Definition (plain)
– Bollinger Bands are a price-overlay indicator that shows a security’s recent average price and a volatility range around that average. The indicator consists of three lines: a middle moving average and an upper and lower band placed a set number of standard deviations away from that average.
Who created them
– John Bollinger, a technical analyst active since the 1980s, developed the bands to combine a moving average with statistical dispersion (standard deviation) so traders could see when price is relatively high or low and how volatile the market is.
How the bands are built (step-by-step)
1. Choose the lookback period for the middle line (typical default: 20 periods). This is usually a simple moving average (SMA) of closing prices.
2. Compute the standard deviation of those same closing prices for the same period.
3. Select how many standard deviations to use for the outer bands (common default: 2).
4. Calculate:
– Middle band = SMA(period)
– Upper band = SMA + (k × standard deviation)
– Lower band = SMA − (k × standard deviation)
where k is the chosen multiplier (commonly 2).
5. Plot the three lines on the price chart. Most chart platforms will compute these automatically.
Why those parameters
– Using two standard deviations ties to the normal-distribution idea: roughly 95% of values fall within ±2 standard deviations if returns were normally distributed. In practice, price returns are not perfectly normal, so the ±2 rule is a guideline, not a strict law.
Key interpretations (what traders commonly read from the bands)
– Width = volatility: Wide bands indicate higher volatility; narrow bands indicate lower volatility.
– Price near upper band: often interpreted as relatively high (potentially “overbought”) price; may mark resistance.
– Price near lower band: often interpreted as relatively low (potentially “oversold”) price; may mark support.
– Middle band: acts as
a dynamic trend benchmark — typically the n‑period simple moving average (SMA). Traders treat the middle band as a reference for trend direction and mean reversion: prices above the middle band suggest bullish bias, prices below suggest bearish bias, and crosses of the middle band can signal shifts or help confirm other signals.
Common signals and patterns (how traders read the bands)
– Squeeze (band narrowing): When the bands contract, volatility is low. Narrow bands often precede bigger moves, but they do not indicate direction. A breakout above the upper band or below the lower band following a squeeze signals a potential start of a higher‑volatility trend. Confirm with volume or a momentum indicator before trading the breakout.
– Breakout: A close outside a band is not, by itself, a buy or sell signal. Breakouts show strength in the breakout direction; traders look for follow‑through (additional closes outside the band) or confirmation from other tools.
– Riding the band: In a strong trend, prices may “ride” the upper band in an uptrend or the lower band in a downtrend. This indicates persistent momentum; the middle band then becomes support (in uptrends) or resistance (in downtrends).
– Reversal/Failure swings: If price touches or exceeds an outer band but then fails to sustain and crosses back through the middle band, that can indicate a weakening move and a possible reversal.
– Double tops/bottoms using bands: A classic setup is a lower high near the upper band (for bears) or a higher low near the lower band (for bulls). Combine with volume decline on the second touch for added conviction.
Key formulas (standard implementation)
– Middle band (SMA): SMA_n = (1/n) * sum_{i=1}^{n} Close_i
– Standard deviation (SD): SD_n = sqrt[(1/n) * sum_{i=1}^{n} (Close_i − SMA_n)^2] (many platforms use the population formula; some use n−1 — check your platform)
– Upper band = SMA_n + k * SD_n
– Lower band = SMA_n − k * SD_n
Typical defaults: n = 20 periods, k = 2.
Worked numeric example (20‑period, k = 2)
1. Suppose the 20 most recent daily closes average (SMA_20) = 50.00.
2. Calculate the 20‑period SD and find SD_20 = 1.50.
3. Upper band = 50.00 + 2 * 1.50 = 53.00.
4. Lower band = 50.00 − 2 * 1.50 = 47.00.
Interpretation: A daily close above 53.00 is outside the upper band; a close below 47.00 is outside the lower band. A move from 51.00 up into 53.50 shows momentum beyond the recent average plus volatility; whether to act depends on your plan and confirmation signals.
