are curves drawn in and around the price structure usually consisting of a moving average the middle band , an upper band, and a lower band that answer the question as to whether prices are high or low on a relative basis. Bollinger Bands work best when the middle band is chosen to reflect the intermediate-term trend, so that trend information is combined with relative price level data.

Here are a couple of practical examples of the usage of Bollinger Bands and the classic Bollinger Band tools along with a volume indicator, Intraday Intensity:. Click chart to enlarge.

Chart 1: On 20 July prices tagged the upper Bollinger Band while day Intraday Intensity was deep in negative territory setting up a sell alert. The first down day was the sell signal and entry. The red triangle is a negative PowerShift. We have come a long way since the bands were developed.

Today we have a suite of Bollinger Bands tools with at least one tool in every major technical analysis indicator category. And with more on the way; wherever you are, whatever you trade, Bollinger Bands and the related tools will be there for you. The corridor will be smoother as the period increases.

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However, it does not mean the accuracy of the indicator will increase as well. Whenever the price is touching or nearing one of the outer averages, the most probable scenario is a change in price direction. If the price breaks the line and goes beyond it, you can expect the beginning of the trend in the direction of the breakout. If the price is moving in a narrow corridor for a long time, it is usually a sign of market consolidation before a strong price movement.

The best thing to do is to use the Bollinger Bands together with another indicator. The confluence of two different technical indicators can make your trading signals more accurate.

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Bollinger Bands® Simple Explanation

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