Average True Range: Measuring Realized Price Movement

Average true range (ATR), introduced by J. Welles Wilder Jr., estimates the magnitude of recent price movement. It improves on the simple high-low range by incorporating gaps from the previous close. ATR rises when realized ranges expand and falls when they contract. It contains no positive or negative sign, so it cannot establish bullish or bearish direction by itself.

Start with true range#

For each completed period after the first, true range (TR) is the largest of:

Current high - Current low

Absolute value of current high - previous close

Absolute value of current low - previous close

The high-low range is enough when the full move occurs inside the current bar. The previous-close comparisons matter when price gaps. For example, a market can open above yesterday’s close and trade in a narrow intraday range; high minus low would miss much of the close-to-close displacement, while true range captures it.

The first observation has no prior close. Implementations may use high minus low, omit it, or begin after more history is available.

Smooth true range into ATR#

The conventional lookback is 14 periods. Initial ATR is commonly the arithmetic mean of the first 14 true ranges. Wilder’s recursive update is then:

ATR today = ((Prior ATR × (n - 1)) + TR today) / n

For (n = 14), the new true range contributes one-fourteenth and prior smoothed history contributes thirteen-fourteenths. Some platforms instead apply an EMA or rolling SMA. Those methods can produce different values, especially after a volatility shock.

Reproducible analysis specifies the smoothing method, lookback, session, price data, and treatment of overnight gaps. A daily ATR built from a 24-hour session differs from one built from a restricted session.

Interpret level and change#

ATR is expressed in the instrument’s price units. An ATR of 5 may be small for a 2,000-unit instrument and enormous for a 10-unit instrument. A normalized version supports comparison:

ATR percentage = ATR / Price × 100

A rising ATR shows that recent realized movement is expanding. It does not show whether expansion favors buyers or sellers. A declining ATR shows contraction, which may accompany a quiet range or an orderly trend. Low ATR does not mean low future risk; an unscheduled announcement can immediately make historical calm irrelevant.

ATR is often used to scale analytical distances, but a multiple of ATR remains a convention rather than a guaranteed safe boundary.

Worked example: gaps and smoothing#

Suppose the previous close is 100, while the next period has a high of 104 and a low of 101. The three candidates are:

• high-low: 104 - 101 = 3
• high-previous close: |104 - 100| = 4
• low-previous close: |101 - 100| = 1

True range is 4, correctly including the upward gap.

For a shortened three-period illustration, suppose the first three true ranges are 2.5, 4.0, and 6.0. Initial ATR is:

(2.5 + 4.0 + 6.0) / 3 = 4.17

If the next true range is 3.0, Wilder’s update gives:

((4.17 × 2) + 3.0) / 3 = 3.78

At a price of 103, normalized ATR is about 3.78 / 103 × 100 = 3.67%. Volatility has eased from the initial sample, but the value does not forecast the direction or exact size of the next period.

Practical ATR checklist#

1. Confirm the session definition and whether overnight gaps are included.
2. Record lookback, smoothing method, price units, and warm-up history.
3. Normalize ATR when comparing instruments with different price scales.
4. Distinguish current ATR from a forecast of future or event volatility.
5. Test any ATR multiple across quiet, trending, gapping, and stressed regimes.
6. Model spread and slippage, which often widen as ATR rises.
7. Recalculate analytical exposure when volatility changes rather than assuming a fixed range.

Completed-bar values should be used when a rule depends on the final high, low, or close.

Limitations and false signals#

ATR is backward-looking and can react after a large move has already occurred. A volatility spike may inflate it after risk has materialized, while a long quiet period may compress it just before a gap. Because it is directionless, attaching a directional interpretation to rising ATR requires separate evidence.

Values are sensitive to market hours and contract construction. Futures rolls, equity splits, stale prices, and erroneous highs or lows can create artificial ranges. Percentage ATR improves scale comparison but does not make liquidity or tail risk comparable. An ATR-based stop can still fill beyond its intended level, and an ATR-based size rule can underestimate losses when correlations rise or markets gap. Historical multiples also invite overfitting if selected to avoid every past loss.

Key takeaways#

• True range includes both intraperiod movement and gaps from the previous close.
• Standard ATR uses 14 periods and Wilder smoothing.
• ATR measures magnitude, not direction.
• Percentage ATR is more useful than raw ATR for cross-price comparison.
• Session choices, event gaps, data errors, and delayed response limit the indicator.

This guide is for general education only and is not personal investment advice or a recommendation. Historical range cannot cap future loss; gaps, liquidity changes, slippage, and leverage can produce outcomes far beyond an ATR estimate.