Shrunk Correlation Matrix

Compute an asset correlation matrix as a convex linear combination of an asset correlation matrix and a target correlation matrix, the target correlation matrix being either:

• An equicorrelation matrix made of 1s
• An equicorrelation matrix made of 0s
• An equicorrelation matrix made of -1/(n-1), with n the number of assets
• An equicorrelation matrix made of the average correlation of the elements of the asset correlation matrix
• The correlation matrix obtained after truncating the eigendecomposition of the asset correlation matrix, as described in the 3rd reference
• A provided correlation matrix

References

• Steiner, Andreas, Manipulating Valid Correlation Matrices
• Kwan, Clarence C. Y. (2017) Shrinkage of the Sample Correlation Matrix of Returns Towards a Constant Correlation Target: A Pedagogic Illustration Based on Dow Jones Stock Returns, Spreadsheets in Education (eJSiE): Vol. 10: Iss. 1, Article 3.
• Jose Menchero and Lei Ji, Advances in Estimating Covariance Matrices, Vol. 19, No. 3, (2021), pp. 60–80