(6月24日）概率统计学术报告

题目： Improved Global Minimum Variance Portfolio via Tail Eigenvalues Amplification

报告人： Dr. Chengguo Weng，University of Waterloo，Canada

报告时间：6月24日下午4:00---5:00

报告地点： 数学中心5楼报告厅

摘要:

We discuss how a manipulation of sample eigenvalues affects the actual portfolio risk when a two-step method is used to construct a global minimum variance portfolio (GMVP). For special structures of the true covariance matrix, both a shrinkage on a head eigenvalue and an amplification on a tail eigenvalue are shown to have a marginal effect of reducing the actual risk. In a high-dimensional setting, the marginal effect of amplifying a tail eigenvalue becomes dominant compared with that of shrinking a head eigenvalue. This leads us to propose a new concept called a tail eigenvalues amplification (TEA) method. In the TEA method, the first few eigenvalues are kept unchanged, while the last few eigenvalues are amplified to infinity. This modified covariance matrix is used for constructing a GMVP. Both simulation and empirical results show that the TEA method with the number of eigenvalues to amplify selected using a cross-validation method has an improved actual portfolio risk reduction effect and smaller turnover compared with the “shrinkage towards identity" method. Lastly, when there is a larger gap (in terms of the magnitude) between the off-diagonal elements and the diagonal elements in the true covariance matrix, the TEA method results in a higher percentage actual portfolio risk reduction.

报告人简介：

    Chengguo Weng is an Associate Professor of Actuarial Science at the University of Waterloo. He received a Ph.D. in Actuarial Science from the University of Waterloo, a Master of Mathematics and a Bachelor of Science (both in Statistics) from Zhejiang University. His research interests span a wide range of topics in actuarial science and finance, in both theoretical and applied aspects. His latest research focuses on optimal decision, stochastic modelling and predicting problems from the fields of insurance and finance. Here is his personal homepage: www.chengguoweng.comChengguo Weng is an Associate Professor of Actuarial Science at the University of Waterloo. He received a Ph.D. in Actuarial Science from the University of Waterloo, a Master of Mathematics and a Bachelor of Science (both in Statistics) from Zhejiang University. His research interests span a wide range of topics in actuarial science and finance, in both theoretical and applied aspects. His latest research focuses on optimal decision, stochastic modelling and predicting problems from the fields of insurance and finance. Here is his personal homepage: www.chengguoweng.com

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联系人：苏中根（suzhonggen@zju.edu.cn) 张奕(zhangyi63@zju.edu.cn)