Correlation: How Two Investments Move in Relation to Each Other

Correlation measures how strongly two variables move in relation to each other. In finance, it usually refers to how the returns of two assets move together.

• A correlation near +1 means they tend to move in the same direction.
• A correlation near 0 means there is little consistent relationship.
• A correlation near -1 means they tend to move in opposite directions.

Correlation matters because diversification works best when portfolio holdings do not all move together at the same time.

Correlation is about the pattern of co-movement. The closer the points align in one direction, the stronger the relationship.

Why Correlation Matters

Investors do not build portfolios one asset at a time in isolation. They build combinations of assets.

An individual stock may be volatile on its own, but when combined with assets that behave differently, the overall portfolio can become more stable. That is why correlation is central to portfolio construction, asset allocation, and risk management.

Two investments can each look attractive separately, yet still create an undiversified portfolio if they are highly correlated.

The Correlation Coefficient

The standard formula is:

Where:

• \(\operatorname{Cov}(X,Y)\) is the covariance between the two return series
• \(\sigma_X\) is the standard deviation of asset X
• \(\sigma_Y\) is the standard deviation of asset Y

The result is scaled to lie between -1 and +1.

High positive correlation

If U.S. large-cap stocks and another U.S. large-cap index fund have correlation close to +1, owning both may not add much diversification.

Low or moderate correlation

If stocks and high-quality bonds show lower correlation, combining them can reduce overall portfolio volatility.

Negative correlation

If one asset often rises when another falls, the combination may provide even stronger diversification benefits, although strong negative correlation is uncommon and can change over time.

Worked Example

Suppose an investor owns:

• a broad stock fund
• a government bond fund

Each fund has its own expected return and volatility. What matters for diversification is not just the risk of each holding, but also how their returns interact.

If stock returns fall sharply during a risk-off period while bond returns hold steady or rise, the portfolio’s total volatility can be lower than the volatility of the stock fund alone. That benefit comes from correlation being below +1.

Correlation and Diversification

Correlation does not eliminate risk, but it helps explain why diversification can reduce portfolio volatility.

That relationship shows up directly in portfolio math. For a two-asset portfolio, portfolio variance depends on:

• each asset’s weight
• each asset’s volatility
• the correlation between them

Lower correlation usually means a larger diversification benefit.

Important Limits

Correlation is useful, but it is not permanent or perfectly reliable.

• Correlations can rise during crises.
• Historical correlation may not match future correlation.
• Correlation does not prove causation.
• Two assets can have low correlation and still lose money at the same time under specific stress conditions.

This is why investors often combine correlation analysis with stress testing, scenario analysis, and business-level judgment.

Correlation vs. Covariance

Covariance tells you whether two assets tend to move together and in what direction, but it is not scaled. Correlation standardizes that relationship, making it easier to compare across assets and markets.

That is why portfolio discussions usually refer to correlation rather than raw covariance.

Related Terms

• Covariance: The raw measure of how two return series move together.
• Standard Deviation: Measures the volatility of an asset or portfolio.
• Portfolio Variance: Uses correlation and volatility to measure portfolio risk.
• Diversification: Spreads exposure across assets to reduce risk concentration.
• Asset Allocation: Determines how capital is divided across asset classes and strategies.

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