What ATR is

What the height of a bar leaves out 

The obvious measure of how far an instrument moved during a period is already drawn on the chart. Subtracting a bar's low from its high gives the range of that period, expressed in the instrument's own price units, and for most bars that number is an adequate description of the ground covered. Nothing more elaborate is needed for the great majority of the chart.

It fails in one specific circumstance, and the circumstance is common enough to matter. Trading in most markets stops and restarts. A share market closes overnight and at weekends, an index contract pauses, a currency pair breaks between the last quote of the week and the first of the next. When trading restarts, the first price is under no obligation to be the last one. The distance between where one period finished and where the next one began is real movement, and it belongs to neither bar's high and neither bar's low.

Measured on its own, a period that opened a long way from the previous close and then traded within a narrow band looks like a quiet period. That is not a rounding problem. A measure of movement that discards jumps understates movement precisely where movement was most abrupt, which is the opposite of what a measure of movement exists to do.

The true range of a single bar 

True range repairs the omission by refusing to measure a bar in isolation. It compares three distances and keeps the largest of the three. The first is the bar's own high minus its own low. The second is the distance from the bar's high to the previous period's close. The third is the distance from the bar's low to the previous period's close. The second and third are taken as distances rather than as signed differences, so neither can be negative, and the largest of the three candidates is the true range of that bar.

The previous close is the part doing the work, and it is the reason the measure carries the word true. It anchors the bar to the price at which the last period actually came to rest, so any jump between the two bars falls inside at least one of the three candidates instead of falling between them. Without that anchor each bar is measured as though the chart began at its own open.

Two properties follow directly from the construction. Where a bar opens inside the previous bar's range, the first candidate is always the largest, so true range and plain range are the same number and the extra arithmetic changes nothing. The second and third candidates can only win where the bar has opened away from the previous close, which is exactly the case the plain range mishandles. True range is therefore never smaller than the bar's own high minus low, and it is larger only when a gap occurred.

Averaging the range 

One bar's true range is a fact about one period, and read on its own it is far too jumpy to describe anything. A single unusual session produces a single unusual figure, and the next session may return to whatever preceded it. Averaging true range over a fixed lookback, conventionally fourteen periods, produces a slower quantity that describes the recent character of the instrument's bars rather than the last one. That average is the indicator.

The first value in the series is a plain mean: the true ranges of the first fourteen bars are totalled and divided by fourteen. Every value after it is conventionally produced by a smoothing step instead. The previous average is multiplied by one less than the lookback, the current bar's true range is added, and the total is divided by the lookback. The effect is that an old bar's contribution fades gradually rather than dropping out of the window in one step, so a single very tall bar keeps influencing the reading long after it has scrolled away.

Neither averaging method is the correct one. They are answers to different questions, one asking what the last fourteen bars measured and the other asking what a persistently updated estimate looks like, and a reader comparing a figure quoted in one place with a figure on their own screen is often comparing the two methods rather than disagreeing about the data.

The measure has no sign 

Every one of the three candidates is a distance, and a distance has no direction. A bar that fell heavily and a bar that rose by the same amount, from the same previous close, produce an identical true range. Reflecting an entire chart upside down leaves the average true range line unchanged from end to end. There is no arrangement of prices that makes the reading negative, and no reading that distinguishes a rise from a fall.

This is worth stating flatly because the line moves, and a line that moves invites interpretation. A rising average true range does not mean price is rising. It means the bars are getting taller, and they can get taller while price falls, while price rises, or while price ends the window exactly where it began after travelling a long way in both directions. Two instruments carrying the same reading may be doing entirely opposite things. Whatever question is being asked about direction, this indicator is not answering it, and the answer it does give is a description of the window that has already closed.

Why later lessons use it as a distance 

Those two properties, price units and no direction, are the reason this is the one indicator the later risk lessons in this curriculum return to. A quantity carrying a direction cannot serve as a unit of measurement, and a quantity carrying no units cannot be converted into a number of points on a chart. Average true range carries units and no direction, which makes it usable as a yardstick: a distance can be stated as a multiple of it rather than as a fixed number of points.

The difference that makes is arithmetic rather than rhetorical. A fixed number of points is a different proposition on an instrument whose bars are typically short than on one whose bars are typically tall, and it is a different proposition on the same instrument in a quiet stretch than in a violent one. A distance stated as a multiple of recent range converts into a different number of points on each of those charts, by construction, without anyone adjusting it.

Volatility based sizing traditions build on exactly that conversion, and the lesson on position sizing in the risk module sets out the calculation in full. Two limits on the practice are stated by the practitioners who use it most, and they belong here rather than there. The multiple is arbitrary. It is chosen by convention or by preference, no value of it is derived from anything, and the practice of adjusting the multiple until the historical distances look convincing is fitting the setting to the chart it will be judged on. And the measure looks backwards. It reports the fourteen bars that have closed, so it is at its smallest immediately before range expands and at its largest immediately after, which is the opposite ordering to the one a distance derived from it would need.

What the reading does not contain 

The reading is a summary of the height of the bars behind it. Four things it does not contain are worth stating plainly, because a moving line invites each of them.

1. It contains no direction, and no combination of readings produces one. A rising line, a falling line and a flat line are each consistent with price going up, going down, or ending where it began.
2. It contains no ceiling on the next bar. An average of fourteen ranges is an average, not a bound, and a single bar can exceed every range in the window that produced the reading. Range traditions describe tall bars as tending to cluster, and disagree about how far that description extends beyond the periods already observed.
3. It contains no statement about a level. Support, resistance, a trend line and a swing point are all statements about where price is. This measure is a statement about how far bars travel, and the two answer unrelated questions.
4. It does not make a distance reachable or unreachable. A gap is movement that crossed a range of prices without trading in it, and the same gapping this indicator was constructed to measure is the mechanism by which an instruction resting inside that range is filled at a price beyond it. A distance derived from past range does not change that, and no figure appears on this page for how often any distance is exceeded, because such a figure would depend entirely on the lookback, the smoothing method and the multiple chosen before the counting began.

Where practitioners disagree 

The first disagreement is about the lookback. Fourteen is inherited from the account in which the indicator was first published rather than derived from any test a reader can inspect, and it is the same number that arrived with several other indicators from the same source. A shorter lookback produces a reading that responds to a single tall bar almost immediately and falls away just as fast. A longer one produces a reading that barely notices individual bars and lags a genuine change in character by weeks. Neither is a better description of the instrument, because they are descriptions of different windows.

The second is about whether the gap component earns its place. On a currency pair quoted around the clock through the trading week, the second and third candidates rarely win, so true range and plain range agree on nearly every bar and the extra step is close to ornamental. On a share, an index or any instrument with a long overnight break, the gap component is the entire reason the measure exists and skipping it produces a systematically understated figure. The same construction is therefore near redundant on one class of instrument and load bearing on another, which is a fact about market hours rather than about the arithmetic.

The third and largest disagreement is about what a measure of past range can be used for. The sceptical account is that range is being measured on the same bars already drawn on the chart, that the reading is arithmetic rather than information, and that a quantity known to lag by construction is a poor basis for anything sized in advance. The answer from practitioners is narrower than it is often taken to be: that the measure gives a consistent, instrument independent unit in which distances can be expressed, and that a consistent unit is worth having whether or not it forecasts anything. That second claim is about comparability, not about prediction, and the honest statement is that average true range is a description of how far recent bars travelled, whose usefulness beyond that description is disputed rather than established.