What ADX is

What the panel contains 

The construction was published as a set of three related lines and it is usually plotted as all three. The positive directional indicator measures how much of recent movement extended above the previous period's high. The negative directional indicator measures how much extended below the previous period's low. The average directional index measures how far apart those two lines are, smoothed. All three are drawn on the same panel on a scale running from nought to one hundred, and only the third of them is what the name of the indicator refers to.

A good deal of charting software plots the third line by itself, and a reader who meets it in that form is meeting one third of the construction with the other two thirds hidden. The gap the index reports is not inspectable unless the two lines producing it are on the panel as well, which is why they are described here first and why the index is described last.

What counts as directional movement 

The inputs are the high and the low of each period together with the previous period's close, so unlike an oscillator built on closes alone this construction reads the whole span of the period. Each period is compared with its predecessor in two ways. The distance by which this period's high extends above the previous high is measured. The distance by which this period's low extends below the previous low is measured. Only the larger of the two is recorded, and the other is set to nought. Where neither extends beyond the previous period at all, which is what happens whenever a period's whole range sits inside its predecessor's, both are nought and the period contributes nothing to either side.

That rule has a consequence worth stating at the outset, because it governs everything the index can subsequently report. A period contributes to at most one side of the calculation. A period that made both a higher high and a lower low than its predecessor, which is the most genuinely two sided period a chart can contain, is recorded as though it had moved only in the direction of its larger excess, and the smaller excess is discarded without trace.

From two distances to three lines 

Recorded movement is measured in the instrument's own price units, so on its own it cannot be compared between one instrument and another, or between a quiet stretch and an active one on the same instrument. The next step removes the units. Each period's recorded movement is divided by that period's true range, which is the greatest of three quantities: the period's own high to low span, the distance from the previous close up to this period's high, and the distance from the previous close down to this period's low. What comes out of that division is a proportion of the period's total travel rather than a price.

Those proportions are then smoothed over a lookback, conventionally fourteen periods, by the method the same author used throughout his work: the running total is reduced by one fourteenth of itself and the current period is added to what remains. Older periods therefore fade out of the calculation gradually rather than dropping out of a window all at once. Multiplying each smoothed proportion by one hundred produces the two directional indicators as they appear on the panel.

The third line is built entirely from the first two and reads nothing else. The difference between them is taken, the sign of that difference is thrown away, and the remaining quantity is divided by the sum of the two. The result, multiplied by one hundred, is the directional index for that period: nought when the two lines are equal, one hundred when one of them is nought, and a measure of how lopsided they are everywhere in between. The average directional index is that quantity smoothed over the same lookback a second time.

Why the index cannot report a direction 

One step in the calculation above is the reason this indicator behaves unlike almost every other panel on a chart, and it is the step that discards the sign of the difference. Once the sign is gone, the calculation can no longer distinguish which of the two lines was the larger. A market in which the positive indicator dominates the negative by a given margin, and a market in which the negative dominates the positive by the same margin, arrive at precisely the same index.

This is why the two directional indicators are part of the construction rather than an optional extra. Direction lives in them and separation lives in the index, and the panel was published as a set because neither half answers the other half's question. A reading taken from the index alone describes how one sided recent movement was without recording which side it was on.

The bounds follow from the same arithmetic. The index cannot fall below nought, which would require the difference between two positive quantities to be negative after its sign has been removed. It cannot rise above one hundred, which would require the difference to exceed the sum. It reaches one hundred only where one of the two directional indicators has been nought across the whole smoothed window, meaning no period in that window reached beyond its predecessor in that direction at all.

The lines drawn across the panel 

Most charting packages draw one horizontal line across the panel, at twenty five, and some draw a second at twenty. The original published account treated readings below twenty as movement too evenly divided to describe as directional, and later practice moved the line up. Readings above forty, and again above fifty, are conventionally described as strongly directional. Technical traditions attach the phrase trend strength to the whole scale, which is a name for the separation between the two lines and not a measurement of anything else.

