Linearly Shrunk Empirical Covariance Matrix

Compute a linearly shrunk empirical asset covariance matrix, which is a convex combination of the empirical covariance matrix of these assets and a target covariance matrix, the target covariance matrix being either:

• A constant variance covariance matrix (i.e., a multiple of the identity matrix)
• An unequal variance covariance matrix (i.e., a diagonal matrix)
• A constant variance-covariance covariance matrix (i.e., the sum of a multiple of the identity matrix and of a matrix with 0s on its diagonal and 1s elsewhere)
• A constant correlation covariance matrix (i.e., the sum of a diagonal matrix and of a multiple of a particular matrix with 0s on its diagonal)

References

• Olivier Ledoit, Michael Wolf, The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation, Journal of Financial Econometrics, Volume 20, Issue 1, Winter 2022, Pages 187–218
• Gianluca De Nard, Oops! I Shrunk the Sample Covariance Matrix Again: Blockbuster Meets Shrinkage, Journal of Financial Econometrics, Volume 20, Issue 4, Fall 2022, Pages 569–611
• O. Ledoit, M. Wolf, Honey, I Shrunk the Sample Covariance Matrix, The Journal of Portfolio Management Summer 2004, 30 (4) 110-119
• Schafer J, Strimmer K. A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Stat Appl Genet Mol Biol. 2005;4:Article32
• Guillaume Becquin and Saher Esmeir. 2023. Semantic Similarity Covariance Matrix Shrinkage. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 9977–9992, Singapore. Association for Computational Linguistics