Research on Risk Measurement in Financial Market Based on GARCH-VaR and FHS An Example of Chinese Bond Market

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1 Applied Economics and Finance Vol. 5, No. 4; July 018 ISSN E-ISSN Published by Redfame Publishing URL: hp://aef.redfame.com Research on Risk Measuremen in Financial Marke Based on GARCH-VaR and FHS An Example of Chinese Bond Marke Shaozhen Chen 1, Bangqian Zhang 1 & Jinjin Deng 1 1 Finance Deparmen of Inernaional Business School, Jinan Universiy, Qianshan Road 06#, Zhuhai Ciy, Guangdong Province, China Correspondence: Jinjin Deng, Finance Deparmen of Inernaional Business School, Jinan Universiy, Qianshan Road 06#, Zhuhai Ciy, Guangdong Province, Pos No , China. Received: May 7, 018 Acceped: June 19, 018 Available online: June, 018 doi: /aef.v5i URL: hps://doi.org/ /aef.v5i Absrac Accuraely measuring he risk of bond marke is very imporan for improving he risk managemen level of bond marke and mainaining he sabiliy of he financial sysem. Taking ChinaBond New Composie Wealh (gross) Index as he research objec, his paper selecs he closing price from January 1, 00 o March 30, 018, esablishes he GARCH, EGARCH and GJR-GARCH model based on normal disribuion and disribuion, and finds ou he volailiy aggregaion and he leverage effec of he bond marke. Then, his paper use wo mehods o measure he risk of he bond marke: firs, we esimae he value a risk (VaR) of he bond marke by he parameer mehod, using condiional variance esimaed by he GARCH models, and we carry ou backesing analysis and he Kupiec failure rae es on measuremen accuracy of VaR. The resuls show ha disribuion hypohesis and eliminaion of auocorrelaion of he yield rae can improve he accuracy and robusness of he esimaion of he VaR; second, we simulae he fuure revenue pah of he bond marke and compare i wih he acual loss, using Filered Hisorical Simulaion (FHS) based on Boosrap mehod. The resuls show ha he bond marke has leverage effec. The maximum possible loss under exreme condiions can be far greaer han he maximum possible revenue. Bu he esimaed VaR under 95% confidence level can predic fuure risks very well. Finally, according o he conclusion, his paper pus forward some suggesions for regulaors and invesors from he perspecive of risk managemen. Keywords: volailiy, leverage, GARCH models, VaR, FHS 1. Inroducion The Asian financial crisis ha broke ou in 1997 gives us a lesson ha he developmen of muli-level capial markes, especially he bond marke, is of grea significance o he sabiliy and prosperiy of finance and economy in a region and even a counry. The developmen of he bond marke will help expand he financing channels, esablish indirec conrol mechanisms, promoe he reform of ineres rae liberalizaion and hen increase he efficiency of he allocaion of financial resources. Therefore, how o ensure he healhy developmen of he bond marke and le he bond marke risk buffer play heir full role, or how o accuraely measure he risk of he bond marke and improve he level of risk managemen are of grea pracical significance. Since Chinese governmen resumed issuing naional deb in 1981, he bond marke has so far achieved rapid developmen. Regulaory sysem has been gradually improved; bond ypes have become increasingly diverse; a unified layered marke sysem including hree submarkes, which are iner-bank bond marke, exchange bond marke, and commercial bank over-he-couner marke has gradually emerged. The bond marke plays an imporan role in he implemenaion of he macroeconomic regulaion carrier while playing a financing funcion. The regulaory auhoriies regulae he money supply hrough open marke operaions such as cash coupon rading and repurchase in he bond marke o achieve moneary policy goals; hey can also achieve financial policy goals hrough he scienific arrangemen of he size, iming, and erm srucure of governmen bond issuance; hey can guide he flow of bond financing as well by raionally adjusing he srucure of bond issuers o opimize he indusrial srucure and achieve he purpose of healhy indusrial developmen. A he end of 017, he sock size of China's bonds was rillion yuan, and he bond marke issued a oal of 40.8 rillion yuan in various bonds. Among hem, he scale of bonds issued by he iner-bank bond marke reached

