**History of Bollinger Bands**

Bollinger Bands are a technical analysis trading tool created by John Bollinger, a long-time technician of the markets, in the early 1980s. They arose from the need for adaptive trading bands and the observation that volatility was dynamic, not static as was widely believed at the time, and since they can be used to measure the highness or lowness of the price relative to previous trades they became widely accepted.

**John Bollinger** developed the technique of using a moving average with two trading bands above and below it. Unlike a percentage calculation from a normal moving average, Bollinger bands simply add and subtract a standard deviation calculation. Note: Standard deviation is a mathematical formula that measures volatility, showing how the stock price can vary from its true value. By measuring price volatility, Bollinger Bands adjust themselves to market conditions. This is what makes them so handy for traders: they can find almost the entire price data needed between the two bands.

**John Bollinger, CFA, CMT**

John Bollinger is the president and founder of Bollinger Capital Management. He personally governs all investment decisions for Bollinger Capital Management clients.

John Bollinger is a Chartered Financial Analyst (CFA) and a Chartered Market Technician (CMT). He is known to the public for his many years of market analysis and commentary on television -- first on Financial News Network, where he was the Chief Market Analyst -- and subsequently on CNBC.

John Bollinger is also well known to professional investors. An avid researcher, he has developed a number of widely used investment tools and analytical techniques. His technical analysis trading tools have been integrated into most of the analytical software and charting platforms currently in use.

**BollingerBands.com** is wholly owned by Bollinger Capital Management, Inc., a California corporation.

His book, "Bollinger on Bollinger Bands" was published by McGraw Hill in 2001 and has been translated into seven languages. John Bollinger is also the founder of several web sites for investors.

He is an active member of the financial community and a frequent lecturer at national and international investment seminars. His articles have appeared in Technical Analysis of Stocks and Commodities, Active Trader and the Market Technicians Association Newsletter. He is a former board member of the Market Technicians Association and the International Federation of Technical Analysts.

**Bollinger Capital Management Inc.** is an investment management company that provides technically driven portfolio management services to individuals, families, trusts, corporations, and retirement plans. Bollinger Capital Management also develops and provides proprietary research for institutions and individuals.

**Definition**

A technical analysis technique in which lines are plotted two standard deviations above and below a moving average, and at the moving average itself. Because standard deviation measures volatility, these bands will be wider during increased volatility and narrower during decreased volatility. Some technical analysts consider a market which approaches the upper band to be overbought, and a market which approaches the lower band to be oversold.

**Use As an Indicator**

Bollinger Bands are a very powerful technical indicator. Some traders will swear that solely trading these Bands is the key to their winning systems. The Bands are drawn within and surrounding the price structure of a stock. It provides relative boundaries of highs and lows.

The Bands consist of a set of three curves drawn in relation to securities prices. The middle band is a measure of the intermediate-term trend, usually a simple moving average that serves as the base for the upper band and lower band. Most stock charting applications default the middle band to a 20 period moving average.

The interval between the upper and lower bands and the middle band is determined by volatility, typically the standard deviation of the same data that were used for the average. The default parameters, 20 periods and two standard deviations, may be adjusted to suit your purposes.

**Bollinger Bands consist of:**

• a Middle Band being an N-period simple moving average (MA)

= 20 period moving average (most charting packages use the simple moving average)

• an Upper Band at K times an N-period standard deviation above the middle band (MA + Kσ)

= Middle band + 2 standard deviations

• a Lower Band at K times an N-period standard deviation below the middle band (MA − Kσ)

= Middle band - 2 standard deviations.

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

S&P 500 with 20 day, two standard deviation Bollinger Bands, %b and BandWidth.

**A Calculation of Bollinger Bands**

** ML = SUM [CLOSE, N]/N**

The top line, TL, is the same as the middle line a certain number of standard deviations (D) higher than the ML.

**TL = ML + (D*StdDev)**

The bottom line (BL) is the middle line shifted down by the same number of standard deviations.

** BL = ML — (D*StdDev)**

Where: N — is the number of periods used in calculation;

SMA — Simple Moving Average;

StdDev — means Standard Deviation.

StdDev = SQRT(SUM[(CLOSE — SMA(CLOSE, N))^2, N]/N)

It is recommended to use 20-period Simple Moving Average as the middle line, and plot top and bottom lines two standard deviations away from it. Besides, moving averages of less than 10 periods are of little effect.

**A Simplified Explanation**

Bollinger Bands are a good tool to give traders a feel for what the volatility is in the market and how high or low prices are relative to the recent past. The basic premise of Bollinger Bands is that price should normally fall within two standard deviations (represented by the upper and lower band) of the mean which is the center line moving average. As this is the case, trend reversals often occur near the upper and lower bands. As the center line is a moving average which represents the trend in the market, it will also frequently act as support or resistance.

**Use on Stock Patterns**

The bands will expand and contract as the price action of an issue becomes volatile (expansion) or becomes bound into a tight trading pattern (contraction).

**Example 1.**

**Example 2.**

**Notes**

1. When the average used in the calculation of the Bands is changed from a simple moving average to an exponential or weighted moving average, it must be changed for both the calculation of the middle band and the calculation of standard deviation.

2. The Bands use the population method of calculating standard deviation, thus the proper divisor for the sigma calculation is n, not n − 1.

**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. Writing upperBB for the upper band, lowerBB for the lower band, and last for the last (price) value:

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

BandWidth tells you 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.

**Use Outside of Finance**

In a paper published in 2006 by the Society of Photo-Optical Engineers, "Novel method for patterned fabric inspection using Bollinger Bands", Henry Y. T. Ngan and Grantham K. H. Pang present a method of using Bollinger Bands to detect defects in patterned fabrics. From the abstract: "In this paper, the upper band and lower band, which are sensitive to any subtle change in the input data, have been developed for use to indicate the defective areas in patterned fabric."

**Interpretation and Use**

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 band or sell when price falls below the lower band. Moreover, the use of Bollinger Bands is not confined to stock traders; options traders, most notably implied volatility traders, often sell options when the Bands are historically far apart or buy options when the Bands are historically close together, in both instances, expecting volatility to revert back towards the average historical volatility level for the stock.

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.

Traders are often inclined to use Bollinger Bands with other indicators to see if there is confirmation. In particular, the use of an oscillator like Bollinger Bands will often be coupled with a non-oscillator indicator like chart patterns or a trend line; if these indicators confirm the recommendation of the Bands, the trader will have greater evidence that what they forecast is correct.

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