Definition
Correlation is a statistic between −1 and +1 that measures how closely two return series move together in a straight-line sense. A value of +1 means they move in perfect step, 0 means no linear relationship, and −1 means they move in exactly opposite directions.
How it works
The usual measure, the Pearson coefficient, equals the covariance of two return series divided by the product of their standard deviations. It should be computed on returns, not price levels, because two trending price series can look strongly correlated even when their returns are unrelated.
Correlation depends on the window and data frequency, and it is not stable: relationships estimated in calm periods often strengthen in market stress. It captures only linear co-movement, says nothing about causation, and is not beta, which also depends on relative volatility.
Formula / convention
ρ(X, Y) = Cov(X, Y) ÷ (σ(X) × σ(Y)), where −1 ≤ ρ ≤ +1, computed on returns
Illustrative example
Illustrative: two fictional funds have monthly return standard deviations of 2.0% and 1.5%, and their covariance is 0.00018. Correlation = 0.00018 ÷ (0.020 × 0.015) = 0.00018 ÷ 0.0003 = 0.60, a moderately strong tendency to move together.
What to watch for
A correlation of 0.60 does not mean the two move together 60% of the time, and a low or negative reading in one sample is no guarantee of protection in another. Outliers can dominate the coefficient, and nonlinear relationships can hide behind a near-zero value.