2 rillion; he issuance of governmen bonds reached 3.9 rillion yuan; he issuance of local governmen bonds reached 4.4 rillion yuan; he issuance of financial bonds reached 5 rillion yuan; governmen-sponsored insiuional bond issuance reached 86 billion yuan; asse-backed securiies reached 1.5 rillion yuan; inerbank cerificaes issued amouned o 0. rillion yuan; corporae credi bonds issued amouned o 5.5 rillion yuan. I can be seen ha he bond marke has become an imporan place for direc financing in China. I is no only an imporan par of he financial marke, bu also an imporan plaform for naional macroeconomic regulaion and conrol. Bond marke plays an increasingly imporan role in he sable developmen of he naional economy. However, compared wih he developed bond marke, China s bond marke is sill a developing marke wih a shor developmen period, a weak sysem, and a srucure ha needs improvemen. The lack of risk managemen ools and he deficiencies in risk conrol mechanisms have aggravaed he risk accumulaion in he bond marke. According o Wind saisics, here have been 140 bond defauls since 014, involving a balance of billion yuan. Among hem, 35 new defaul bonds were issued in 017, involving a balance of billion yuan, which was sill a grea amoun of money despie a 7.58% year-on-year decrease. In response, China's supervisory auhoriies have successively inroduced a number of policy measures since 017 o srenghen pre-, inra- and ex pos managemen of various bond risks. However, auhoriies no only need o formulae various policies and regulaions on he micro level, bu also needs o undersand he overall marke risk siuaion on a macro level in order o manage risk of he bond marke. The fuures crisis in he lae 1990s and he financial crisis ha broke ou in 008 all underscore he imporance of overall financial risk conrol. This also pus forward higher requiremens for financial risk measuremen. How o accuraely measure risks and improve risk managemen levels o ensure he healhy developmen of he bond marke and give full play o he role of he risk buffer in he bond marke is a major issue ha we urgenly need o resolve.. Lieraure Review In he sudy of risk in he bond marke, foreign scholars sared earlier. The research conen mainly includes hree aspecs: firs, he sudy of bond liquidiy and volailiy risk; second, he facors ha conribue o bond premium risk; hird, he influencing facors on he pricing of corporae bonds. Chordia e al. (003) sudied he mechanism of ineracion beween liquidiy, rading aciviy, yield, and volailiy beween he sock marke and he bond marke. The resuls showed ha he sock marke and bond markes had similar liquidiy paerns. The ineracion beween volailiy and liquidiy did exis, ha is, here were he same influencing facors ha affeced each oher sysemaically. John and Monika (005) sudied he characerisics of he ime variaion of expeced excess bond yields, and conduced a regression analysis of he one-year excess reurn of he iniial forward rae. A single en-shaped long-erm ineres rae linear combinaion was used o predic he excess reurns of 1- o 5-year bonds, and he regression resuls showed ha R was as high as Heinke (006) sudied he relaionship beween bond credi risk premiums, volailiy, and credi raings. He used panel daa o compare credi spreads before and afer changes in credi raings. Using -es o sudy how volailiy changes depend on he credi raing, Heinke drew he conclusion ha here is an inverse relaionship beween raings and volailiy. Ludger e al. (009) empirically sudied he risk premiums of he European Cenral Governmen and he sub-naional governmens of Germany, Spain and Canada and found ha he cenral governmen's risk premium has a posiive response o deb and deficis. Jürgen e al. (011) sudied he spreads of governmen bonds denominaed in US dollars and euros relaive o benchmark bonds in he Unied Saes and Germany before and afer he 008 financial crisis. The empirical evidence showed ha afer he crisis, he spread of non-benchmark bonds rose sharply due o he increase in he degree of general risk aversion. German bonds had acquired similar safe-haven invesmen saus as he Unied Saes. Darbha and Dufour (014) sudied he relaionship beween he risk of defaul in a counry and he insufficiency of liquidiy in issuing bonds. Empirical evidence showed ha he non-liquidiy of bonds depended on he level of marke developmen in he counry. The sovereign deb defaul decision made he liquidiy of he subordinae bond marke insufficien hrough deb ransfer channels. Liang e al. (016), under he framework of he srucural model, consruced a corporae bond indiscriminae pricing model for credi-level migraion by condiionally applying credi raing migraion boundaries. Using dynamic programming heory, Liang e al. analyzed he impac of model parameers on indiscriminae pricing. Pan (016) buil a corporae bond pricing model based on risk hedging by inroducing sochasic recovery rae and defaul inensiy, and found ha inensiy and recovery parameers were imporan facors affecing bond credi spreads. Claudia e al. (017) used he DCC-GARCH model o analyze he correlaion beween he credi spreads of he U.S. and Canadian corporae bond markes. The empirical evidence showed ha he correlaion beween he wo markes during he normal period was weak, bu he correlaion increased suddenly during he crisis. Thomas (018) sudied he characerisics of he ime variaion of governmen bond yields based on he global asse-reurn pricing model. Empirical evidence showed ha 40% o 70% of he ime variaion in US dollar-denominaed bond income was relaed o he global bond marke and exchange rae risk. China's researches on he risk of bond marke mainly focus on he heoreical discussion of marke managemen mechanism. The empirical research conen is mainly focused on he credi risk of municipal bonds and corporae bonds. 103

3 A few sudies are focused on liquidiy risks. Ba Shusong (000) described he impac of he developmen of he bond marke on he counry's moneary policy and poined ou how o manage he ineres rae risk of he bond marke from he perspecive of ineres rae risk. Li Yan (003) clarified how o correcly undersand he credi risk of corporae bonds, and suggesed ha he consrucion of corporae bond marke requires informaion disclosure sysem and believed ha he governmen mus srenghen he supervision of informaion disclosure. Liu Shangxi and Zhao Xiaojing (005) believed ha here are public risks and fiscal risks in he issuance of municipal revenue bonds. The ways o preven risks were o improve he relevan laws and regulaions, design a marke framework for municipal revenue bonds, and reform he governmen invesmen sysem. Yang Qinyan (007) used he KMV model o measure he credi risk of municipal bonds in Hangzhou and Ningbo, wo economically more developed ciies, and hen proposed policy recommendaions based on empirical resuls from he perspecive of marke insiuional norms. Zhang Rui (010) esablished an error correcion model o sudy he impac of differen influencing facors on he liquidiy of he bond marke. Empirical evidence showed ha domesic money supply was he main driving force of he curren bond marke liquidiy, and ha inernaional capial marke risk had a negaive impac on bond marke liquidiy. The impac of he major inernaional exchange rae flucuaions and inernaional capial coss would affec he bond marke liquidiy in a long-erm way hrough various channels. Zhang Yuyan and Lu Jin (01) poined ou ha self-discipline managemen was of grea significance in he bond marke. Promoing self-discipline managemen would conribue o he developmen and innovaion of he Chinese bond marke. Hou Xianping (016) conduced a mulidimensional analysis of he bond marke risk based on he GAHCH family model and VaR mehod. The applicaion scope and accuracy of various models were compared and sudied hrough rigorous poserior analysis, and hen he applicaion values of differen ypical facs in risk managemen were analyzed. Zong Jun (017) poined ou he curren general risks and oher srucural impacs of China's bond marke, and proposed a mehodology for macro-managemen of bond marke risks, and a risk managemen oolbox o be adoped. From he perspecive of credi risk, Sun Jifeng (017) used he DS model and he KMV model o sudy he bond defauls of lised companies in China. The empirical resuls showed ha when he issuer's credi raing was a or above level A, he credi saus of he issuer was beer and he defaul disance was bigger. However, when he bond issuer s credi saus was below level A, he beer he credi saus of he issuer, he greaer he defaul disance. Song Meiyi and Hu Yuji (018) esablished a hreshold model o capure he non-linear effecs of marke ineres raes on he credi risk of he bond marke. The empirical resuls showed ha long-erm ineres raes had a posiive impac on credi risk as a whole, and shor-erm ineres raes had an opposie effec on credi risk, depending on he degree of currency liquidiy. Judging from he focus of research, when sudying he risks of he bond marke boh a home and abroad, more micro-perspecives are aken o sudy he credi risk of municipal bonds and corporae bonds. There is lile research on he overall risk measuremen of he bond marke. However, in he sock marke, research on financial marke risk measuremen is maure. The mos widely used financial risk quaniaive measure is he loss disribuion meric mehod, and he mos common one is he VaR and ES measure echnology. The concep of VaR was proposed by he Bank for Inernaional Selemens in The calculaion mehods include parameer mehod, hisorical simulaion mehod and semi-parameric exreme value heory. The parameric mehod generally assumes ha he rae of reurn belongs o he posiion-scale disribuion family, ha is, he rae of reurn can be represened by he mean, he sandard deviaion (also called he volailiy) of he yield, and he random error. Because he average yield rae has lile effec on VaR, researchers mainly focus on he volailiy and error disribuion. The volailiy esimaion is generally based on GARCH model and SV model. The error disribuion assumes ha he residual obeys Gaussian disribuion, disribuion, GED disribuion and so on. Applicaions in his area include Siu e al. (000), Tang and Shieh (006), Wua and Shiehb (007). The hisorical simulaion mehod is considered o be he mos convenien mehod for esimaing VaR. I is no necessary o make assumpions abou he enire disribuion of reurns, and he sample quanile of he hisorical income disribuion is used as an esimae of VaR. Barone e al. (1998) showed ha he hisorical simulaion mehod had good predicion performance. In response o he limiaions of he hisorical simulaion mehod, Barone e al. (00) inroduced he Filered Hisorical Simulaion (FHS) mehod. The significan advanage is refleced in he expansion of he scope of hisorical scenarios hrough a weighing facor, and he improvemen of he ail porion of he revenue. Therefore, i has received grea aenion in he field of risk managemen. Adesi e al. (001), Prisker (006), and Sukcharoensin (010) used he FHS echnique o measure VaR and achieved good resuls. The semi-parameric exreme value heory (EVT) is he sudy of modeling and saisical analysis of exreme variabiliy of random variables ha rarely occur, bu ha have a significan impac once hey occur. A presen, he POT model based on generalized Pareo disribuion is he mainsream of exreme value heory. Bali (007) found ha EVT mehod using he Box-Cox generalized exreme value disribuion can more accuraely reflec he exreme risks of financial insiuions. Bhaacharyya e al. (008) combined he GARCH model and he EVT model o consruc a VaR measuremen model for he dynamic volailiy and nonnormaliy of sock reurn, and concluded ha he dynamic VaR model is he bes model for measuring VaR. 104

4 In summary, mos scholars a home and abroad sudied he bond marke from he perspecives of credi risk, liquidiy risk and marke managemen, bu seldom measured he overall risk of he bond marke from he perspecive of financial measuremen. Therefore, his paper will use he muli-dimensional volailiy GARCH model for he bond marke using he daa of China Bond New Comprehensive Wealh (Gross Value) Index from January 1, 00 o March 30, 018, and measure he dynamic risk value of he marke (VaR). Then his paper will perform back es analysis and Kupiec failure rae es on differen GARCH-VaR o obain a robus volailiy model. Finally, based on a robus GARCH model, his paper will use FHS o simulae he fuure yield pah and obain VaR afer Backes analysis. Based on he above empirical resuls, his aricle can provide marke regulaors and invesors wih relevan risk managemen recommendaions. 3. Theoreical Model 3.1 GARCH Model Volailiy agglomeraion is a salien feaure of financial ime series, especially he reurn rae series. When characerizing volailiy accumulaion, he mos commonly used models are he GARCH model and he SV model. This aricle uses he GARCH model o empirically analyze he bond marke index, and is mehods briefly are as follows GARCH (p, q) The GARCH model is an exension of he ARCH model, proposed by T. Bolerslev in 1986, and is paricularly applicable o he analysis and predicion of volailiy. The model equaion for GARCH (p, q) is: p q Where ω 0, α i 0, β i 0, αi βi 1 i 1 j EGARCH (p, q) y x, ~ (0, φ u u N σ ) p q σ ω αiu i β jσ j i 1 j 1 Nelson (1991) proposed he EGARCH model, which is a model ha can reflec he asymmery of financial marke volailiy. The EGARCH (p, q) model equaion is: y x, ~ (0, φ u u N σ ) ln r p u q σ u k i ln ω θk αi β j σ j k 1 σ k i 1 σ i j 1 Where θ 0 means ha he impac of exernal shocks on flucuaions is asymmerical; where θ 0 means ha he influence of negaive shock on he price flucuaion of financial producs is greaer han he impac of posiive shock, ha is Leverage effec GJR-GARCH (p, q) GJR-GARCH was proposed by Glosen, Jagannahan and Runkle in Like EGARCH, i conains a leverage erm o characerize asymmeric flucuaions in financial markes. Is equaion can be expressed as: y, ~ (0, xφ u u N σ ) p q q σ ω αiu i β jσ γ D σ j 1 j j j i 1 j 1 j 1 Where D 1 is a dummy variable, and mee he following condiions. D j 0, u i 0 D j 1, u i 0 If 0 γ, hen negaive shocks have greaer impac on condiional variance han posiive shocks, suggesing a "leveraging effec" in he marke. 105

5 3. VaR Measure Based on GARCH Model VaR (Value a Risk) is inerpreed lierally as "risk value". Is meaning refers o he maximum possible loss of he value of a cerain financial asse or porfolio wihin a cerain period of ime a a cerain probabiliy level (confidence). When Q sands for loss and p sands for probabiliy level, VaR wihin period can be expressed as: Pr Q VaR( p) p A he assumpion of coninuous compounding, wih day as a measuremen of ime, he derivaion of VaR is as follows: Firs define he log yield And hen we ge he following expression Y log P log P 1 p Pr( P P 1 VaR( p)) Pr( P 1( e Y 1) VaR( p)) Pr Y VaR( p) 1 log 1 σ P 1 σ Because VaR( p) / P 1 1, represening ( Y σ) wih F y (), making γ( p ) equals as below. 1 F y ( p), we can lis a new equaion For a small 1 F y ( p) σ 1 VaR( p) (exp( F y ( p) σ) 1) P, The VaR of a uni asse can be approximaed as: 1 VaR( p) σγ( pp ) In his paper, when esimaing VaR, we use he GARCH family model of Secion 3.1 o calculae he condiional sandard deviaion. Subsiuing he above formula, we can ge he dynamic VaR based on GARCH. 3.3 Kupiec Failure Rae Tes The accuracy es of he VaR model refers o he degree of coverage of he acual losses by he measuremen resuls of he VaR model. Therefore, examining he probabiliy ha acual losses exceed VaR is he mos direc mehod of accuracy esing. This paper selecs he Kupiec likelihood raio es as a backesing model for furher analysis. The idea of he failure frequency es proposed by Kupiec is o assume ha he VaR esimaion has a ime independence, and hen we record he acual daily loss exceeding he VaR esimae as failure, and record he acual loss below he VaR esimae as successful. If i is assumed ha each even has ime independence, he binomial resul of he failed observaion represens a series of independen Bernoulli ess. Assumed acual days of inspecion o be T and he Number of days failed o be N, hen we can ge probabiliy of failure as p N T. If he seleced confidence level is q, and he probabiliy of failure is expeced o be P 1 q, hen we can ge he null hypohesis as p p. Kupiec proposed ha he mos appropriae es for he null hypohesis p T N N N T N N N LR ln 1 p p ln 1 T T 1 p is he likelihood raio es: Saisics LR obeys he chi-square disribuion wih a degree of freedom of 1. A a level of significance of 5%, he criical value of Chi-square saisics is Therefore, when LR 3.84,we can rejec he null hypohesis and he model as well. In general, he smaller he number of failures, he smaller he LR, ha is, he more accurae he model and he higher he credibiliy. However, a small number of failures means ha he model is oo conservaive, which can someimes cause he LR o be oo large and rejec he null hypohesis. 3.4 Boosrap Resampling The Boosrap mehod is a simulaed sampling saisical inference mehod. I is based on he original daa and can be 106

6 used o sudy he disribuion characerisics of a saisic for a group of daa. I is paricularly applicable o problems such as inerval esimaion and hypohesis esing ha are difficul o derive by using convenional mehods. The basic idea is o consruc an esimaed confidence inerval wih he help of muliple sampling of parial samples when all samples are unknown. The algorihm flow is as follows: Targe:For a sample x1, x,..., x n,he parameers of is overall probabiliy disribuion θ such as mean, median is unknown. Now we wan o ake advanage of his limied sample o ge an esimae of ˆθ. Sep1 Selec he number of resampling i ; Sep Rerieving N imes from he sample x1, x,..., xn N i ; Sep3 Repea Sep wih i imes, and calculae ˆθ for each sample; Sep4 Use he resuling daa θˆ, ˆ,..., ˆ 1 θ θ i as a sample, and we can ge he value when is quanile is α ; The percenage posiion can be calculaed according o Equaion 1 α 100% and Equaion ( 1 α ) 100%. A he same ime he confidence inerval θ, θ α (1 α ) of he parameer θ wih significance level α can be furher obained. 3.5 Filer Hisory Simulaion Filered Hisorical Simulaion (FHS) is a new nonparameric hisorical simulaion mehod proposed by Barone-Adesi G and Giannopoulos K. As he radiional hisorical simulaion mehod assumes ha he fuure changes of marke facors are compleely consisen wih hisorical changes, i canno handle he exreme siuaions of he marke well. Under exreme circumsances, i will underesimae marke risks. The advanage of he FHS is ha i can simulae exreme evens in a sysemaic way, so ha i can well characerize he ail of he income disribuion and beer measure marke risks. Take AR(1)-GARCH(1,1) as an example, he FHS implemenaion seps are as follows: Sep1 Sandardized processing:sandardize he residual error sequence (sample) obained by he GARCH model o obain he residual sequence ha obeys i.i.d. e ε σ Sep Iniial value selecion:assume ha he curren ime is, and hen draw samples of reurn rae r, sandardized residual e and Volailiy σ a ime from Sep1, as a random error in he simulaion of he firs day's reurn rae series. Afer ha we can ge The reurn rae and volailiy a +1, rˆ ρr ε 1 σˆ ω αε βσ 1 Sep3 Ieraive simulaion:use Boosrap mehod o draw he normalized residual from Sep1 as a random error of he reurn rae sequence a he ime of p in he fuure, and also we can obain he asse reurn rae and volailiy a p 1. Repea Sep3 o ge he asse's reurn rae sequence: εˆ p e p σ ˆ p rˆ p 1 ρrˆ p εˆ p ˆ σˆ p 1 ω αε p βσˆ p Afer several simulaions of he bond index, we can ge he cumulaive reurns for he nex N days. According o he cumulaive disribuion funcion (CDF), we can obain he VaR a a cerain confidence level from he quanile. 4. Empirical Research 4.1 Daa Selecion and Descripion ChinaBond New Composie Index is issued by China Cenral Deposiory & Clearing Co., Ld. (CCDC) o reflec he overall price rend and revenue of he bond marke in China. Compared wih oher indexes, ChinaBond New Composie Index covers a wider range and reflecs a more comprehensive rend of price movemens in China's bond marke. Therefore, based on he discussion above, his paper akes ChinaBond New Composie Wealh (gross) Index as he 107

7 research objec, and selecs he daa from January 1, 00 o March 30, 018 as he sample, wih a oal of 4065 daa. The sample covers hree saes of he bond marke including he bull marke, bear marke and shock marke. Therefore, he saisics derived from he sample can well describe he normal siuaion and exreme siuaion of he marke. The daa in his paper comes from he Wind daabase. 4. Descripive Saisics and Sabiliy Tes 4..1 Descripive Saisics This paper denoes he daily yield rae of he bond marke by r, which is defined as follows: r P 100 ln P in which, P sands for he daily closing price of he bond index, 1,,..., N. The logarihmic yield is muliplied by 100; we do so in order o reduce he esimaed error. Wih he help of MATLAB, we can ge he descripive saisical resuls and he yield rae ime series diagrams of he bond marke, as shown in Table 1 and figure 1. Table 1. Descripive saisics of he yield rae of ChinaBond New Composie Wealh (gross) Index Mean Median Max Min S.D. Skewness Kurosis J-B Prob(J-B) Figure 1. Yield rae ime series diagrams of ChinaBond New Composie Wealh (gross) Index From able 1, we can see ha he yield rae of ChinaBond New Composie Index is rejeced by he normal disribuion hypohesis, and shows a significan characerisic of fa ails wih skewness, which can be seen more inuiively by drawing he QQ diagram as shown in Figure. From Figure 1, i is clear ha, from 004 o 005, from 008 o 009, in he second half of 013 and in 015, he volailiy of he yield rae of ChinaBond New Composie Index ends o enlarge obviously and shows he effec of volailiy aggregaion. In rerospec, i is known ha in 004 he cenral bank led he cenral ineres rae down, urning he bear marke ino bull marke; in 008, he bond marke was hi by he subprime crisis, bear marke came again; in 013, he cenral bank ighened up money supply, he marke faced money shorage; in 015, afer he sock marke s prosperiy and following huge flucuaion, he currency poured ino he bond marke. In a word, he yield rae of ChinaBond New Composie Index can well reflec he volailiy of he marke and depic marke risks. 108

8 4.. Sabiliy Tes Figure. QQ diagram of ChinaBond New Composie Wealh (gross) Index In order o avoid spurious regression, we need o es he sabiliy of sequences. In his paper, we use ADF es o es he yield series of ChinaBond New Composie Wealh (gross) Index. The resuls are shown in Table. Table. ADF es resuls of ChinaBond New Composie Wealh (gross) Index 4.3 GARCH Model Auocorrelaion and Parial Correlaion Tes Augmened Dickey-Fuller es saisic % level Tes criical 5% level values 10% level We carry ou he auocorrelaion and parial correlaion es of he yield of ChinaBond New Composie Wealh (gross) Index. I can be seen from figure 3 ha here is a cerain auocorrelaion and parial correlaion in he yield sequence Mean Equaion Figure 3. Auocorrelaion and parial correlaion es The sochasic volailiy model of yield rae in financial ime series is generally as follows: r μ ε ε N σ, ~ (0, ) σ is condiional variance. Because he mean value of in which, μ is condiional mean for yield, ε is residual, yield rae in financial ime series is much smaller han is sandard deviaion (see Table 1), he condiional mean can be regarded as 0. On he oher hand, he esimaion of he mean of yield rae has lile influence on VaR, plus i was proved ha AR (1) can well describe he condiional mean of yield. Therefore, his paper chooses he following wo as he mean equaion of GARCH: 109

9 4.3.3 Tes of ARCH Effec r ε ε N σ, ~ (0, ) r c ρr ε ε N σ 1, ~ (0, ) We carry ou ARCH-LM es on he residual sequence obained from he mean equaion. As shown in Table 3, under he significan level of 5%, he LM es wih he lag order of 1 rejecs he null hypohesis, so he GARCH model can be esablished. Table 3. Tes of ARCH effec Hypohesis Probabiliy F-saisic Criical Value Mean= AR(1) Noe. In he column Hypohesis, 1 indicaes he rejecion of null hypohesis and he exisence of ARCH effec Parameer Esimaion Previous resuls show ha he yield sequence of financial marke no only has auocorrelaion and volailiy aggregaion, bu also has he characerisics of leverage effec and fa ails. Because GARCH (1,1) model can well describe he marke s volailiy aggregaion, his paper akes GARCH (1,1) as he basic funcion. In order o deermine more accuraely wheher he bond marke has his feaure, his paper uses he GJR (1,1) model and he EGARCH (1,1) model o verify i when leverage effec is aken ino consideraion. We assume ha he yield residual is subordinae o disribuion and compare i wih he normal disribuion hypohesis when aking he fa ails disribuion in he yield sequence ino consideraion. The esimaed resuls are shown in Table 4. Table 4. Tes resul of parameer esimaion of GARCH model Noe. The numbers in he figure are parameer esimaors; he numbers in parenhesis are heir saisics; numbers wih underline mean ha he parameers are no significan a 5% significan level DoF refers o he degree of freedom of disribuion, and from he able 4 we can know ha he all DoF ess are significan a he 5% significan level. I can be seen from he resuls of parameer esimaion in able 4 ha: (a) he esimaion resuls for he parameer ρ of AR (1) are significan a 5% significan level, indicaing ha he AR (1) process assumpion of he condiional mean μ is reasonable; (b) he degree of freedom es based on disribuion is significan, indicaing ha he yield sequence has characerisic of fa ails disribuion; (c) he esimaion of GARCH coefficiens β is significan in each model, 1 indicaing ha he volailiy of he preceding period significanly affecs he volailiy of his period, and he volailiy 110

