حسن قدرتی قزاانی

This paper aims to investigate the portfolio optimization under various market risk conditions using copula dependence and extreme value approaches. According to the modern portfolio theory, diversifying investments in assets that are less correlated with one another allows investors to assume less risk. In many models, asset returns are assumed to follow a normal distribution. Consequently, the linear correlation coefficient explains the dependence between financial assets, and the Markowitz mean-variance optimization model is used to calculate efficient asset portfolios. In this regard, monthly data-driven information on the top 30 companies from 2011 to 2021 was the subject to consideration. In addition, extreme value theory was utilized to model the asset return distribution. Using Gumbel’s copula model, the dependence structure of returns has been analyzed. Distribution tails were modeled utilizing extreme value theory. If the weights of the investment portfolio are allocated according to Gumbel’s copula model, a risk of 2.8% should be considered to obtain a return of 3.2%, according to the obtained results.

The purpose of this study is to make investment decisions with the approach of data envelopment analysis and making decision on selection of optimal stock portfolio employing meta heuristic algorithms for multi-objective functions subject to real-life constraints. The statistical population of this research in capital decision-making and selection of the optimal capital composition is 183 of the selected companies of Tehran Stock Exchange, which were finally 42 companies as justified investment options. After measuring the risk and return of efficient companies, the real limitations of the budget, requirements and expectations of the investor, determination and composition of the investment were formulated as a multi-objective model. For optimal decision, the modified genetic meta heuristic algorithm and MATLAB software with dual operators were used. Elimination of the risk minimization function in sensitivity analysis improved the level of decision return but also led to more risk. Eliminating the maximizing return function improved decision-making risk but also reduced investment return. Elimination of investment requirements and expectations improved returns and increased investment risk, but more companies became involved in optimal investment.

One of the main concerns of investors is the evaluation of the return on investment, which is conducted using various models such as the CAPM (single-factor model), Fama-French three/five-factor models, and Roy and Shijin’s six-factor model and other models known as multi-factor models. Despite the widespread use of these models, their major drawbacks include sensitivity to unexpected changes, sudden shocks, high turbulence of price bubble, and so on. To eliminate such negatives, the multi-factor model using the penalty function method is used, in which, instead of averaging, the optimization and avoidance of the effects of abnormal changes and other factors affecting the capital market are considered. In order to evaluate stock returns, it is possible to select effective factors, to simulate and develop a model appropriate to the conditions governing the capital market in Iran. In the present study, by forming portfolios of investments and identifying and refining effective factors, the classification and estimation of the hybrid model of penalty and multi-factor (P & PCA) functions were performed based on the functional data during 2007-2017. The results of this study indicated that the extensive use of the simulation algorithm for the penalty function in the form of P & PCA estimation method improves the efficiency of multi-factor methods in stock return evaluation, and that the use of the hybrid algorithm of penalty and multi-factor functions, compared to the exclusive use of multi-factor models, brings a higher accuracy in estimating stock returns.