Bollinger Bands
Bollinger Bands are a technical analysis tool developed by John Bollinger in the early 1980s consisting of three bands plotted on a price chart: a middle band (simple moving average of closing prices), an upper band (the SMA plus a multiple of the rolling standard deviation), and a lower band (the SMA minus the same multiple), designed to measure volatility and identify potential overbought or oversold conditions.
Key takeaways
- The standard settings are a 20-period SMA as the middle band with upper and lower bands at ±2 standard deviations, meaning approximately 95% of closing prices should fall within the bands under normal conditions.
- Band width (distance between upper and lower bands) contracts during periods of low volatility ('the squeeze') and expands during high-volatility periods, with squeezes often preceding significant price breakouts.
- When price touches or exceeds the upper band, the asset may be statistically 'overbought' relative to recent volatility; touching the lower band may indicate 'oversold' — but trending markets can sustain extended touches without reversal.
- Bollinger Bands are most effective as a relative measure of volatility — providing context for current price movement — rather than as standalone buy/sell signals.
- The %B indicator (measuring where the current price is relative to the bands, from 0 at the lower band to 1 at the upper band) and BandWidth (normalized band width) are commonly derived indicators.
Explanation
John Bollinger developed his bands from the concept of 'trading envelopes' — fixed percentage bands above and below a moving average — recognizing that a volatility-adaptive envelope (using standard deviations instead of fixed percentages) would be more responsive to changing market conditions. By using the statistical properties of normal distributions as a reference, he created a framework that automatically widens during volatile periods and narrows during quiet periods.
The construction is mathematically straightforward: the middle band is a 20-period simple moving average (SMA) of the closing price. The standard deviation is calculated over the same 20-period lookback. The upper band is SMA + 2σ and the lower band is SMA − 2σ. Under the assumption that returns are normally distributed and the lookback window is representative, approximately 95% of observations should fall within ±2σ — meaning only about 5% of observations should be outside the bands. In practice, financial return distributions have fat tails, so bands are violated somewhat more frequently than 5%.
The Bollinger Band 'squeeze' is one of the most actionable signals derived from the indicator. Periods of unusually low volatility — manifesting as very narrow bands (low BandWidth relative to its historical range) — tend to precede periods of elevated volatility. The direction of the subsequent move is not predicted by the squeeze itself; it is typically confirmed by the initial direction of the breakout. John Bollinger notes that the squeeze identifies when markets are coiling, but traders should use other indicators (MACD divergence, RSI, or fundamental catalysts) to determine directional bias.
For systematic quantitative strategies, Bollinger Bands have been incorporated as features in mean-reversion models (fade the touch of the upper/lower band in range-bound markets) and momentum models (trade in the direction of a confirmed breakout beyond the bands). Academic research on Bollinger Band strategies shows modest but statistically significant predictive power in highly liquid, mean-reverting markets (foreign exchange pairs, equity index futures) with appropriate signal confirmation filters, but limited effectiveness on individual stocks with idiosyncratic volatility regimes.
Formula
Middle Band = SMA(Close, n) Upper Band = SMA(Close, n) + k × σ(Close, n) Lower Band = SMA(Close, n) - k × σ(Close, n) %B = (Close - Lower Band) / (Upper Band - Lower Band) BandWidth = (Upper Band - Lower Band) / Middle Band
Example
Gold futures are trading at $1,980/oz, with the 20-day SMA at $1,970 and standard deviation of $25. The upper Bollinger Band is at $2,020 (1,970 + 2×25) and the lower band at $1,920 (1,970 − 2×25). BandWidth is $100, or 5.1% — well above its 52-week median of 3.2%, indicating elevated volatility. As gold consolidates over the next two weeks, the bands narrow to $70 (BandWidth = 3.5%), approaching the annual low — a textbook Bollinger squeeze. A breakout above $2,000 on high volume provides the directional signal, and a systematic trend-following system triggers a long entry. Gold subsequently rallies to $2,060 over the next 3 weeks as the geopolitical catalyst driving the initial volatility resolves in a risk-off direction — demonstrating the squeeze-and-breakout pattern.
Related terms
Average True Range Breakout Doji Equity Equity Index Exchange Exponential Moving Average Fat Tails Gold Macd Moving Average Convergence Divergence Moving Average Overbought