A Novel Approach for Portfolio Optimization Using Fuzzy AHP Based on Gustafson Kessel Clustering Algorithm
Portfolio management involves modeling risk-return relationships. However, the diverse factors impacting financial markets introduce uncertainty into future portfolio selection. The aim of this study is to propose a portfolio selection model to assist investors in creating the most suitable investme...
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Mehmet Akif Ersoy University
2024-12-01
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| Series: | Mehmet Akif Ersoy Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3865520 |
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| author | Yeşim Akbaş Türkan Erbay Dalkılıç Serkan Akbaş |
| author_facet | Yeşim Akbaş Türkan Erbay Dalkılıç Serkan Akbaş |
| author_sort | Yeşim Akbaş |
| collection | DOAJ |
| description | Portfolio management involves modeling risk-return relationships. However, the diverse factors impacting financial markets introduce uncertainty into future portfolio selection. The aim of this study is to propose a portfolio selection model to assist investors in creating the most suitable investment plan in the financial market uncertainty. In this context, a preliminary reduction step is applied to the stocks using the Gustafson-Kessel (GK) algorithm, a fuzzy clustering method, to select portfolio stocks. Later, trapezoidal fuzzy numbers (TrFNs) were defined instead of triangular fuzzy numbers (TFNs) used in the Constrained Fuzzy Analytic Hierarchy Process (AHP) for portfolio selection problems. By using new fuzzy numbers, the weights of the criteria were obtained as TrFNs. Then, a linear programming problem was modeled using the weights of the obtained criteria as a TrFN. For this purpose, a method available in the literature was used that uses price variables in the objective function as TFNs. In this study, a linear programming model that uses these variables as TrFNs is proposed as an alternative to the method that uses the price variables in the objective function as TFNs. In this proposed model, the weights obtained from the Constrained Fuzzy AHP using TrFNs are used as price variables in the objective function of the created linear programming problem. Proposed model then applied to the 48-month return data set of stocks in the Istanbul Stock Exchange 100 (ISE-100) index to determine which stocks the investor should choose and the investment rates investor should make in these stocks. In addition, in order to examine the effectiveness of the proposed model within the scope of the study, portfolio distributions were obtained with different portfolio optimization methods using the same data set and the results were compared. |
| format | Article |
| id | doaj-art-b62c867397404d25bb0f959d3f360c3a |
| institution | Kabale University |
| issn | 2149-1658 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Mehmet Akif Ersoy University |
| record_format | Article |
| series | Mehmet Akif Ersoy Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi |
| spelling | doaj-art-b62c867397404d25bb0f959d3f360c3a2025-01-27T12:39:37ZengMehmet Akif Ersoy UniversityMehmet Akif Ersoy Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi2149-16582024-12-011141436145610.30798/makuiibf.1469103273A Novel Approach for Portfolio Optimization Using Fuzzy AHP Based on Gustafson Kessel Clustering AlgorithmYeşim Akbaş0https://orcid.org/0000-0001-7590-6139Türkan Erbay Dalkılıç1https://orcid.org/0000-0003-2923-599XSerkan Akbaş2https://orcid.org/0000-0001-5220-7458KARADENIZ TECHNICAL UNIVERSITYKARADENIZ TECHNICAL UNIVERSITYKaradeniz Technical UniversityPortfolio management involves modeling risk-return relationships. However, the diverse factors impacting financial markets introduce uncertainty into future portfolio selection. The aim of this study is to propose a portfolio selection model to assist investors in creating the most suitable investment plan in the financial market uncertainty. In this context, a preliminary reduction step is applied to the stocks using the Gustafson-Kessel (GK) algorithm, a fuzzy clustering method, to select portfolio stocks. Later, trapezoidal fuzzy numbers (TrFNs) were defined instead of triangular fuzzy numbers (TFNs) used in the Constrained Fuzzy Analytic Hierarchy Process (AHP) for portfolio selection problems. By using new fuzzy numbers, the weights of the criteria were obtained as TrFNs. Then, a linear programming problem was modeled using the weights of the obtained criteria as a TrFN. For this purpose, a method available in the literature was used that uses price variables in the objective function as TFNs. In this study, a linear programming model that uses these variables as TrFNs is proposed as an alternative to the method that uses the price variables in the objective function as TFNs. In this proposed model, the weights obtained from the Constrained Fuzzy AHP using TrFNs are used as price variables in the objective function of the created linear programming problem. Proposed model then applied to the 48-month return data set of stocks in the Istanbul Stock Exchange 100 (ISE-100) index to determine which stocks the investor should choose and the investment rates investor should make in these stocks. In addition, in order to examine the effectiveness of the proposed model within the scope of the study, portfolio distributions were obtained with different portfolio optimization methods using the same data set and the results were compared.https://dergipark.org.tr/en/download/article-file/3865520fuzzy ahpgustafson-kessel algorithmportfolio selectiontrapezoidal fuzzy numbersfuzzy ahpgustafson-kessel algorithmportfolio selectiontrapezoidal fuzzy numbers |
| spellingShingle | Yeşim Akbaş Türkan Erbay Dalkılıç Serkan Akbaş A Novel Approach for Portfolio Optimization Using Fuzzy AHP Based on Gustafson Kessel Clustering Algorithm Mehmet Akif Ersoy Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi fuzzy ahp gustafson-kessel algorithm portfolio selection trapezoidal fuzzy numbers fuzzy ahp gustafson-kessel algorithm portfolio selection trapezoidal fuzzy numbers |
| title | A Novel Approach for Portfolio Optimization Using Fuzzy AHP Based on Gustafson Kessel Clustering Algorithm |
| title_full | A Novel Approach for Portfolio Optimization Using Fuzzy AHP Based on Gustafson Kessel Clustering Algorithm |
| title_fullStr | A Novel Approach for Portfolio Optimization Using Fuzzy AHP Based on Gustafson Kessel Clustering Algorithm |
| title_full_unstemmed | A Novel Approach for Portfolio Optimization Using Fuzzy AHP Based on Gustafson Kessel Clustering Algorithm |
| title_short | A Novel Approach for Portfolio Optimization Using Fuzzy AHP Based on Gustafson Kessel Clustering Algorithm |
| title_sort | novel approach for portfolio optimization using fuzzy ahp based on gustafson kessel clustering algorithm |
| topic | fuzzy ahp gustafson-kessel algorithm portfolio selection trapezoidal fuzzy numbers fuzzy ahp gustafson-kessel algorithm portfolio selection trapezoidal fuzzy numbers |
| url | https://dergipark.org.tr/en/download/article-file/3865520 |
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