Constructing a Bollinger band-width trend filter

From envelope to band width

Bollinger Bands are a volatility envelope placed a stated number of standard deviations above and below a moving average of ordered price. A common construction centers a 20-day moving average and places the upper and lower bands two standard deviations from that average.

Band width is the gap between those bands, usually divided by the same moving average so the series is comparable through time. Under that construction, the distance between the bands divided by the 20-day moving average equals four standard deviations over the same average.

A very low reading on that width series is treated as a compressed-volatility, trend-ready state after a quiet market, on the premise that a later directional expansion may follow consolidation.

Width as a trend filter

A trend filter is a constructed series from ordered price over a defined lookback that marks the presence, absence, pace, or readiness of a directional regime. The Average Directional Index is read that way: a rising line marks a trend in progress, a sideways or falling line marks a range, and a low reading marks a trend-ready condition.

The same width series can be applied as a trend filter in that Average Directional Index manner, with a rising width accompanying major advances and declines alike.

Lookback, lead time, and reset speed

Lookback is the sampling window used to compute the moving average, standard deviation, or directional-movement average. Compared with a 14-day Average Directional Index, a 20-day width series can turn at the start or end of a trend one or more periods earlier and can fall back toward a compressed reading more quickly after a range narrows.

Because the width lookback is shorter than the nested 14-day Average Directional Index construction, the width series can flag trends that do not develop. Lengthening that lookback is described as reducing short-horizon sensitivity.

Scale, direction, and missed slow trends

A slow, low-momentum trend can leave the width series flat, because standard deviation stays small when price remains close to its moving average. That same standard deviation is the dispersion of price around the moving average that sets both envelope distance and the width of the trend filter.

The width series has no shared 0-to-100 scale across markets and does not indicate trend direction, so another method is required to read which way price is moving.

Worked examples compute the width series with one standard deviation instead of four for vertical scaling only, and they treat a steeper width slope as a faster underlying trend.

TradersWeek editorial note: the width series is a pace and readiness reading, not a direction reading. Pairing it with a separate directional method is part of the construction, not an optional overlay.