# American Institute of Mathematical Sciences

July  2014, 10(3): 905-927. doi: 10.3934/jimo.2014.10.905

## A hybrid approach for index tracking with practical constraints

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

Received  March 2012 Revised  August 2013 Published  November 2013

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.
Citation: Yingjie Li, Xiaoguang Yang, Shushang Zhu, Dong-Hui Li. A hybrid approach for index tracking with practical constraints. Journal of Industrial & Management Optimization, 2014, 10 (3) : 905-927. doi: 10.3934/jimo.2014.10.905
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