Bollinger bands

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 an N-period simple moving average
* an upper band at K times an N-period standard deviation above the middle band
* a lower band at K times an N-period standard deviation below the middle band

Typical values for N and K are 20 and 2, respectively. The default choice for the average is a simple moving average, but other types of averages can be employed as needed. Exponential moving averages are a common second choice. Usually the same average is used for both the middle band and the calculation of standard deviation.

Indicators Derived from Bollinger Bands

There are two indicators derived from Bollinger Bands, %b and BandWidth.

%b, pronounced 'percent b', is derived from the formula for Stochastics and tells you where you are in relation to the bands. %b equals 1 at the upper band and 0 at the lower band.

%b = (last - lowerBB) / (upperBB - lowerBB)

BandWidth tells you how wide the Bollinger Bands are on a normalized basis.

BandWidth = (upperBB - lowerBB) / middleBB

Using the default parameters of a 20-period look back and plus/minus two standard deviations, BandWidth is equal to four times the 20-period coefficient of variation.

Uses for %b include system building and pattern recognition. Uses for BandWidth include identification of opportunities arising from relative extremes in volatility and trend identification.

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. [ [http://www.bollingerbands.com] second paragraph, center column]

Interpretation

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.

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.

Effectiveness

Bollinger Band trading strategies may be effective in the Chinese marketplace as concluded by a recent study that states, "Finally, we find significant positive returns on buy trades generated by the contrarian version of the moving average crossover rule, the channel breakout rule, and the Bollinger band trading rule, after accounting for transaction costs of 0.50 percent." Nauzer J. Balsara, Gary Chen and Lin Zheng "The Chinese Stock Market: An Examination of the Random Walk Model and Technical Trading Rules" [ [http://findarticles.com/p/articles/mi_qa5466/is_200704/ai_n21292807/pg_1?tag=artBody;col1] The Quarterly Journal of Business and Economics, Spring 2007]

Statistical Properties

Security prices have no known statistical distribution, Normal or otherwise; they are known to have fat tails, compared to the Normal. [Rachev; Svetlozar T., Menn, Christian; Fabozzi, Frank J. (2005), Fat Tailed and Skewed Asset Return Distributions, Implications for Risk Management, Portfolio Selection, and Option Pricing, John Wiley, New York]

The sample size typically used, 20, is too small for statistical techniques like the Central Limit Theorem to be used reliably.

Such techniques usually require the sample to be independent and identically distributed which is not the case for a time series like security prices.

For these three primary reasons, it is incorrect to assume that the percentage of the data outside the Bollinger Bands will always be limited to a certain amount. So, instead of finding about 95% of the data inside the bands, as would be the case if normally distributed, one will typically find less; how much less is usually an indication of a security's volatility.

Further reading

* "Bollinger on Bollinger Bands", John Bollinger, ISBN 0071373683

External links

* [http://www.bollingerbands.com John Bollinger's website]
* [http://www.bollingeronbollingerbands.com John Bollinger's Bollinger Band analytics website]

Notes