Bollinger Bands: Volatility Around a Moving Average

Bollinger Bands place a volatility envelope around a moving average. The centre describes recent average price, while the outer bands expand and contract with the dispersion of the same observations. That makes the indicator adaptive: a two-unit move may be ordinary in one regime and unusually large in another. The bands organize price relative to recent variability, but they do not establish a statistical promise that price will remain inside them.

Calculate the middle and outer bands#

The common configuration uses 20 periods and two standard deviations:

Middle band = 20-period SMA

Upper band = Middle band + 2 × standard deviation

Lower band = Middle band - 2 × standard deviation

The standard deviation is calculated from the prices in the moving window, usually closes. Many charting packages use population standard deviation, dividing squared deviations by (n); some implementations use sample standard deviation, dividing by (n - 1). That choice changes band width. Price adjustments, rounding, timeframe, and session definitions can also explain platform differences.

When the window advances, both the average and dispersion are recalculated, so the envelope’s location and width can change at the same time.

Interpret location without inventing certainty#

A touch of the upper band means price is high relative to its recent mean and dispersion. It is not automatically overvalued or ready to fall. In a strong advance, closes can repeatedly track the upper band. Likewise, repeated lower-band contact can accompany a persistent decline.

A close outside a band is possible and should not be treated as a calculation error. Standard deviation describes the observed window; market returns are not guaranteed to follow a stable normal distribution. Fat tails, gaps, and changing volatility make extreme observations more common than a simple bell-curve interpretation suggests.

The middle band can act as a trend reference, but it is still an SMA—not a guaranteed support or resistance level.

Use bandwidth and percent B carefully#

Two related measures make observations easier to compare:

Bandwidth = (Upper band - Lower band) / Middle band

Percent B = (Price - Lower band) / (Upper band - Lower band)

Low bandwidth identifies relative contraction, often called a squeeze. Contraction can precede expansion because volatility clusters, but it does not reveal the direction of the next move. Percent B equals 0 at the lower band, 0.5 at the middle band, and 1 at the upper band. Values can fall below 0 or rise above 1 when price moves outside the envelope.

Both measures require historical context. “Low” bandwidth for one instrument may be normal for another.

Worked example: a five-price envelope#

Use a shortened window with closes of 98, 100, 101, 99, and 102. Their mean is:

(98 + 100 + 101 + 99 + 102) / 5 = 100

Deviations from the mean are -2, 0, 1, -1, 2. Their squared values total 10. Using population standard deviation:

Variance = 10 / 5 = 2

Standard deviation = square root of 2 = 1.414

At two standard deviations, the upper band is 100 + 2.828 = 102.83, and the lower band is 100 - 2.828 = 97.17. For the latest close of 102:

Percent B = (102 - 97.17) / (102.83 - 97.17) ≈ 0.85

Bandwidth is approximately 5.66 / 100 = 5.66%. The close sits near the upper band, but it remains inside. Nothing in those numbers alone establishes continuation or reversal.

Practical Bollinger Bands checklist#

1. Confirm lookback, deviation multiplier, standard-deviation convention, and price input.
2. Compare current bandwidth with the instrument’s own historical distribution.
3. Determine whether price is ranging, trending, or reacting to a discrete event.
4. Treat a squeeze as a volatility condition, not a directional signal.
5. Require a separately defined rule for any breakout or mean-reversion interpretation.
6. Evaluate closes and executable prices rather than relying on temporary intrabar touches.
7. Include gaps, spread, slippage, and failed breakouts in testing.

The multiplier and lookback should remain fixed during evaluation unless a documented rule changes them.

Limitations and false signals#

Band width is backward-looking. A quiet window can produce narrow bands just before an event, but it cannot quantify the size or direction of the event gap. Conversely, bands can stay wide after volatility has already peaked. Mean-reversion assumptions are vulnerable when a new trend begins, while breakout assumptions are vulnerable when price briefly exits and returns.

The middle average and standard deviation use the same price sample, so the three lines are not independent signals. Normal-distribution shortcuts can also understate tail risk. Changing parameters by instrument after inspecting outcomes introduces overfitting, and same-close backtests may assume fills that were unavailable. Confirmation should add different evidence, such as structure or participation, rather than another transformation of the same closes.

Key takeaways#

• Bollinger Bands combine a moving average with a volatility-based envelope.
• Band touches describe relative location, not mandatory reversals.
• A squeeze signals contraction but does not predict breakout direction.
• Percent B measures location; bandwidth measures relative envelope width.
• Distribution assumptions, regime shifts, and execution reality limit simple rules.

This guide is general education, not personal investment advice or a recommendation. Volatility can expand abruptly, prices can gap beyond intended controls, and liquidity, execution, and leverage risks can create substantial losses.