Miha Kralj
6.2 KiB
PRS: Price Relative Strength
| Property | Value |
|---|---|
| Category | Momentum |
| Inputs | Source (close) |
| Parameters | smoothPeriod (default 1) |
| Outputs | Single series (PRS) |
| Output range | Varies (see docs) |
| Warmup | smoothPeriod bars |
TL;DR
- Category: Momentum Also known as: Relative Strength Comparison, Price Ratio, Performance Ratio
- Parameterized by
smoothperiod(default 1). - Output range: Varies (see docs).
- Requires
smoothPeriodbars of warmup before first valid output (IsHot = true). - Validated against TA-Lib, Skender, and Tulip reference implementations where available.
Category: Momentum
Also known as: Relative Strength Comparison, Price Ratio, Performance Ratio
Pine Script Implementation of PRS
Overview
Price Relative Strength (PRS) measures the performance of one asset relative to another by calculating the ratio between their prices. This indicator helps identify which asset is outperforming and is fundamental for sector rotation, pairs trading, and relative performance analysis.
Unlike the Relative Strength Index (RSI) which measures momentum within a single asset, PRS compares two different price series. A rising PRS indicates the base asset is outperforming the comparison asset; a falling PRS indicates underperformance.
Core Concepts
- Ratio-based: Simply divides base price by comparison price
- Trend interpretation: Rising = outperformance, Falling = underperformance
- Optional smoothing: EMA with bias compensation removes noise while maintaining responsiveness
- Scale-independent: Can compare assets with vastly different price levels
- Cross-market analysis: Compare stocks, indices, commodities, or any tradeable assets
Parameters
| Parameter | Default | Description | When to Adjust |
|---|---|---|---|
| smoothPeriod | 1 | EMA smoothing period (1 = no smoothing) | Increase for trend analysis, decrease for signal sensitivity |
Pro Tip: Use smoothPeriod=1 for raw ratio analysis, smoothPeriod=10-20 for trend identification, and smoothPeriod=50+ for longer-term relative strength trends.
Calculation
Simplified Explanation: PRS divides the base asset's price by the comparison asset's price, then optionally smooths the result with an EMA.
Technical Formula:
Raw Ratio = Base Price / Comparison Price
Smoothed = EMA(Raw Ratio, smoothPeriod)
With bias-compensated EMA for accurate warmup:
α = 2 / (smoothPeriod + 1)
EMA_biased = α × (ratio - EMA_prev) + EMA_prev
compensation = 1 / (1 - (1-α)^n)
Smoothed = compensation × EMA_biased
Implementation Note: When smoothPeriod=1, the raw ratio is returned without any smoothing. Division by zero (comparison = 0) returns NaN.
Interpretation Details
Trend Analysis:
- PRS rising: Base asset outperforming comparison (bullish for base)
- PRS falling: Base asset underperforming comparison (bearish for base)
- PRS flat: Both assets moving in tandem
Common Comparisons:
- Stock vs. sector ETF (stock relative to its sector)
- Sector vs. broad market index (sector rotation)
- Growth vs. Value ETFs (style performance)
- Emerging markets vs. developed markets
- Commodity vs. currency (inflation dynamics)
Trading Signals:
- PRS crossover above prior high: Breakout in relative strength
- PRS crossover below prior low: Breakdown in relative strength
- Divergence: Price makes new high, PRS does not = warning
Performance Profile
Operation Count (Streaming Mode)
PRS with smoothing is three scalar operations: one division for the raw ratio, one FMA for the EMA update, and one divide for the bias compensation factor. Without smoothing (smoothPeriod = 1), the bias step is skipped entirely.
| Operation | Count | Cost (cycles) | Subtotal |
|---|---|---|---|
| Input validation (IsFinite checks) | 2 | 1 | ~2 |
| Raw ratio: base / comparison | 1 | 8 | ~8 |
| EMA update (FMA: α×ratio + decay×prev) | 1 | 4 | ~4 |
| Bias factor update (1 − (1−α)^n) | 1 | 5 | ~5 |
| Compensated output (ema / bias) | 1 | 8 | ~8 |
| Total | 6 | — | ~27 cycles |
O(1) per bar. The dominant cost is the two floating-point divisions (ratio + bias correction). With smoothPeriod = 1, reduces to ~10 cycles (just the ratio division). WarmupPeriod = smoothPeriod.
Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
|---|---|---|
| Raw ratio (base / comp element-wise) | Yes | VDIVPD across full span |
| EMA smoothing pass | No | Recursive IIR dependency; each EMA value depends on previous |
| Bias compensation | Partial | Bias factor is a scalar per-bar sequence; precomputable for batch |
| NaN guard (division by zero) | Yes | VCMPPD mask + VBLENDVPD for zero-denominator replacement |
The SIMD bottleneck is the recursive EMA. A batch-mode implementation can precompute the raw ratio span via vectorized division (VDIVPD at 4 doubles/cycle on AVX2), then apply a scalar EMA sweep for the smoothing pass. This hybrid approach achieves roughly 2× throughput versus fully scalar for large series.
Limitations and Considerations
- No absolute measure: Tells you relative performance, not absolute value
- Base dependency: Results depend on which asset is the numerator
- Lagging indicator: Smoothed version lags the raw ratio
- Volume ignored: Pure price comparison, volume not considered
- Currency effects: Cross-currency comparisons may include FX impact
References
- Murphy, J. J. (1999). Technical Analysis of the Financial Markets. New York Institute of Finance.
- Pring, M. J. (2002). Technical Analysis Explained. McGraw-Hill.
- Sector rotation and relative strength analysis literature
See Also
- ROC/ROCP/ROCR: Single-asset rate of change variants
- RSI: Single-asset momentum oscillator
- Beta: Statistical measure of relative volatility
- Correlation: Measures how two assets move together