Time-limited Metaheuristics for Cardinality-constrained Portfolio Optimisation

TL;DR

This paper introduces a time-limited testing approach for metaheuristics in constrained portfolio optimization, comparing their performance within fixed computational durations to assess solution quality and speed.

Contribution

It proposes a standardized evaluation method for metaheuristics by limiting computation time, enabling fairer comparison of solution quality and efficiency.

Findings

Simulated annealing achieved near-optimal solutions within 5 seconds in most datasets.

Genetic algorithm produced the lowest quality solutions among tested metaheuristics.

Time limits of 1, 5, and 25 seconds reveal trade-offs between solution quality and computational speed.

Abstract

A financial portfolio contains assets that offer a return with a certain level of risk. To maximise returns or minimise risk, the portfolio must be optimised - the ideal combination of optimal quantities of assets must be found. The number of possible combinations is vast. Furthermore, to make the problem realistic, constraints can be imposed on the number of assets held in the portfolio and the maximum proportion of the portfolio that can be allocated to an asset. This problem is unsolvable using quadratic programming, which means that the optimal solution cannot be calculated. A group of algorithms, called metaheuristics, can find near-optimal solutions in a practical computing time. These algorithms have been successfully used in constrained portfolio optimisation. However, in past studies the computation time of metaheuristics is not limited, which means that the results differ in both quality and computation time, and cannot be easily compared. This study proposes a different way of testing metaheuristics, limiting their computation time to a certain duration, yielding results that differ only in quality. Given that in some use cases the priority is the quality of the solution and in others the speed, time limits of 1, 5 and 25 seconds were tested. Three metaheuristics - simulated annealing, tabu search, and genetic algorithm - were evaluated on five sets of historical market data with different numbers of assets. Although the metaheuristics could not find a competitive solution in 1 second, simulated annealing found a near-optimal solution in 5 seconds in all but one dataset. The lowest quality solutions were obtained by genetic algorithm.