##### Bollinger Bands

Bollinger Bands are a type of statistical chart characterizing the prices and volatility over time of a financial instrument or commodity, using a formulaic method propounded by John Bollinger in the 1980s. Financial traders employ these charts as a methodical tool to inform trading decisions, control automated trading systems, or as a component of technical analysis. Bollinger Bands display a graphical band and volatility in one two dimensional chart.

Two input parameters chosen independently by the user govern how a given chart summarizes the known historical price data, allowing the user to vary the response of the chart to the magnitude and frequency of price changes, similar to parametric equations in signal processing or control systems. Bollinger Bands consist of an N-period moving average (MA), an upper band at K times an N-period standard deviation above the moving average (MA + Kσ), and a lower band at K times an N-period standard deviation below the moving average (MA − Kσ). The chart thus expresses arbitrary choices or assumptions of the user, and is not strictly about the price data alone.

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 days 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 period is used for both the middle band and the calculation of standard deviation.

Purpose

The purpose of Bollinger Bands is to provide a relative definition of high and low prices of a market. 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.

Indicators derived from Bollinger Bands

BBImpulse measures price change as a function of the bands; percent bandwidth (%b) normalizes the width of the bands over time; and bandwidth delta quantifies the changing width of the bands.

%b (pronounced "percent b") is derived from the formula for stochastics and shows where price is in relation to the bands. %b equals 1 at the upper band and 0 at the lower band. Writing upperBB for the upper Bollinger Band, lowerBB for the lower Bollinger Band, and last for the last (price) value:

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

Bandwidth tells how wide the Bollinger Bands are on a normalized basis. Writing the same symbols as before, and middleBB for the moving average, or middle Bollinger Band:

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.

Interpretation

The use of Bollinger Bands varies widely 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 towards the average historical volatility level for the stock.

When the bands lie close together, a period of low volatility is indicated. Conversely, as the bands expand, an increase in price action/market volatility is indicated. When the bands have only a slight slope and track approximately parallel for an extended time, the price will generally be found to oscillate between the bands as though in a channel.

Traders are often inclined to use Bollinger Bands with other indicators to confirm price action. In particular, the use of oscillator like Bollinger Bands will often be coupled with a non oscillator indicator like chart patterns or a trendline. If these indicators confirm the recommendation of the Bollinger Bands, the trader will have greater conviction that the bands are predicting correct price action in relation to market volatility.