None of those levels is derived from a test a reader can inspect. They are conventions, and they interact with everything else that has been chosen. A shorter lookback carries the reading across any given line far more often, and a longer one carries it across rarely, so the same prices produce different sets of crossing dates under different settings. Some instruments spend most of their history on one side of the line, at which point the line divides nothing on that chart, and practitioners who work on those instruments move it. The practice of adjusting a threshold until the historical crossings look convincing on the chart it will be judged on is fitting the setting to the answer.

There is also no agreement about what a reading between the conventional lines describes. One tradition treats the region below the line as evidence of a range, on the reasoning that a market moving without a consistent lean produces two similar directional indicators and therefore a small difference. Another points out that a small difference is also what a strong move produces during a pause inside it, and that the index cannot separate the two cases because both are periods in which neither side dominated.

Why a rising reading describes the past 

The index is smoothed twice. The two directional indicators are smoothed over the lookback, and the quantity derived from them is smoothed over the lookback again. Everything a reader sees in the third line has therefore been through two averaging steps, and each of them delays the effect of any single period by design, since the purpose of an average is to prevent one period from moving the result very far.

So a rising reading is a statement in the past tense. It states that recent movement was more one sided than the movement before it, over a window that has already closed. The reverse statement, that a rising reading means movement will go on being one sided, is not something the arithmetic contains, and the delay makes the point sharper than that: the reading can still be rising for several periods after the underlying quantity has peaked and begun to fall, because each new value, though lower than the last, is still above the average it is being folded into.

What a reading does not mean 

The reading is a twice smoothed summary of the periods behind it. Five things it does not contain are worth stating flatly, because the vocabulary attached to the indicator invites every one of them.

1. It does not say which way price moved, and it cannot be made to. The sign is discarded before the index exists, and a rising market and a falling market of the same shape return the identical number.
2. It does not say that a move will continue. A high reading describes windows that have closed, and the smoothing means those windows are further behind the current period than the shape of the line suggests.
3. It does not measure the size of a move. Recorded movement is divided by the true range of the same period, so the quantity is a proportion of that period's travel, and an instrument that moved a long way and one that moved a short way can produce the same reading.
4. It does not say when a reading will cross a threshold, or that a crossing will happen within any period a reader is watching. This page publishes no figure for what follows a crossing, and the omission is deliberate: any such figure would depend on the lookback, the smoothing, the threshold and the holding period chosen before the counting began.
5. It is not a verdict, and it is not combined here with any other reading to produce one. A number that aggregates several indicators into a single rating is a different kind of object from a description of past prices, and this page does not construct one.

Where practitioners disagree 

The first disagreement is about the double smoothing. One position is that smoothing the derived quantity a second time is what makes the line legible, since the underlying quantity moves violently from period to period and a chart of it is difficult to read. The other is that the second smoothing costs more than it buys, because it delays the line by a further stretch of periods in exchange for a cosmetic improvement, and that a reader who wants the underlying quantity should plot it directly. Both lines can be drawn from the same data and they tell noticeably different stories about when anything changed.

The second is about the word strength. The index measures the separation between two smoothed proportions, and separation is not the same property as size, persistence or conviction, all of which the word invites. Practitioners who are careful about this describe the reading as a measure of how one sided recent movement has been and stop there. Others use the shorter word and accept the imprecision, which is a defensible choice about vocabulary and an indefensible one if the imprecision is then reasoned from.

The third and largest disagreement is whether the panel adds anything to the chart above it. The sceptical account is that the sequence of highs and lows is already visible in the price, that a reader who can identify swing points can see whether one side has been dominating without an arithmetic restatement of it, and that a bounded scale mostly makes a persistent lean look like an event because it has nowhere else to put one. The answer from practitioners is that the eye is a poor judge of degrees of one sidedness across instruments and across periods, and that a bounded, comparable number is a discipline against reading a shape into a chart. Both positions are held by people who read charts for a living, and the honest statement is that the reading is a description of past highs, lows and closes whose predictive content is disputed rather than established.