Average True Range (ATR): Master Stop-Loss Placement and Position Sizing

Average True Range (ATR) measures how much an asset moves per bar — including overnight gaps that a simple High minus Low calculation would miss. It tells you the market's current pulse: fast or slow, wide or tight. ATR does not predict direction. It quantifies magnitude.

Section 1: Core Mechanics

ATR was developed by J. Welles Wilder Jr. and published in his 1978 book New Concepts in Technical Trading Systems. The same book introduced RSI and the Parabolic SAR.

Formula

The first step is the True Range (TR) — the largest of three measurements for each bar:

The second measurement captures upward gaps; the third captures downward gaps. This is why ATR is more accurate than a simple High-Low range for assets that gap overnight.

ATR is then a Wilder-smoothed average of TR over N periods:

For the first bar, (simple average of the first N true ranges). Default N = 14.

Inputs

• High: Bar high
• Low: Bar low
• Close: Previous bar close (for gap measurement)

Parameters

Output

ATR outputs a single positive value per bar on a separate sub-panel, expressed in the same unit as price (dollars for stocks, pips for forex, points for futures). Higher ATR = wider price swings. Lower ATR = quieter, tighter price action.

Visual Behavior

• Rising ATR → volatility expanding — market becoming more active
• Falling ATR → volatility contracting — market quieting down
• ATR at multi-month lows → pre-breakout squeeze or extended low-volatility environment

Section 2: Interpretation & Signals

ATR is not a buy/sell signal generator. It is a measurement tool that powers three critical trade management functions.

Three Uses of ATR

ATR Stop-Loss Logic

A fixed stop of $2.00 is too tight on a stock with ATR = $4.00 and too wide on one with ATR = $0.80. ATR-based stops adapt automatically:

Volatility Filter Signal

Section 3: Pass vs. Live — Real-Time Reliability

ATR on a live (unclosed) bar updates in real time as the high and low expand. The true range will only be finalized at bar close. For stop-loss calculations, always use the ATR from the prior closed bar — not the current live bar — to avoid sizing your stop on an ATR that hasn't finished forming.

Section 4: Practical Use Cases

Real example — Position sizing: Account $50,000, risk 1% per trade = $500 maximum risk. AAPL ATR(14) on daily = $3.20. Position size = $500 ÷ $3.20 = 156 shares. Stop = entry price minus 1× ATR = entry minus $3.20. If AAPL is at $175.00, stop goes at $171.80. This size and stop risk exactly $499.20 — within the 1% rule.

Section 5: Pseudo Code

INPUT: high[], low[], close[], period=14

PROCESS:
  Step 1: Calculate True Range for each bar i (starting from bar 1, not bar 0)
            tr[i] = max(
              high[i] - low[i],
              abs(high[i] - close[i-1]),
              abs(low[i] - close[i-1])
            )
  Step 2: Seed the first ATR value using a simple average
            atr[period] = mean(tr[1 : period+1])
  Step 3: Apply Wilder smoothing for all subsequent bars
            atr[i] = ((atr[i-1] * (period - 1)) + tr[i]) / period

OUTPUT: atr[] — array of ATR values, NaN for first (period - 1) bars
EDGE CASES:
  - Fewer than period bars: return all NaN
  - First bar (i=0): no previous close, so tr[0] = high[0] - low[0]
  - Gap open: |High - PrevClose| or |Low - PrevClose| will exceed High-Low — ATR captures this correctly
  - Period = 1: ATR equals TR of each bar (no smoothing)

Section 6: Parameters & Optimization

Standard ATR Period Conventions

ATR Multiplier Reference

Section 7: Synergies & Conflicts

Section 8: Common Mistakes

Section 9: Cheat Sheet