Indicator library · Momentum
Momentum, Price Minus Price, n Bars Back
The simplest speed measurement there is: today’s close minus the close n bars ago. Identical in shape to the rate of change and different in one respect that decides how it may be used; the answer is in the instrument’s own currency.
The calculation
Momentum = close − close n periods ago. That is the entire formula. A reading of +3 means price is three units higher than it was n bars back; zero means unchanged over the window regardless of the route taken to get there.
Two properties follow immediately and both matter more than the setting. The output is denominated in the instrument’s own currency, so readings cannot be compared between instruments or across a stock split. And it is unbounded, so there are no natural extremes and no level that means the same thing twice.
Points against per cent
The distinction between this measure and the rate of change is worth seeing in numbers, because it is the reason two charts labelled "momentum" can disagree by orders of magnitude. Below are the last five sessions of the series above, in both forms.
| Session | Close | Momentum (points) | Rate of change (%) |
|---|---|---|---|
| 26 | 89.6 | -9.10 | -9.22 |
| 27 | 88.4 | -8.10 | -8.39 |
| 28 | 89.5 | -4.70 | -4.99 |
| 29 | 91.0 | -1.60 | -1.73 |
| 30 | 92.8 | -0.90 | -0.96 |
The two columns turn together and cross zero on the same session; they are the same measurement. What differs is portability. The percentage column can be placed beside the same calculation on any other instrument and ranked; the points column cannot, because it is partly a statement about the price level. On a stock at 400 the same percentage move produces a momentum reading four times larger than on one at 100, and neither number is wrong.
Reading it
There are three readings and only the first has a fixed meaning.
The zero line. Above it, price is higher than n bars ago. This is a fact rather than an inference, and it is the least fragile thing the indicator offers, though it is also late by construction, since price must travel back past a bar that is itself moving forward.
Deceleration. A positive but falling reading describes an advance covering less ground per bar than it was. This is the observation worth having, and it needs to persist over several bars before it is anything more than noise. Trends decelerate frequently and resume just as frequently.
Divergence. Price makes a higher high while momentum makes a lower one, meaning the second push covered less ground in the same time. Because the line is unsmoothed it produces a great many apparent divergences, most of which mean nothing, which is exactly the problem the Price Momentum Oscillator was built to address by smoothing this same input twice.
Why it survives as a component
Nobody trades momentum on its own any more, and that is not a criticism of it. Its value is that it is the shortest possible statement about speed, two closes and a subtraction, with nothing between the reading and the prices it came from. Everything more sophisticated in the momentum family is this number with something done to it.
The Price Momentum Oscillator smooths it twice. The rate of change divides it by the earlier close so it can be ranked. The Relative Momentum Index feeds the same n-bar comparison into Wilder's smoothing and bounds the result. Knowing what the raw quantity does — where it peaks, when it crosses zero, what a window exit can do to it — is what makes the behaviour of those three explicable rather than mysterious.
Where it misleads
| Situation | What goes wrong |
|---|---|
| Compared across instruments | The output carries the price level. A reading of 4 is four dollars on one chart and four cents on another. |
| Absolute thresholds | Unbounded and volatility-dependent, so no level transfers, not even between two eras of the same instrument. |
| Unadjusted prices | A split creates one enormous reading that persists for the whole length of the lookback. |
| Route ignored | Only two closes enter the calculation. A quiet drift and a violent round trip can produce identical readings. |
| Window-exit artefacts | The line can move sharply on a quiet session because the bar leaving the back of the window was unusual. |
| Crossings traded directly | Late in a trend, constant in a range. Inherent to a difference of two points, not a settings problem. |
What volume adds
Momentum reads two closing prices and nothing else, so it cannot distinguish a rapid advance that absorbed heavy selling from one that drifted upward through an empty book. Both produce the same reading, and they are not the same event.
The habit that costs nothing is to read the speed from this line and the participation from the volume beside it. A steep reading on expanding volume describes a move that required someone large to be on the other side; the same reading on the thinnest sessions of the month describes an absence of sellers, which reverses as soon as any arrive.
Frequently asked questions
What is the difference between momentum and rate of change?
The operation, not the idea. Momentum subtracts the close n bars ago; the rate of change divides by it and multiplies by 100. Over a short window on one instrument the two lines have almost identical shape, and the difference matters the moment you compare anything: momentum carries the instrument’s currency, so a reading of 4 means four dollars on one chart and four cents on another. Only the percentage form can be ranked across a universe.
Why is momentum unbounded?
Because there is no denominator to constrain it. RSI divides one average by another and maps the result onto 0–100, which is what makes its levels transferable. Momentum is a raw difference of two prices, so its natural range is whatever the instrument happens to move, a few cents on a utility, tens of dollars on a high-priced stock. Any threshold quoted in general is describing whatever chart the author had open.
What lookback should I use?
The one that matches the decision, and 10 or 12 sessions if you have no reason to prefer another. A short lookback produces a line that crosses zero constantly and describes the last week; a long one is steadier and describes a move you may already have missed. The number is a choice of horizon rather than a quality setting, and choosing it from the length of the swings you actually trade leaves you with something to defend afterwards.
What does the zero line mean?
That price is exactly where it was n bars ago. Above zero it is higher, below it lower, that is the whole of the reading with a fixed meaning, and it is comparative rather than predictive. Because the comparison is against a bar that keeps moving forward, the line can cross zero on a session where nothing happened, purely because the bar that dropped out of the window was unusual.
Why does the line peak before price does?
Because it measures speed, not level. Momentum is largest where the n-bar change is largest, which is the middle of a strong move rather than its end. A falling momentum reading with price still rising describes an advance that is decelerating, the most useful thing this indicator says, and the easiest to over-read, since trends routinely decelerate and then continue for months.
Is a zero-line crossing a signal?
It is a fact about the last n bars and a poor trigger on its own. In a trending market the crossings arrive late, after a meaningful part of the move; in a range they arrive constantly and reverse. This is inherent to a difference of two points on the same series and cannot be tuned away, which is why momentum is more often used as an input to something else than traded directly.
How do splits and dividends affect it?
Severely, and more than they affect a percentage measure. An unadjusted two-for-one split halves the price, so the difference against the close n bars back becomes an enormous negative number that persists for the length of the lookback. Always compute on an adjusted series. Even on adjusted data, a large price-level change over years means momentum readings from different eras are not comparable with each other.
What is momentum used for, if not traded directly?
As a component. It is the raw input the Price Momentum Oscillator smooths twice, the quantity the rate of change expresses as a percentage, and a common filter inside larger systems, take signals only while momentum is positive, for instance. Its value is that it is the simplest possible statement about speed, with nothing between the reading and the two prices it came from.