Robust enhanced index tracking problem with mixture of distributions. (1st September 2022)

• Record Type: Journal Article
• Authors: Kang, Zhilin; Yao, Haixiang; Li, Xingyi; Li, Zhongfei
• Is Part Of: Expert systems with applications. Volume 201(2022)
• Publication Date: 2022-09-01
• Subjects: Enhanced indexing -- Lower partial moment -- Mixture model -- Robust optimization -- ϕ-divergence -- Sortino index; Expert systems (Computer science) -- Periodicals; Systèmes experts (Informatique) -- Périodiques; Electronic journals; 006.33
• DOI: 10.1016/j.eswa.2022.117110
• Languages: English
• ISSNs: 0957-4174

Abstract

Abstract: Enhanced index tracking (EIT) is a popular form of investment strategy, which seeks to create a portfolio to generate excess return relative to a given benchmark index without purchasing all the index components. In this paper we develop an EIT model with mixture distribution under a lower partial moment (LPM) framework. Furthermore, we formulate the EIT problem as a robust and tractable model by integrating uncertain information on the proportions of Gaussian mixture distribution specified by the ϕ -divergence. By applying Lagrange duality theory, we demonstrate that the EIT problem on the basis of the worst-case LPMs of degree 1 and 2 can be transformed into a mathematically tractable optimization problem. Out-of-sample experiments using the FTSE100 and S&P500 data sets show that the portfolios based on our proposed model exhibit better performance than those from the benchmark index in most cases. Highlights: A lower partial moment framework for the enhanced index tracking (EIT) problem. The robust EIT that deals with the uncertainty in the proportions of mixture distribution is introduced. The robust problem remains tractable under the type of Phi-divergence uncertainty. Experiments for tracking the FTSE100 index and S&P500 index.