A robust linear programming model for index fund construction

Abstract

In this study, the strategy of effective asset allocation under uncertainty with the capability of risk control, transaction cost reduction and favorable return realization is investigated. In order to implement this strategy and to overcome the shortfalls of classic portfolio optimization models in dealing with uncertainty, the formation of an index fund using a robust approach and considering cardinality constraint became the agenda. Accordingly, in order to solve the index tracking problem, a linear programming model as minimizing the absolute deviation between the expected return of the index fund and that of the benchmark is presented. Considering the dimension of the solution space, a Meta heuristic genetic algorithm was implemented to solve the robust counterpart of the problem. The results of the analysis imply on the selection of 20 stocks as the index fund composition and indicate good performance of the index tracking funds based on criteria such as correlation, root mean square error and the excess return using out of sample data.

Keywords

• index fund
• index tracking
• linear programming
• robust optimization. instructer