QuanTAlib/lib/volatility/atrp/Atrp.md

ATRP: Average True Range Percent

"Volatility without context is noise. ATRP gives you context."

ATRP normalizes the Average True Range (ATR) as a percentage of the closing price. This transforms an absolute volatility measure into a relative one, enabling meaningful comparisons across different price levels and different assets.

A $5 stock and a $500 stock might both have an ATR of 2.0, but their volatility profiles are completely different. ATRP reveals the truth: the $5 stock is moving 40% while the $500 stock is moving 0.4%.

Historical Context

ATRP is a derivative of J. Welles Wilder Jr.'s ATR, introduced in his 1978 work New Concepts in Technical Trading Systems. While Wilder focused on absolute range, traders quickly realized that percentage-based normalization was necessary for portfolio-level analysis and cross-asset comparison.

The indicator gained prominence with the rise of systematic trading strategies that needed to compare volatility across diverse asset classes—equities, commodities, forex—without the distortion of absolute price differences.

Architecture & Physics

ATRP builds on ATR's foundation and adds a single normalization step:

1. True Range (TR): Captures the "real" distance price traveled, including gaps.
2. RMA Smoothing: Wilder's smoothing method (\alpha = 1/N) provides the characteristic slow decay.
3. Percentage Normalization: Divides by current close price and multiplies by 100.

Why Percentage Matters

Consider two scenarios:

• Stock A: Price = $100, ATR = 5.0 → ATRP = 5%
• Stock B: Price = $10, ATR = 2.0 → ATRP = 20%

ATR alone suggests Stock A is more volatile. ATRP reveals Stock B moves four times more in percentage terms—critical information for position sizing and risk management.

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 High
• L_t: Current Low
• C_{t-1}: Previous Close

2. Average True Range (ATR)

ATR_t = RMA(TR, N)

Expanding the RMA:

ATR_t = \frac{ATR_{t-1} \times (N-1) + TR_t}{N}

3. ATRP (Percentage)

ATRP_t = \frac{ATR_t}{C_t} \times 100

Where C_t is the current closing price.

Performance Profile

Metric	Score	Notes
Throughput	10	High; O(1) calculation via RMA + single division.
Allocations	0	Zero-allocation in hot paths.
Complexity	O(1)	Constant time regardless of period.
Accuracy	10	Matches ATR-based calculation exactly.
Timeliness	4	Inherits ATR's lag due to RMA smoothing.
Overshoot	0	Bounded by mathematical definition.
Smoothness	8	Smooth decay from RMA; slight additional noise from close price variation.

Validation

ATRP is validated by computing ATR from external libraries and applying the same percentage formula.

Library	Status	Notes
QuanTAlib	✅	Validated.
TA-Lib	✅	Validated via (TA_ATR / Close) × 100.
Skender	✅	Validated via (GetAtr / Close) × 100.
Tulip	✅	Validated via (atr / Close) × 100.
Ooples	✅	Validated via (CalculateAverageTrueRange / Close) × 100.

Use Cases

Position Sizing

ATRP enables volatility-adjusted position sizing:

Position Size = Risk Capital / (ATRP × Entry Price)

This ensures each position carries equivalent percentage risk regardless of the asset's absolute price.

Cross-Asset Comparison

Compare volatility across:

• Different price levels (penny stocks vs. blue chips)
• Different asset classes (equities vs. commodities)
• Different time periods (adjusting for price drift)

Regime Detection

• ATRP < 1%: Low volatility regime—expect consolidation, mean reversion strategies favored.
• ATRP 2-4%: Normal volatility—standard trend-following conditions.
• ATRP > 5%: High volatility regime—crisis conditions, wider stops required.

Common Pitfalls

• Lag: ATRP inherits ATR's lag. It tells you what volatility was, not what it will be.
• Close Price Sensitivity: A sharp close price move affects both the numerator (via TR) and denominator (close), creating transient spikes. Use multiple periods for confirmation.
• Zero/Near-Zero Prices: Assets approaching zero will show extreme ATRP values. Ensure minimum price thresholds in screeners.
• Dividend Adjustments: Unadjusted price data can create artificial gaps around ex-dividend dates, inflating TR.

Related Indicators

• ATR: The absolute volatility measure ATRP normalizes.
• NATR: Similar concept; some implementations differ in smoothing or warmup handling.
• ATRN: ATR normalized to [0,1] range based on historical min/max.
• Volatility Ratio: Compares current TR to average TR for breakout detection.