Trapezoidal fuzzy efficiency and cross-efficiency data envelopment analysis with network structure in order to find the optimal investment portfolio

Increasing shareholders' wealth is one of the most important financial management goals. This matter is always intertwined with the concepts of risk and return simultaneously so that shareholders always seek to increase portfolio returns by controlling and minimizing risk or reducing risk at a certain level of expected return. For this purpose, investors mainly use the concepts of fundamental analysis, which means paying attention to the internal structure and financial performance of companies, or technical concepts, which means paying attention to the changes and price fluctuations of stocks in the market, or a combination of both methods. The main objective of the present research is to provide a combined model that pays attention to both financial structure as a fundamental approach and stock price fluctuations in the historical chart as a technical approach. Ultimately, using the network concept in data envelopment analysis, it aims to investigate the impact of financial performance on the company's market value.  In addition, the concept of trapezoidal fuzzy numbers has been used to consider the uncertainty in returns.

In this research, we will combine the Markowitz model with fuzzy returns and the network data envelopment analysis model to create a multi-objective model. By considering company performance based on certain financial ratios, its impact on stock market value, and price fluctuations, we aim to introduce stock portfolios in the best possible scenarios in terms of risk, return, and portfolio efficiency. Ultimately, to utilize the model for selecting an optimal stock portfolio, 50 companies from various industries actively traded on the Tehran Stock Exchange were chosen, and the proposed model was applied to them. Additionally, a multi-objective genetic algorithm with non-dominated sorting was employed to solve the model.

The results obtained from the implementation of the model on 50 companies active in the stock exchange show that the use of the proposed model has better results in terms of efficiency than the use of any of the Markowitz models or network data coverage analysis alone, and also compared to the non-network model. It provides investors with risk and efficiency and has a more comprehensive approach than the previously presented models.

Originality/Value:

 The current research introduces a model that simplifies the decision-making process for choosing the optimal portfolio by combining the views of investors with a fundamental approach and investors with a (technical) price volatility approach. The presented method tries to express the uncertainty in the returns in terms of trapezoidal fuzzy numbers and also measures the effect of the companies' efficiency on the market value and the increase of the shareholders' wealth by using the data envelopment analysis network model.