Exploring the (Efficient) Frontiers of Portfolio Optimization

Abstract

The cardinality-constrained portfolio optimization problem is NP-hard. Its Pareto front (or the Efficient Frontier - EF) is usually calculated by stochastic algorithms, including EAs. However, in certain cases the EF may be decomposed into a union of sub-EFs. In this work we propose a systematic process of excluding sub-EFs dominated by others, enabling us to calculate non-dominated sub-EFs. We then calculate whole EFs to a high degree of accuracy for small cardinalities, providing an alternative to EAs in those cases. We can use also this to provide insight into EAs on the problem.