PRS: Price Relative Strength

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

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

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