Concept
Bollinger Bands, created by John Bollinger, consist of a middle line (20-day simple moving average) and an upper and lower band around it. The bands widen and narrow with how spread out recent prices are (the standard deviation).
- When price swings grow, the bands widen; when things calm down, they narrow.
- Statistically the price stays inside the bands most of the time, but moving outside them is also common.
Find a stretch on the chart where the bands become very narrow and then widen sharply. Change the standard deviation multiplier to 1 or 3 to see how the band width changes.
How it is calculated
Middleₜ = SMA(N)ₜ
σₜ = √( Σ(Pᵢ − Middleₜ)² ÷ N ) (last N days)
Upperₜ = Middleₜ + k × σₜ, Lowerₜ = Middleₜ − k × σₜ
Bandwidthₜ = (Upperₜ − Lowerₜ) ÷ Middleₜ
- The defaults are N = 20 and k = 2.
- The standard deviation is the population standard deviation, divided by N (Bollinger’s definition). Some tools divide by N − 1, so values can differ slightly.
Cautions when reading it
- Touching the upper band ≠ a top: in strong trends the price can keep climbing along the upper band (“walking the band”).
- Touching the lower band ≠ a bottom: the same happens in downtrends.
- Squeeze: narrow bands are said to precede big moves, but they do not tell you the direction.
- Limits of the normal-distribution assumption: stock returns have more extreme moves than a normal distribution, so “inside the bands 95% of the time” is not accurate.
Chart shapes and indicators summarize past prices. The same shape is sometimes right and sometimes wrong depending on the market, and this page does not tell you when to buy or sell any stock. To practice yourself, try the chart lab or mock trading.