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