Kernel Search: An application to the index tracking problem

In this paper we study the problem of replicating the performances of a stock market index, i.e. the so-called index tracking problem, and the problem of out-performing a market index, i.e. the so-called enhanced index tracking problem. We introduce mixed-integer linear programming (MILP) formulations for these two problems. Furthermore, we present a heuristic framework called Kernel Search. We analyze and evaluate the behavior of several implementations of the Kernel Search framework to the solution of the index tracking problem. We show the effectiveness and efficiency of the framework comparing the performances of these heuristics with those of a general-purpose solver. The computational experiments are carried out using benchmark and newly created instances.

► MILP formulations of the problems allow to include real-life features.
► Good out-of-sample behaviors of the optimized portfolios.
► Good performances of the Kernel Search framework solving large-scale instances.
► New contributions to the heuristic algorithm show better results than the original one.