Overview

Bollinger Bands are similar to moving average envelopes. 
The difference between Bollinger Bands and envelopes is 
envelopes are plotted at a fixed percentage above and 
below a moving average, whereas Bollinger Bands are 
plotted at standard deviation levels above and below 
a moving average. Since standard deviation is 
a measure of volatility, the bands are self-adjusting: 
widening during volatile markets and contracting 
during calmer periods.

Bollinger Bands were created by John Bollinger.

Interpretation

Bollinger Bands are usually displayed on top 
of security prices, but they can be displayed 
on an indicator. These comments refer to bands 
displayed on prices.

As with moving average envelopes, the basic interpretation 
of Bollinger Bands is that prices tend to stay within 
the upper- and lower-band. The distinctive characteristic 
of Bollinger Bands is that the spacing between the bands 
varies based on the volatility of the prices. 
During periods of extreme price changes (i.e., high volatility), 
the bands widen to become more forgiving. 
During periods of stagnant pricing (i.e., low volatility), 
the bands narrow to contain prices.

Mr. Bollinger notes the following characteristics of Bollinger Bands.

- Sharp price changes tend to occur after the bands tighten, 
as volatility lessens.

- When prices move outside the bands, a continuation 
of the current trend is implied.

- Bottoms and tops made outside the bands followed 
by bottoms and tops made inside the bands call 
for reversals in the trend.

- A move that originates at one band tends to go 
all the way to the other band. This observation is 
useful when projecting price targets.

Calculation

Bollinger Bands are displayed as three bands. 
The middle band is a normal moving average. 
In the following formula, "n" is the number of 
time periods in the moving average (e.g., 20 days).

1.bmp

The upper band is the same as the middle band, 
but it is shifted up by the number of standard deviations 
(e.g., two deviations). In this next formula, "D" is 
the number of standard deviations.

2.bmp

The lower band is the moving average shifted down 
by the same number of standard deviations (i.e., "D").

3.bmp

Mr. Bollinger recommends using "20" for the number of 
periods in the moving average, calculating the moving average 
using the "simple" method (as shown in the formula for 
the middle band), and using 2 standard deviations. 
He has also found that moving averages of less then 
10 periods do not work very well.