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Bollinger Bands: Formula, %B, Bandwidth and the Squeeze

Bollinger Bands sit 2 standard deviations around a 20-day average. How %B and bandwidth are calculated and what a squeeze describes.

Reviewed · Sources at the end · How Vyreon measures
Vyreon's per-security reports are not live yet; this page describes what they will measure. Examples are illustrative.

Bollinger Bands are lines drawn two standard deviations above and below a 20-day moving average of the closing price. The bands widen when recent prices have been volatile and narrow when they have been calm. %B shows where the price sits within the bands, and bandwidth shows how wide they are.

Bollinger Bands Formula

Over the last 20 sessions:

  • Middle band = 20-day simple moving average of the close
  • Standard deviation (sd) of the same 20 closes
  • Upper band = middle + 2 × sd
  • Lower band = middle − 2 × sd

John Bollinger's definition uses the population standard deviation (dividing by 20, not 19), and so does Vyreon. Some charting tools use the sample version, which gives slightly wider bands.

What Is %B?

%B = (close − lower band) ÷ (upper band − lower band)

At the lower band %B is 0, at the middle band 0.5 and at the upper band 1. Vyreon shows it as a percentage: 0% is the lower band and 100% the upper band. Above 100% means the close is above the upper band; below 0% means it is below the lower band.

What Is Bollinger Bandwidth?

Bandwidth = (upper band − lower band) ÷ middle band

Because the bands sit 2 sd either side of the middle, bandwidth equals 4 × sd ÷ the 20-day average: a measure of recent volatility relative to price.

Illustrative example: a 20-day average of 100 and a standard deviation of 2 give bands at 104 and 96 and a bandwidth of 8%. A close of 103 gives a %B of (103 − 96) ÷ 8 = 87.5%.

What Is A Bollinger Squeeze?

A squeeze is a period when bandwidth falls to a low level compared with its own recent history: the price has been unusually quiet. Traders watch squeezes because, in Bollinger's description, quiet periods are followed by more active ones, but the bands say nothing about the direction of any move, or when it comes. Vyreon measures bandwidth every session, so a squeeze shows up as a low point in that series.

Touching Or Closing Outside The Bands

A close at or beyond a band is not, on its own, a signal. In a strong trend prices can stay near one band for weeks. Prices are not normally distributed, and daily returns have fatter tails than a normal distribution, so the "95% within two standard deviations" rule of thumb from the normal distribution does not apply to the bands.

How Vyreon Calculates It

  • Bollinger Bands (20, 2) on daily closes adjusted for splits and dividends, with the population standard deviation.
  • Vyreon reports the upper, middle and lower bands, %B and bandwidth.

What Bollinger Bands Do Not Tell You

  • They describe the last 20 sessions. They do not predict where the price goes next.
  • The 20-day window and the factor of 2 are conventions; band touches and squeezes are not rules.

Related: moving averages · price channels · ATR · realized volatility · RSI

Sources

  • John Bollinger, Bollinger on Bollinger Bands (2001): the bands, %B, bandwidth and the squeeze, with the population standard deviation.
  • Benoit Mandelbrot, "The Variation of Certain Speculative Prices", Journal of Business (1963), and Eugene F. Fama, "The Behavior of Stock-Market Prices", Journal of Business (1965): price changes with fatter tails than a normal distribution.