Cluster-Based Shrinkage of Correlation Matrices for Portfolio Optimization

The estimation of correlation and covariance matrices from asset return time series is a critical step in financial portfolio optimization. Although sample estimates are reliable when the length of time series is very large compared to the number of assets, in high-dimensional settings estimation issues arise. To reduce estimation errors and mitigate their propagation to out-of-sample performance of portfolios based on noisy estimates, shrinkage methods are applied. In this paper we consider several shrinkage methods for correlation matrix estimation and define a cluster-based shrinkage procedure which introduces information about the structures of communities identified in asset dependence graphs. To test the considered shrinkage methods we apply them in a portfolio optimization scenario using the global minimum variance portfolio, and perform backtests on a large sample of NYSE daily stock return data. We find that shrinkage methods generally improve out-of-sample portfolio performance, and the proposed cluster-based method yields improved results and portfolios which outperform other considered methods.