Bollinger Bands are
a technical analysis tool invented by John Bollinger in the
1980s. Having evolved from the concept of trading bands,
Bollinger Bands can be used to measure the highness or lowness
of the price relative to previous trades.
The bands cannot, as some have supposed, be used to make
reliable statements regarding what fraction of an equity's
prices will lie within a certain distance of the mean value.
This is because an individual equity's price does not obey
known distribution functions (see stochastic process). For
example, if the bands for plus or minus two standard
deviations (2SD) are computed, it is wrong to suppose that
~95% of an equity's closing prices will, on average, lie
within the Bollinger bands. That would require, among other
things, that the prices be normally distributed, which they
are generally not. It would further require that the true
standard deviation be known. The standard deviation calculated
as above, however, is only an uncertain estimate of the true
standard deviation. Furthermore, it should be realized that
the "standard deviations" of stock prices for finite time
periods are not fixed parameters as required to apply
classical statistical theory, but instead are variables in
constant flux depending on price volatility. The bands give a
visual picture of a stock's price volatility. Nevertheless,
the bands can be useful in the technical analysis of prices or
returns and by Chebyshev's inequality contain at least 75% of
prices. These occurrences should be considered in relation to
other factors before making investment decisions.
It is of interest to note that faulty interpretation of a
price touching or breaching a band based on incorrect
statistical assumptions has become so widespread that some
traders now use these events alone as trading signals and by
so doing may have unwittingly injected significance into these
band-touching events that should otherwise be absent.
Nevertheless, anyone can observe over time, that for a
diversified group of mutual funds, say, the proportion of
daily adjusted close prices that breach their 1-month 2SD
Bollinger bands varies between 5% and 15% of days, with each
fund having a fairly constant, characteristic long-term breach
probability descriptive of its long-term, relative volatility.
When the bands lie close together a period of low volatility
in stock price is indicated. When they are far apart a period
of high volatility in price is indicated. When the bands have
only a slight slope and lie approximately parallel for an
extended time the price of a stock will be found to oscillate
up and down between the bands as though in a channel.
The use of Bollinger Bands varies wildly among traders. Some
traders buy when price touches the lower Bollinger Band and
exit when price touches the moving average in the center of
the bands. Other traders buy when price breaks above the upper
Bollinger Band or sell when price falls below the lower
Bollinger Band. Moreover, the use of Bollinger Bands is not
confined to stock traders; options traders, most notably
implied volatility traders, often sell options when Bollinger
Bands are historically far apart or buy options when the
Bollinger Bands are historically close together, in both
instances, expecting volatility to revert back towards the
average historical volatility level for the stock. |
