Advances in Mathematical Finance and Application (AMFA)

Advances in Mathematical Finance and Application (AMFA)

Advances in Mathematical Finance and Application, Volume 8, Issue 3, Summer 2023 (مقاله علمی وزارت علوم)

مقالات

۱.

A review of meta-heuristic methods for solving location allocation financial problems(مقاله علمی وزارت علوم)

کلید واژه ها: Location routing meta-heuristic Hybridization Financial problems

حوزه های تخصصی:
تعداد بازدید : ۱۲۷ تعداد دانلود : ۹۹
In this article, we will examine the financial issues related to multi-period routing and positioning and the related costs, and we will examine the related limitations. These decisions are made about location allocation, inventory and routing in a three-tier supply chain, including suppliers, warehouses and customers. We are looking for new ways to make location and routing decisions simultaneously and efficiently. In order to maximize the search space and achieve optimal results, exploratory and meta-heuristic methods have been used. The meta-heuristic technique is usually used to increase the performance of the hybrid technique. Therefore, this paper provides an overview of meta-heuristic methods and their combination to solve problems. It also examines the advantages and disadvantages of the proposed methods to solve these problems in order to provide more efficient methods.
۲.

Explaining stock anomalies using multifactorial asset pricing models(مقاله علمی وزارت علوم)

کلید واژه ها: Excess stock returns multifactorial models stock anomalies unexplained returns

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تعداد بازدید : ۱۹۰ تعداد دانلود : ۱۱۱
This study investigates the effects of stock anomalies on excess stock and unexplained returns of multifactorial models in the companies listed at the Tehran Stock Exchange. We selected a sample of 120 companies listed at the Tehran Stock Exchange from 2008 to 2019 using the Fama-Macbeth [18] regression approach. The results revealed that stock anomalies led to considerable differences in excess stock returns of different portfolios, implying that stock returns at different anomaly levels significantly differ. In addition, it was found that the anomalies related to stock characteristics greatly impacted explaining excess stock returns in the three-factor and five-factor models suggested by Fama and French. Besides, in different portfolios of the anomalies, the unexplained return rates were significantly different from each other. Moreover, in Fama and French's three-factor and five-factor models, different anomaly portfolios show significant differences in explaining excess stock returns.
۳.

The Empirical Test of the relationship between information asymmetry, Overvalued Equities and Stock Price Crash Risk(مقاله علمی وزارت علوم)

کلید واژه ها: stock price Crash risk Equity overvaluation information asymmetry

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تعداد بازدید : ۱۱۷ تعداد دانلود : ۸۲
This study examines empirically the effect of equity overvaluation on future stock price crash risk in companies with greater information asymmetry. Using the information asymmetry and crash risk indicators, the question that whether overvalued firms are more prone to future crash risk is investigated. Accordingly, the first purpose of this study is to investigate the relation between overvaluation and the future stock price crash risk. With the increase of information asymmetry between a firm and the market, managers have more abilities and opportunities to withhold bad news and accelerating the release of good news. As a result, it is expected that the information asymmetry between managers and investors increases future stock price crash risk. In so doing, we identify one main hypothesis and three subsidiary ones and the data of 111 listed companies of Tehran Stock Exchange for the period between 2009 and 2017 were analyzed and A panel data approach has been used to test of research hypotheses. According to the results, there is a positive and significant relationship between the overvaluation and the future stock price crash risk of companies which are operating in monopolistic markets and this relation intensified by the information asymmetry.
۴.

Performance Analysis and Sustainability Assessment of International Markets: Iran versus some other countries(مقاله علمی وزارت علوم)

کلید واژه ها: Performance in international markets Economic and non-economic indicators Performance sustainability Performance of Iran

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تعداد بازدید : ۱۱۱ تعداد دانلود : ۱۰۷
Evaluating the performance of countries in international markets and measuring how they utilize allocated resources provides a lucid picture of the state of business management in countries also assessing performance sustainability in international markets, is one of the important issues in predicting international trade. In international markets knowledge of countries' performance leads to the recognition of their economic and non-economic management statuses even more it is used to allocate financial support of global organization. In the present article, an attempt was made to design a model capable of examining the performance of nations in international markets by both economic and non-economic dimensions in the presence of undesirable factors and two preparation and exploitation stages of existing platforms and also assessing the sustainability of countries' performance in the studied period which is quite innovative. Then, data from 21 countries, from 2010 to 2017 were evaluated to test the model. The results indicated that the model is capable of examining the performance of countries and assess the sustainability of the countries over a period of time. According to the results of this model, an attempt was made to evaluate Iran's performance status among homogeneous countries and provide a roadmap for enhancing Iran's performance
۵.

