Constructing on-balance volume as a signed running total

The signed running total

On-balance volume is built as a running total that adds a session's full volume when the close is higher than the prior close and subtracts that volume when the close is lower.

Each increment can be written as session volume multiplied by the sign of the close-to-close change. A flat or tiny close change contributes little, while a directional close contributes the entire session's volume. That signed-volume increment is then added to the running total.

The summation is intended to quiet the day-to-day swing of raw volume bars while still encoding whether each close was up or down. The construction is aimed at instruments with substantial, repeated participation, because many large trades across many sessions reduce the weight of any single spike.

Origin date and volume universe

A distant origin date can bury recent signed increments. A stated construction choice is to begin about one year back at a notable low and not more than two years back.

The volume universe is the share or contract series whose volume is signed and summed, such as one listing or the combined volume of all futures months. For futures, early contract-month volume can be too thin for a stable total, so a common substitute volume universe is the summed volume of all listed contracts.

New extremes and noncoincident advances

Extra smoothing, further summation, or momentum overlays on the raw running total were not shown to improve on the unadorned series' most useful chart event: a new extreme, a fresh high or low on the cumulative line.

Because each increment is the full session volume, a sharp price break signed onto comparatively few shares can leave the cumulative line well above its own prior floor even as price undercuts a prior price floor.

When later up-closes no longer lift the cumulative line with price, the same signed-volume rule is reporting that those advances are being posted on sparse volume. That stretch is a noncoincident advance, in which price and the cumulative line stop printing new ground together.