Bollinger Bands

Because the width is set by the standard deviation of recent closes, the bands are a direct, visible measure of how volatile the security has been. Quiet periods pull them together; violent ones push them apart. The middle line is an ordinary moving average and carries the trend information.

The bands are therefore two indicators in one picture: a trend measure in the centre and a volatility measure in the width. Most of the confusion about how to read them comes from treating the width as if it said something about direction.

Two standard deviations would contain roughly 95 percent of observations if returns were normally distributed. Financial returns are not normally distributed: extreme moves occur far more often than a normal distribution predicts, which is exactly why band touches are so much more common than the statistics would suggest.

There is a second, subtler problem. The standard deviation is computed from the same recent window the bands are describing, so a period of large moves widens the bands and makes the next large move look less exceptional. The measure adapts to what it is measuring.

When the bands narrow to an unusually tight width, realised volatility has fallen. Because volatility tends to cluster and to alternate between quiet and active regimes, a squeeze is often described as preceding an expansion.

It carries no directional information whatsoever. A squeeze says a move may be larger when it comes; it does not say which way, and reading a direction into it is reading something that is not there.

• Bandwidth: the distance between the bands as a percentage of the middle line, so squeezes are comparable across securities and across time.
• Percent B: where price sits within the bands, 0 at the lower band and 1 at the upper, which turns a visual position into a number.

Both exist for the same reason: the raw bands are a picture, and a picture cannot be screened. Bandwidth in particular is what makes it possible to ask which securities in a market are currently at their tightest range in a year.

Two derived measures turn the bands into numbers that can be compared across securities and across time, which the bands themselves cannot be.

Bandwidth is the more useful of the two because it makes the squeeze objective. Rather than judging by eye whether the bands look narrow, it can be compared against its own history: a reading in the lowest decile of the last two years is a defined condition rather than an impression.

The bands are placed two standard deviations from a moving average, and it is routinely said that this contains about ninety-five percent of observations. That figure comes from the normal distribution, and returns are not normally distributed.

• Return distributions have fat tails: extreme moves occur far more often than a normal distribution predicts.
• Volatility clusters, so large moves follow large moves, which violates the independence the statistic assumes.
• The standard deviation is computed over a short rolling window, so it is itself a noisy estimate.
• The mean is a moving average rather than a constant, which is a different construction from the textbook case.

In practice, price sits outside the bands more often than the statistical reading implies, and it does so in clusters during exactly the periods when the bands are being watched most closely.