Bollinger Bands: Standard Deviation, the Squeeze and Walking the Band

How the bands are built

Bollinger Bands put a measure of volatility on the price chart itself. John Bollinger introduced them in the early 1980s. Three lines are drawn:

• The middle band is a 20-period simple moving average of the close.
• The upper band is the middle band plus two standard deviations of the same 20 closes.
• The lower band is the middle band minus two standard deviations.

The standard deviation is the one from the mathematics of spread: the square root of the average squared distance of each close from their mean, σ = √( Σ(x − μ)² / n ). Because it is recomputed every bar from the last 20 closes, the bands widen when price has been swinging and narrow when it has been quiet. That is the feature that distinguishes them from a fixed percentage envelope: the bands are a volatility gauge drawn in price units.

Two derived readings are often shown. %B locates price within the bands, %B = (P − Lower) / (Upper − Lower): 1 at the upper band, 0 at the lower, 0.5 at the middle, above 1 outside the top. Bandwidth measures how wide the bands are relative to the middle, Bandwidth = (Upper − Lower) / Middle, which makes the width comparable across time and across instruments.

What a band touch means

If prices were normally distributed around the moving average, about 95% of closes would fall within two standard deviations. They are not, and the average is estimated from the same twenty closes it is compared against, so in practice Bollinger reports that around 88 to 89% of closes fall inside bands set at 20 periods and two deviations. A close outside the bands is therefore unusual but not rare: it happens roughly one bar in nine.

The common misreading is that a touch of the upper band is a sell and a touch of the lower band a buy. In a trend, the opposite is closer to the truth. A market that is trending strongly walks the band: it closes at or outside the upper band for bar after bar, and each touch is a sign of strength, not exhaustion. The bands tell you that price is extended relative to the last twenty bars. Whether that is an extreme to fade or a trend to follow is decided elsewhere, by the trend on a higher timeframe, by RSI and its divergences, or by what price does on the bar after the touch.

The squeeze

The most reliable thing the bands say is about volatility itself. Volatility is cyclical: quiet periods are followed by active ones and vice versa. When bandwidth falls to its lowest level in roughly six months the bands are in a squeeze, and an expansion usually follows. The squeeze gives no direction; it says that a large move is becoming likely and that the breakout, when it comes, is worth taking seriously. A false start, where price pokes out of one band and then reverses through the other, is common enough that the first move out of a squeeze is often the wrong one.

Settings

The 20-period, two-deviation setting is the default for a reason: the moving average and the deviation are computed over the same window, and twenty bars gives a stable estimate without making the bands too slow. Shorter windows need a smaller multiplier (Bollinger suggests 1.9 at 10 periods) and longer ones a larger (2.1 at 50) to keep roughly the same share of closes inside. Changing the multiplier without changing the window simply moves the bands and changes how often they are touched.

On the desk

The symbol pages overlay Bollinger Bands on the candles beside the moving averages, and the same standard deviation, measured from daily closes and annualised, is what sizes the ranges and the risk meter in the analysis notebooks, so a range quoted there is the instrument's own volatility rather than a round number.