Differential Evolution and Combinatorial Search for Constrained Index Tracking

Index-tracking is a low-cost alternative to active portfolio management. The implementationof a quantitative approach, however, is a major challenge from an optimizationperspective. The optimal selection of a group of assets that can replicate the index ofa much larger portfolio requires both to find the optimal subset of assets and to fine-tunetheir weights. The former is a combinatorial, the latter a continuous numerical problem.Both problems need to be addressed simultaneously, because whether or not a selection ofassets is promising depends on the allocation weights and vice versa. Moreover, the problemis usually of high dimension. Typically, an optimal subset of 30–150 positions out of100–600 need to be selected and their weights determined. Search heuristics can be a valuablealternative to traditional methods, which often cannot deal with the problem. In thispaper, we propose a new optimization method, which is partly based on Differential Evolution(DE) and on combinatorial search. The main advantage of our method is that it cantackle the index-tracking problem as complex as it is, generating accurate and robust results.