Portfolio Selection Problem Using CVaR Risk Measures Equipped with DEA, PSO, and ICA Algorithms

Abdelouahed Hamdi, Arezou Karimi, Farshid Mehrdoust and Samir Brahim Belhaouari
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Abdelouahed Hamdi: Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, Doha 2713, Qatar
Arezou Karimi: Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht P.O. Box 41938-1914, Iran
Farshid Mehrdoust: Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht P.O. Box 41938-1914, Iran
Samir Brahim Belhaouari: Division of Information and Computing Technology, College of Science and Engineering, Hamad Bin Khalifa University, Doha 582500, Qatar

Mathematics, 2022, vol. 10, issue 15, 1-26

Abstract: Investors always pay attention to the two factors of return and risk in portfolio optimization. There are different metrics for the calculation of the risk factor, among which the most important one is the Conditional Value at Risk (CVaR). On the other hand, Data Envelopment Analysis (DEA) can be used to form the optimal portfolio and evaluate its efficiency. In these models, the optimal portfolio is created by stocks or companies with high efficiency. Since the search space is vast in actual markets and there are limitations such as the number of assets and their weight, the optimization problem becomes difficult. Evolutionary algorithms are a powerful tool to deal with these difficulties. The automotive industry in Iran involves international automotive manufacturers. Hence, it is essential to investigate the market related to this industry and invest in it. Therefore, in this study we examined this market based on the price index of the automotive group, then optimized a portfolio of automotive companies using two methods. In the first method, the CVaR measurement was modeled by means of DEA, then Particle Swarm Optimization (PSO) and the Imperial Competitive Algorithm (ICA) were used to solve the proposed model. In the second method, PSO and ICA were applied to solve the CVaR model, and the efficiency of the portfolios of the automotive companies was analyzed. Then, these methods were compared with the classic Mean-CVaR model. The results showed that the automotive price index was skewed to the right, and there was a possibility of an increase in return. Most companies showed favorable efficiency. This was displayed the return of the portfolio produced using the DEA-Mean-CVaR model increased because the investment proposal was basedon the stock with the highest expected return and was effective at three risk levels. It was found that when solving the Mean-CVaR model with evolutionary algorithms, the risk decreased. The efficient boundary of the PSO algorithm was higher than that of the ICA algorithm, and it displayed more efficient portfolios.Therefore, this algorithm was more successful in optimizing the portfolio.

Keywords: portfolio optimization; DEA; PSO; ICA; CVaR (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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