A Mathematical Model for Measuring Corporate Governance using Multi-Criteria Decision Making (MCDM)Technique(مقاله علمی وزارت علوم)

کلید واژه ها: Corporate Governance Comprehensive index for corporate Governance Multi-criteria decision model

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تعداد بازدید : ۱۲۱ تعداد دانلود : ۱۰۷
There has not been presented any comprehensive index for Corporate Governance in spite of its crucial role in resolution and responsiveness. Although diverse methods have been sought for measuring the Corporate Governance in the previous studies, in this study, a comprehensive index is proposed for measuring Corporate Governance taking other indexes into account through mathematical equations. For testing the designed model’s functionality, a set of data related to 149 firms from 2014 to 2019 has been used jointly, too. To do so, a questionnaire, which asks the experts their idea about the weight and significance of the criteria of measuring the Corporate Governance of the firm, is made and distributed and the weight and significance of the criteria were determined through one method of multi-criteria decision model (Shannon Entropy). To measure the changeable hidden relationship which exists in this study of the Corporate Governance, provided with the measurement items, a confirmatory factorial analysis was taken, too; results show that the supposed model has been a proper index for Corporate Governance. This mixed index includes criteria such as the board of directors' size, independence, meetings, and its education, the CEO's permanence, the size, independence, financial specialty, financial experience, tenure and the meetings of the auditors hip committee, ownership concentration, organizational ownership, governmental ownership, deals with the dependent persons, the quality of the disclosure, proper information and weaknesses if the internal controls,
۶.

The role of effective variables on the relationship between tax avoidance and investment efficiency(مقاله علمی وزارت علوم)

کلید واژه ها: Tax Avoidance investment efficiency comparability Readability of Financial Statements information environment competitive power

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تعداد بازدید : ۱۴۱ تعداد دانلود : ۹۶
The present study explained the effective components' role in the relationship between investment efficiency and tax avoidance. The study's statistical population is the firms listed on the Tehran Stock Exchange. Using the systematic elimination sampling method, 128 companies were selected as the research sample in the 8 years between 2014 and 2021. Data for measuring the variables were collected from the Codal website and the companies' financial statements; preliminary calculations were made in Excel; then, the research hypotheses were analysed and tested using a multivariate regression model with panel data in Stata and Eviwes software. The results show that tax avoidance has a negative effect on investment efficiency. Also, the comparability and readability of financial statements have an inverse effect on the relationship between tax avoidance and investment efficiency. It can be concluded that the comparability and readability of financial statements weaken the inverse relationship between tax avoidance and investment efficiency. Other findings showed that the company's information environment has a direct and significant effect on the relationship between tax avoidance and investment efficiency, and competitive power does not significantly affect the relationship between tax avoidance and investment efficiency.
۷.

CEO Overconfidence and Over investment: Role of Exchange Rate(مقاله علمی وزارت علوم)

کلید واژه ها: CEO overconfidence Over investment Exchange Rate

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تعداد بازدید : ۱۱۳ تعداد دانلود : ۹۶
The financial anomalies, which have brought about challenges for the nature of efficient-market hypothesis, provide ample experimental evidence on the deviation of market from rationality. According to the efficient-market hy-pothesis, investors avail themselves of all the information available in the market, and then attempt a thorough and painstaking interpretation of it. The empirical evidence, however, reveals that most investors fail to imple-ment rigorous information processing, thereby rendering to a number of behavioral theories concerning market inefficiency and biased information processing. The current research sets out to identify and scrutinize the im-pact of the CEO’s perceptual biases in judgment and economic decision-making on the reporting quality of the firms listed on the Tehran Stock Ex-change. The Purpose of this study CEO Overconfidence and Overinvestment by Role of Economic moderators Tehran Stock Exchange (TSE). One hun-dred five companies were selected as the sample size by systematic removal sampling reviewed in 2012-2019. Due to its dichotomous dependent variable, this study uses probit regression to test the research hypotheses. The results indicated the significant positive effect of CEO overconfidence on overin-vestment. It was also noted that Exchange Rate strengthens the positive effect of CEO overconfidence on overinvestment. Based on these results, the CEO's decisions as a decision-maker in charge of any company, especially under inflationary conditions, can play a substantial role in future corporate investment levels. The findings reveal that the indices of the CEO’s percep-tual biases in judgment and economic decision-making exert a significantly negative effect on financial reporting reliability and competitiveness.
۸.

Sociological Analysis of Accounting Measurement Theories(مقاله علمی وزارت علوم)

کلید واژه ها: Accounting Measure Theories Sociological Paradigms positivism interpretive thematic analysis

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تعداد بازدید : ۱۵۲ تعداد دانلود : ۱۲۲
Due to the existence of various paradigms and theories in accounting and various methods introduced to measure accounting values, as well as the lack of a complete and well-defined framework of these theories in terms of sociological paradigms, we decided to analyze sociology from theories. To achieve this goal, we used the content analysis method. In this way, first by examining the schools and theories of sociology and the main paradigm of positivism, interpretiveness, identification and components that were the characteristics of these paradigms were extracted and categorized from the themes and then the outputs were approved by sociology professors. And then accounting measurement theories and various theories using the method of taking notes from books and texts and articles extracted and sociological components in the context of accounting theories are searched and analyzed and at the end of accounting theories according to The extracted themes and their analytical codes are classified and analyzed and interpreted based on the obtained results. The results of the analysis of themes, new theories of accounting measurement tend to interpretism in which the role of the accountant is more prominent and historical cost theory is classified as a positivist sociological theory.
۹.

Determining the appropriate weights of criteria in multi-criteria decision-making using cooperative game: A case study of bank(مقاله علمی وزارت علوم)

کلید واژه ها: Data encelopment analysis Shannon Entropy Shapley value TOPSIS

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تعداد بازدید : ۱۲۵ تعداد دانلود : ۷۹
Criteria weighting is a crucial step in the entire decision-making process. Determining the appropriate weights will lead to more reliable results. This study aims to use a coalitional game method for calculating proper criteria weights in multi-criteria decision-making (MCDM). In this paper, the Shapley value method is used to determine the weight of criteria. A numerical case study of 65 banks has been used to explain the efficiency of the proposed method. To this end, using the TOPSIS technique, the alternatives are ranked once in Shapley value and again in the Shannon entropy weighted matrix. Then the results are obtained applying Spearman rank correlation coefficient are compared to efficiency-based ranking using data envelopment analysis (DEA) as a powerful benchmarking method. In the proposed method, unlike many conventional weighting methods, the selection of criteria weights is made in a coalitional game with the participation of all criteria; the obtained weights are both intuitively and objectively fairer, and more reliable rankings are provided. According to the logical and fair calculation of weights, having a simple and understandable mathematical method, and no need for experts’ judgment, the proposed method can be used in real problems. Especially where realistic ranking has a significant impact on the equitable allocation and absorption of resources.
۱۰.

Predicting the Top and Bottom Prices of Bitcoin Using Ensemble Machine Learning(مقاله علمی وزارت علوم)

کلید واژه ها: Algorithmic Trading top and bottom price prediction ensemble machine learning Xgboost LightGBM

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تعداد بازدید : ۱۴۱ تعداد دانلود : ۱۲۰
The purpose of the present study is to use the ensemble learning model to combine the predictions of Random Forest (RF), Long-Short Term Memory (LSTM), and Recurrent Neural Network (RNN) models for the Top and Bottom Prices of Bitcoin. To this aim, in the first stage, Bitcoin's top and bottom prices are predicted using three machine learning models. In the second stage, the outputs of the models are presented as feature variables to the Extreme Gradient Boosting (Xgboost) and Light Gradient Boosting Machine (LightGBM) models to predict the price tops and bottoms. Then, in the third stage, the outputs of the second stage are combined through the voting ensemble classifier pattern to predict the next top and bottom prices. The data of top and bottom Bitcoin prices in the 1-hour time frame from 1/1/2018 to the end of 6/30/2022 are used as target variables and 31 technical analysis indicators as feature variables for the three models in the first stage. 70% of the data is regarded as learning data, and the remaining 30% is considered for the second and third stages. In the second phase, 50% of the data is considered for learning the output of the previous stage and 50% for the test data. Finally, the prediction values are evaluated with real data for the three models and the proposed ensemble learning model. The results reveal the improvement of the performance, precision, and accuracy of the ensemble model compared to weak learning models.
۱۱.

Evaluating the Performance and Ability Explain of Market Index Returns by Selected Stock Portfolios Based on Throughput Accounting Criteria in Comparison with the New Network Matrix Model(مقاله علمی وزارت علوم)

کلید واژه ها: Active Portfolio Management New Network Matrix Model Throughput Accounting Portfolio performance

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تعداد بازدید : ۱۲۱ تعداد دانلود : ۱۰۶
One of the strategies used in active portfolio management is the "network matrix model "which can be used to form different portfolios with different characteristics of stocks or companies. In this study, with the data of 156 companies listed on the Tehran Stock Exchange during the period 2011 to 2018 using the network matrix model and based on throughput accounting criteria, portfolio formation and their performance with the portfolios of the new network matrix model (Defensive, neutral and aggressive stocks) and market portfolio were compared. The results show that the proposed network matrix model portfolios based on throughput accounting criteria have higher performance than the new network matrix model in terms of Sharpe, Sortino, upside potential, and omega criteria. Also, portfolios consisting of stocks of companies with high system performance, in addition to the above criteria, have higher performance in terms of Jensen's Alpha criteria than the new network matrix model, and in terms of upside potential and omega criteria, have higher performance than the market portfolio. The performance of portfolios consisting of stocks of companies with low system performance has a stronger correlation with the market portfolio compared to the new network matrix model.
۱۲.

Optimization of estimates and comparison of their efficiency under stochastic methods and its application in financial models(مقاله علمی وزارت علوم)

کلید واژه ها: Stochastic Differential Equation random sequence Quasi-random sequence (Quasi) Monte Carlo simulation

حوزه های تخصصی:
تعداد بازدید : ۷۲ تعداد دانلود : ۵۸
In this paper, first, the stochastic differential equations are introduced as well as the definition and basic theories about Monte Carlo and quasi-Monte Carlo and Sobel and Halton sequences are expressed. Indeed, we introduce and use simulations under these methods to compare the efficiency of the solutions, which the results show that the approximation of the resulting Sobel sequence is much better than other stochastic methods. The comparison of the efficiency of random and quasi-random methods, the geometric Brownian movement and the price index of Tehran stock (equal weight and weight-value) is studied. The results show that the quasi-Monte Carlo method is better than other methods.
۱۳.

Deep Learning Application in Rainbow Options(مقاله علمی وزارت علوم)

کلید واژه ها: deep learning European options Asian options Monte-Carlo simulation descent gradient method

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تعداد بازدید : ۸۸ تعداد دانلود : ۷۶
Due to the rapid advancements in computer technology, researchers are attracted to solving challenging problems in many different fields. The price of rainbow options is an interesting problem in financial fields and risk management. When there is no closed-form solution to some options, numerical methods must be used. Choosing a suitable numerical method involves the most appropriate combination of criteria for speed, accuracy, simplicity and generality. Monte Carlo simulation methods and traditional numerical methods have expensive repetitive computations and unrealistic assumptions on the model. Deep learning provides an effective and efficient method for options pricing. In this paper, the closed-form formula or Monte-Carlo simulation are used to generate data in European and Asian rainbow option prices for the deep learning model. The results confirm that the deep learning model can price the rainbow options more accurately with less computation time than Monte-Carlo simulation.
۱۴.

Designing a Model of Financial Flexibility Functions for Industrial Infrastructure Development of Abadan Oil Refining Company(مقاله علمی وزارت علوم)

کلید واژه ها: Propositional Themes of Financial Flexibility Functions Total Interpretive Structural Modelling Abadan Oil Refining Company

