A robust optimization approach for index tracking problem

Abstract

Index tracking is an investment approach where the primary objective is to keep portfolio return as close as possible to a target index without purchasing all index components. The main purpose is to minimize the tracking error between the returns of the selected portfolio and a benchmark. In this study, quadratic as well as linear models are presented for minimizing the tracking error. The uncertainty is considered in the input data using a tractable robust framework that controls the level of conservatism while maintaining linearity. The linearity of the proposed robust optimization models allows a simple implementation of an ordinary optimization software package to find the optimal robust solution. The proposed model of this study employs Morgan Stanley Capital International Index as the target index and the results are reported for six national indices including Japan, the USA, the UK, Germany, Switzerland and France. The performance of the proposed models is evaluated using several financial criteria e.g., information ratio, market ratio, Sharpe ratio and Treynor ratio. The preliminary results demonstrate that the proposed model lowers the amount of tracking error while raising values of portfolio performance measures.