An elastic volume-weighted moving average from a share-count lookback

Calendar length versus a share-count lookback

A calendar-length volume-weighted average drops every observation older than a fixed bar count even when later volume still implies those prints belong in the average. An N-volume construction sets the window by a fixed share total rather than by K bars, with N chosen near the volume typically printed over those K periods.

The float parameter

N is set well below total shares outstanding because a large block of stock is often locked, and that choice controls sensitivity the way period length does in a K-bar average. In this construction the chosen share budget is the float parameter: a smaller budget makes the recurrence react faster, analogous to shortening a calendar window. The window itself is a share-count lookback, defined by a fixed quantity of shares rather than by a fixed number of calendar bars.

The elastic volume-weighted moving average

A hard N-volume window still forgets prices once cumulative volume exceeds N, so a recursive elastic update is introduced to keep a running approximation instead of truncating a tail. The elastic volume-weighted moving average updates after each trade or bar by replacing a volume-sized slice of that share budget, valued at the prior average, with the new price. The update assumes sellers of the next volume v paid the prior average and replaces that slice of a share budget N at the new price p by taking the prior value times N minus v, plus v times p, then dividing by N.

A worked path of prints

Starting from 1,000 shares issued at 10, successive prints of 100 at 15, 200 at 20, and 100 at 25 yield approximated paid averages of 10.50, 12.40, and 13.66 under that seller-paid-the-prior-mean assumption.

Seeding from daily close and volume

When trade-level prints are missing, daily close and daily volume can be treated as one aggregated trade and the recurrence can be seeded with that day's price.

Volume-backed jumps and low-volume undershoots

High-volume bars pull the elastic series toward the current price, while price declines that print little volume leave the series nearly unchanged. A 20-bar unweighted average can take 12 to 20 bars to absorb a volume-backed jump and can later show a delayed bump, on the order of 10 bars, after a low-volume undershoot that the elastic update barely records.

Companion statistics

The same paid-price distribution used to justify the mean update can be reused to construct companion statistics such as standard deviation, moments, or kurtosis.