Momentum Indicator: Two Closes Subtracted
The momentum indicator is today's closing price minus the closing price a fixed number of bars ago, plotted as a line. Almost every oscillator in common use is a smoothed or rescaled version of this calculation, which is why they all move together.
How it works
Take today’s close. Subtract the close from ten bars ago. Plot the answer. That is the entire indicator.
Some platforms show it as a ratio instead — today’s close divided by the old one, times 100 — and call it rate of change. Same calculation, different presentation, and the readings behave identically.
Its simplicity is worth stating as a virtue. There is nothing hidden in it, no smoothing constant, no convention inherited from the 1970s. Above zero means price is higher than it was N bars ago. That is the whole claim.
The relationship that explains the whole indicator menu
Nearly every oscillator in common use is this calculation with modifications. The relative strength index separates the up moves from the down moves and expresses the ratio on a 0–100 scale. The MACD takes the difference between two smoothings, which is a smoothed rate of change. The stochastic rescales position within a range, which is the same information as distance travelled.
On this site’s shared 576-bar history, bar-to-bar changes in 10-period momentum correlate at 0.71 with a 14-period relative strength index, 0.66 with the moving average convergence divergence histogram, 0.61 with the stochastic and 0.53 with the commodity channel index.
Every one of those tools is more complicated than this one and none of them moves independently of it. That is the practical content of the whole “which oscillator should I use” question, and it is answerable with a correlation matrix rather than an argument.
In practice: the two real weaknesses
No fixed range is the first weakness. A momentum reading of 3 means something different on a $40 stock than on a $400 one, and something different again after the instrument has doubled. The bounded oscillators exist mostly to fix this, and that is a genuine improvement rather than a decoration.
Depending on exactly two bars is the second. Everything between them is ignored entirely. A period that rose steadily and one that crashed and recovered give identical readings if the endpoints match.
Which produces a drop-off effect stronger than any moving average has. When the bar from N periods ago is replaced by a different one, the reading can swing sharply on a day price barely moved. A simple moving average spreads that jolt across N bars; here it lands on one.
Volume is absent, as it is from the whole family.
Lengthen the lookback and it converges on a trend measure. 200-period momentum is “is price higher than it was 200 bars ago,” which is the same question a long moving average answers with more smoothing.
A gap produces the largest readings on the indicator, because the endpoint moved a long way with no intervening trading. Maximum momentum, zero transactions.
And it produces no level. Like every oscillator, it cannot tell you where to place a stop; that has to come from structure or volatility.
Each zero cross traded costs 2% of a typical bar’s range in round-trip costs on this history, and an unsmoothed line crosses zero far more often than a smoothed one.
And there is no momentum in the market to measure. The word is borrowed from physics, where momentum is a conserved quantity. Price has no mass and no inertia; what the indicator reports is a difference between two numbers.
What the momentum indicator is not
It is not a physical quantity. Nothing is conserved and nothing carries forward on its own.
It is not a different measurement from the smoothed oscillators. It is the un-smoothed version of them.
It is not comparable across instruments. Unbounded output in the instrument’s own units.
And it is not lagging in the same way an average is. It has no smoothing at all — it just requires N bars to have elapsed, which is a different kind of delay.
When it fails
In a range it oscillates around zero with no useful structure. Price is higher than it was, then lower, then higher, and each crossing looks like a signal because there is no smoothing to suppress it.
The second failure is the drop-off jolt. A large bar leaving the back of the window moves the line sharply on a quiet day, and traders look for news to explain something that is purely arithmetic.
A third is comparing readings across time. After a large price change, the same percentage move produces a bigger absolute reading, so a “record momentum” observation is often a record price level.
A fourth is treating it as leading. It is a difference between two past closes. Nothing about it arrives before price does.
And a fifth is stacking it with a smoothed oscillator for confirmation. At 0.71 correlation with the relative strength index on this data, the second tool agrees because it was built from the same subtraction.
The original data
Bar-to-bar change correlations for 10-period momentum on this site’s shared 576-bar history: 0.71
against the relative strength index, 0.66 against the moving average convergence divergence histogram,
0.61 against the stochastic, 0.53 against the commodity channel index. The full five-by-five matrix is
in research/series-measurements.json, produced by site/measure_series.py.
The most useful thing you can do with this page is an experiment that takes five minutes. Put plain momentum on a chart beneath whichever oscillator you normally use, and look at the two shapes. If the turns line up, the more complicated tool is this one with smoothing and a rescaled axis — which is worth knowing before spending any more time choosing between oscillators, and which the correlation figures above say is what you should expect to find.
Related
RSI is this calculation split into up and down moves and bounded 0–100. MACD histogram is a smoothed version of the same idea. And choosing indicators carries the measured question of how much of the menu is one calculation.
Plotting plain momentum next to my usual oscillators was the cheapest lesson I have had. The shapes were the same. Everything I had been choosing between was this calculation with different amounts of smoothing and a different scale on the axis.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.