markowitz mean-variance model

This study introduces a novel approach integrating a support vector machine (SVM) with an optimal portfolio construction model. Leveraging the Radial Basis Function (RBF) kernel, the SVM identifies assets with higher growth potential. However, due to inherent uncertainties, some input points may not be precisely classified into their respective classes in various applications. To mitigate the influence of noise, a new fuzzy support vector machine (NFSVM) is employed to select assets. Here, each sample point is assigned a membership value using a fuzzy membership function, as documented in existing literature [1]. Additionally, the SVM model incorporates principal component analysis (PCA)to eliminate correlated technical indicators. Further, Markowitz’s mean-variance model (MV model) with cardinality constraints and without cardinality constraints is employed for the assets selected by SVM, FSVM, and NFSVM for optimal portfolio construction.The performance of the proposed model is experimentally assessed using a data set derived from the Nifty 50 and Euro Stoxx 50 index. The experimental results demonstrate that the optimal portfolio obtained from the NFSVM with the Markowitz mean-variance model outperforms the one generated by the SVM. This outcome substantiates the effectiveness and efficiency of the proposed model as an advanced approach for optimizing investment portfolios.

In the dynamic world of financial investment, crafting an optimal stock portfolio that judiciously balances risk, return, and efficiency emerges as a critical challenge. Despite the wealth of research on financial portfolio optimization, prevailing methodologies predominantly emphasize either risk minimization or return maximization, often overlooking the imperative for a holistic strategy that simultaneously boosts efficiency and effectiveness. Addressing this gap in the literature, this study introduces an innovative four-objective model that intricately blends risk, return, and efficiency considerations for the strategic selection of stock portfolios. This model ingeniously integrates the foundational principles of Markowitz's mean-variance analysis with the sophisticated network data envelopment analysis (NDEA) techniques, significantly refining the portfolio selection methodology. It further distinguishes itself by incorporating returns represented as trapezoidal intuitionistic fuzzy numbers, adeptly capturing the inherent uncertainties in financial returns. Additionally, the model employs the network data envelopment analysis's cross-efficiency principle, providing a nuanced measure of company performance. To effectively navigate the complexities of this model, we deploy the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and a multi-objective genetic algorithm, demonstrating the model's capability to unearth optimal solutions efficiently. The comparative analysis highlights that the proposed model significantly outperforms the efficiency and effectiveness of existing models, marking a substantial advancement in portfolio optimization strategies.