Bollinger Bands
 | This article's factual accuracy is disputed. (March 2008) |
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.
Bollinger Bands consist of:
- a middle band being a N-period simple moving average
- an upper band at K times a N-period standard deviation above the middle band
- a lower band at K times a N-period standard deviation below the middle band
Typical values for N and K are 20 and 2, respectively. The simple moving average is of the trailing type, not the centered type; in the trailing type, the average is plotted at the time-coordinate of the n-th price, not at the median time-coordinate of the set of N prices.
Purpose
The purpose of Bollinger Bands is to provide a relative definition of high and low. By definition prices are high at the upper band and low at the lower band. This definition can aid in rigorous pattern recognition and is useful in comparing price action to the action of indicators to arrive at systematic trading decisions.[1]
Predictive value
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The bands cannot, as some have supposed, be used to make absolutely 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. The standard deviation calculated as above is only an uncertain estimate of the overall, long-term standard deviation. 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. Chebyshev's inequality can be used to show that at least 75% of the data lies between the Bollinger Bands. This is applicable, because this probability statement applies separately to each pairs of points of the band which are calculated, for one point in time, for which the moving average and moving standard deviation are fixed quantities, at that point in time. Non-random counter examples can be concocted, but it is to random variables, like price, to which this applies.
It is of interest to note that interpretation of a price touching or breaching a band based on these 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 too much significance into these band-touching events. 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.
Interpretation
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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.-technical analysis
Further reading
- Bollinger on Bollinger Bands, John Bollinger, ISBN 0071373683