We study large-scale portfolio optimization problems in which the aim is to maximize a multi-moment performance measure extending the Sharpe ratio. More specifically, we consider the adjusted for skewness Sharpe ratio, which incorporates the third moment of the returns distribution, and the adjusted for skewness and kurtosis Sharpe ratio, which exploits in addition the fourth moment. Further, we account for two types of real-world trading constraints. On the one hand, we impose stock market restrictions through cardinality, buy-in thresholds, and budget constraints. On the other hand, a turnover threshold restricts the total allowed amount of trades in the rebalancing phases. To deal with these asset allocation models, we embed a novel hybrid constraint-handling procedure into an improved dynamic level-based learning swarm optimizer. A repair operator maps candidate solutions onto the set characterized by the first type of constraints. Then, an adaptive $$\ell _1$$ℓ 1 -exact penalty function manages turnover violations. The focus of the paper is to highlight the importance of including higher-order moments in the performance measures for long-run investments, in particular when the market is turbulent. We carry out empirical tests on two worldwide sets of assets to illustrate the scalability and effectiveness of the proposed strategies, and to evaluate the performance of our investments compared to the strategy maximizing the Sharpe ratio.

In this paper, the main goal is to tackle a sustainable portfolio optimization problem in which we aim to minimize a tail-dependence risk measure. More specifically, the considered risk measure is represented by the Delta Conditional Value-at-Risk, a tail-dependence measure meant to quantify the potential losses of a portfolio due to the riskiness associated with an individual asset or a group of assets. In addition, in the portfolio construction, we take into account some real-world trading constraints. On the one hand, we impose stock market restrictions through buy-in thresholds and budget constraints. Moreover, a minimum level of guaranteed expected return is required. On the other hand, a turnover threshold restricts the total amount of trades allowed in the rebalancing phases. Finally, in order to meet the growing appetite for sustainable investment, we introduce a green threshold into the portfolio’s design. To deal with these asset allocation models, in this paper we develop an improved hybrid Particle Swarm Optimizer (PSO) that is dynamically adjusted by a neural network architecture embedded with a suitable constraint-handling procedure. The neural network paradigm is fundamental for enhancing the basic PSO’s performance and improving the quality of estimating the Delta Conditional Value-at-Risk. Finally, we conduct empirical tests on two different American datasets to illustrate the effectiveness of the proposed strategies and evaluate the performance of our investments as the sustainable preferences vary.

In the last five years, extreme events such as the COVID-19 pandemic and the Ukrainian crisis have highlighted the importance of corporate social responsibility and sustainable principles. Consequently, the investment process is changing toward more ethical choices. In this context, we extend the classical optimization framework under the cumulative prospect theory (CPT) in two directions. We first consider an agent who maximizes a financial CPT-value function preselecting the assets to be included in the portfolio based on their environmental, social, and governance (ESG) scores. Then, we develop a bi-objective model that optimizes financial and sustainable CPT-value functions at the same time. Numerical results obtained on an investable universe from the constituents of the STOXX Europe 600 show that introducing ESG information improves the portfolio’s financial performance. JEL classification numbers: C63, G11, G17. Keywords: Cumulative prospect theory, ESG scores, portfolio optimization, genetic algorithm, European stock exchange.