Bollinger Bands

The formula

For each bar, take the last 20 closes. Find their average, and their standard deviation, which measures how far the closes spread around that average. The bands sit 2 standard deviations above and below the average. Many tools use the population standard deviation, dividing by 20, and some use the sample version, dividing by 19, so values differ a little.

A worked example

Take the first 20 made-up closes in the picture, from 100 to 113. Their average is 105.75. The standard deviation of those closes is 4.02. The upper band is 105.75 + 2 x 4.02 = 113.80 and the lower band is 105.75 - 2 x 4.02 = 97.70. The last close, 113, sits inside. The bandwidth is 15.2 percent of the middle line.

As the path moves on the window slides. The price speeds up, and the average and the standard deviation both rise. The bands follow, but the average lags, so the price can run outside the upper band while the average is still behind it.

Bandwidth, the squeeze and the expansion

Bandwidth is the gap between the bands as a percent of the middle line. In the made-up path it is 15.2 percent in the first window and 34.7 percent in the last, so the bands have widened as the price sped up. Traders talk about a squeeze when bandwidth is low and an expansion when it rises. Bandwidth only describes how much the price has moved, and a narrow band does not tell you which way the next move goes, or whether there will be one.

What the bands do and do not mean

• They measure recent spread, not the future. A narrow band means the last 20 bars moved little. It does not say the next move will be small or large.
• A touch is not a signal. The 95 percent figure belongs to a bell curve. Real price changes have fatter tails and cluster, so closes outside the bands are more common.
• Trends walk the band. In a strong trend the price can sit near or beyond one band for many bars in a row.

How a bot misuses them

The popular bot rule is mean reversion: buy at the lower band, sell at the upper. In a range it can earn small gains. In a trend it keeps selling into a rising price. In this made-up path a rule that sold at each close above the upper band would have sold 7 times while the price kept rising. If it also adds each time, it is averaging against the trend, the same shape as a martingale, with the same risk of one large loss. The average down calculator shows how the average price moves as you add.

How to check a rule that uses the bands

Test it in a range, an uptrend and a downtrend, and count the trades in each. Include the spread and slippage, since a band rule trades often. Do not tune the period and the width to the best past result, which is overfitting. Keep data back and test once, as in backtesting. Look at the max drawdown, which is where mean reversion rules usually show their cost.

What this page does not tell you

It does not say that any setting works. The prices are made up. The bands describe recent spread and nothing more, and this page is education, not a signal.