Direct Answer
Log correlation is the correlation between two series measured on logarithmic returns, ln(P_t / P_(t-1)), rather than on price levels or simple returns. Log returns add across time and behave better statistically than levels. It is read like any correlation, from -1 to +1.
Log Correlation: Formula, Meaning, Signals, Examples and How to Use It
How Is Log Correlation Calculated?
Log correlation is the correlation between two series measured on logarithmic returns, ln(P_t / P_(t-1)), rather than on price levels or simple returns. Log returns add across time and behave better statistically than levels.
Formula: r_t = ln(P_t / P_(t-1)) for each asset; then Pearson correlation of the two log-return series over the window
Inputs:
- Two aligned price series
- Window length
Worked example. A price move from 100 to 105 is a log return of 0.0488, compared with a simple return of 5 percent. The inputs are illustrative numbers, not market data.
Reading it. It is read like any correlation, from -1 to +1. Using log returns avoids the spurious correlation that trending price levels produce, so it describes co-movement of changes rather than of drift.
Limits. For small moves log and simple returns are nearly identical, so the choice matters little day to day. Like all correlations it is linear and unstable in short windows.
What is Log Correlation?
Log correlation is the correlation between two series measured on logarithmic returns, ln(P_t / P_(t-1)), rather than on price levels or simple returns. Log returns add across time and behave better statistically than levels.
How to use Log Correlation
It is read like any correlation, from -1 to +1. Using log returns avoids the spurious correlation that trending price levels produce, so it describes co-movement of changes rather than of drift. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- Log returns add exactly across periods, so a gain and a loss of the same log size cancel and multi-period sums stay exact.
- Working on returns rather than levels avoids the spurious high correlation that two unrelated trending price series show.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- Correlation of daily log returns does not equal correlation of monthly log returns, so the sampling interval has to be stated.
- Log returns of assets do not sum into a portfolio log return, so the correlation is not an exact input for portfolio-level sums.
- Correlated indicators can create false confidence by repeating the same underlying information.
Editorial and risk note
This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance.
Frequently Asked Questions
Is Log Correlation a buy or sell signal?
No. It is read like any correlation, from -1 to +1. For small moves log and simple returns are nearly identical, so the choice matters little day to day. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions.
What is the best setting for Log Correlation?
Log Correlation takes these inputs: two aligned price series; window length. There is no universal best setting for the tunable ones, so test them across instruments, regimes and out-of-sample periods and favor stable parameter regions over one historical winner.
Can Log Correlation be used by itself?
For small moves log and simple returns are nearly identical, so the choice matters little day to day. Like all correlations it is linear and unstable in short windows. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does Log Correlation work on every timeframe?
The calculation (r_t = ln(P_t / P_(t-1)) for each asset; then Pearson correlation of the two log-return series over the window) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it.
Why does Log Correlation give false signals?
Correlation of daily log returns does not equal correlation of monthly log returns, so the sampling interval has to be stated. Log returns of assets do not sum into a portfolio log return, so the correlation is not an exact input for portfolio-level sums. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should Log Correlation be backtested?
Rebuild Log Correlation from two aligned price series using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline.