ارزيابي توان تبيين نظريه ارزش فرين (حدي) و مدل‌هاي كاپولا-گارچ در پيش‌بيني ارزش در معرض ريسك و ريزش مورد انتظار پرتفوي

The assessment of extreme value theory and Copula - Garch models in prediction of value at risk and the expected short fall in portfolio Investment Company in Tehran stock exchange.

ﻫﺪف اﺻﻠﯽ اﯾﻦ ﭘﮋوﻫﺶ اراﺋﻪ ﯾﮏ ﻣﺪل دﻗﯿﻖﺗﺮ ﺑﺮاي ﻣﺤﺎﺳﺒﻪ رﯾﺴﮏ ﺑﺎﻧﮏﻫﺎ و ﻣﺆﺳﺴﺎت ﻣﺎﻟﯽ ﺑﻮده اﺳﺖ. از ﻫﻤﯿﻦ رو ﺑﺎ ﻣﻄﺎﻟﻌﻪ روشﻫﺎي ﺟﺪﯾﺪ در ﺣﻮزه ﻣﺪﯾﺮﯾﺖ رﯾﺴﮏ ﻣﺰﯾﺖ اﺳﺘﻔﺎده از ﺗﻮاﺑﻊ ﮐﺎﭘﻮﻻ ﻣﺸﺨﺺ ﺷﺪه اﺳﺖ. ﻫﻤﭽﻨﯿﻦ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﺰاﯾﺎي ﻣﻌﯿﺎر ارزش در ﻣﻌﺮض رﯾﺴﮏ ﺑﺮاي ﻣﺤﺎﺳﺒﻪ رﯾﺴﮏ ﭘﺮﺗﻔﻮي، از اﯾﻦ ﻣﻌﯿﺎر در ﭘﮋوﻫﺶ اﺳﺘﻔﺎده ﺷﺪه اﺳﺖ و ﺑﺎ ﺗﺮﮐﯿﺐ آن ﺑﺎ ﺗﻮاﺑﻊ ﮐﺎﭘﻮﻻ، ﺑﻪ ﻣﻌﺮﻓﯽ ﻣﺪل)ARIMA- GARCH- COPULA ( ﭘﺮداﺧﺘﯿﻢ. ﺑﺮاي ﺑﻪ دﺳﺖ آوردن ﺗﻮزﯾﻊﻫﺎي iid و ﻫﻤﭽﻨﯿﻦ ﺗﺨﻤﯿﻦ وارﯾﺎﻧﺲ، ﺑﻪﺗﺼﺮﯾﺢ و ﺗﺨﻤﯿﻦ ﻫﻢزﻣﺎن ﻣﺪل ﻣﯿﺎﻧﮕﯿﻦ و وارﯾﺎﻧﺲ ﺷﺮﻃﯽ در اﯾﻦ ﭘﮋوﻫﺶ ﭘﺮداﺧﺘﻪﺷﺪه اﺳﺖ. ﺑﺪﯾﻦ ﻣﻨﻈﻮر از ﻣﺘﺪوﻟﻮژي ﺑﺎﮐﺲ- ﺟﻨﮑﯿﻨﺰ )ARIMA( ﺑﺮاي ﻣﺪلﺳﺎزي ﻣﯿﺎﻧﮕﯿﻦ ﺑﺎزده داراﯾﯽﻫﺎي ﭘﮋوﻫﺶ و ﻣﺪلﻫﺎي ﻧﺎﻫﻤﺴﺎﻧﯽ وارﯾﺎﻧﺲ )GARCH( ﺑﻪ ﻣﻨﻈﻮر ﻣﺪلﺳﺎزي وارﯾﺎﻧﺲ ﺷﺮﻃﯽ ﭘﮋوﻫﺶ ﺑﻬﺮه ﺑﺮده ﺷﺪه اﺳﺖ ﺑﻪﻣﻨﻈﻮر ﻣﻘﺎﯾﺴﻪ ﻣﺪلﻫﺎي ﻣﺨﺘﻠﻒ ﺗﺨﻤﯿﻦ ارزش در ﻣﻌﺮض رﯾﺴﮏ از ﻣﻌﯿﺎر ﻣﯿﺎﻧﮕﯿﻦ ﺧﻄﺎ و ﺑﺮاي آزﻣﻮن آﻣﺎري ﻧﺘﺎﯾﺞ، از روشﻫﺎي ﭘﺲ آزﻣﺎﯾﯽ اﺳﺘﻔﺎده ﮐﺮدهاﯾﻢ. ﻣﻌﯿﺎر ﻣﯿﺎﻧﮕﯿﻦ ﺧﻄﺎ ﯾﮑﯽ از ﻣﻬﻢﺗﺮﯾﻦ ﺷﺎﺧﺺﻫﺎ در ارزﯾﺎﺑﯽ ﺗﻮان و دﻗﺖ و ﻗﺪرت ﻣﺪلﻫﺎ در ﺗﺨﻤﯿﻦ اﯾﻦ ﺳﻨﺠﻪ ﻣﯽﺑﺎﺷﻨﺪ ﮐﻪ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ اﯾﻦ ﻣﻌﯿﺎر ﻣﺪل ﭘﯿﺸﻨﻬﺎدي ﭘﮋوﻫﺶ ﺣﺎﺿﺮ ﻣﺪل) COPULA-ARIMA-GARCH ( ﺑﻬﺘﺮﯾﻦ ﻋﻤﻠﮑﺮد و دﻗﺖ را داﺷﺘﻪ اﺳﺖ. ﭘﺲ از آن ﻣﺪل GEV ﮐﻪ ﺑﺎ اﺳﺘﻔﺎده از ﺗﺌﻮري ﻣﻘﺎدﯾﺮ ﻓﺮﯾﻦ )ﺣﺪي( ﺣﺎﺻﻞ ﺷﺪه اﺳﺖ در رﺗﺒﻪ دوم ﻗﺮار ﮔﺮﻓﺘﻪ اﺳﺖ. ﻧﺘﺎﯾﺞ ﺗﺴﺖ ﭘﻮﺷﺶ ﻏﯿﺮ ﺷﺮﻃﯽ ﻧﺸﺎن دادﻧﺪ ﮐﻪ ﺗﻘﺮﯾﺒﺎً ﺗﻤﺎﻣﯽ روشﻫﺎي ﻣﻘﺎﯾﺴﻪ ﺷﺪه ﺑﻪﺟﺰ ﻣﺪل وارﯾﺎﻧﺲ-ﮐﻮوارﯾﺎﻧﺲ از ﻧﻈﺮ آﻣﺎري در ﻣﺤﺎﺳﺒﻪ VAR از دﻗﺖ ﮐﺎﻓﯽ ﺑﺮﺧﻮردار ﻫﺴﺘﻨﺪ، وﻟﯽ ﻧﺘﺎﯾﺞ روش رﺗﺒﻪﺑﻨﺪي داو ﺑﺴﯿﺎر ﺑﻪ ﯾﮑﺪﯾﮕﺮ ﻧﺰدﯾﮏ ﻫﺴﺘﻨﺪ. ﻃﺒﻖ روش رﺗﺒﻪﺑﻨﺪي