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تعداد بازدید : ۹۲ تعداد دانلود : ۷۰
The purpose of this study was designing a model of financial flexibility functions for industrial infrastructure development of َAbadan oil refining com In this study,12 financial management specialists at the university level and the company participated as panel members in the quality department. In fact, in the qualitative part, which used Meta-synthesis and Delphi analysis, the aim was to identify the propositions of financial flexibility functions for the development of industrial infrastructure, and then in a small part with the participation of 18 managers and deputies of Abadan Oil Refining Company, Findings: Therefore, relying on meta-synthesis, first 14 studies were reviewed as a basis for evaluation to determine the themes of the statements of financial flexibility functions for the development of industrial infrastructure in the form of critical evaluation, based on which, 24 themes of selected propositions were entered into Delphi analysis in a checklist manner to determine the theoretical adequacy. In this stage, 4 propositions were removed during the two stages of Delphi analysis and a total of 20 propositions entered the quantitative analysis section, ie Total Interpretive Structural Modelling. In this section, the results show the themes of the statements of financial agility in the development of industrial infrastructure (P12); Reduction of financial constraints in providing resources for industrial infrastructure development (P17) and dynamics of evaluation of industrial infrastructure development plans (P18) were selected as the last level of the most effective reasons for financial flexibility for industrial infrastructure development in Abadan Oil Refining Company.
۱۵.

Stock Liquidity and Return Predictability; Is There a Connec-tion? (Evidence from an Emerging Market)(مقاله علمی وزارت علوم)

کلید واژه ها: Liquidity spread Return Predictability market efficiency Tehran Stock Exchange

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تعداد بازدید : ۸۵ تعداد دانلود : ۱۱۲
This study examines the relationship between stock liquidity and return predicta-bility of 116 publicly-traded firms in Tehran Stock Exchange (TSE). To this end, we constructed a dated-regular frequency of time series with total 40128 stock-firm observations. After calculating daily bid-ask spreads and stock returns, the observations were classified based on liquidity into three classes and the return predictability was investigated across different classes using a set of parametric tests. The results exhibit signs of return autocorrelation and non-independence over three liquidity groups. Our findings didn’t show a connection between stock liquidity and market efficiency. The Hurst exponent also revealed mean reversion of returns series across different liquidity classes. We conclude that stock liquidity doesn’t play a significant role in market efficiency and return predictability of stocks in TSE. In case of TSE as other emerging markets, due to the small num-ber of traders (the need for more trading activity) and low market making activi-ties, both the cost of trading increases and the reaction to stock price information is delayed, resulting in predictability of price /return.
۱۶.

Modelling Optimal Predicting Future Cash Flows Using New Data Mining Methods (A Combination of Artificial Intelligence Algorithms)(مقاله علمی وزارت علوم)

کلید واژه ها: Future Cash Flows Neural Network Model Genetic Algorithm Particle swarm Algorithm

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تعداد بازدید : ۱۳۰ تعداد دانلود : ۱۰۴
The purpose of this study was to present an optimal model Predicting Future Cash Flows optimized neural network with genetic (ANN+GA) and particle swarm algorithms (ANN+PSO). In this study, due to the nonlinear relationship among accounting information, we have tried to predict future cash flows by combining artificial intelligence algorithms. Variables of accruals components and operating cash flows were employed to investigate this prediction; therefore, the data of 137 companies listed in Tehran Stock Exchange during (2009-2017) were analysed. The results of this study showed that both neural network models optimized by genetic and particle swarm algorithms with all variables presented in this study (with 15 predictor variables) are able to provide an optimal model Predicting Future Cash Flows. The results of fitting models also showed that neural network optimized with particle swarm algorithm (ANN+PSO) has lower error coefficient (better efficiency and higher prediction accuracy) than neural network optimized with ge-netic algorithms (ANN+GA).
۱۷.

Using A Multivariate Statistical Method of Factor Analysis and Grounded Theory to Review the Theory of Agency in Developing Countries (A Case Study of Iran)(مقاله علمی وزارت علوم)

کلید واژه ها: Agency Theory Corporate Governance Reward Risk Aversion Supervision

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تعداد بازدید : ۱۱۱ تعداد دانلود : ۱۲۱
The asymmetry of information between managers and shareholders significantly affects the company's investment decisions and exacerbates the problems of agency. It seems that these problems in developing markets such as Iran are more than developed markets. This research is an exploratory study, and it aims at reviewing the theory of agency in Iran. In the present study, based on the research paradigm, first, data acquisition strategy is selected based on a qualitative approach, and then qualitative study and analysis, quantitative approach, and factor analysis approach have been used to confirm the validity of the extracted model. Statistical analysis of research data shows that among the hypotheses of agency theory, risk aversion, supervision, and reward are revised dimensions in Iran like examples of developing countries.The results confirm the existence of assumptions; 1. Conflict of interests of manager and owner, 2. Information asymmetry, 3. Reverse choice, 4. Ethical risk, 5. Maximizing the expected utility, 6. Forcing and 7. Failure to confirm the assumption is the ability to predict the future and receive information. due to the existence of information asymmetry, higher investment risks of minority shareholders and transparency problems, the lack of ability to predict the future and receive information is necessarily confirmed.
۱۸.

