🌡️ ATR — Average True Range
ATR measures how much an asset typically moves in a single period, in absolute price units, independent of direction. It is the workhorse volatility measure behind most stop-loss and position-sizing rules.
💡 Financial Meaning
A simple high-minus-low range ignores overnight or gap moves; ATR fixes this by using the True Range, which also accounts for gaps relative to the previous close. Traders place stops at a multiple of ATR (e.g. "2×ATR below entry") so that the stop automatically widens in volatile conditions and tightens in calm ones, rather than using a fixed price distance that is too tight in fast markets and too loose in quiet ones.
🔢 Mathematical Formulas
-
True Range — the largest of three candidates, capturing gaps as well as the intraday range:
\[ TR_t = \max\big(H_t - L_t,\; \left| H_t - C_{t-1} \right|,\; \left| L_t - C_{t-1} \right|\big) \] -
Average True Range — a smoothed moving average (Wilder's SMMA) of the True Range:
\[ ATR_t = SMMA_N(TR) \]
⚙️ Parameters
| Parameter | Key | Default | Description |
|---|---|---|---|
| Period (\(N\)) | period |
14 | Smoothing window applied to the True Range, in sessions. |
🎛️ Signal Processing Equivalent — Smoothed Rectified Envelope
Taking \(\max(\cdot)\) of three absolute-difference candidates is a form of full-wave rectification with gap compensation — it converts a signed, direction-agnostic quantity (price range) into a strictly positive "energy" measure. Smoothing that rectified signal with an SMMA (a one-pole IIR low-pass, same structure as the EMA) produces a running envelope estimate, conceptually the same role an envelope detector plays in an AM radio demodulator.
flowchart LR
H["📈 High"] --> TR["🌡️ True Range = max(H−L, |H−C_prev|, |L−C_prev|)"]
L["📉 Low"] --> TR
Cp["💹 Previous Close"] --> TR
TR --> SMMA["🔁 SMMA(N)"]
SMMA --> ATR["🌡️ ATR(t)"]ATR has no upper bound
Because ATR is expressed in price units, its scale grows with the instrument's price level over time. When comparing volatility across different assets — or the same asset at very different price levels — use NATR instead.