Materiali di discussione Differential Evolution and Combinatorial Search for Constrained Index Tracking Differential Evolution and Combinatorial Search for Constrained Index Tracking

Thiemo Krink, Stefan Mittnik, Sandra Paterlini, Thiemo Krink, Stefan Mittnik, Sandra Paterlini
2008 unpublished
Index tracking is a valuable low-cost alternative to active portfolio management. The implementation of a quantitative approach, however, is a great challenge from an optimization perspective: the optimal selection of a group of assets that can replicate the index of a much larger portfolio requires both to find the optimal asset positions and to fine-tune their allocation weights. The former is a combinatorial problem, whereas the latter is a continuous numerical problem. Both optimization
more » ... th optimization problems need to be tackled simultaneously, because whether a selection of asset positions is promising or not depends on the actual allocations and vice versa. Moreover, the problem is usually high dimensional; typically an optimal subset of 30-150 positions out of 100-600 need to be selected and their asset allocation weights need to be determined. Search heuristics can be a viable and valuable alternative to traditional methods, which often cannot deal with the problem. In this work, we describe a new optimization method, which is partly based on Differential Evolution (DE) and on combinatorial search. The main advantages of our method are that it can tackle the index tracking problem as complex as it is while obtaining very accurate and robust results.