Portfolio Risk of Chinese Stock Market Measured by VaR Method

Transcription

1 Vol.53 (ICM 014), pp.6166 hp://dx.doi.org/ /asl Porfolio Risk of Chinese Sock Marke Measured by VaR Mehod Wu Yudong School of Basic Science,Harbin Universiy of Commerce,Harbin Absrac. Taking he new composie index of Shanghai Sock Exchange (SSE) as sample, his paper calculaed he VaR of GARCH, EGARCH and PARCHES models as well as heir corresponding GARCHM, EGARCHM and PARCH M models, analyzed he applicabiliy of he model a differen confidence levels under differen disribuional assumpions and evaluaed he models by loss funcion es mehod. The resuls show ha: 1) he VaR under disribuion is grealy overesimaed, so disribuion does no apply o Chinese sock marke; ) he generalized error disribuion describes he marke risk more accuraely han he normal disribuion and he VaR calculaed in PARCH (1,1) model under generalized error disribuion is he bes; 3)he VaRPARCH (1,1)GED model is more suiable o measure he invesmen risk of Chinese sock marke. Keywords: VaR, GARCH model, loss funcion es 1 Inroducion Changes of he marke indexes can reflec he flucuaions of sock marke. Currenly, he essence of he marke indexes of he wo sock exchanges in Shanghai and Shenzhen is an asse porfolio, a proporional funcion of he marke value of he invesmen porfolio. Is amoun of increase or decrease is he yield of he porfolio. Porfolio heory ells us ha invesing in porfolio can diversify risk. However, he porfolio can only reduce nonsysemaic risk bu no sysemic risk, so he risk of he sock marke composie index (i.e. sysemic risk) canno be eliminaed. How o accuraely measure he marke risk and beer operae he marke are commonly concerned by he invesors and securiies insiuions. The economy and finance of China are growing rapidly, so i is necessary o research he sock price index of Chinese sock marke while making considerable progresses in securiies marke, especially he sock marke[14]. ISSN: ASTL Copyrigh 014 SERSC

2 Vol.53 (ICM 014) Basic characerisics of he daily yield rae series of Chinese sock marke index.1 Selecion of he sample daa In his paper, he composie index daa is seleced from he sofware of Tonghuashun Caiong Securiies, including 143 daa of SSE from January 5h, 009 o February 1h, Characerisics analysis of he daily yield rae series Yield rae is he firs difference logarihmic form, where r is he yield of day and p is he closing price of day. Then: r ln ( p / p ) 1 (1) Fig.1. Logarihmic daily yield rae ime series of SSE new composie index Seen from Fig.1, i is found ha he volailiy of he sample series is grea during some period and small during oher period wih explosiveness and gregariousness, indicaing ha his series has heeroskedasiciy. We need esablish GARCH model..3 Resuls and analysis of VaR of Chinese sock marke index.3.1 Esablish GARCH model Seen from he above analysis, he logarihmic daily yield rae series of SSE new composie index is saionary wih no auocorrelaion, so he income equaion is general average regression equaion. Afer repeaed rials, he model is esablished as GARCH (1, 1) model. r, where N (0, ) () 6 Copyrigh 014 SERSC

3 Vol.53 (ICM 014) , 0, (3).3. VaR resuls of SSE new composie index under differen disribuions calculaed by GARCH model (1) Resuls analysis and accuracy es under normal disribuion Table 1. Parameers and Zes probabiliy esimaes of SSE daily yield rae under normal disribuion Model GARCH(1,1) EGARCH(1,1) PARCH(1,1) GARCH(1,1) M EGARCH(1,1) M PARCH(1,1)M A Seen from Zes probabiliy of he corresponding esimaed parameers in Table 1, only he parameers of PARCH (1, 1) model and PARCH (1, 1)M model are no significan a he confidence level of. When do ARCH es o he residual effecs of he model, i is found ha here were no significan heeroscedasiciy, indicaing ha he above model is able o beer characerize he heeroskedasiciy of he daily yield rae of SSE new composie index. 1 1 The aenuaion coefficien ( ) reflecs he persisence of he impac of a shock on he volailiy of he variable. I can be found ha he aenuaion coefficiens of GARCH, PARCH, GARCHM and PARCHM models under normal disribuion are less han 1 while he aenuaion coefficiens of EGARCH and EGARCHM models were greaer han 1, indicaing ha he impac of he shock on share price flucuaions has an indefinie exending endency, prolonging he marke memory. An imporan feaure of EGARCH and PARCH models is ha hey inroduced parameer in he condiional variance o describe he asymmeric impac of a shock on price flucuaions. I can be seen form from he able ha is no equal o 0, indicaing ha he impac of he shock on he share price is asymmeric and in Copyrigh 014 SERSC 63

