مدل بهبوديافته رديابي شاخص با درنظر گرفتن هزينه هاي معاملاتي

An enhanced model for the index tracking problem with transaction costs

ﭼﮑﯿﺪه ﻣﺴﺌﻠﻪ ﻣﺪﯾﺮﯾﺖ و ﺑﻬﯿﻨﻪﺳﺎزي ﭘﻮرﺗﻔﻮي ﺳﺮﻣﺎﯾﻪﮔﺬاري، ﯾﮑﯽ از ﻣﺒﺎﺣﺚ ﺑﺴﯿﺎر ﻣﻬﻢ در ﺑﺎزارﻫﺎي ﻣﺎﻟﯽ اﺳﺖ. ﺑﺮاي ﻣﺪﯾﺮﯾﺖ ﭘﻮرﺗﻔﻮي دو اﺳﺘﺮاﺗﮋي ﻣﻨﻔﻌﻼﻧﻪ و ﻓﻌﺎﻻﻧﻪ وﺟﻮد دارد ﮐﻪ اﯾﺠﺎد ﯾﮏ ﭘﻮرﺗﻔﻮي ردﯾﺎب ﺷﺎﺧﺺ ﯾﮑﯽ از ﺟﻨﺒﻪ ﻫﺎي روﯾﮑﺮد ﻣﻨﻔﻌﻼﻧﻪ ﺑﺮاي ﻣﺪﯾﺮﯾﺖ ﺳﺒﺪ ﺳﻬﺎم ﻣﯽﺑﺎﺷﺪ. اﺳﺎس ﺳﺒﺪ ردﯾﺎب ﺷﺎﺧﺺ، دﺳﺘﯿﺎﺑﯽ ﺑﻪ ﻋﻤﻠﮑﺮدي ﻣﻄﺎﺑﻖ ﺑﺎ ﺑﺎزدهﺷﺎﺧﺺ ﺑﺎ ﺗﺸﮑﯿﻞ ﺳﺒﺪي ﻣﺤﺪود از ﺳﻬﺎم اﺳﺖ ﮐﻪ درﭘﯽآن ﻫﺰﯾﻨﻪﻫﺎي ﻣﻌﺎﻣﻼﺗﯽ ﺑﺮاي ﺳﺮﻣﺎﯾﻪﮔﺬار ﮐﺎﻫﺶ ﭘﯿﺪا ﺧﻮاﻫﺪ ﮐﺮد. در اﯾﻦ ﭘﮋوﻫﺶ، ﺑﺎ درﻧﻈﺮ ﮔﺮﻓﺘﻦ ﻣﺤﺪودﯾﺖﻫﺎي ﻫﺰﯾﻨﻪ ﻣﻌﺎﻣﻼﺗﯽ، ﻣﺪﻟﯽ ﺑﺮاي ﺗﺸﮑﯿﻞ ﭘﻮرﺗﻔﻮي ردﯾﺎب اراﺋﻪ ﺷﺪه اﺳﺖ ﮐﻪ ﺗﺎ ﺟﺎي ﻣﻤﮑﻦ ﺑﺘﻮان اﺧﺘﻼف ﺑﺎزده ﭘﻮرﺗﻔﻮي و ﺷﺎﺧﺺ را در ﺟﻬﺖ ﻣﺜﺒﺖ)اﻧﺤﺮاف ﻣﻄﻠﻮب( ﺑﯿﺸﯿﻨﻪ و ﻧﯿﺰ اﯾﻦ اﺧﺘﻼف را در ﺟﻬﺖ ﻣﻨﻔﯽ)اﻧﺤﺮاف ﻧﺎﻣﻄﻠﻮب( ﮐﻤﯿﻨﻪ ﮐﺮد. ﺑﻤﻨﻈﻮر ﺣﻞ ﻣﺪل ﺗﻮﺳﻌﻪ داده ﺷﺪه از اﻟﮕﻮرﯾﺘﻢ ژﻧﺘﯿﮏ اﺳﺘﻔﺎده ﺷﺪه اﺳﺖ. ﻣﺪل ﻣﻮرد ﻧﻈﺮ ﺑﺮ روي ﭼﻬﺎر ﺻﻨﻌﺖ ﺑﺰرگ ﺑﻮرس اوراق ﺑﻬﺎدار ﺗﻬﺮان در ﺑﺎزه زﻣﺎﻧﯽ 1395/1/31 اﻟﯽ 1395/10/30 ﭘﯿﺎدهﺳﺎزي ﺷﺪه ﮐﻪ اﯾﻦ ﺑﺎزه ﻧﯿﺰ ﺑﻪ دو دوره آﻣﻮزش و ﺳﻨﺠﺶ ﺗﻘﺴﯿﻢ ﺷﺪه اﺳﺖ. ﻫﻤﭽﻨﯿﻦ ﻣﻘﻄﻌﯽ از زﻣﺎن را ﻧﯿﺰ ﺑﺮاي ﺑﺎزﻧﮕﺮي در ﭘﻮرﺗﻔﻮي ﺑﺎ اﻋﻤﺎل ﻣﺤﺪودﯾﺖﻫﺎي ﻫﺰﯾﻨﻪ ﻣﻌﺎﻣﻼﺗﯽ در ﻣﺪل در ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪه اﺳﺖ. ﺑﺮاي ﺑﺮرﺳﯽ ﮐﺎراﯾﯽ ﻣﺪل از آزﻣﻮن ﻣﻘﺎﯾﺴﻪ زوﺟﯽ ﺑﻬﺮه ﮔﺮﻓﺘﻪ ﺷﺪه و ﻧﺘﺎﯾﺞ ﺑﺪﺳﺖ آﻣﺪه ﻧﺸﺎن ﻣﯽدﻫﺪ ﮐﻪ ﻣﺪل ﭘﯿﺸﻨﻬﺎدي ﻋﻤﻠﮑﺮد ﺧﻮﺑﯽ در ردﯾﺎﺑﯽ ﺷﺎﺧﺺ ﻣﺮﺑﻮﻃﻪ و دﺳﺘﯿﺎﺑﯽ ﺑﻪ ﺑﺎزده ﻣﺎزاد ﺑﺮ

Portfolio optimization is one of the most important issues in financial sciences. Various strategies have been used to manage stock portfolios, which can be categorized into types: active and passive strategies. One of the most important passive portfolio management approaches is to form an index tracking portfolio. The purpose of index tracking portfolio is to its performance replicate market index as benchmark as closely as possible with a limited stocks in portfolio which will result in lower transaction costs for investor. In this research, a model for index tracking problem is proposed which aims to minimize undesirable deviations and maximize desirable deviations. Finally, a genetic algorithm is used to solve the leading model. To evaluate the performance of the model, data from four major industries of Tehran Stock Exchange has been used. The results show that the proposed model has a suitable performance in tracking the relevant index and achieving excess return over the benchmark.