Multi-Index Shrinkage Estimation

Abstract

The authors present an improved method for estimating the asset class covariance matrix for input into a mean variance optimizer. Starting with the Ledoit and Wolf [2003] stock level Bayesian shrinkage estimator, they derive a multi-index shrinkage estimator for capturing the actual asset class return structure and for estimating the covariance matrix. They test this multi-index estimator relative to the historical covariance matrix and single-index estimator. Using annual return data for 13 asset classes over the period 1960 through 2002, they find that the multi-index estimator outperforms both of the alternative estimation methods in terms of mean squared error in forecasting the actual covariance matrix and in terms of forming one-, two-, and three-years-ahead minimum-risk portfolios.