An exact algorithm for small-cardinality constrained portfolio optimisation

Abstract

Real-world portfolio optimisation problems are often NP-hard, their efficient frontiers (EFs) in practice being calculated by randomised algorithms. In this work, a deterministic method of decomposition of EFs into a short sequence of sub-EFs is presented. These sub-EFs may be calculated by a quadratic programming algorithm, the collection of such sub-EFs then being subjected to a sifting process to produce the full EF. Full EFs of portfolio optimisation problems with small-cardinality constraints are computed to a high resolution, providing a fast and practical alternative to randomised algorithms. The method may also be used with other practical classes of portfolio problems, complete with differing measures of risk. Finally, it is shown that the identified sub-EFs correspond closely to local optima of the objective function of a case study evolutionary algorithm.

Keywords:

• Portfolio selection
• cardinality constraint
• deterministic methods
• quadratic programming
• evolutionary algorithm
• operational research

Acknowledgements

The authors thank the Centre for Mathematical Sciences at the University of Plymouth for research support during the preparation of this work. Thanks also go to T. Alotaibi for translation of a preliminary version of the MAPLE code to the R language.

Disclosure statement

No potential conflict of interest was reported by the authors.