10 has obvious aggregaion effec; (d) he coefficiens of he model are significan in mos cases, indicaing ha he fiing effec of he model is good; (e) he coefficiens of he leverage effec are significan under he normal disribuion hypohesis whereas under he hypohesis of disribuion, only he coefficien of EGARCH model is significan. The resuls above show ha he bond marke has leverage effec. 4.4 Esimaion and Backesing of VaR VaR Esimaion and Backesing Display We can derive he condiional variance σ from he GARCH model, and hen differen GARCH-VaR esimaors can be obained based on he VaR formula in 3.. Taking GARCH (1,1)-N as an example, using he curren price P, confidence level α, and condiional variance esimae σ ˆ, we can calculae he esimaed value of he maximum loss of asses wih a holding period of 1 days. Because he logarihmic yield in his paper is magnified 100 imes, he price loss correspondingly enlarges 100 imes. The VaR esimae is shown in Figure 4. Figure 4. VaR esimaion under differen confidence levels based on GARCH (1,1) For a vivid visual represenaion of GARCH-VaR and backesing es resuls, we compare he VaR value of he firs 100 days wih he acual loss. As shown in Figure 5, under he confidence level of 99%, he esimaion of VaR is more conservaive, so he number of failure is less. 111

11 4.4. Backesing Based on Kupiec Failure Frequency Tes Figure 5. The effec of Backesing We carry ou Kupiec failure frequency es on VaR resuls esimaed by differen GARCH models. The es resuls are shown in Table 5. Table 5. Kupiec failure frequency es resuls of differen GARCH models model 95% 99% Acual P(LR) Hypohesis Acual P(LR) Hypohesis failure rae failure rae GARCH(1,1)-N 3.5% % EGARCH(1,1)-N 3.% % GJR(1,1)-N 3.49% % GARCH(1,1)- 1.97% % DoF= EGARCH(1,1)- 1.57% % DoF=4.143 GJR(1,1)-.44% % DoF= AR(1)-GARCH(1,1)-N 3.59% % AR(1)-EGARCH(1,1)-N 3.37% % AR(1)-GJR(1,1)-N 3.49% % AR(1)-GARCH(1,1)-.31% % DoF=4.104 AR(1)-EGARCH(1,1)- 1.8% % DoF=3.441 AR(1)-GJR(1,1)- DoF=4.11.9% % Noe 1: indicaes he rejecion of null hypohesis, 0 means he accepance of null hypohesis, so when hypohesis in he above able equals 0, he model is more robus. From he resuls of Kupiec failure rae es, we can see ha mos of he models rejec he null hypohesis, bu he acual failure rae is less han 3.59% under differen confidence levels, indicaing a good esimaion effec. From he principle of Kupiec failure rae es we can derive ha he esimaors of mos of he GARCH-VaR models buil in his paper are conservaive, and he number of failures is so small ha LR is oo big. Thus, he null hypohesis of Kupiec failure rae es is rejeced. 11

12 More specifically: (a) mos of he VaR esimaion models under normal disribuion hypohesis are able o pass he Kupiec es, and he models are more robus. However, he VaR esimaion model under he disribuion hypohesis has lower failure rae, which indicaes ha disribuion can beer reflec he exreme siuaion of he marke, and ha is condiional variance is greaer and he esimaion is more conservaive; (b) when we compare he siuaion where condiional mean equals 0 wih he corresponding AR (1) model, he acual failure rae is no very differen from ha of he Kupiec es. However, he esimaion of AR (1) model is more conservaive, which can be derived from he P value of LR; (c) when he leverage erm is added ino he model, he acual failure rae becomes lower, he model more robus, and VaR's esimaion more conservaive. 4.5 Filered Hisorical Simulaion Based on Boosrap Sandardizaion and Auocorrelaion Tes Afer he esimaion equaion of GARCH, he residual sequence can be obained. Because he FHS heory requires he residual sequence o obey he independen idenical disribuion (i.i.d.), plus many sudies showed ha he normalized residual of he yield sequence is subordinae o i.i.d., we sandardize he residual sequence. We selec he more robus AR (1) -EGARCH (1,1) -N as he research objec and find ha here is a cerain auocorrelaion in he normalized residual sequence. In order o eliminae he auocorrelaion, he AR (5) -EGARCH (1,1) -N model is esablished in his paper. The auocorrelaion ess of residual and residual squared are shown in Figure 6. The sandardized residual can be approximaed as he absence of auocorrelaion. Figure 6. Auocorrelaion ess of residual and residual squared A he same ime, he effec of eliminaing auocorrelaion or no on VaR esimaion is also examined. As shown in Table 6, eliminaion of auocorrelaion makes he acual failure rae of VaR esimaion lower and he model more robus. Table 6. The effec of auocorrelaion on VaR esimaion Model 95% 99% Acual failure rae P(LR) Hypohesis Acual failure rae P(LR) Hypohesis AR(1)-EGARCH(1,1)-N 3.37% % AR(5)-EGARCH(1,1)-N 3.35% % FHS Using he normalized residual sequence, under he same iniial condiion, we simulae he fuure revenue pah by Boosrap mehod. The holding ime of he asses is one monh, ha is, 0 rading days. We simulae 0000 imes a day. Then he cumulaive disribuion funcion (CDF) and he probabiliy densiy funcion (PDF) can be obained, as shown in Figure

