Weighted Moving Average (WMA)

The weighted moving average (WMA), also called the linearly weighted moving average, assigns more importance to recent prices by giving each price a weight that rises in a straight line from oldest to newest. In a 5 period WMA, the newest price is multiplied by 5, the previous by 4 and so on down to 1. The result reacts faster than a simple moving average and, unlike the EMA, completely forgets prices older than its window.

The formula#

WMA = (n × Pₙ + (n−1) × Pₙ₋₁ + ... + 1 × P₁) ÷ (n + (n−1) + ... + 1)

The denominator is the sum of the weights, which equals n × (n + 1) ÷ 2.

Comparing WMA, SMA and EMA#

In practice, a WMA and an EMA of similar length look much alike on a chart. The WMA tends to hug price slightly more closely over short windows.

When traders use the WMA#

• Short term trend tracking, where faster reaction than an SMA is wanted.
• As a component of other indicators. The best known is the Hull moving average.

The Hull moving average#

Alan Hull designed an average to reduce lag while staying smooth. It combines WMAs:

HMA(n) = WMA( 2 × WMA(n/2) − WMA(n), √n )

The result follows price very closely with less noise than a short WMA. Many traders use it to spot trend changes early, accepting that faster signals still bring some false ones.

Trading with the WMA#

The uses are the same as other moving averages:

1. Trend direction: price above a rising WMA suggests an uptrend.
2. Pullback entries: reactions near the WMA in trending markets.
3. Crossovers: a fast WMA crossing a slow one, or price crossing the WMA.
4. Filters: only trade in the direction of a longer WMA's slope.

Because it reacts faster, the WMA suits shorter timeframes and faster strategies more than long term trend filtering, where the 50 and 200 day SMAs remain the standard references. See Moving Averages Explained.

Choosing between them#

There is no universally better average. Choose based on purpose:

• Long term trend and widely watched levels: SMA.
• Responsive trend tracking: EMA or WMA.
• Low lag with smoothing: Hull moving average.
• Volume emphasis: VWMA. See Volume-Weighted Moving Average (VWMA).

Test the same strategy with different averages; often the difference is smaller than expected, and the rules around entries, exits and risk matter more.

Common mistakes#

• Switching averages constantly to fit recent price action.
• Expecting a faster average to remove lag entirely. All moving averages lag.
• Using fast averages in choppy markets, which produces many false signals.

Frequently asked questions#

What is a weighted moving average?#

A moving average that multiplies each price by a weight that increases linearly for more recent periods, making it more responsive than a simple average.

Is the WMA the same as the EMA?#

No. Both weight recent prices more, but the WMA uses linear weights over a fixed window, while the EMA uses exponentially decaying weights and never fully drops old data.

What is the Hull moving average?#

A low lag moving average built from weighted moving averages, designed to follow price closely while remaining smooth.

Next, learn the volume weighted version: the Volume-Weighted Moving Average (VWMA).