Portfolio Variance and Correlation Matrices

Executive Summary. The fact that portfolio variances must be positive implies that the correlation matrix for asset returns should be positive definite. As such, a test for positive definiteness in the correlation matrix should be routinely implemented prior to any portfolio optimization exercise. A program is developed to test for positive definiteness in correlation matrices and to detect correlation coefficients that violate the positive definiteness condition. The correlation matrices from five randomly selected papers are tested and violations revealed in larger correlation matrices. Where violations are detected, the portfolio manager or analyst should proceed with the optimization exercise only if the alternative bounds on the correlation coefficients computed by our program are acceptable.