4 Vol.53 (ICM 014) EGARCH and EGARCHM models are less han 0, indicaing ha lising has leverage effec. Models GARCH(1, 1) EGARCH( 1,1) PARCH(1, 1) GARCH(1, 1)M EGARCH( 1,1)M PARCH(1, 1)M Confide nce coefficien Table. VaR and reurned es values of he esimae models Mea n VaR Maxi mum VaR Mini mum VaR Sandard deviaion of VaR Expeced failure days Re al failure days Fai lure rae LR sai sics Table shows ha he mean VaR of hese six models calculaed a he confidence level of and, respecively, are no significanly differen.seen from he poin view of failure rae, a he confidence level of, only he failure rae of PARCHM model is higher han 5% while a he confidence level of, he failure raes of all models are higher han 1%, so he error es is no passed. Seen from he poin of view of es resuls of LR saisic, a he confidence level of, he LR es values of he models are less han 3.84, so he null hypohesis canno be rejeced; a he confidence level of, he LR es values of he models are greaer han 6.63, so he model is rejeced. i is unreasonable o assume ha he ime series of daily yield rae is normal disribuion. Similarly he parameers of EGARCH (1, 1), PARCH (1, 1), GARCH (1, 1)M, EARCH (1,1)M and PARCH (1,1)M models are no significan a he significance level of 5%, a he confidence level of, he saisical LR of each model is greaer han 3.84 excep he PARCH model, so he null hypohesis is rejeced. A he confidence level of, he saisical LR of each model is less han 6.63 excep GARCH model, so he null hypohesis canno be rejeced and only he PARCH mode passed he accuracy es a he confidence levels of and. Combined wih he number of failure days, i can be concluded ha VaR esimaes under disribuion are oo conservaive and overesimae he risk value, so i is unreasonable o assume ha he ime series is disribuion. 64 Copyrigh 014 SERSC

5 Vol.53 (ICM 014) Similarly he esimaed ail parameers under GED disribuion are less han ( n ), indicaing ha he yield rae is no normal disribuion. Seen from he corresponding Zes probabiliies of he esimaed parameers, he parameers of he models are no significan a he confidence level of excep he GARCH model. Seen from he aenuaion coefficiens, he aenuaion coefficiens of GARCH, EGARCH, PARCH and GARCHM models are less han 1 while hose of EGARCH M and PARCHM models are greaer han 1 bu close o 1, indicaing ha he impac caused by he shock on price flucuaions has an indefinie exending endency, prolonging he marke memory and he impac of policies on he sock marke will be longerm. The general saisical characerisics of he esimaed VaR values, he failure days and he corresponding failure rae go by reurn es mehods under GED disribuion. The mean VaR of hese six models have no significan difference a he confidence levels of and,seen from he number of failure days and he failure raes, GED disribuion can beer characerize he volailiy of he sock marke han normal disribuion. Seen from he es resuls of he LR saisics, he LR es values of he models are less han 3.84 a he confidence level of, so he null hypohesis canno be rejeced. A he confidence level of, he LR es values of he models are less han 6.63, so he model canno be rejeced. Combing failure rae and he LR es values, i can be concluded ha PARCH model is more applicable a confidence levels of and. 3 Conclusion According o he resuls of he VaR and he kupiec failure frequency es of SSE new composie index, he following conclusions can be go: 1) seen from he poin of view of disribuion, disribuion does no apply o Chinese sock marke; GED disribuion measures Chinese sock marke invesmen risk more accuraely han normal disribuion; ) seen from he perspecive of models, PARCH (1,1) model is more suiable for Chinese sock marke risk measuremen and in places wih obvious and greaer risk volailiy, describing he condiional variance wih PARCH model can esimae VaR values more reasonably; 3) under GED disribuion, he esimaed VaR resuls from he PARCH model showed ha he esimaed VaR of SSE new composie index was.% a he confidence level and was 3.5% a he confidence level of. The analysis of he VaR (loss value form) of he PARCH (1, 1)GED model indicaes ha under GED disribuion, he esimaed mean VaR of SSE new composie index is a he confidence level of and is a he confidence level of. Acknowledgmens. This research was suppored by he Deparmen of Educaion of Heilongjiang Province under Gran No , Gran No and he Harbin Universiy of Commerce Naural Science Foundaion of Young Teachers under Gran No HCUL This work was also financially suppored by he funding (funding number: ) from he Heilongjiang Educaion Deparmen. Copyrigh 014 SERSC 65

6 Vol.53 (ICM 014) References 1. Mehme Orhan, Bülen Köksal. A comparison of GARCH models for VaR esimaion[j]. Exper Sysems Wih Applicaions, Vol 39,358359, (01).. Rombous, Jeroen V. K.; Verbeek, Marno. Evaluaing porfolio ValueaRisk using semiparameric GARCH models[j]. Quaniaive Finance, Vol 9, ,(009). 3. Yan yuxin. Marke Risk Assessmen of China's Sock Index Fuures Based on VaR GARCH Model[D]. Ocean universiy of China, 10, (011). 4. Shi Tianxiong, Qian Jinye. Marke risk measuremen of sock index in China based on VaR models[j]. Journal of China Universiy of Geosciences(Social Sciences Ediion), Vol 04, 11914, (010). 66 Copyrigh 014 SERSC