Eigen Portfolio Selection: A Robust Approach to Sharpe Ratio Maximization

Abstract

We show that even when a covariance matrix is poorly estimated, it is still possible to obtain a robust maximum Sharpe ratio portfolio by exploiting the uneven distribution of estimation errors across principal components. This is accomplished by approximating an investor’s view on future asset returns using a few relatively accurate sample principal components. We discuss two approximation methods. The first method leads to a subtle connection to existing approaches in the literature; while the second one is novel and able to address main shortcomings of existing methods.

Keywords: Portfolio optimization, Estimation error, Approximation error, Spectral cut-off method, Spectral selection method

JEL Classification: G11