Useful derived indicators
– %B: (Price − Lower) / (Upper − Lower). Scales price relative to bands: 0 = at lower band, 1 = at upper band. Helpful for systematic rules.
– BandWidth: (Upper − Lower) / Middle. A normalized measure of band width; useful to quantify squeezes.
Practical checklist before using Bollinger Bands
1. Confirm parameters (n and k) and understand your charting platform’s SD formula (population vs. sample).
2. Identify market context (trending vs. ranging). Bands perform differently in each.
3. Look for confirmation: volume, RSI/ADX, MACD, or a trend filter (e.g., longer SMA).
4. Define risk: entry trigger, exact stop loss (e.g., just inside the middle band on a failure), and position size.
5. Backtest or paper‑trade your rules on the specific instrument and timeframe.
Limitations and caveats
– Bands are lagging: they derive from past prices. Signals are not predictive by themselves.
– Non‑normal returns: The “±2 SD ≈ 95%” heuristic assumes normality; asset returns deviate from normality, so expect more frequent band breaches.
– False breakouts: In choppy markets, many false signals occur. Use filters and confirmatory indicators.
– Parameter sensitivity: Shorter n or smaller k makes bands tighter and signals more frequent but noisier; longer n or larger k smooths and reduces signals.
Parameter tuning and common variations
– Shorter
– Shorter n (lookback length) and smaller k (standard‑deviation multiplier) make the bands tighter and generate more frequent signals, but increase noise and false signals. Longer n and larger k smooth the bands and reduce signal frequency, at the cost of slower reaction to real changes.
Common parameter choices and why they matter
– Typical default: n = 20, k = 2. That balances responsiveness and filtering for many liquid stocks and indices on daily charts.
– Mean‑reversion tuning: traders often shorten n to 10–14 and reduce k to 1–1.5 to catch quicker bounces around a central mean.
– Breakout tuning: traders seeking volatility expansion may lengthen n to 30–50 and keep k at 2–2.5 to reduce whipsaws and focus on stronger breakouts.
– Moving average type: simple moving average (SMA) is standard; exponential moving average (EMA) weights recent prices more and produces slightly different bands.
– Standard‑deviation convention: most implementations use population standard deviation (divide by n). If you use sample standard deviation (divide by n−1), bands will be marginally wider—be consistent in backtests.
Useful derived indicators (formulas and short definitions)
– %B (percent B): location of price within the bands, scaled 0–1.
Formula: %B = (Price − Lower Band) / (Upper Band − Lower Band)
Interpretation: %B ≈ 1 means price at upper band; ≈ 0 at lower band; >1 or 1 or <0 occur when price is outside the bands.
– Bandwidth (or the related “squeeze” concept):
– Very low bandwidths → low volatility; traders watch for breakouts but direction is not given by bandwidth.
– Bandwidth expansion after a squeeze signals increasing volatility; confirm direction with price and other indicators.
Limitations and caveats
– Bands are based on historical volatility; they do not predict direction, only relative volatility and deviation from a moving average.
– Different software may use population (STDEV.P) or sample (STDEV.S) SD; this changes band levels slightly—check your data source.
– Short-period SMAs (like 5) react faster but produce wider, noisier bands; longer-period SMAs (like 20) smooth noise but lag price.
– Avoid relying on Bollinger Bands alone — combine with volume, trend indicators, or price action for more robust signals.
Worked-note on the SD method used here
– This example used population standard deviation: variance = Σ(x − μ)^2 / n. Many textbooks and some platforms use sample standard deviation (divide by n−1); for small n the difference is material.
References
– Investopedia — Bollinger Bands overview: https://www.investopedia.com/terms/b/bollingerbands.asp
– John Bollinger (official): https://www.bollingerbands.com
– CBOE — Volatility and indicators education: https://www.cboe.com/education
Educational disclaimer
This explanation is for educational purposes only and is not individualized investment advice. Use it to learn calculation and interpretation; consult a licensed professional before making trading decisions.