A Regression-Based Interpretation of the Inverse of the Sample Covariance Matrix

Abstract

The usefulness of covariance and correlation matrices is well-known in various academic fields. Matrix inversion, if required in an analytical setting, tends to mask the intuition in interpreting the corresponding empirical or experimental results. Drawing on the finance literature in mean-variance portfolio analysis, this paper presents pedagogically a regression-based interpretation of the inverse of the sample covariance matrix. Microsoft ExcelTM plays an important pedagogic role in this paper. The availability of various Excel functions and computational tools for numerical illustrations provides flexibility for instructors in the delivery of the corresponding analytical materials.