Correlation Coefficient

What Is a Correlation Coefficient?

A correlation coefficient is a statistical measure of the relationship between two sets of data, most often expressed as the Pearson correlation coefficient, which is denoted by the letter r. It ranges from -1 to +1. A value of +1 means the two variables move in perfect lockstep in the same direction, -1 means they move in perfectly opposite directions, and 0 means there is no linear relationship between them. Values in between indicate the strength of the tendency: values near +1 or -1 show a strong relationship, while values near 0 show a weak one.

Correlation measures association, not cause. Two series can be correlated because one drives the other, because both respond to a third factor, or purely by coincidence.

How It Is Calculated

The Pearson version divides the covariance of two series by the product of their standard deviations. In plain terms, it asks how much the two series deviate from their averages together, scaled so the result always falls between -1 and +1:

r = Σ(xi − x̄)(yi − ȳ) / √[Σ(xi − x̄)² × Σ(yi − ȳ)²]

Here xi and yi are individual observations, and x̄ and ȳ are their averages. In practice, spreadsheet and data software compute this automatically from paired series, such as the daily percentage changes of two stocks over the same period.

Why It Matters to Investors

Investors use correlation to understand how assets behave relative to each other. Stocks with low or negative correlation to one another can reduce the overall volatility of a portfolio through diversification, because losses in one holding may be offset by gains or smaller losses in another. Highly correlated holdings tend to fall together, so owning several of them may provide less protection than the number of holdings suggests.

Correlations are not fixed. They can rise sharply during market stress, and estimates based on past data may not hold in the future. The coefficient also captures only linear relationships, so it can miss strong but non-linear patterns.