Average True Range

Technical Analysis · basic · CC-BY-4.0

Average True Range (ATR) is a technical indicator developed by J. Welles Wilder that measures market volatility by calculating the exponential moving average of a security's 'true range'—defined as the greatest of: the current high minus the current low, the absolute value of the current high minus the prior close, and the absolute value of the current low minus the prior close—over a specified lookback period, typically 14 periods. ATR quantifies the magnitude of price movement without direction, making it a pure volatility measure used for position sizing, stop-loss placement, and breakout confirmation.

Key takeaways

True Range = max(High - Low, |High - Prior Close|, |Low - Prior Close|); the inclusion of the prior close captures overnight gaps and limit-move scenarios that the simple High-Low range misses.
ATR does not indicate direction—high ATR means high volatility; low ATR means low volatility. Sustained low ATR periods often precede significant directional breakouts.
Traders use ATR multiples as volatility-adjusted stop-loss levels: a common rule is to set stops at 2× or 3× ATR below the entry price, ensuring the stop is beyond normal random price variation.
Position sizing based on ATR: Risk per trade / ATR gives the number of units to trade to achieve consistent dollar risk per position regardless of the underlying's volatility level.
ATR is relative, not absolute—a $10 ATR on a $500 stock (2% ATR) indicates the same relative volatility as a $2 ATR on a $100 stock (2% ATR); comparing ATRs across assets requires normalization.

Explanation

Average True Range was introduced by Wilder in his 1978 book 'New Concepts in Technical Trading Systems,' alongside RSI and Parabolic SAR. Wilder designed ATR specifically to address the limitation of the simple high-low range in markets with gaps: when a futures market moves limit-up overnight, the day's low may still be above the prior day's high, making the intraday high-low range uninformative about the actual price change experienced by a position holder. By incorporating the prior close in the true range calculation, ATR captures this gap risk.

The calculation proceeds as follows: (1) Compute True Range for each period; (2) Average the True Range over the lookback period (Wilder used a 14-period smoothed average, which applies a weight of 1/14 to the current value: ATR_t = (ATR_{t-1} × 13 + TR_t) / 14). The result is an exponentially smoothed measure of recent volatility that rises during high-volatility episodes and declines during quiet markets. The 14-period lookback is standard but practitioners adjust it—shorter periods (7-10) create more responsive but noisier readings; longer periods (20-30) create smoother, slower-reacting indicators.

The most rigorous application of ATR is in systematic position sizing. The concept of 'volatility-normalized position sizing' (as popularized by the Turtle Traders and subsequently by systematic CTAs) uses ATR to ensure that each position in a portfolio risks the same dollar amount regardless of the asset's underlying price level or historical volatility. The formula: Position Size = Risk Per Trade / ATR. If a trader risks $1,000 per trade and Apple has a 14-day ATR of $5.00, they trade 200 shares (stop placed 1 ATR below entry). If gold has an ATR of $25 and the same $1,000 risk budget applies, the position is 40 ounces. This approach prevents low-volatility positions from being overweighted (risking too little) and high-volatility positions from being underweighted (risking too much) relative to the portfolio's actual risk budget.

In breakout trading, ATR serves as a threshold filter. Many systematic breakout strategies trigger entries when price moves more than N×ATR from a reference level (a prior high, a moving average, or the prior day's close), filtering out noise while capturing genuine regime changes. The underlying logic is that a move of less than 1 ATR is within the normal random variation of the asset and does not constitute a statistically meaningful break; a move of more than 2 ATR suggests a genuine shift in supply/demand dynamics.

Formula

True Range = max(High - Low, |High - Prior Close|, |Low - Prior Close|)
ATR(n) = (ATR(n-1) × (n-1) + TR) / n  [Wilder's smoothing]
Position Size = Risk Budget / ATR
Volatility-adjusted stop: Entry ± (N × ATR)

Example

A systematic futures trader is sizing a position in crude oil (WTI) futures. The 14-day ATR is $2.80 per barrel, and each WTI futures contract represents 1,000 barrels. The trader's risk budget per position is $5,000. Position size = $5,000 / ($2.80 × 1,000 barrels) = 1.79 contracts, rounded to 2 contracts. Entry is at $82.00; stop is placed at $82.00 - (2 × $2.80) = $76.40, approximately 6.8% below entry. If oil's ATR expands to $4.50 following an OPEC announcement, the trader's position sizing algorithm reduces the position to 1 contract for new trades (keeping dollar risk constant). This volatility-adjusted sizing ensures that a volatile period does not expose the portfolio to disproportionate drawdown from a single position.

Average True Range

Key takeaways

Explanation

Formula

Example

Related terms