## Bollinger Bands Indicators

An Introduction to the Bollinger Bands® Indicators

John Bollinger, CFA, CMT

Very shortly after the invention of Bollinger Bands it became obvious that it was possible, indeed necessary, to create technical indicators based on the bands. The first two indicators were %b™ (pronounced ‘percent b’), which tells us where we were in relation to the bands and BandWidth™, which tells us how wide the bands are. Together with Bollinger Bands, those two indicators form the

core of the Bollinger Band Suite. Let’s start with Bollinger Bands and then work our way through the indicators.

Bollinger Bands are curves drawn in and around the price structure that define whether prices are high or low on a relative basis. They consist of a middle band, a simple moving average, and upper and lower bands spread above and below the middle band by a measure of volatility. In most applications the length of the average for the middle band is selected to be descriptive of the intermediate-term trend. So, from a certain perspective Bollinger Bands can be seen as a combination of trend and volatility information. It is this informational nexus that allows Bollinger Bands to provide robust definitions of high and low.

The key to Bollinger Bands is volatility. We use the calculation for standard deviation, which measures dispersement around the average. When the data are close to the average the bands are tight and when the data are distant from the average the bands are wide. We can’t make the usual statistical assumptions regarding the percent of data one would expect to find inside the bands. There are two main reasons; security prices do not follow a normal distribution and the sample size we use is generally too small. The bottom line is that instead of finding the expected 95% of the data inside the bands, we generally find a bit less than 90%.

Bollinger Bands provide a definition of whether prices are high or low on a relative basis. One interesting way of exploiting that definition is to compare relative highs and lows to absolute highs and lows – more on this later. A major aspect of the importance of these relative definitions is that they allow users to create rigorous trading approaches that help eliminate emotions from the trading process. Typical Bollinger Band approaches that use these definitions include pattern recognition, signal generation, stop creation, breakouts and breakdowns…

Once we have our definitions of high and low, we can ask: How high? or How low? To answer that question I created %b. %b is derived from the formula for the Stochastic Oscillator popularized by George Lane. The Stochastic Oscillator answers the question: Where are we in the n-day range? %b answers a similar question: Where are we in relation to the Bollinger Bands? The formula for the raw

Stochastic, %k, is:

%k = (last – lowest(n)) / (highest(n) – lowest(n))

Which resolves to one if we are at an n-day high and zero if we are at an n-day low. A simple substitution of the upper and lower bands for the highest and lowest results in %b.

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

There is one crucial difference, the Stochastic calculation is bounded by one and zero, but since price can and does rise above the upper band and fall below the lower band, %b can assume a value above one or less than zero. A %b reading of 1.10 says the we are 10% of the width of the bands above the upper band and a %b reading of -0.20 says that we are 20% of the width of the bands below the lower band, which bring us to BandWidth, the second Bollinger Band indicator.

BandWidth measures the width of the Bollinger Bands. It is the distance from the upper band to the lower band divided by the middle band. It is a percentage and has a ‘normal’ range of approximately five to fifty percent. The most popular use of BandWidth is for locating extremes where the bands are either quite narrow or very wide, areas that have been shown to have forecasting ability. These areas are known as the Squeeze and the Bulge and are defined as the lowest and highest values of BandWidth in the past 125 periods, which brings us to the question of periods and defaults.

BandWidth = (upperBB – lowerBB) / middleBB Squeeze = Lowest(BandWidth, 125)

Bulge = Highest(BandWidth, 125)

We always discuss Bollinger Bands in terms of periods, as they are applicable in most time frames, from the very short to the very long. So a five minute bar is a period, as is an hourly bar, a day, a week and so on. In each case, the bar consists of the highest, lowest, first and last prices of that period. The only limitation is that there must be enough activity in each bar to give a good picture of the price-formation mechanism.

The defaults for Bollinger Bands are a 20-period calculation window and a multiplier of two times the standard deviation of the same data used in the average to determine the distance to the upper and lower bands from the middle band. These may be changed to suit your application, but if you get down towards 10 periods or up towards 50, consider changing the length of the periods and push the Bollinger Band parameters back towards 20.

The default Bollinger Band multiplier of two determines the distance to the upper and lower bands from the middle band. As you lengthen the bands you may want to increase the width to maintain the

same percentage containment. And as you shorten the calculation period you may want to decrease the width to maintain the same percentage containment.

Now that we have handle on Bollinger Bands, %b and BandWidth, let’s see them in action. The following charts illustrate basic Bollinger Band techniques: “W” bottoms where we make a new absolute low but not a new relative low, Three Pushes to a High, and the use of BandWidth to diagnose the beginning and end of a trend via the Squeeze and the Bulge.

Chart 1, ESRX, Express Scripts: A pair of W bottoms dominate this chart, both featuring Ws where the second low was a new low in price but not a new low relative to the Bollinger Bands. Note also the false W on the way down to the first real W bottom. One can filter out such false signals by noting that price is strong enough to close above the middle band and that the middle band does not turn up. Chart 2, GLD, the gold bullion ETF: Tops are often more complex than bottoms, so I chose the classic Three Pushes to a High pattern in gold to illustrate a BB topping formation. Note the sequence of lower peaks in %b versus higher peaks in price and the downturn in BandWidth on the second push – the momentum peak – and after the first leg down, in both cases indicating an end to the current trend. Note also the low reading in BandWidth – a Squeeze – in early June just before the continuation rally started.

Finally, in recent years we have expanded the Bollinger Band Suite greatly. Examples include Bollinger Envelopes – a version of Bollinger Bands derived from highs and lows rather than closes, BBTrend – a measure of trendiness, BBPersist – a measure of directionality, BBImpulse – a measure of instantaneous strength and BBStops – a progressive stop approach that includes a time component.

Come visit us at www.BBands.com or www.EquityTrader.com to see what we have been up to.

Good trading.

John Bollinger, CFA, CMT

www.BollingerBands.com

Nov23

- Glen

- Brandon Kirk Davis

- Brandon Kirk Davis