Introduction
In quantitative finance, correlation matrices are essential for portfolio optimization, risk management, and asset allocation. However, real-world data often results in correlation matrices that are invalid due to various issues:
- Merging Non-Overlapping Datasets: If correlations are estimated separately for different periods or asset subsets and then stitched together, the resulting matrix may lose its positive semidefiniteness.
- Manual Adjustments: Risk/assert managers sometimes override statistical estimates based on qualitative insights, inadvertently making the matrix inconsistent.
- Numerical Precision Issues: Finite sample sizes or noise in financial data can lead to small negative eigenvalues, making the matrix slightly non-positive semidefinite.
