报 告 人：戚厚铎 教授
报告题目：An Optimization Study of Diversification Return Portfolios
Houduo Qi is a professor at the department of applied mathematics, The Hong Kong Polytechnic University. He received the BSc in Statistics from Peking University in 1990, MSc and PhD in Operational Research and Optimal Control, respectively from Qufu Normal University (1993) and the Institute of Applied Mathematics, Chinese Academy of Sciences (CAS) in 1996. He has been postdoctoral fellows at the Institute of Computational Mathematics, CAS, the Hong Kong Polytechnic University, and the University of New South Wales before joining the University of Southampton in 2004 as a lecturer in Operational Research, rising to Professor and Chair of Optimization.
He was awarded the prestigious Queen Elizabeth II Fellowship (QEII Fellow) by the Australian Research Council (2003) and Turing Fellow in 2019 by the Alan Turing Institute, UK’s national institute of data science. He recently joined the Hong Kong Polytechnic University. He is mainly interested in Mathematical Optimization, especially in matrix optimization with applications to finance and statistics. He is currently the area editor (Optimization) of Asia-Pacific Journal of Operational Research, associate editor for Mathematical Programming Computation and Journal of Operations Research Society of China. From 2010, he has been a college member of Engineering and Physical Sciences Research Council, UK.
The concept of Diversification Return (DR) was introduced by Booth and Fama in 1990s and it has been well studied in the finance literature mainly focusing on the various sources it may be generated. However, unlike the classical Mean-Variance (MV) model of Markowitz, DR portfolios lack optimization theory for justifying their often-outstanding empirical performance. In this paper, we first explain what the DR criterion tries to achieve in terms of portfolio centrality. A consequence of this explanation is that practically imposed norm constraints in fact implicitly enforce constraints on DR. We then derive the maximum DR portfolio under given risk and obtain the efficient DR frontier. We further develop a separation theorem for this frontier and establish a relationship between the DR frontier and Markowitz MV efficient frontier. In the particular case where the variance vector is proportional to the expected return vector of the underlining assets, the two frontiers yield same efficient portfolios.The proof techniques heavily depend on recently developed geometric interpretation of the maximum DR portfolio. Finally, we use DAX30 stock data to illustrate the obtained results and demonstrate an interesting link to the maximum diversification ratio portfolio studied by Choueifaty and Coignard.