Bollinger Bands

Definition

Bollinger Bands (John Bollinger’s construction) draw an envelope of ±k standard deviations of price around an N-bar SMA — a moving, volatility-scaled band. Price position within the band normalizes “how far from the mean” by recent volatility; band WIDTH is itself a volatility gauge (squeeze = compression, expansion = regime shift underway).

How it works / structure

• Formula: middle = SMA(N); bands = SMA(N) ± k × σ(N), with σ the standard deviation of price over N (20 and 2.0 are the conventions).
• Parameters (engine-executable): N, k, price input, and the signal convention — band touch/close-outside (reversion reading), %B (position within the band, 0-1), bandwidth (squeeze threshold as percentile of its own history), or breakout-after-squeeze (the volatility-cycle reading).
• Two opposite readings, same event: close outside a band is a reversion trigger in range regimes and a breakout confirmation in trending ones — the same regime fork as stochastics/Donchian, resolved outside the indicator.
• σ vs ATR: close-to-close standard deviation ignores gaps and intrabar range that ATR captures; the two scale units differ most exactly when it matters (gappy tape).

When it applies

Reversion triggers with volatility-adaptive thresholds (a fixed ±5% envelope is wrong for both a utility and a small-cap; ±2σ adapts); squeeze detection as a volatility-regime flag (regime-volatility compression before expansion); %B as a normalized input to systematic rules.

Risk profile & failure modes

• Band walks: strong trends ride the outer band for many bars — serial band touches are trend evidence, not repeated reversion signals; fading a band walk is the canonical Bollinger loss.
• σ estimation noise: 20 observations estimate σ poorly; bands jitter with sampling error, and outliers inflate them just after the shock (the ATR lag problem in σ form).
• Squeeze direction is unknown: compression predicts expansion, not direction — squeeze-breakout systems still need the directional leg to be right.
• Convention overfitting: N and k are two more fitted parameters; 20/2.0 has no demonstrated optimality.

Evidence & limits

Bollinger (2001) is the construction source. Direct academic tests are sparse and unflattering: Lento et al (2007) found simple Bollinger rules did not outperform buy-and-hold after costs in their samples. Volatility clustering (the squeeze logic’s foundation) is robustly documented (regime-volatility); directional band rules are unproven-to- negative after friction. Band lore (“a close outside means reversal”) is folklore, labeled.

Falsifiable-thesis examples

Illustrations only, not signals:

• “X, closing below its −2σ band without news, will close above the 20-day SMA within 15 sessions” — falsified at the mark.
• “Bandwidth in its lowest decile predicts above-median 10-day realized volatility on universe U this year” — falsified by the tally.

Cross-references

• Components: indicator-sma; alternative scale: indicator-atr
• The regime fork: strategy-mean-reversion vs strategy-breakout
• The squeeze’s foundation: regime-volatility
• Method caveats: lens-technical