Title: Enhanced Sharpe ratio via eigen portfolios selection
Authors: Chengguo Weng - University of Waterloo (Canada) [presenting]
Abstract: The aim is to show how to pick optimal portfolios by modulating the impact of estimation risk in the covariance matrix. The portfolios are selected to maximize their Sharperatios. Each eigenvector of the covariance matrix corresponds to a maximum Sharpe ratio(MSR) portfolio for a different set of expected returns. Assuming the portfolio manager has views on the future expected returns, a portfolio consistent with her views can be approximated by the first K eigenvectors of the covariance matrix. Since the estimation error in the 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. We show the equivalence between the expected returns approximation approach and the spectral cut-off method of regularizing a precision matrix. We introduce a more general spectral selection method, which uses non-consecutive eigenvectors to approximate the expected excess returns. The spectral methods, when applied to empirical data yield Sharpe ratios consistently higher than those of equally weighted portfolios.