Angie · learn

Bollinger bands

A moving average with bands drawn two standard deviations above and below it. Price at a band is unusual relative to its own recent range, not relative to any other stock.

Updated 2026-09-03

Bollinger bands draw a moving average with two lines either side of it, placed a set number of standard deviations away. The bands widen when the market is volatile and narrow when it is calm, so they describe a range that adapts to conditions.

upper band = 20-period SMA + 2 × standard deviation

Lower band subtracts the same. Roughly 95 percent of observations fall inside two standard deviations if returns were normally distributed, which they are not.

That last caveat matters more than the formula. Financial returns have fat tails, so price touches the bands far more often than the statistics suggest, and the extreme events that matter most are the ones the normal distribution says should essentially never happen.

Price touching the upper band is not a sell signal. In a strong trend price can ride the upper band for weeks, and a strategy that sells every touch will short every good rally. The useful reading is the width itself: a sustained narrowing means volatility has compressed, and compressed volatility tends to resolve into a large move in an unknown direction.

See also

  • Z-score — How many standard deviations today's price sits from its recent average. Two sigma below means a move this far down happened on roughly one day in forty.
  • Mean reversion — The tendency of a stretched price to drift back toward its own average. Angie measures how often that actually happened for a name rather than assuming it will.
  • RSI — A 0 to 100 gauge of how one-sided recent moves have been. Conventionally below 30 is oversold and above 70 overbought, though a strong trend can hold an extreme for weeks.

← See this one in the deck

Educational content, not investment advice. Angie explains how a valuation is built so you can judge it yourself. What you do with that is your call.

IsiofiaIsiofia