Correlation Coefficient

Risk & Portfolio

Updated Apr 2026 • Has calculator

Measures how consistently two return series move together, from −1 (perfect inverse) to +1 (perfect positive).

What is Correlation?

The Pearson correlation coefficient quantifies the linear relationship between two return series. A value of +1 means the two assets always move in the same direction by proportional amounts; −1 means they always move in opposite directions; 0 means no linear relationship. In portfolio construction, correlation is critical because combining assets with low or negative correlations reduces the portfolio's overall volatility without necessarily reducing expected return — the key insight behind diversification. For example, adding an asset that is negatively correlated with the rest of a portfolio can reduce total risk even if the asset itself is volatile in isolation.

Formula

ρ = Σ[(Aᵢ−Ā)(Bᵢ−B̄)] / √[ Σ(Aᵢ−Ā)² × Σ(Bᵢ−B̄)² ]

Worked Example

Annual returns 2019–2023

Step 1 S&P 500 annual returns (%): 31.5, 18.4, 28.7, −18.1, 26.3

Step 2 US Agg Bond annual returns (%): 8.7, 7.5, −1.5, −13.0, 5.5

Step 3 Covariance ≈ 62.4; σ_SPX ≈ 18.6%; σ_Bond ≈ 7.8%

Step 4 ρ = 62.4 / (18.6 × 7.8) = 62.4 / 145.1 ≈ 0.43

Step 5 → Moderate positive correlation: bonds partially but not fully dampen equity swings

Source: S&P Dow Jones Indices & Bloomberg Index Services (2024-01-31)

Calculate Correlation

Asset A Returns (%)

Enter comma-separated returns for the first asset

Asset B Returns (%)

Enter comma-separated returns for the second asset (same number of periods)

Correlation

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Not investment advice.

How to Interpret Correlation

< -0.5

Strong Negative — excellent diversification benefit

-0.5 – 0

Weak Negative — good diversification

0 – 0.5

Weak Positive — limited diversification benefit

> 0.5

Strong Positive — assets move together; low diversification

📚 Risk Metrics — Complete the path

Sources