What is Correlation?
Correlation measures the strength and direction of the linear relationship between two assets' return series. It ranges from −1 (perfect inverse relationship) to +1 (perfect positive relationship), with 0 indicating no linear relationship. Portfolio diversification relies on combining assets with low or negative correlation: uncorrelated assets reduce portfolio volatility without necessarily reducing expected return. Correlation is not constant: assets that appear uncorrelated in normal markets often become highly correlated in a crisis (correlation spikes toward 1 during sell-offs). Historical correlation is backward-looking and may not predict future correlation, especially across different market regimes.
Formula
ρ(X,Y) = Cov(X,Y) / (σ_X × σ_Y)
Cov(X,Y) = Σ[(X_i − X̄)(Y_i − Ȳ)] / (n−1)
σ_X, σ_Y = standard deviations of X and Y return series
n = number of observations
Calculator
How to Use
- 1Enter paired returns: Enter matching-period returns for Asset X and Asset Y (e.g., monthly returns for both over 36 months).
- 2Calculator computes correlation: The tool computes the Pearson correlation coefficient from the data.
- 3Interpret: ρ > 0.7: highly correlated (move together). ρ < 0.3: low correlation (good diversifier). ρ < 0: negative correlation (hedge).
- 4Use in portfolio construction: Combine assets where ρ < 0.5 to achieve meaningful diversification benefit.
Worked Example
Example: Stocks vs bonds (simplified)
Cov(S,B)
−0.0008
σ_Stocks
15%
σ_Bonds
7%
ρ = −0.0008 / (0.15 × 0.07) = −0.076. Near-zero slight negative correlation, historically typical for US equities vs investment-grade bonds (the "60/40 diversification"). In 2022, this correlation became positive as both fell simultaneously, illustrating the regime-dependency of correlation.