报告题目：Eigen Portfolio Selection: A Robust Approach to Sharpe Ratio Maximization
报 告 人：Chengguo Weng (Associate Professor，University of Waterloo)
In this paper, we study how to pick optimal portfolios by modulating the impact of estimation risk in large covariance matrices. We discover that if the expected returns vector lies in a subspace of the eigenvector space of the sample covariance matrix, the sample-based maximum Sharpe ratio portfolio also lies in the same subspace. Due to the uneven distribution of estimation errors across different sample eigenvalues and eigenvectors, it is desirable that the portfolio estimator lies in a space spanned by a few sample eigenvectors that relatively well estimate their population counterparts. Therefore, we propose approximating the expected returns vector in a lower-dimensional subspace and use the approximation for the construction of portfolio. As long as the approximation is close to the original vector, we benefit from the reduced exposure to the estimation error without much loss in the information of the expected returns. We introduce two concrete regularization methods for approximating the expected returns, and analyze the choice of turning parameters for the methods. We conduct simulation studies and use three real-world stock returns datasets to assess the effectiveness of the two methods. Our results show that both methods mitigate the effect of the estimation error more effectively in a high-dimensional setting than a low-dimensional setting.
Dr. Chengguo Weng graduated from Zhejiang University with a Bachelor of Science in 2001 and a Master of Mathematics in Statistics in 2003. He started graduate studies in Actuarial Science at University of Waterloo in May 2006 and graduated with a Ph.D. degree in 2009. Dr. Weng worked as an Assistant Professor at Townson University in Maryland, USA for about one year before he moved back to University of Waterloo and worked there as Assistant Professor in June 2010. Dr. Weng is currently an Associate Professor at University of Waterloo. His research interests span a broad spectrum of scientific disciplines, ranging from actuarial science, and finance to probability, statistics, and stochastic optimization. He is interested in both theoretical and applied research topics. His research team are currently working on: (1) Monte Carlo simulation methods for optimal control problems; (2) Construction of vast portfolios; (3) Optimal insurance contract design; (4) Predictive Analytics for insurance and finance. One can find more information about Dr. Weng on the website: https://chengguoweng.com.