An Introduction to Shrinkage Estimation of the Covariance Matrix: A Pedagogic Illustration

Shrinkage estimation of the covariance matrix of asset returns was introduced to the finance profession several years ago. Since then, the approach has also received considerable attention in various life science studies, as a remedial measure for covariance matrix estimation with insufficient observations of the underlying variables. The approach is about taking a weighted average of the sample covariance matrix and a target matrix of the same dimensions. The objective is to reach a weighted average that is closest to the true covariance matrix according to an intuitively appealing criterion. This paper presents, from a pedagogic perspective, an introduction to shrinkage estimation and uses Microsoft ExcelTM for its illustration. Further, some related pedagogic issues are discussed and, to enhance the learning experience of students on the topic, some Excel-based exercises are suggested.