Covariance Cleaning and Estimators

This lecture covers the rationale behind covariance matrix cleaning, emphasizing the drawbacks of using the sample covariance matrix for portfolio optimization. It delves into rotationally invariant estimators, hierarchical clustering, and bootstraps. The instructor discusses the empirical spectrum of correlation matrices, eigenvalue clipping, and a formal approach to correlation/covariance cleaning. The lecture explores the concept of a good covariance estimator, focusing on minimizing the distance with the true matrix and building an optimal estimator for portfolio optimization. Additionally, it introduces the linear shrinkage method and the concept of optimal rotationally invariant estimators.