BOLLINGER BANDS

1. Origins and History

Bollinger Bands were developed by John Bollinger in the early 1980s while he was working as a capital markets analyst for the Financial News Network (FNN). Bollinger was searching for a method of defining whether prices were high or low on a relative basis — a deceptively simple question that had resisted easy answers in classical technical analysis.

Prior to Bollinger’s work, traders used fixed percentage envelopes drawn at a constant distance above and below a moving average (for example, 3% or 5% bands). While useful, these static envelopes had a critical flaw: market volatility is not constant. 

Bollinger’s key insight was to replace the fixed percentage offset with a measure of the market’s own volatility — specifically, the statistical standard deviation of price. By anchoring the width of the bands to actual observed price dispersion, the bands would naturally expand when volatility was high and contract when the market was quiet. 

Bollinger first introduced the concept publicly in the early 1980s via his appearances on FNN and through his market letter. He continued to refine the indicator throughout the decade. The bands gained widespread adoption after being incorporated into popular charting software platforms in the late 1980s and 1990s. 

In 2011, Bollinger Bands were awarded a Dow Award by the Market Technicians Association (now the CMT Association), one of the most prestigious recognitions in technical analysis.

2. Calculation

Bollinger Bands consist of three lines plotted directly on a price chart. Their construction requires three parameters: the period n (typically 20), the moving average type (simple, by default), and the multiplier k (typically 2).

2.1The Middle Band

The middle band is a simple moving average (SMA) of the closing price over the chosen period:

Middle Band  =  SMA(Close, n)

Where n is the lookback period. This acts as a trend baseline.

2.2 Standard Deviation

The standard deviation is calculated over the same n-period window. 

σ  =  √ [ (1/n) × Σ (Closeᵢ – SMA)² ]

2.3 Upper and Lower Bands

The upper and lower bands are placed at k standard deviations above and below the middle band:

Upper Band  =  SMA(Close, n)  +  k × σ

Lower Band  =  SMA(Close, n)  –  k × σ

With the default settings of n = 20 and k = 2, the bands reflect two standard deviations of recent price dispersion around the 20-period moving average.

3. Statistical Background and Caveats

3.1 The 95% Claim

It is frequently stated that with k = 2, approximately 95% of price observations will fall within the Bollinger Bands. This claim is derived from the normal distribution: in a perfectly Gaussian distribution, exactly 95.45% of observations fall within two standard deviations of the mean.

This is a useful rule of thumb, but it comes with significant statistical caveats that any serious practitioner must understand.

3.2 Why the Claim is Not Statistically Rigorous

The standard application of the normal distribution to financial prices rests on assumptions that do not hold in practice:

• Fat tails: Financial return distributions are well-documented to have heavier tails than the normal distribution. Extreme price moves occur far more frequently than a Gaussian model predicts. 
• Rolling window non-stationarity: The standard deviation used to construct the bands is calculated over a rolling n-period window. The 95% property of the normal distribution applies to a stationary distribution, not a rolling one.
• Price levels, not returns: Bollinger Bands are applied to price levels, not to returns. Price levels are non-stationary by construction.

The correct interpretation of Bollinger Bands is not that 95% of prices will always fall within the bands. Rather, the bands adaptively represent recent volatility: a price touching or breaching a band signals that the current price is statistically unusual relative to recent behaviour, as measured by local standard deviation.

3.3  Practical Implications

Despite these statistical limitations, the Bollinger Band framework is robust in practice because it does not require strict adherence to normality to be useful. The bands serve as a relative measure: they tell the trader where the current price stands relative to recent volatility.

4. Trading Strategies

4.1  Bollinger Bands as a Continuation Signal

In trending markets, Bollinger Bands are most powerfully used as a continuation tool. 

The Squeeze

A Squeeze occurs when the bands narrow significantly. This reflects a period of low volatility and typically signals consolidation or range-bound price action. Bollinger himself describes the Squeeze as “the most powerful signal Bollinger Bands give.”

The rationale is rooted in the cyclical nature of volatility: periods of low volatility tend to precede periods of high volatility. A narrowing of the bands therefore sets up for an eventual expansion — a breakout. The bands do not, by themselves, indicate the direction of the breakout; additional tools are required to assess directional bias.