داو در ﺳﻄﺢ ﻣﻌﻨﯽداري 5% ﻣﺪل GEV ﮐﻤﺘﺮﯾﻦ ﺗﺎﺑﻊ زﯾﺎن و در ﺳﻄﺢ ﻣﻌﻨﯽداري 1% ﻣﺪل ﺷﺒﯿﻪﺳﺎزي ﺗﺎرﯾﺨﯽ داراي ﮐﻤﺘﺮﯾﻦ ﺗﺎﺑﻊ زﯾﺎن ﺑﻮده اﺳﺖ. ﻫﻤﭽﻨﯿﻦ ﻣﺤﺎﺳﺒﺎت رﯾﺰش ﻣﻮرد اﻧﺘﻈﺎر ﻧﯿﺰ ﺑﺮاي 4 ﻣﺪل ﻣﺬﮐﻮر ﺻﻮرت ﮔﺮﻓﺖ ﮐﻪ ﻣﺪل) ARIMA-GARCH- COPULA( ﮐﻤﺘﺮﯾﻦ زﯾﺎن را ﺣﺎﺻﻞ ﻧﻤﻮد. ﻟﺬا ﺑﻪﻋﻨﻮان ﻧﺘﯿﺠﻪﮔﯿﺮي ﮐﻠﯽ ﻣﯽﺗﻮان ﮔﻔﺖ ﻣﺪل ﭘﯿﺸﻨﻬﺎدي ﭘﮋوﻫﺶ ﻣﺪل )-ARIMA GARCH- COPULA( ﺑﻬﺘﺮﯾﻦ ﻋﻤﻠﮑﺮد و دﻗﺖ را ﻫﻢ در ﻣﺤﺎﺳﺒﻪ ارزش در ﻣﻌﺮض رﯾﺴﮏ و رﯾﺰش ﻣﻮرد اﻧﺘﻈﺎر داﺷﺘﻪ و ﭘﺲ از آن ﻣﺪل GEV ﮐﻪ ﺑﺎ اﺳﺘﻔﺎده از ﺗﺌﻮري ﻣﻘﺎدﯾﺮ ﻓﺮﯾﻦ ﺣﺎﺻﻞ ﺷﺪه اﺳﺖ در رﺗﺒﻪ دوم ﻗﺮار ﮔﺮﻓﺘﻪ است

The present study has endeavored to represent a more precise model to calculate the risk of banks in this study by ARIMA-GARCH-COPULA Model has been introduced.In obtaining the iid distributions and variance estimation the mean model and conditional variance have been determined and estimated simultaneously.In so doing, the ARIMA methodology has been employed to model the average return on assets of the study, and for modeling the research conditional variance of GARCH have been applied. Also mean error criterion has been used to compare the different models of VAR estimation, and for the purpose of testing statistical results backtesting methods have been employed. Based on mean error criterion, the proposed model of the study at hand has demonstrated the most accuracy The GEV model derived from the EVT has been ranked second The output of the Dow ranking method, however, has been very similar to one another According to Dow ranking method, the GEV model has had the lowest loss function at 5% level of significance, and at 1% level of significance, the HS model has demonstrated the least loss function. ES calculations have also been carried out for the four models with ARIMA-GARCH-COPULA model showing the least loss.