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Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com> Co-authored-by: aider (openrouter/anthropic/claude-sonnet-4) <aider@aider.chat> Co-authored-by: Warp <agent@warp.dev>
128 lines
4.8 KiB
Markdown
128 lines
4.8 KiB
Markdown
# ATRP: Average True Range Percent
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> "Volatility without context is noise. ATRP gives you context."
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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.
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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 $500 stock is moving 0.4%.
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## Historical Context
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ATRP is a derivative of J. Welles Wilder Jr.'s ATR, introduced in his 1978 work *New Concepts in Technical Trading Systems*. While Wilder focused on absolute range, traders quickly realized that percentage-based normalization was necessary for portfolio-level analysis and cross-asset comparison.
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The indicator gained prominence with the rise of systematic trading strategies that needed to compare volatility across diverse asset classes—equities, commodities, forex—without the distortion of absolute price differences.
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## Architecture & Physics
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ATRP builds on ATR's foundation and adds a single normalization step:
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1. **True Range (TR)**: Captures the "real" distance price traveled, including gaps.
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2. **RMA Smoothing**: Wilder's smoothing method ($\alpha = 1/N$) provides the characteristic slow decay.
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3. **Percentage Normalization**: Divides by current close price and multiplies by 100.
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### Why Percentage Matters
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Consider two scenarios:
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* **Stock A**: Price = \$100, ATR = 5.0 → ATRP = 5%
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* **Stock B**: Price = \$10, ATR = 2.0 → ATRP = 20%
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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.
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## Mathematical Foundation
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### 1. True Range (TR)
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$$
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TR_t = \max(H_t - L_t, |H_t - C_{t-1}|, |L_t - C_{t-1}|)
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$$
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Where:
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* $H_t$: Current High
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* $L_t$: Current Low
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* $C_{t-1}$: Previous Close
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### 2. Average True Range (ATR)
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$$
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ATR_t = RMA(TR, N)
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$$
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Expanding the RMA:
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$$
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ATR_t = \frac{ATR_{t-1} \times (N-1) + TR_t}{N}
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$$
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### 3. ATRP (Percentage)
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$$
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ATRP_t = \frac{ATR_t}{C_t} \times 100
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$$
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Where $C_t$ is the current closing price.
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## Performance Profile
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| Metric | Score | Notes |
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| :--- | :--- | :--- |
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| **Throughput** | 10 | High; O(1) calculation via RMA + single division. |
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| **Allocations** | 0 | Zero-allocation in hot paths. |
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| **Complexity** | O(1) | Constant time regardless of period. |
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| **Accuracy** | 10 | Matches ATR-based calculation exactly. |
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| **Timeliness** | 4 | Inherits ATR's lag due to RMA smoothing. |
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| **Overshoot** | 0 | Bounded by mathematical definition. |
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| **Smoothness** | 8 | Smooth decay from RMA; slight additional noise from close price variation. |
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## Validation
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ATRP is validated by computing ATR from external libraries and applying the same percentage formula.
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| Library | Status | Notes |
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| :--- | :--- | :--- |
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| **QuanTAlib** | ✅ | Validated. |
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| **TA-Lib** | ✅ | Validated via `(TA_ATR / Close) × 100`. |
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| **Skender** | ✅ | Validated via `(GetAtr / Close) × 100`. |
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| **Tulip** | ✅ | Validated via `(atr / Close) × 100`. |
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| **Ooples** | ✅ | Validated via `(CalculateAverageTrueRange / Close) × 100`. |
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## Use Cases
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### Position Sizing
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ATRP enables volatility-adjusted position sizing:
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```
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Position Size = Risk Capital / (ATRP × Entry Price)
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```
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This ensures each position carries equivalent percentage risk regardless of the asset's absolute price.
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### Cross-Asset Comparison
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Compare volatility across:
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* Different price levels (penny stocks vs. blue chips)
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* Different asset classes (equities vs. commodities)
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* Different time periods (adjusting for price drift)
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### Regime Detection
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* **ATRP < 1%**: Low volatility regime—expect consolidation, mean reversion strategies favored.
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* **ATRP 2-4%**: Normal volatility—standard trend-following conditions.
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* **ATRP > 5%**: High volatility regime—crisis conditions, wider stops required.
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## Common Pitfalls
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* **Lag**: ATRP inherits ATR's lag. It tells you what volatility *was*, not what it *will be*.
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* **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.
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* **Zero/Near-Zero Prices**: Assets approaching zero will show extreme ATRP values. Ensure minimum price thresholds in screeners.
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* **Dividend Adjustments**: Unadjusted price data can create artificial gaps around ex-dividend dates, inflating TR.
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## Related Indicators
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* **ATR**: The absolute volatility measure ATRP normalizes.
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* **NATR**: Similar concept; some implementations differ in smoothing or warmup handling.
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* **ATRN**: ATR normalized to [0,1] range based on historical min/max.
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* **Volatility Ratio**: Compares current TR to average TR for breakout detection. |