A correlation matrix is a square table where each cell shows the Pearson correlation coefficient between two assets or risk factors, describing how their returns move in relation to each other. Coefficients range from -1 (perfect negative relationship) to 1 (perfect positive relationship), with 0 indicating little or no linear relationship. The matrix is usually calculated from historical return data over a chosen period and can be shown for a specific window or market regime.
In risk and portfolio analysis, the correlation matrix helps assess diversification and redundancy among assets. It is related to the covariance matrix; Cov(i,j) equals Corr(i,j) times the standard deviation of asset i times the standard deviation of asset j. Practitioners use it to understand how shifts in one asset may coincide with shifts in others, influence portfolio variance, and identify clusters of assets that tend to move together. It is common to monitor how the matrix evolves over time or under different conditions to capture potential shifts in relationships.
Correlation is a historical measure and can change over time; relying on a single period may understate or overstate the degree of co-movement in future conditions. In risk modeling, the matrix serves as a building block for calculating portfolio risk and for scenario analysis.
In a three-asset set, the matrix shows pairwise correlations; for example, Asset A and Asset B have a correlation of 0.25, Asset A and Asset C -0.10, Asset B and Asset C 0.05.
Correlation · Covariance Matrix · Diversification · Portfolio Variance · Standard Deviation · Covariance