Large-Scale Portfolio Optimisation with Heuristics

Abstract

Heuristic optimisation techniques allow to optimise financial portfolios with respect to different objective functions and constraints, essentially without any restrictions on their functional form. Still, these methods are not widely applied in practice. One reason for this slow acceptance is the fact that heuristics do not provide the “optimal” solution, but only a stochastic approximation of the optimum. For a given problem, the quality of this approximation depends on the chosen method, but also on the amount of computational resources spent (e.g., the number of iterations): more iterations lead (on average) to a better solution. In this paper, we investigate this convergence behaviour for three different heuristics: Differential Evolution, Particle Swarm Optimisation, and Threshold Accepting. Particular emphasis is put on the dependence of the solutions’ quality on the problem size, thus we test these heuristics in large-scale settings with hundreds or thousands of assets, and thousands of scenarios.