مقايسه توزيع فريشه (FD) و توزيع پارتو تعميم يافته (GPD) در برآورد ارزش در معرض ريسك (VAR) و ارزش در معرض ريسك شرطي (CoVaR) شاخص بورس اوراق بهادار تهران

Comparing the Frechet Distribution and the Generalized Pareto Distribution in Estimating Value at Risk and Conditional Value at Risk in Tehran Stock Exchange

ﭼﺎﻟﺶ اﺳﺎﺳﯽ در ﻣﺤﺎﺳﺒﻪ رﯾﺴﮏ اﻧﺘﺨﺎب روﺷﯽ اﺳﺖ ﮐﻪ ﺑﺘﻮاﻧﺪ دﻗﯿﻖ ﺗﺮﯾﻦ ﻣﻘﺪار رﯾﺴﮏ را ﻣﺤﺎﺳﺒﻪ ﮐﻨﺪ. ﻫﺪف اﯾﻦ ﻣﻄﺎﻟﻌﻪ ﻣﻘﺎﯾﺴﻪ ﺑﺮآورد ارزش در ﻣﻌﺮض رﯾﺴﮏ VAR)( و ارزش در ﻣﻌﺮض رﯾﺴﮏ ﺷﺮﻃﯽ CoVaR)( در ﺑﻮرس اوراق ﺑﻬﺎدار ﺗﻬﺮان ﺑﺎ اﺳﺘﻔﺎده از ﺗﻮزﯾﻊ ﻓﺮﯾﺸﻪ )FD( و ﺗﻮزﯾﻊ ﭘﺎرﺗﻮ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ )GPD( ﻫﺴﺖ. در اﯾﻦ ﭘﮋوﻫﺶ از ﺑﺎزده داده ﻫﺎي 21 و 63 روزه ﺳﺮي زﻣﺎﻧﯽ ﺷﺎﺧﺺ ﮐﻞ، ﺷﺎﺧﺺ ﺳﻬﺎم آزاد ﺷﻨﺎور و ﺷﺎﺧﺺ 50 ﺷﺮﮐﺖ ﻓﻌﺎل ﺑﻮرس اوراق ﺑﻬﺎدار ﺗﻬﺮان در ﻓﺎﺻﻠﻪ زﻣﺎﻧﯽ 1391/01/01 اﻟﯽ 1398/12/29 اﺳﺘﻔﺎده ﮔﺮدﯾﺪ. ﺑﺮاي ﭘﺬﯾﺮش ﻣﺪل ﻫﺎ ﺑﻪ ﻟﺤﺎظ آﻣﺎري از آزﻣﻮن ﻫﺎي ﭘﺲ آزﻣﺎﯾﯽ ﮐﻮﭘﯿﮏ و آزﻣﻮن ﭘﻮﺷﺶ ﺷﺮﻃﯽ ﮐﺮﯾﺴﺘﻮﻓﺮﺳﻦ اﺳﺘﻔﺎده ﺷﺪ. ﻣﻘﺎﯾﺴﻪ ﻣﺪل ﻫﺎ از ﻃﺮﯾﻖ ﺗﻮاﺑﻊ زﯾﺎن دوم ﻟﻮﭘﺰ و ﺑﻼﻧﮑﻮ -اﯾﻬﻞ اﻧﺠﺎم ﺷﺪ. ﺑﺮاي رﺗﺒﻪ ﺑﻨﺪي ﻣﺪل ﻫﺎي CoVaR ﻧﯿﺰ دو ﺗﺎﺑﻊ زﯾﺎن ﺷﺎﻣﻞ ﻣﯿﺎﻧﮕﯿﻦ ﻗﺪر ﻣﻄﻠﻖ ﺧﻄﺎﻫﺎ )MAE( و ﻣﺠﺬور ﻣﯿﺎﻧﮕﯿﻦ ﻣﺮﺑﻌﺎت اﻧﺤﺮاف ﻫﺎ )RMSE( ﺑﻪ ﮐﺎر رﻓﺖ. ﻧﺘﺎﯾﺞ ﻧﺸﺎن داد ﻃﺒﻖ ﺧﺮوﺟﯽ آﻣﺎره ﺗﺎﺑﻊ زﯾﺎن دوم ﻟﻮﭘﺰ، ﺗﻮزﯾﻊ ﭘﺎرﺗﻮ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ در ﺑﺮآورد VaR ﺑﺎزده ﺷﺎﺧﺺ ﮐﻞ و ﺑﺎزده ﺷﺎﺧﺺ 50 ﺷﺮﮐﺖ ﺑﺮﺗﺮ ﺑﻬﺘﺮ از ﺗﻮزﯾﻊ ﻓﺮﯾﺸﻪ ﻋﻤﻞ ﻧﻤﻮد، اﻣﺎ ﺑﺮاي ﺷﺎﺧﺺ آزاد ﺷﻨﺎور، ﺗﻮزﯾﻊ ﻓﺮﯾﺸﻪ ﻋﻤﻠﮑﺮد ﺑﻬﺘﺮي دارد. ﻧﺘﺎﯾﺞ ﻃﺒﻖ ﻣﻘﺎدﯾﺮ ﺗﺎﺑﻊ زﯾﺎن ﺑﻼﻧﮑﻮ-اﯾﻬﻞ ﻣﺨﺎﻟﻒ ﻧﺘﺎﯾﺞ آﻣﺎره ﺗﺎﺑﻊ زﯾﺎن دوم ﻟﻮﭘﺰ ﺑﻮد. ﻧﺘﺎﯾﺞ ﻣﯿﺎﻧﮕﯿﻦ ﻗﺪر ﻣﻄﻠﻖ ﺧﻄﺎﻫﺎ و ﻣﺠﺬور ﻣﯿﺎﻧﮕﯿﻦ ﻣﺮﺑﻌﺎت اﻧﺤﺮاف ﻫﺎ ﻧﺸﺎن از ﺑﺮﺗﺮي ﺗﻮزﯾﻊ ﻓﺮﯾﺸﻪ در ﺑﺮآورد CoVaR ﻧﺴﺒﺖ ﺗﻮزﯾﻊ ﭘﺎرﺗﻮ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ داﺷﺖ.

Selecting the most accurate method of risk measurement is the main challenge in risk estimation. This study aims to measure value at risk (VaR) and conditional value at risk (CoVar) in Tehran Stock Exchange (TSE) using the Frechet distribution (FD) and the generalized Pareto distribution (GPD). It used the data from 21 and 63-day time series of TEPIX, free-float, and the indices of the top 50 TSE companies between 2012-3-20 and 2020-3-19. It used COPIC post-test and Christoffersen’s conditional coverage test for models statistical confirmation. It applied Lopez and Blanco-Ihle’s second loss functions for model comparison. The CoVaR models were ranked by two loss functions, including Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). Results indicated according to the statistics measured in Lopez’s second loss function, GPD performed better than FD in measuring VaR of TEPIX and the return index of the selected 50 companies, however, FD performed better for the free-float index. Blanco-Ihle’s loss function results contradicted the ones derived from Lopez’s second loss function. MAE and RMSE results indicated FD is better in estimating CoVaR.