Indicators, and what the readings mean

ATR: true range, and why a volatility reading has no direction in it

ATR answers one question: how far does this market normally travel in a bar? It is the only common indicator that is a unit rather than an opinion, and it says nothing whatsoever about which way price is going.

About 10 minutes to read. Free, no account.

True range: the three candidates, and the one that matters

The obvious measure of a bar’s movement is its high minus its low. That measure misses everything that happened between the previous close and this bar’s open - the gap. True range fixes it by taking the largest of three distances.

True range

candidate 1   this high        minus  this low
candidate 2   this high        minus  the previous close
candidate 3   the previous close  minus  this low

true range  =  the largest of the three, ignoring sign

Work a gap up. The previous bar closed at 100.00, and this bar trades between 101.00 and 103.00 - it never traded back down to yesterday’s close at all.

A bar that gapped up

previous close  100.00      this high  103.00      this low  101.00

candidate 1   103.00 - 101.00  =  2.00
candidate 2   103.00 - 100.00  =  3.00
candidate 3   100.00 - 101.00  =  1.00 (ignoring sign)

true range    =  3.00        high minus low would say  2.00

The bar moved three points away from where the market last traded, and only candidate 2 saw it. A gap down works the same way through candidate 3: a previous close of 100.00 with a bar between 96.00 and 99.00 gives candidates of 3.00, then 1.00, then 4.00 - true range 4.00.

From true range to ATR

ATR is an average of true range over N bars, 14 by convention. The plain version is an arithmetic mean:

The simple version

the last 14 true ranges sum to   28.00
ATR(14)  =  28.00 / 14           =   2.00

The standard version uses Wilder’s smoothing, the same recurrence the RSI lesson describes: keep (N-1)/N of yesterday’s average and add today’s true range divided by N.

Wilder’s step, with today’s true range of 3.00

ATR(today)  =  (previous ATR times 13  +  today’s true range) / 14

            =  (2.00 times 13  +  3.00) / 14
            =  (26.00 + 3.00) / 14
            =  29.00 / 14   =   2.07

A true range half again as large as the average moved the average by seven hundredths of a point. That inertia is the defining property of the reading, and the next section is about how much it costs you.

ATR lags, and here is how much

Put a genuine shock through it. The average true range is 2.00 and one bar arrives with a true range of 16.00 - eight times normal.

One enormous bar

ATR  =  (2.00 times 13  +  16.00) / 14
     =  (26.00 + 16.00) / 14
     =  42.00 / 14   =   3.00

the bar was 8 times the average;  the average rose by half

So ATR tells you what normal was, not what normal is. It rises after volatility arrives and it falls after volatility leaves, and in both cases the thing it is describing happened first. A low ATR is a statement that the last fourteen bars were calm. It is not a forecast that the next one will be, and quiet periods are precisely where violent bars tend to be found.

Shortening the period makes ATR react faster and jump around more; lengthening it makes the reading steadier and later. There is no setting at which an average of past bars describes the next bar.

Why ATR is a unit, not a direction

Every candidate in the true range calculation ignores sign. A bar that fell 3.00 points and a bar that rose 3.00 points contribute identically. There is no information about direction inside ATR, and no setting can put any there. Anyone telling you a rising ATR is bullish is reading a quantity that cannot answer the question.

What it is genuinely good for is turning distances into a comparable measure. Raw ATR is in the coin’s price units, so divide by price to compare markets:

ATR as a percent of price

coin A    ATR 2.07        price 104.00     2.07 / 104.00    =  1.99%
coin B    ATR 0.00012     price 0.0024     0.00012 / 0.0024 =  5.00%

coin B normally travels about two and a half times as far per bar

And distances on the chart become counts of normal bars. A level 2.50 points below a price of 104.00, with ATR at 2.07:

A distance in ATRs

2.50 / 2.07  =  1.21 ATRs

which reads: about one and a fifth normal bars away

That sentence is useful in a way "2.50 points" is not, because 2.50 points is a different-sized obstacle on a sleepy market than on a frantic one. Expressing a distance in ATRs is measurement. What to do about the measurement - how wide a stop to accept, whether to take the trade - is your decision, and the school will not make it for you.

Timeframe changes the number, roughly predictably

ATR(14) on a 15-minute chart and ATR(14) on a 4-hour chart are different quantities: one averages fourteen quarter-hours, the other averages fourteen four-hour stretches. A 4-hour bar is sixteen 15-minute bars long, and if moves accumulated independently the range would grow with the square root of time:

The rough scaling

4 hours / 15 minutes      =  16 times the span
square root of 16         =   4

so expect the 4-hour ATR near 4 times the 15-minute one

Treat that as an order-of-magnitude check, not a law. It assumes each interval is independent of the last, and markets trend and mean-revert in ways that break the assumption in both directions. If your two readings are wildly out of line with it, the useful question is which timeframe is carrying an outlier.

What ATR cannot do

It cannot tell you direction. Sign is discarded in the first line of the calculation.
It cannot tell you volatility is about to change. It is a trailing average, so it reports arrivals and departures after they happen.
It cannot be compared across coins in raw form. Divide by price first, or you are comparing price tags.
It cannot tell you a move was unusual in context. A true range of 16.00 against an ATR of 2.00 is eight times normal for this market and this window - and a news event, a listing and a liquidation cascade all look identical from inside the arithmetic.

Used well, ATR is the unit the rest of the chart should be quoted in. A signal arrives with a distance between entry and stop already in it; knowing that distance in ATRs tells you whether it is a wide plan or a tight one for this market, which is worth knowing before anything happens. See how a signal is built.

The terms, defined

True range: The largest of three distances - high to low, high to the previous close, and the previous close to the low - taken without regard to sign.
ATR: Average true range. The average of true range over N bars, 14 by convention, usually using Wilder’s smoothing.
Wilder’s smoothing: Keep (N-1)/N of the previous average and add the new value divided by N. The same recurrence RSI uses, and the source of ATR’s inertia.
Gap: A move between one bar’s close and the next bar’s range with no trading in between. Invisible to high minus low, which is why true range exists.
ATR percent: ATR divided by price. The comparable form - raw ATR is in the price units of whatever you are charting.
Volatility: How far a market moves, in either direction. A size, never a direction.

What this means in practice

Use true range, not high minus low, and know why: the gap between bars is real movement.
Divide ATR by price before comparing two coins. Raw ATR compares price tags.
Quote chart distances as counts of ATRs. "About one normal bar away" is a sentence; "2.50 points" is not, until you know the market.
Never read direction into ATR, rising or falling. The sign was thrown away in the first line of the calculation.
Remember a low ATR describes the last fourteen bars and promises nothing about the next one.
Expect roughly the square root of the timeframe ratio between two ATRs, and investigate when it is far off rather than averaging them.

Nothing in this lesson is financial advice or an instruction to trade. See the risk disclaimer. We never recommend a leverage setting - that decision is yours.