Miha Kralj
a7b7207801
- Updated mathematical foundations and performance profiles where necessary to maintain clarity and coherence.
3.2 KiB
ATR: Average True Range
"Volatility is the only thing that is real. Everything else is just a guess."
The Average True Range (ATR) is the definitive measure of market "heat." It ignores direction completely to focus on the raw magnitude of price movement. When ATR is high, the market is screaming; when it's low, the market is whispering.
Most traders mistakenly use ATR to find entries. Its true power is in exits and sizing. It answers the critical question: "How far can this asset move against me in a single day?"
Historical Context
J. Welles Wilder Jr. introduced ATR in his 1978 masterpiece, New Concepts in Technical Trading Systems. This is the same book that gave us RSI, ADX, and the Parabolic SAR.
Wilder was a mechanical engineer turned real estate developer turned trader. He approached markets with an engineer's obsession for robust systems. He realized that simply looking at the High-Low range was flawed because it ignored gaps. If a stock closes at $100 and opens at $110, the High-Low range of the new bar might be small, but the true volatility was massive. ATR captures this "invisible" volatility.
Architecture & Physics
ATR is built on two concepts: True Range (TR) and Wilder's Smoothing (RMA).
- True Range: The "real" distance price traveled, accounting for overnight gaps.
- RMA: An exponential moving average with a specific alpha (
\alpha = 1/N) that places significant weight on history. This gives ATR its characteristic "inertia"—it rises fast on shocks but decays slowly.
The Gap Problem
Standard range (High - Low) fails when markets gap.
- Scenario: Close = 100. Next Open = 110. High = 112. Low = 109.
- Standard Range:
112 - 109 = 3. - True Range:
112 - 100 = 12.
ATR correctly identifies the volatility as 12, not 3.
Mathematical Foundation
1. True Range (TR)
TR_t = \max(H_t - L_t, |H_t - C_{t-1}|, |L_t - C_{t-1}|)
Where:
H_t: Current HighL_t: Current LowC_{t-1}: Previous Close
2. Average True Range (ATR)
ATR_t = RMA(TR, N)
Which expands to:
ATR_t = \frac{ATR_{t-1} \times (N-1) + TR_t}{N}
Performance Profile
ATR is computationally cheap but mathematically robust.
| Metric | Complexity | Notes |
|---|---|---|
| Throughput | ~5ns / bar | Simple arithmetic + 1 EMA update |
| Allocations | 0 bytes | Hot path is allocation-free |
| Complexity | O(1) | Constant time per update |
| Precision | double |
Required for accurate gap measurement |
Validation
Validation is performed against TA-Lib and Skender.Stock.Indicators.
- Accuracy: Matches external libraries to 9 decimal places.
- Edge Cases: Correctly handles the first bar (where
C_{t-1}is undefined) by usingH-L.
Common Pitfalls
- Directionality: ATR is non-directional. A crashing market has high ATR. A rallying market has high ATR. Do not use it to predict direction.
- Scale Dependence: ATR is absolute, not relative. An ATR of 5.0 on a $100 stock is different from an ATR of 5.0 on a $10 stock. Use
ATRP(ATR Percent) for comparisons across assets. - Lag: Because it uses RMA (a slow-decaying average), ATR lags actual volatility spikes. It tells you what has happened, not what will happen.