Walking the Bands

Once a strong trend is established, price tends to “walk” along the outer band — repeatedly tagging or closing near the upper band in an uptrend, or the lower band in a downtrend. In this context, a tag of the upper band is not a sell signal but a sign of trend strength. Traders should resist the impulse to fade the band during a strong directional move.

4.2  Bollinger Bands as a Reversal Signal

In ranging markets, Bollinger Bands can be used as a contrarian reversal tool. The classic reversal patterns are the “W-Bottom” and “M-Top,”.

W-Bottom (Bullish Reversal)

A W-Bottom consists of two reaction lows. The first low tags or breaches the lower Bollinger Band. A subsequent bounce and then a re-test forms the second low, which ideally does not reach the lower band. A rally from the second low that breaks above the most recent reaction high and the middle band confirms the reversal.

M-Top (Bearish Reversal)

The M-Top is the mirror image. A first push reaches or breaches the upper band. A reaction pullback and then a second push higher that fails to reach the upper band signals weakening momentum.

5. Combining Bollinger Bands with Other Tools

Bollinger Bands are most effective when used in conjunction with other analytical tools: the following combinations are widely used by practitioners.

5.1  Bollinger Bands with Momentum Oscillators

Volume and momentum oscillators help confirm or deny the significance of a band tag:

• RSI: An upper band tag accompanied by RSI below 70 (non-overbought) suggests trend continuation. An upper band tag with RSI above 80 and beginning to turn down raises reversal risk. Bullish and bearish divergences between RSI and price at band extremes are particularly powerful signals.
• MACD: A bullish MACD crossover as price tests the lower band strengthens the case for a long entry. Conversely, divergence between MACD and price at a band extreme warns of potential reversal.
• Stochastic Oscillator: A %K/%D crossover in oversold territory coinciding with a lower band test provides a combined timing trigger that many traders find more reliable than either signal alone.

5.2  Bollinger Bands with Trendlines

Trendlines can be combined with Bollinger Bands to identify high-probability setups:

• Trendline break confirmed by band position: A break of a downtrend trendline that occurs simultaneously with price moving above the middle Bollinger Band is a stronger continuation buy signal than either event alone. 
• Convergence zones: When a trendline and the lower (or upper) Bollinger Band converge at approximately the same price level on the same bar, the resulting zone carries additional support or resistance significance. 
• Squeeze breakout direction: During a Bollinger Band Squeeze, plotting trendlines on the price action within the squeeze can help anticipate the breakout direction. A pattern of higher lows within a squeeze often precedes an upside breakout and viceversa.

5.3  Bollinger Bands with Support and Resistance Levels

Support and resistance levels derived from prior price structure are among the most important confirming tools for Bollinger Band analysis:

• Band-level alignment with structural support / resistance: A lower band test that occurs at or near a known prior support level produces a much higher-confidence reversal or bounce setup. The structural level provides a rationale for a price floor; the band provides confirmation that the price is statistically stretched. The same is true the other way round. Traders may use this confluence to time profit-taking or entries in a range-bound environment.
• Middle band as dynamic support/resistance: In a trending market, the middle band frequently acts as dynamic support in an uptrend or dynamic resistance in a downtrend. Pullbacks to the middle band in a strongly trending market are often optimal continuation entry points, particularly when the middle band also aligns with a static support or resistance zone.
• False breakout identification: A price that breaks above a resistance level but closes back inside the Bollinger Band on the same bar — or that breaches the upper band without volume confirmation — is more likely to be a false breakout. 

6. Summary

Bollinger Bands represent one of the most versatile and widely adopted tools in technical analysis. Their adaptive volatility-based construction addresses a fundamental weakness of earlier static envelope methods, and their dual role as both a trend-following and mean-reversion tool makes them applicable across a broad range of market conditions.

Practitioners should, however, be clear-eyed about their statistical limitations: the claim that 95% of price observations fall within the bands rests on assumptions of normality that financial markets routinely violate. The appropriate interpretation is relative and contextual — the bands describe where price is relative to recent volatility, not where it must or will go.

Used in conjunction with momentum oscillators, trendlines, and structural support and resistance levels, Bollinger Bands provide a coherent, rule-based framework for identifying both trend continuation and reversal opportunities. This multi-tool approach, consistently applied with disciplined risk management, is the foundation of professional-grade Bollinger Band analysis.