Title: Eigen portfolio selection: A robust approach to Sharpe ratio maximization
Authors: Danqiao Guo - University of Waterloo (Canada) [presenting]
Phelim Boyle - Wilfrid Laurier University (Canada)
Chengguo Weng - University of Waterloo (Canada)
Tony Wirjanto - University of Waterloo (Canada)
Abstract: It is shown how to pick optimal portfolios by modulating the impact of estimation risk in large covariance matrices. The portfolios are selected to maximize their Sharpe ratios. Each eigenvector of the covariance matrix corresponds to a maximum Sharpe ratio (MSR) portfolio for a different set of expected returns. Assuming that the portfolio manager has views on the future expected returns, a portfolio consistent with her views can be approximated by the first few eigenvectors of the sample covariance matrix. Since the estimation error in a large sample covariance matrix tends to be most severe in the eigenvectors associated with the smallest eigenvalues, the elimination of the tail eigenvectors reduces estimation error. We substitute the vector of expected excess returns by its lower-dimensional approximation so that the MSR portfolio is not contaminated by the estimation errors in the tail. To seek a balance between the approximation error and the estimation error, we set a tolerance limit for the former and make best efforts to control the latter. We further introduce a more general spectral selection method, which uses non-consecutive eigenvectors to approximate the expected excess returns. According to simulation and real-data studies, the advantage of the spectral selection method becomes apparent when the number of assets is large compared with the sample size.