# Bollinger Bands®

Bollinger Bands consist of three bands that can be overlayed over a normal price chart or an indicator. The first, the middle band is a simple moving average and it is recommended that a period of 20 be used.
• The middle band is a simple moving average calculated from the previous 20 periods.
• b is the number of periods over which to make the calculation, the default is 20 periods.
• a -> b is a backward count of the number of periods to be included in the calculation.
• "Close a" is the latest close.

• The upper band is the moving average plus 2 standard deviations
• b is the number of periods, usually 20 by default.
• D is the standard deviation, 2 standard deviations from the moving average is the default.
• "Close a" is the latest close.
• Middle Band is a simple moving average

• The lower band is the moving average minus 2 standard deviations
• b is the number of periods, usually 20 by default.
• D is the standard deviation, 2 standard deviations from the moving average is the default.
• "Close a" is the latest close.
•  Middle band is a simple moving average.

John Bollinger invented this indicator, which looks very much like an envelope and is overlayed on a price chart as an envelope would be. This indicator is unique because it's influenced by the changing volatility of the market. It is a function of the addition and subtraction of twice the standard deviation from the moving average. It stands to reason then that when the market is vibrant it will be reflected in volatility and therefore the bands will widen. Conversely when volatility wanes reflecting a quiet market the bands should logically narrow. This is a relative measure of course.

How to use Bollinger Bands
To use the Bollinger Bands as intended by their inventor one must either subscribe to or at least be empathetic with the following premises about market behaviour. Fortunately most of these assumptions can be verified statistically and therefore hold greater credence.

• Low volatility (order) tends to predicate sharp price changes (chaos)
• If and when the market moves outside the bands the move should continue
• If the market tops or bottoms, first outside the bands and then within the bands, the market is likely to reverse the recent trend
• A move that's starts at one of the upper or lower bands, should go all the way to the other

In the example below arrow 1 shows the market extending above the upper bands and issuing a buy signal in the process. A sell signal is not generated until arrow 3, once a top has been made within the bands following a top outside the bands at arrow 2. That top then produces a move to the lower band at arrow 4.