Index tracking optimization with cardinality constraint: a performance comparison of genetic algorithms and tabu search heuristics

The aim of this study was to compare the performance of the well-known genetic algorithms and tabu search heuristics with the financial problem of the partial tracking of a stock market index. Although the weights of each stock in a tracking portfolio can be efficiently determined by means of quadratic programming, identifying the appropriate stocks to include in the portfolio is an NP-hard problem which can only be addressed by heuristics. Seven real-world indexes were used to compare the above techniques, and results were obtained for different tracking portfolio cardinalities. The results show that tabu search performs more efficiently with both real and artificial indexes. In general, the tracking portfolios obtained performed well in both in-sample and out-of-sample periods, so that these heuristics can be considered as appropriate solutions to the problem of tracking an index by means of a small subset of stocks.

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