Correlation Matrix
A table displaying the pairwise correlation coefficients between all assets in a portfolio.
What is Correlation Matrix?
A correlation matrix is a square table showing the Pearson correlation coefficients between every pair of assets in a portfolio or a broader set of securities. Each cell represents the linear relationship between two assets' return series, ranging from −1 (perfect inverse correlation) to +1 (perfect positive correlation), with 0 indicating no linear relationship. Portfolio construction uses correlation matrices to identify diversification opportunities: adding assets with low or negative correlations to existing holdings reduces overall portfolio volatility without necessarily sacrificing expected return. Correlation matrices are an input to mean-variance optimization (Markowitz framework), risk parity strategies, and factor models. A critical limitation is that correlations are not stable — they tend to spike toward 1 during market crises, precisely when diversification benefits are most needed. Dynamic correlation models and stress-tested scenarios account for this 'correlation breakdown' phenomenon.
Example
A portfolio contains US stocks, international stocks, bonds, and gold. The correlation matrix shows US and international stocks are correlated at +0.75, stocks and bonds at −0.20, and stocks and gold at +0.05. Adding gold to the portfolio slightly reduces volatility because it is nearly uncorrelated with equities. During the 2020 COVID crash, correlations between asset classes temporarily spiked, reducing short-term diversification benefits.