Metaheuristics for portfolio optimization : application of NSGAII, SPEA2, and PSO algorithms

This work looks for the optimal allocation of different assets, namely, the G7 stock indices, commodities (gold and WTI crude oil), cryptocurrencies (Bitcoin and Ripple), and S&P Green Bond, over four periods: before the COVID-19 crisis, during the COVID-19 crisis and before the Russia-Ukraine war, during the COVID-19 crisis and Russia-Ukraine war, and after the COVID-19 pandemic and during the Russia-Ukraine war. Metaheuristics, Non-dominated Sorting Genetic Algorithm (NSGAII), Strength Pareto Evolutionary Algorithm (SPEA2), and Particle Swarm Optimization (PSO) are applied to find the best allocation. The results reveal that there a significant preference for the S&P Green Bond during the four periods of study according to three algorithms, thanks to its portfolio diversification abilities. During the COVID-19 pandemic and the geopolitical crisis, the most optimal portfolio was Nikkei 225 because of its quick recovery from the pandemic and poor reliance on the Russia-Ukraine markets, while WTI crude oil and both dirty and clean cryptocurrencies were poor contributors to the investment portfolio because these assets are sensitive to geopolitical problems. After the end of the pandemic and during the ongoing Russia-Ukraine war, the three algorithms obtained remarkably different results: the NSGAII portfolio was invested in various assets, 32% of the SPEA2 portfolio was allocated to the S&P Green Bond, and half of the PSO portfolio was allocated to the S&P Green Bond too. This may be due to changes in investors' preferences to protect their fortune and to diversify their portfolio during the war. From a risk-averse perspective, NSGAII does not underestimate the risk, while in terms of forecasting accuracy, PSO is an adequate algorithm. In terms of time, NSGAII is the fastest algorithm, while SPEA2 requires more time than the NSGAII and PSO algorithms. Our results have important implications for both investors and risk managers in terms of portfolio and risk management decisions, and they highlight the factors that influence investment choices during health and geopolitical crises.