A hybrid approach for index tracking with practical constraints

Yingjie Li; Xiaoguang Yang; Shushang Zhu; Dong-Hui Li

doi:10.3934/jimo.2014.10.905

Article Contents

2014, Volume 10, Issue 3: 905-927. Doi: 10.3934/jimo.2014.10.905

This issue Previous Article A nonlinear conjugate gradient method for a special class of matrix optimization problems Next Article Finite-time optimal consensus control for second-order multi-agent systems

A hybrid approach for index tracking with practical constraints

1.
Institute of Systems Science, Chinese Academy of Science, Beijing 100190
2.
Department of Finance and Investment, Sun Yat-Sen University, Guangzhou 510275
3.
School of Mathematical Sciences, South China Normal University, Guangzhou, 510631

Received: March 2012

Revised: August 2013

Published: July 2014

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Abstract

Index tracking is a popular way for passive fund management, which aims to reproduce the performance of a market index by investing in a subset of the constituents of the index. The formulation of index tracking with some realistic constraints always leads to an optimization problem that is very hard to solve. In this paper, we propose an approximate formulation to the original optimization problem and analyze the approximation error bound. It is shown that the approximation can be reasonably close to the original problem. We consider both cases where the mean absolute error and mean square error are used as the tracking error measurements. The mean absolute error measurement results in a mixed-integer linear programming problem and can be solved by some standard solvers, such as CPLEX. The mean square error measurement leads to a mixed-integer quadratic programming problem. An efficient hybrid heuristic method is given to solve this problem. We do some numerical experiments by the use of five data sets from OR-Library. The results are promising.

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Mathematics Subject Classification: Primary: 65K15; Secondary: 90C11.

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