Correlation Coefficient

A value of +1 means a perfect positive relationship: when one variable rises, the other always rises in exact proportion. A value of −1 means a perfect negative relationship. A value of 0 means there is no straight-line relationship. Values in between show weaker or stronger tendencies.

The most common version, the Pearson correlation coefficient, is calculated by dividing the covariance of two variables by the product of their standard deviations. This standardises the measure so it does not depend on the units of the data.

For example, two funds whose monthly returns have a covariance of 1.63, with standard deviations of about 1.58 and 1.12, have a correlation coefficient of about 0.92. That is a strong positive relationship, suggesting holding both funds would provide little diversification.

As a rough guide, values above about 0.7 or below about −0.7 are often described as strong, and values close to 0 as weak, although interpretation depends on the context.

The correlation coefficient only captures straight-line relationships. Two variables can be strongly related in a curved way yet show a correlation near zero. It is also sensitive to outliers, and with small samples it can be misleading.