Shrinkage of the Sample Correlation Matrix of Returns Towards a Constant Correlation Target: A Pedagogic Illustration Based on Dow Jones Stock Returns

Abstract

This paper extends the introduction to shrinkage estimation in a recent paper from the same journal. The extension, which is in a portfolio investment context, is on shrinkage of the sample correlation matrix of returns towards a constant correlation target. Here, shrinkage estimation is about finding a weighted average of the sample correlation matrix and the target matrix, for a balance between reducing overall forecast errors and maintaining some existing idiosyncrasies in the individual correlations. Excel plays an important pedagogic role here. Besides illustrating the computations involved, the use of Excel also enables students to gain valuable hands-on experience in shrinkage estimation, by working with the Dow Jones stock returns in an Excel file accompanying this paper.