Bollinger Bands

August 24, 2024 Trading

Bollinger Bands explained: moving-average and standard-deviation formulas, bandwidth, a calculation example, practical interpretations, and limitations.

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Bollinger Bands are volatility-adjusted price bands placed above and below a moving average. The common configuration uses a 20-period simple moving average and bands two standard deviations away, creating a relative framework for judging whether price is high or low compared with its recent distribution.

A band touch is not automatically a reversal signal. In a strong trend, price can repeatedly move along or beyond one band.

Key Takeaways

The middle band is usually a moving average; the outer bands expand and contract with recent standard deviation.
Common defaults are 20 periods and a multiplier of 2, but settings must be stated.
BandWidth describes relative band width, while %B describes price location within the bands.
Narrow bands indicate lower recent dispersion, not certainty that a breakout is imminent.
The bands are based on historical prices and do not create a normal-probability forecast.

Bollinger Bands diagram showing narrow bands during compression and wider bands after price expansion.

Formula

For lookback n and standard-deviation multiplier k:

$$ Middle_t = SMA_n(P_t) $$

Upper_t = Middle_t + k\sigma_n

Lower_t = Middle_t - k\sigma_n

where sigma is the standard deviation of the selected price series over the same lookback.

Two related measures are:

BandWidth_t = \frac{Upper_t-Lower_t}{Middle_t}

\%B_t = \frac{P_t-Lower_t}{Upper_t-Lower_t}

%B = 1 places price at the upper band, 0.5 at the middle of the bands, and 0 at the lower band. Values can exceed 1 or fall below 0.

Simple Example

Suppose a stock’s 20-day moving average is $100, its 20-day standard deviation is $2, and k = 2.

$$ Upper = 100 + 2(2) = 104 $$

$$ Lower = 100 - 2(2) = 96 $$

A close at $105 is above the upper band. It shows that the close is high relative to this moving average and standard-deviation setting. It does not establish that the stock must decline or that $105 is fundamentally expensive.

How Bollinger Bands Are Interpreted

Observation	What it describes	What it does not prove
Price near upper band	High relative price within the current envelope	Price is overvalued or must fall
Price near lower band	Low relative price within the current envelope	Price is undervalued or must rise
Bands narrow	Recent price dispersion declined	The timing or direction of a breakout
Bands widen	Recent dispersion increased	Volatility will remain elevated
Price walks a band	Persistent directional movement	A risk-free trend

The same upper-band touch can support a trend-following rule in one strategy and a mean-reversion observation in another. The trading rule, not the band itself, determines the interpretation.

Bollinger Bands Versus Fixed Envelopes

Feature	Bollinger Bands	Fixed-percentage envelope
Center	Usually a moving average	Usually a moving average
Distance from center	Standard-deviation multiple	Fixed percentage
Response to volatility	Expands and contracts	Remains fixed unless parameters change
Main sensitivity	Price distribution and lookback	Chosen percentage and moving average

Bollinger Bands are also distinct from range-based channels that use average true range instead of standard deviation.

How to Evaluate a Bollinger Rule

Confirm the price field, lookback, moving-average type, standard-deviation convention, and multiplier.
State whether the rule uses a touch, close beyond a band, return inside a band, BandWidth, or %B.
Check whether the market is trending or range-bound.
Test the rule on data not used to select its settings.
Include spreads, fees, slippage, gaps, and realistic order timing.

Risks and Limitations

Parameter sensitivity: Different lookbacks and multipliers materially change the bands.
Distribution assumptions: Two standard deviations do not guarantee a fixed percentage of future prices will remain inside the bands.
Lag: Both the moving average and standard deviation depend on historical observations.
Band walking: Strong trends can remain near one band longer than a mean-reversion rule can tolerate.
Volatility shock: Bands widen only after new price movement enters the calculation.
Data differences: Adjusted prices, session boundaries, and vendor methods can change readings.

John Bollinger’s official explanation describes the bands as a relative-price framework and distinguishes BandWidth and %B. The CFTC Futures Glossary provides public definitions for volatility and technical analysis. Neither source guarantees the performance of a Bollinger-based rule.

FAQs

Does touching the upper Bollinger Band mean sell?

No. It means price reached a high relative level under the selected settings. In a strong uptrend, repeated upper-band touches can reflect persistence rather than immediate exhaustion.

Does a Bollinger squeeze guarantee a breakout?

No. Narrow bands show that recent dispersion declined. They do not determine when volatility will expand or which direction price will move.

Are prices expected to stay inside the bands 95% of the time?

No fixed percentage is guaranteed. Market returns are not necessarily normally distributed, and the moving mean and standard deviation change with each observation.

Standard Deviation: A measure of dispersion around an average.
Moving Average: A rolling average used as the middle band.
Breakout: Price movement beyond a defined level or range.
Price Volatility: Variation in market prices over time.

This article is educational and does not provide personalized investment or trading advice. Bollinger Bands cannot guarantee gains or limit losses.

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