Exact and Heuristic Approaches for the Index Tracking Problem with UCITS Constraints.

Passive asset management aims at implementing cheap investment strategies that allow to repli- cate the performance of an index or benchmark. Such strategies can be determined as solutions of a constrained optimization problem where the objective function to be minimized is a dis- tance measure between the index and the tracking portfolio. Beyond replicating the index performance, the tracking portfolio should be cheap to maintain and update, have low turnover, and should avoid large positions in few assets, as required by the European Union Directive UCITS (Undertaking for Collective Investments in Transferable Securities) rules. In this paper, we present the first mixed integer quadratic programming formulation for the constrained index tracking problem with the UCITS rule compliance. This allows us to obtain exact solutions for small and medium-size problems based on real-world datasets and to compare them with the ones provided by a state-of-art stochastic search heuristic.