Overlays · Indicator
VWAP with volume-weighted standard-deviation bands at plus and minus one, two and three sigma, marking how stretched price is from fair value.
Overview
VWAP Bands add standard-deviation envelopes around the volume weighted average price at plus and minus one, two and three sigma. They identify statistically stretched intraday moves and potential mean-reversion levels relative to volume-weighted fair value. Where plain VWAP tells you which side of the session's average price you are on, the bands tell you how far away you are in units that account for how volatile the session has actually been.
The deviation is volume-weighted like the average itself, so bars where a lot of trading took place contribute more to the measure of dispersion. A session that opened with a violent range and then settled will show wide bands reflecting that early activity; a session that has traded quietly in a narrow range all day will show tight bands, and a move that would be unremarkable on the first day looks extreme on the second.
Because the bands are cumulative from the anchor, they behave differently through the day. They start wide and unstable when only a few bars have accumulated, then narrow and stabilise as volume builds. The one-sigma band is crossed routinely, the two-sigma band marks a genuinely extended move, and three-sigma excursions are uncommon and usually associated with news.
How it is calculated
VWAP is computed first as the cumulative volume-weighted average from the anchor. The variance is then accumulated the same way, weighting each bar's squared distance from the running VWAP by that bar's volume, and the square root of that variance gives the volume-weighted standard deviation, sigma.
Each band is placed a whole number of sigma above and below the VWAP line, giving seven plotted series in total: the VWAP itself plus three bands on each side.
VWAP = sum(P * V) / sum(V), cumulative from the anchor Variance = sum(V * (P - VWAP)^2) / sum(V) Sigma = sqrt(Variance) Upper band k = VWAP + k * Sigma (k = 1, 2, 3) Lower band k = VWAP - k * Sigma (k = 1, 2, 3)
Inputs
How to read it
Treat the bands as a map of how unusual the current price is for this session. Inside plus or minus one sigma is ordinary two-way trade. Beyond two sigma the market has moved well outside the range where most of the session's business was done, and beyond three sigma it is in territory that only occurs a handful of times a month on most instruments.
The bands are used in two opposite ways depending on regime. In balanced, rotational sessions the outer bands act as fade levels and price tends to revert towards VWAP. In trending sessions price can ride the one-sigma band for hours, and the two-sigma band becomes a marker of trend strength rather than a reversal point. The slope of the VWAP line is the usual way to decide which regime is in force.
Band width itself is informative. Bands that stay tight through the middle of the session describe a market in balance, and a break beyond them after a long period of narrowness often marks the start of the day's real move. Bands that are already very wide say the session has been volatile, and a further excursion is less remarkable than the same distance would be on a quiet day.
Signals to look for
In a rotational session, a probe beyond the two-sigma band that fails to hold is a common mean-reversion reference, with VWAP itself as the natural target. It depends entirely on the session being balanced rather than trending.
Price holding between the one-sigma and two-sigma band on the same side for an extended run, with VWAP sloping in that direction, is read as sustained one-way pressure rather than an extreme.
A move outside bands that have been compressed for much of the session marks a departure from balance, and is watched as the point where the market stops rotating and starts trending.
Limitations
Frequently asked questions
VWAP with volume-weighted standard-deviation bands at plus and minus one, two and three sigma, marking how stretched price is from fair value.
Treat the bands as a map of how unusual the current price is for this session. Inside plus or minus one sigma is ordinary two-way trade. Beyond two sigma the market has moved well outside the range where most of the session's business was done, and beyond three sigma it is in territory that only occurs a handful of times a month on most instruments.
Two-sigma fade: In a rotational session, a probe beyond the two-sigma band that fails to hold is a common mean-reversion reference, with VWAP itself as the natural target. It depends entirely on the session being balanced rather than trending.
Sigma is small and unstable in the first bars after the anchor, so the bands can be absurdly tight or wide before enough volume has accumulated to make the deviation meaningful.
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