Cardinality Constraints for Markowitz Efficient Lines

5.5 Conclusion

In this chapter a meta-heuristic was presented that basically combines principles from Simulated Annealing with evolutionary strategies and that uses additional modifications. Having applied this algorithm to the problem of portfolio selection when there are constraints on the number of different assets in the portfolio and non-negativity of the asset weights, we find this algorithm highly efficient and reliable. Furthermore, it is shown that the introduction of evolutionary principles has significant advantages.

The algorithm is flexible enough to allow for extensions in the optimization model by introducing additional constraints such as transaction costs, taxes, upper and/or lower limits for weights, alternative risk measures and distributions of returns, etc. First tests with such extensions led to promising results and supported the findings for the algorithm presented in this chapter.