Selecting The Optimal Multi-Period Stock Portfolio with Different Time Horizons in the Credibility Theory Framework(مقاله علمی وزارت علوم)

کلید واژه ها: Multi-period Portfolio different time horizons fuzzy variables credibility theory

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تعداد بازدید : ۱۰۰ تعداد دانلود : ۷۴
After closing, the multi-period portfolio can be corrected and revised at regular intervals. The philosophy behind using multi-period portfolio models is that investors often have a multi-period view of future changes in assets, which can be the result of technical and fundamental analysis or statistical model analysis. In conventional multi-period portfolio models, it is assumed that the forecast and correction time horizons are the same for all assets. However, one asset may be forecasted over a one-month horizon while another may be forecasted over a two-month horizon, and both may be revised in the future. The purpose of this study is to present a multi-period portfolio model in which assets have different time horizons for corrections or an asset may not be traded for the first few periods and then enter the correction stage. In this model, fuzzy variables defined in a credibility space are used to describe the return, and the credibility measure controls the risk. The model's objective function is to maximize the portfolio's ultimate wealth, and a constraint is used to control portfolio risk, in which the validity of the portfolio's ultimate wealth below a certain threshold is controlled at a certain level of confidence. A combination of particle swarm optimization and simulation is used to find the best solution. Finally, using a numerical example, the model is implemented on a portfolio with 6 assets and 4 monthly time steps on the Tehran Stock Exchange.
۱۹.

Presenting financial and non-financial indices model affecting the credit risk on the Maskan Bank(مقاله علمی وزارت علوم)

کلید واژه ها: Financial and non-financial indicators Credit risk Maskan Bank

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تعداد بازدید : ۹۱ تعداد دانلود : ۱۰۱
Providing credit facilities to clients can be regarded as one of the most important tasks of banks. As a result, the current research is carried out with the aim of developing a model of financial and non-financial factors that influence credit risk in the Maskan Bank. This study was divided into two sections: qualitative and quantitative. In the qualitative portion, the Delphi technique was used to identify financial and non-financial variables impacting credit risk in the Maskan Bank by interviewing 18 experts. In the quantitative section, the selected components of the questionnaire were initially created in a 5-point Likert scale. The questionnaire was then presented to 361 legal clients of Maskan Bank from the statistical sam-ple of the quantitative section. The quantitative component was completed using LISREL software and modeling the structural equations of SEM. Three primary components (financial, market, and management) and 33 sub-components were identified as financial and non-financial indicators impacting credit risk based on the results of the qualitative section. The quantitative findings also revealed that the indicators of guarantee status in the financial component, price level in the market component, and manpower motivation and productivity, as well as man-agement continuity and trade in the management component, had the largest factor loads.
۲۰.

Comparative evaluation of the performance of selected portfoli-os based on AHP and Topsis multi-criteria decision-making techniques with Markowitz mean-variance model(مقاله علمی وزارت علوم)

نویسنده:

کلید واژه ها: Analytic hierarchy process TOPSIS Markowitz Optimization Model Portfolio Performance Evaluation

حوزه های تخصصی:
تعداد بازدید : ۷۶ تعداد دانلود : ۷۴
In this research, using Analytic Hierarchy Process (AHP) and TOPSIS method (TOP) based on financial criteria, earnings per share, dividend per share, operating cash flow growth, earnings per share growth, beta (systematic) risk, volatility Operating profit, stock liquidity and price-to-earnings ratio selected according to the opinions of investment experts, formed a portfolio. Then, the criteria for evaluating the performance of risk-adjusted portfolios according to modern portfolio theory (Sharp, Trainer and Alpha Jensen) were calculated based on monthly stock prices during the 5-year period from 1393 to 1397 and com-pared with the criteria for evaluating portfolio performance according to Marko-witz model. The results showed that the selection of stock portfolio using the mentioned financial criteria and using the Analytic Hierarchy Process (AHP) model leads to the acquisition of adjusted returns with more risk than the Marko-witz optimization model and the TOPSIS model (TOP).

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