Every stock has its own normal amount of movement. A utility can drift 1% in a week and that is a big week. A young growth stock can move 1% before lunch on a quiet day. A fixed rule like "a 5% move is a lot" doesn't work, because 5% means something different for each stock.
Sigma is the standard way to measure normal movement. It is one standard deviation of a stock's returns. Sigma Bands draw that measurement on the chart. Around a one-month average they draw three envelopes, at one, two and three sigma, showing how far the stock is likely to travel over the next 21 trading days.
Sigma Bands on a daily chart. The dashed line is the anchor (the 21-day average close). The shading darkens toward the centre: ±1σ, ±2σ, ±3σ.
What one sigma means
If returns followed a perfect bell curve, the stock would close inside the bands about this often:
| Band | Inside, in theory | How to read it |
|---|---|---|
| ±1σ | ≈ 68% | Normal. Most months end in here. |
| ±2σ | ≈ 95% | Stretched. Something is pushing the stock. |
| ±3σ | ≈ 99.7% | Extreme. News, earnings, or a crowd moving all at once. |
Markets are not perfect bell curves. Big days happen far more often than the table suggests, and real stocks reach the 3σ band several times a year. Use the bands as a measure of how far a move has gone, not as odds.
How the bands are built
Most volatility bands use one lookback window. Sigma Bands blend four measurements, so the bands respond quickly to a change in volatility without jumping on every single day.
| Ingredient | Default weight | What it adds |
|---|---|---|
| 5-day volatility of returns | 25% | Reacts fast when the stock suddenly starts moving more |
| 21-day volatility of returns | 35% | The core: about one month of movement |
| 60-day volatility of returns | 20% | Steadies the blend with about a quarter of history |
| Garman-Klass, 21 days | 20% | Uses open, high, low and close, so intraday swings count too |
The blend gives a daily sigma. It is then scaled to the 21-day horizon and applied around the anchor:
Two details explain the shape you'll see on the chart:
- Why √21? Volatility grows with the square root of time. One month is about 21 trading days, so a month's sigma is the daily sigma times √21 (about 4.6).
- Why ex? Prices move in percentages. Using ex makes the upper band slightly further away than the lower one, just as +10% then −10% doesn't bring you back to where you started. The bands are symmetric in percentage terms, not in dollars.
Every number above is a parameter you can change in the indicator's settings: the horizon, the four weights, and the band multiple.
The three panels underneath
Sigma Bands go over the price. Three more indicators use the same blended sigma, each in its own pane below the chart.
Sigma Annualised: how volatile is the stock right now?
The blended sigma converted to an annual percentage (fc × √252 × 100), so you can compare it with other stocks and with the options market. A dotted line shows its average over the last year. Above that line, the stock is moving more than usual for itself.
Sigma Band Width: is the stock coiling or expanding?
The width of the ±1σ band as a percentage of the anchor, drawn on a log scale. Two dotted guides show this stock's own 20th and 80th percentiles over the last five years:
Below P20, the stock is quiet compared with its own history (a squeeze). Above P80, it is loud.
The percentiles are what make the reading useful. "Narrow" means narrow for this stock. A biotech and a bank have very different normal widths, but both have a quietest fifth of their history.
Z-scores: was today unusual?
Two bar charts that each answer the question "how unusual was today?" on the same scale:
- Price z: today's return measured in standard deviations of the previous 60 days' returns. Guides at ±2 and ±3.
- Volume z: today's volume compared with the median of the previous 60 days. It uses the median, so one earnings day doesn't make every later spike look ordinary.
Both compare today against a baseline that stops at yesterday. If today were included, a big day would raise its own average and spread and score smaller than it really was.
The highlighted day: price z above +2 and volume z above +2 on the same bar.
Five ways to use them
TrendBuy the pullback, not the stretch
In an uptrend with a rising anchor, strong stocks often pull back to the anchor or the −1σ band and then resume. A close up at +2σ or +3σ means the move is already stretched. For a leader, that is often the time to wait rather than chase.
SqueezeA quiet stock is often about to get loud
When Band Width drops below its P20 line, volatility is compressed compared with the stock's own history. Volatility tends to come in waves, so quiet periods are often followed by big moves. A squeeze doesn't tell you the direction. Wait for price to break out of the base before acting.
DemandPrice z and volume z together
A day with price z above +2 and volume z above +2 is an unusually large move on unusually heavy volume. That is often what large buyers look like when they start building a position. A big price move with ordinary volume deserves less trust.
RiskSize the position by sigma, not by feel
A stop placed inside the ±1σ band will be hit by ordinary noise. Placing it just beyond the band, or sizing the position so a 1σ move costs the same dollar amount on every trade, gives each stock room for its normal movement. Use Sigma Annualised to compare: a stock at 60% needs a much smaller position than one at 20%.
ScreenFind them across the whole market
Every line has a screener name, so the same numbers work as columns and filters:
bandPos places the close inside the ±1σ band: 0 at the lower edge, 1 at the upper edge, and below 0 or above 1 when price is outside the band.
What sigma can't tell you
- Direction. The bands measure how big a move may be, not which way it will go.
- Gaps. Earnings and news can jump past every band overnight. Sigma is built from past movement and can't see a scheduled event coming.
- Regime changes. When a quiet stock becomes a momentum stock, the 60-day part of the blend takes weeks to catch up. The 5-day part is there to shorten that delay, but it can't remove it.
Adding them to a chart
- Open Indicators on the chart toolbar.
- Under Volatility Indicators, pick Sigma Bands. They're drawn over the price.
- Add Sigma Annualised, Sigma Band Width and Z-scores if you want them. Each opens in its own pane below the chart.
- Click ⚙ next to any of them to change the horizon, the weights, or the colour of each band.
Find the stocks the bands highlight.
Sigma Bands, squeezes and z-scores across the whole market, in the screener and on the chart.
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