Name, Sometimes Called:
Bollinger Bands
Brief Description:
Bollinger Bands provide a comparison of volatility
and price levels over a prescribed period. The three “bands”
are a simple moving average SMA
between an upper band (SMA plus a number of standard deviations
(SDs)
and a lower band (SMA minus the same number of SDs ).
Definitions, Formulas:
Bollinger Bands allow analysts to compare volatility
versus price levels over a prescribed time period. The three “bands”
are: (1) a simple moving average SMA
between (2) an upper band (SMA plus a number of standard deviations
(SDs)
and (3) a lower band (SMA minus the same number of SDs ). Because
the standard deviation is a volatility measure, the spacing between
the upper and lower bands increases in periods of increased volatility
(extreme price changes) and narrows as volatility decreases (reduced
price fluctuation).
The parameters to be used depend on the period to be examined.
John Bollinger, the TAI’s developer, recommends the following:
- For the short term (roughly 10 days), the top and bottom bands
should be at plus and minus 1.5 standard deviations.
- For the intermediate term (about 20 days), the top and bottom
bands should be at plus and minus 2.0 standard deviations.
- For the long term (such as 50 days), the top and bottom bands
should be at plus and minus 2.5 standard deviations.
We examine the intermediate term.
First, calculate the 20-day SMA, which is the middle band (MB):
MBk = SMA(20)(price)k = 
where
k = the position of day k in the period
Ci = the closing price
on day i
Then calculate the standard deviation:
SDk =
The upper and lower bands are then:
UBk = MBk + 2*SDk
LBk = MBk + 2*SDk
where k is as before.
Positive Development Calculation:
For this TAI, a new positive development (NPD)
occurs when both VPMO is positive
and price crosses under the lower band, that is, when Ck
crosses under LBk. The Bollinger
Bands TAI is an example of a confirming
technical analysis indicator.
This TAI is no longer positive when either VPMO
is no longer positive, or when Ck
x+ LBk.
Here is an important point to remember. When a TAI--or even a group
of TAIs--is no longer positive, it is NOT the same as a “sell”
signal.
If this TAI is still positive tomorrow, it will no longer be new,
but will be a cumulative positive development (CPD).
If this TAI was a new positive development (NPD)
yesterday, and is still positive today, then it becomes a cumulative
positive development (CPD).
History:
This TAI was developed by John A. Bollinger, CFA, CMT
(Bollinger Capital Management, Inc., P.O. Box 3358, Manhattan Beach,
CA 90266; www.bollingerbands.com).
In concept, it resembles the moving average envelope TAI, in that
both provide limiting lines above and below the price line. However,
the older TAI uses a fixed percentage to plot the lines, while the
Bollinger Bands TAI uses a multiple of the standard deviation.
Bollinger suggests using other indicators with his bands to confirm
price action, and does so himself. We do so here as well.
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