Indicator library · Volatility

Average True Range (ATR), Volatility in Points

How far an instrument travels in a typical session, gaps included and direction ignored. Wilder built it for position sizing rather than for signals, and that is still the use it survives best.

The calculation

Two steps, and the first is where all the thought went.

  1. True range: the largest of three distances: high − low, |high − previous close| and |low − previous close|. The second and third capture gaps, which a plain high-low span cannot see.
  2. Average: Wilder smoothing over n periods: ((previous × (n − 1)) + current) ÷ n, seeded with a simple mean of the first n values. Fourteen is the conventional period.

The gap case is not academic. On session 11 of the series charted below, the plain high-low span is 1.20 points while the true range is 4.10, nearly four times larger, because the instrument opened a long way above the previous close and then traded quietly. A measure that reported that session as calm would be describing the clock rather than the market.

Price with its average true rangeThe upper panel shows a price series that trades quietly, gaps sharply upward around the eleventh bar, declines for about ten bars and then settles into a narrow range. The lower panel shows the average true range in points, which is low through the quiet opening, jumps after the gap, stays elevated through the decline and then decays steadily as the range contracts.CLOSEATR 90.99gapPrice with its average true rangeThe upper panel shows a price series that trades quietly, gaps sharply upward around the eleventh bar, declines for about ten bars and then settles into a narrow range. The lower panel shows the average true range in points, which is low through the quiet opening, jumps after the gap, stays elevated through the decline and then decays steadily as the range contracts.CLOSEATR 90.99gap
Fig. 1: schematicComputed at build time by Wilder's method from the high, low and close of every bar in this page's source. Two things are worth reading. The jump at the marked session comes from the gap, which the true range counts and a high-low span would not. And the long decay afterwards is the smoothing rather than the market: Wilder's average keeps a decaying trace of that one session for many bars, which is why the line is still elevated well after the instrument went quiet. The final reading of 0.99 points is 1.91% of the last close.

Points, per cent, and what may be compared

ATR is denominated in the instrument’s own currency, which has the same consequence it has for every unbounded measure on this site: the raw number cannot be compared with the same number on another instrument. An ATR of 2 points is enormous on a twenty-dollar stock and trivial on a two-thousand-dollar one.

Which form to use for which question
QuestionForm
How large a position should I take in this instrument?Points. The stop distance and the money at risk are both in the instrument's currency, so the arithmetic works directly.
Which of these hundred instruments moves most?Per cent, ATR divided by price. This is one of the two definitions a most-volatile screen can use.
Is this instrument more volatile than it was last year?Either, provided the price level has not changed much; per cent if it has.

Position sizing, which is what it is for

Wilder introduced ATR in 1978 as part of a system, and its most defensible use has always been deciding how much to hold rather than what to buy. The logic is short.

Fix the money you are prepared to lose on one position. Fix the stop distance as a multiple of ATR (two is common), so that ordinary movement in that instrument will not reach it. The position size is then the money at risk divided by the stop distance in points. A volatile instrument gets a smaller position and a quiet one a larger position, and a single bad outcome costs roughly the same either way.

What this does not give you is a level the market cares about. A stop set by volatility alone sits wherever the arithmetic puts it, which is sometimes exactly where a great many other stops sit. The measure decides the distance; it has no opinion about the place.

Reading a rising or falling ATR

The line itself is worth a moment, since it is often glanced at and rarely read. A rising ATR says sessions have been covering more ground lately, and nothing else. It rises during declines more often than during advances, because falls are faster and more synchronised, but it also rises on a breakout, and treating it as a warning is reading a direction into a measure that has none.

A falling ATR is the more interesting of the two, because a contracting range changes what every other measure on this site is reporting. A stochastic reaches its extremes more easily, breakout systems produce more false starts, and a stop set at a fixed multiple of the average is now much closer to the price than it was a month ago. The measure has not changed; the market underneath it has.

Where it misleads

Known failure modes
SituationWhat goes wrong
Read as directionalEvery input is a distance. A violent advance and a violent decline produce identical readings.
Compared across instrumentsRaw ATR carries the price level. Use ATR as a percentage of price for any ranking.
Wrong smoothing constantWilder's weight is 1/n. A conventional exponential average uses 2/(n+1) and produces values that look right and are not.
Short historyThe seed is carried forward with a decaying weight; early values depend on where the data starts.
One gap read as a regimeA single gap keeps the average elevated for many bars after the instrument has gone quiet.
Unadjusted pricesA split produces a false gap of enormous size, which the true range faithfully records.

What volume adds

ATR measures how far the price travelled and says nothing about what it took to move it. The two cases it cannot separate are the ones that decide whether a move is worth anything: a wide range on the heaviest volume in weeks, where size was genuinely traded against, and an identical range on the thinnest session of the month, where a modest order walked an empty book.

Read together they answer a question neither can answer alone. Expanding range on expanding volume describes a market changing its mind; expanding range on flat or falling volume describes a book that gave way, and typically reverses as soon as anyone real arrives.

Frequently asked questions

What is the "true" range?

The largest of three distances: today’s high minus today’s low, the distance from yesterday’s close up to today’s high, and the distance from yesterday’s close down to today’s low. The second and third exist to capture gaps. An instrument that opens far above yesterday’s close and then trades in a narrow band has a small high-low range and a large true range, and the true range is the honest description of how far it moved.

Does ATR say anything about direction?

Nothing at all, by construction. Every input is a distance, so a violent decline and an equally violent advance produce the same reading. This is a feature rather than a limitation. It is precisely what makes ATR usable as an input to position sizing and stop placement, where what you need to know is how far the instrument moves, not which way.

How is it smoothed?

With Wilder’s average: the first value is a simple mean of the first n true ranges, and every value after it is ((previous × (n − 1)) + current) ÷ n. That weight is 1/n, not the 2/(n+1) of a conventional exponential average, and using the wrong one is the most common reason two platforms disagree about ATR on the same data. Fourteen is Wilder’s period and remains the default everywhere.

Can ATR be compared between instruments?

Not in its raw form, because it is denominated in the instrument’s own currency, an ATR of 2 is enormous on a $20 stock and negligible on a $2,000 one. Dividing by the price gives ATR as a percentage, which is comparable and is what any cross-instrument volatility screen should rank on. The raw points figure remains the right input for sizing a position in that one instrument.

How is ATR used for position sizing?

By fixing the money at risk rather than the number of shares. Decide what a stop distance should be in units of ATR — two is a common choice — and how much money you are prepared to lose if it is hit; the position size is that money divided by the stop distance in points. The effect is that a volatile instrument gets a smaller position and a quiet one a larger position, so a single bad outcome costs about the same either way. This is the most defensible use of the indicator.

Should stops be placed at a multiple of ATR?

It is a reasonable way to set a distance and it is not a strategy. What ATR gives you is a stop far enough from the price that ordinary movement will not hit it, expressed in the instrument’s own terms rather than in an arbitrary percentage. What it cannot give you is a level anything cares about, and a stop placed by volatility alone will sometimes sit exactly where everyone else’s sits, which is the one place worth avoiding.

What does a rising ATR mean?

That sessions have been covering more ground lately, nothing more. It happens during declines more often than during advances, because falls are faster and more synchronised, so a rising ATR often coincides with weakness. But it also rises on a breakout to the upside, and reading it as a bearish signal is reading a direction into a measure that has none.

Does it need a long history?

More than the period suggests. Wilder smoothing carries its seed forward for ever with a decaying weight, so a 14-period ATR fed twenty bars is still substantially a function of where the data began. Feed at least a few hundred bars if you intend to compare your figures with a platform, and discard the first few multiples of the period.