# Cointegration vs. Correlation in Trading

Written By
Written By
Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.
Updated

We look at the differences between cointegration and correlations and its application in trading.

Imagine a trader observing two assets that seem to move in unison.

Do these assets offer a solid basis for a trading strategy (e.g., eventual convergence if they run apart)?

Noticing this movement alone isn’t sufficient. It’s important to determine whether the relationship stems from short-term correlation or deeper, long-term cointegration.

## Key Takeaways – Cointegration vs. Correlation

• Cointegration:
• Measures the long-term equilibrium relationship between two non-stationary time series (e.g., stock prices)
• If two assets are cointegrated, it means their prices may deviate from each other in the short-run, but they tend to move together over the long-run, maintaining an equilibrium relationship
• Cointegration implies the existence of an error correction mechanism that causes the variables to converge in the long-run
• Useful for pairs trading strategies, where traders look to profit from temporary deviations from the long-term equilibrium
• Correlation:
• Measures the degree of linear relationship between two variables over a specific time period
• Ranges from -1 to 1, with -1 being perfectly negatively correlated, 0 being no correlation, and 1 being perfectly positively correlated
• A high positive/negative correlation implies the variables tend to move in the same/opposite direction in the short-term
• Correlation is a short-term, period-specific concept that doesn’t imply a long-run equilibrium relationship
• Cointegration is more relevant for long-term investing/trading strategies like pairs trading, looking for mean reversion opportunities
• Correlation is more useful for short-term trading, looking at current market conditions and relationships between/among assets
• Uncorrelated but cointegrated assets can exist, where prices diverge in the short-run but maintain a long-run equilibrium

## Defining Correlation

Correlation quantifies how two assets move in relation to each other over a short period.

The essence of correlation lies in its focus on the direction and magnitude of short-term price movements between assets.

## Defining Cointegration

Cointegration, on the other hand, suggests a long-term equilibrium between asset prices, allowing for temporary divergences.

For instance, two stocks in the same sector may deviate in the short term due to specific news but exhibit a consistent, linked trajectory over time.

This relationship is confirmed through statistical tests like the Engle-Granger method.

### Confidence Intervals

Cointegration is defined in the context of confidence intervals.

95% and 90% confidence intervals are most common.

Something can be cointegrated with a 90% confidence interval but not at a 95% confidence interval.

Relationships like this include:

• gold and gold miners
• US nominal Treasury bonds and US inflation-linked Treasury bonds
• stocks and commodities
Dependent Independent Test Statistic p-value 95% Confidence 90% Confidence
VanEck Gold Miners ETF (GDX) SPDR Gold Shares (GLD) -1.669 0.09 Not cointegrated Cointegrated

Dependent Independent Test Statistic p-value 95% Confidence 90% Confidence
iShares 20+ Year Treasury Bond ETF (TLT) iShares TIPS Bond ETF (TIP) -1.686 0.09 Not cointegrated Cointegrated

Dependent Independent Test Statistic p-value 95% Confidence 90% Confidence
iShares S&P GSCI Commodity-Indexed Trust (GSG) SPDR S&P 500 ETF Trust (SPY) -1.782 0.08 Not cointegrated Cointegrated

## Correlation vs. Cointegration – What’s the Difference?

A key distinction is that while highly correlated assets may also be cointegrated, cointegration signifies a more profound and stable relationship – i.e., a long-term equilibrium in their price movements.

### Chart: Correlation vs. Cointegration

 Feature Correlation Cointegration Focus Short-term price movements Long-term price relationship Measure Degree of linear association Existence of a shared trend Statistical Basis Correlation coefficient Cointegration tests Trading Use Identifying trending markets, potential hedges Pairs trading, mean-reverting strategies

## Using Cointegration and Correlation in Trading

Cointegration is used in pairs trading strategies and identifying mispriced assets.

It’s more of a framework for long-term trading or investment decisions.

Conversely, correlation is used in trend-following strategies and short-term hedging, so it can provide insights into immediate market dynamics.

## Cointegration vs. Covariance

Cointegration indicates a long-term relationship where non-stationary time series variables, like asset prices, move together over time, which suggests an underlying equilibrium.

Covariance, conversely, measures how two variables vary together in the short term, without implying any long-term relationship or equilibrium.

• Cointegration assesses the stable linkage in their levels over extended periods.
• Covariance focuses on their concurrent movement in terms of variance and correlation, without considering the long-term trend.

Related: Correlation vs. Covariance

## Conclusion

Understanding the nuances between cointegration and correlation equips traders with ways to statistically analyze the relationship between assets and other time series variables.

A trader can include both concepts to tailor strategies appropriately – and consider the potential to integrate these analyses within other forms of analysis for a comprehensive approach.