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.

This paper introduces a two-phase decision support system based on information theory and financial practices to assist investors in solving cardinality-constrained portfolio optimization problems. Firstly, the approach employs a stock-picking procedure based on an interactive multi-criteria decision-making method (the so-called TODIM method). More precisely, the best-performing assets from the investable universe are identified using three financial criteria. The first criterion is based on mutual information, and it is employed to capture the microstructure of the stock market. The second one is the momentum, and the third is the upside-to-downside beta ratio. To calculate the preference weights used in the chosen multi-criteria decision-making procedure, two methods are compared, namely equal and entropy weighting. In the second stage, this work considers a portfolio optimization model where the objective function is a modified version of the Sharpe ratio, consistent with the choices of a rational agent even when faced with negative risk premiums. Additionally, the portfolio design incorporates a set of bound, budget, and cardinality constraints, together with a set of risk budgeting restrictions. To solve the resulting non-smooth programming problem with non-convex constraints, this paper proposes a variant of the distance-based parameter adaptation for success-history-based differential evolution with double crossover (DISH-XX) algorithm equipped with a hybrid constraint-handling approach. Numerical experiments on the US and European stock markets over the past ten years are conducted, and the results show that the flexibility of the proposed portfolio model allows the better control of losses, particularly during market downturns, thereby providing superior or at least comparable ex post performance with respect to several benchmark investment strategies.

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 ℓ₁-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. 2020 Mathematics Subject Classification: 90C59 (primary); 91G10, 68W50, 90C26 (secondary)

In this work, we propose a hybrid variant of the level-based learning swarm optimizer (LLSO) for solving large-scale portfolio optimization problems. Our goal is to maximize a modified formulation of the Sharpe ratio subject to cardinality, box and budget constraints. The algorithm involves a projection operator to deal with these three constraints simultaneously and we implicitly control transaction costs thanks to a rebalancing constraint. We also introduce a suitable exact penalty function to manage the turnover constraint. In addition, we develop an ad hoc mutation operator to modify candidate exemplars in the highest level of the swarm. The experimental results, using three large-scale data sets, show that the inclusion of this procedure improves the accuracy of the solutions. Then, a comparison with other variants of the LLSO algorithm and two state-of-the-art swarm optimizers points out the outstanding performance of the proposed solver in terms of exploration capabilities and solution quality. Finally, we assess the profitability of the portfolio allocation strategy in the last five years using an investible pool of 1119 constituents from the MSCI World Index.