Robust enhanced index tracking problem with mixture of distributions

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.