Harbor Coffee, our fictional coffee company, averages $66 in two different 20-session windows. Its Bollinger Bands span $62–$70 in the first and $64–$68 in the second. The center is unchanged; the envelope is half as wide.
These invented prices tell a story that the average alone misses. The recent closes have moved closer together. Bollinger Bands make that spread visible, then redraw the envelope as each new close arrives.
What the envelope measures
Bollinger Bands form a volatility envelope: an upper and lower line around a moving average. The average locates the envelope; the spread of recent prices sets its width. Where MACD compares two averages, the bands describe the spread around one.
A common setup uses a 20-period simple moving average, or SMA, as the center. The outer bands sit two standard deviations above and below it. On a daily chart, 20 periods means 20 trading sessions.
Standard deviation measures spread around a mean. Here it measures closing-price levels, such as $64 and $68. That differs from measuring how much percentage returns vary from day to day.
Build Harbor's bands
Use completed regular-session closes in US dollars after Harbor's year 3 snapshot, with no splits or distributions. Each band uses the latest 20 closes.
SMA20 is the average of those closes; SD20 is their standard deviation. The ± means add for the upper band and subtract for the lower.
In window A, Harbor alternates between $64 and $68 for 20 sessions: ten closes at each price. The mean is $66. Every close is $2 from that mean, so SD is $2.
Twice that spread is $4. The upper band is $66 + $4 = $70; the lower is $66 − $4 = $62.
In window B, the 20 closes alternate between $65 and $67. The mean is still $66, but every close is only $1 away. SD is $1, giving bands of $66 ± $2, or $64–$68.
| Window | Mean | SD | Bands |
|---|---|---|---|
| A | $66 | $2 | $62–$70 |
| B | $66 | $1 | $64–$68 |
The average price is identical; the envelope is half as wide, shrinking from $8 to $4.
As in the SMA calculation, the newest close replaces the oldest; now the spread changes along with the mean.
Read narrowing and widening
A band squeeze means the bands are unusually narrow compared with their own history. A band expansion means they are widening.
Compare the same stock with the same settings. A $4 envelope means something different around a $20 stock than around a $200 stock; there is no universal narrow dollar width.
The chart joins A, then B, then five more closes: $69, $70, $71, $72 and $73. It starts at session 20, when the first full window is available. The bands narrow as B replaces A.
At session 40, only B remains, giving the $64–$68 envelope. By session 45, the upper band has risen to about $72.12, yet Harbor closes at $73. That $73 is already included in the calculation. A band can move higher without keeping the price inside.
The lower band falls to about $62.48 while the stock rises. The average moves up, but the spread grows enough to push the lower line down. A smooth climb can widen the bands; it need not involve erratic daily returns.
At session 40, that climb is still in the future. Narrow bands tell you the recent window is quieter. They say neither which way prices will move nor how long the quiet will last.
A band is not a barrier
An upper-band touch puts the price high relative to recent closes. It does not tell you whether the business is overpriced. During a trend, a stock can keep following an outer band as both price and band move.
John Bollinger's own explanation is explicit: a touch alone is not a buy or sell signal. A touch describes a location, not an instruction.
Two standard deviations do not make this a 95% forecast interval. The formula measures the prices you put in; it does not assign odds to the next close landing inside the bands.
For window B, your reading is simple: 20 closes centered on $66, with a tighter $64–$68 envelope. The next direction remains unknown.
True range catches gaps
A candle's high-to-low span can miss an overnight gap. True range includes the previous close to catch it. It takes the largest of high minus low, the absolute distance from high to previous close, and the absolute distance from low to previous close. Average true range (ATR) smooths these ranges, commonly over 14 bars.
In a separate Harbor session, the previous close is $66, the high $63, the low $60 and the close $61. The intraday span is $3; true range is max($3, $3, $6) = $6. One $6 range does not determine ATR; earlier ranges matter too. ATR is measured in dollars here, with no direction.
Bands and ATR describe movement within one stock's history. The core route resumes with relative strength, which compares its performance with a stated benchmark.
In short
- Bollinger Bands combine a moving average with the spread of recent closing-price levels.
- Narrow bands describe a quieter window, not the next move's direction or timing.
- A band touch is not a command, and two standard deviations are not a 95% promise.
- ATR includes gaps in recent trading ranges, without telling you a direction.