A squirrel search algorithm for the multi-objective portfolio optimisation with transaction costs

Abstract

Portfolio optimisation (PO) is the problem of deciding how much of an investor’s wealth should be invested in each asset amongst a universe of assets so as to obtain a reasonable trade-off between return and risk objectives. In this paper, we address this problem including real-life constraints such as cardinality, quantity and pre-assignment constraints by making use of an improved version of the Squirrel Search Algorithm (SSA) described in the literature. The novelty of this work is the application of the improved SSA in the multi-objective portfolio optimisation problem together with transaction costs. There are four major improvements from the classical SSA with the aim of better global convergence ability. The first improvement is to consider the predator presence probability as a variable, the second is to generate the squirrels’ position by using a cloud generator. The third and fourth improvements consist of selecting the best squirrel following successive iteration and to find the optimal dimensions of the position of the best flying squirrel. We test the performance of the algorithm with seven publicly available datasets drawn from two different sources and compare the results with well-known heuristics and the standard SSA. The results obtained proved the efficacy and superiority of the improved algorithm considering both the cases with and without transaction costs. The improved SSA (ISSA) obtained smaller generational distance and inverted generational distance when compared to SSA for most of the test problems except for the S&P 100 index. In terms of the hypervolume indicator it can be seen that the ISSA outperformed all the algorithms as it obtained higher values for all the test problems. For the spacing metric ISSA performed better for most datasets.