13 Figure 7. CDF and PDF of yield rae As shown in Table 7, we can find, hrough he simulaed yield oucome, ha he maximum loss in he following monh is as high as 7% and he maximum income is no more han 7%. I shows ha he marke losses caused by exreme circumsances are huge, bu he maximum income is no as big as he loss, indicaing ha he leverage effec does exis in he marke. In addiion, according o he VaR esimae of confidence level of 95% and 99%, we can know ha he marke loss under normal condiion is no more han -1.4%. Table 7. simulaed oucome of FHS Maximum possible Maximum possible 95% VaR 99%VaR loss revenue Loss percen % 6.897% % % In order o es he simulaion effec of FHS, his paper simulaes he yield rae of asse holding period of 5 days, 10 days, 15 days, 0 days, and compares hem wih he fuure acual loss (April 018). The resuls are shown in Table 8. Table 8. The effec of FHS 5 days 10 days 15 days 0 days 95% VaR % % % % 99% VaR % % % % Acual loss 0.467% 0.630% % % As ime goes on, he VaR esimaion value simulaed by FHS is also magnified. Bu a 95% confidence level, he esimaed value can cover he acual loss, indicaing ha FHS has a good risk-predicion abiliy. 5. Conclusions and Suggesions Accuraely measuring he risk of bond marke is very imporan for improving he risk managemen level of he bond marke and mainaining he sabiliy of he financial sysem. Taking ChinaBond New Composie Wealh (gross) Index as he research objec, his paper consrucs differen bond marke yield volailiy models, uses VaR o measure he risk of he bond marke in China, and compares he measuremen accuracy of various models hrough he backesing analysis and he Kupiec failure rae es mehod. Then, his paper uses he Filered Hisorical Simulaion mehod based on Boosrap mehod o simulae VaR wih differen confidence levels and he maximum possible loss and revenue of he marke under exreme condiions. A he same ime, by comparing wih he acual loss, he risk predicion abiliy of FHS is measured. The resuls of he sudy show ha: (1) The yield rae of he bond marke has he characerisic of hick ails. The acual failure rae of he GARCH-VaR model based on disribuion is lower, and such model can measure he risk of he marke more accuraely. Bu, under he Kupiec es, he robusness of he model is no as good as he one which is based on normal disribuion hypohesis; () The yield rae of he bond marke no only has volailiy aggregaion effec, bu also has leverage effec. The leverage erm provides more effecive informaion in he marke, which can improve he esimaion accuracy and robusness of VaR; (3) The yield rae of he bond marke has a cerain auocorrelaion. Eliminaing he auocorrelaion of yield can effecively improve he esimaion accuracy and robusness of VaR; (4) Filered Hisorical Simulaion mehod based on Boosrap mehod reflecs he exisence of leverage effec in he marke, ha is, he maximum possible loss of he marke is far greaer han he maximum possible revenue in he 114

14 coming period. Using FHS o esimae he risk can effecively measure he acual loss of he marke. The above conclusions have imporan guiding significance in he risk managemen pracice of he bond marke. As we know, oubreaks of exreme risks end o desroy he smooh operaion of he marke and bring grea losses o invesors. Therefore, prevening and resolving exreme risks is of grea significance o he developmen of he bond marke and he safey of invesmen. In order o preven and resolve exreme marke risks, we mus focus on he ypical characerisics of exreme risk measuremen, such as fa ail disribuion, volailiy aggregaion and leverage effec, which have high applicaion value. According o hese characerisics and changes, he regulaory auhoriies can choose appropriae models o describe he risk of he bond marke and formulae corresponding risk managemen measures; invesors can also choose he appropriae model o measure risk and specify heir own invesmen sraegies by aking heir own risk olerance ino consideraion. Meanwhile, boh supervisors and invesors can effecively evaluae he risk of he porfolio by FHS, hus effecively avoiding huge risk. References Ba, S. (000). The developmen of China's bond marke and is impac on ineres rae policy and bank risk managemen, Journal of Financial Research, (), Bali, T. G. (007). An exreme value approach o esimaing ineres-rae volailiy: Pricing implicaions for ineres-rae opions, Managemen Science, 53(), hps://doi.org/10.187/mnsc Barone, A., G., & Giannopoulos, K. (001). Non parameric VaR Techniques. Myhs and Realiies, Economic Noes, 001, 30(), hps://doi.org/ /j x Barone, A. G., Bourgoin, F., & Giannopoulos, K. (1998). Don Look Back, Risk, (8), Barone, A. G., Giannopoulos, K., & Vosper, L. (00). Backesing Derivaive Porfolios wih Filered Hisorical Simulaion (FHS), European Financial Managemen, 8(1), hps://doi.org/ / x Bhaacharyya, M., & Riolia, G. (008). Condiional VaR using EVT Towards a planned margin scheme, Inernaional Review of Financial Analysis, 17(), hps://doi.org/ /j.irfa Champagne, C., Coggins, F., & Sodjahin, A. (017). Corporae bond marke inerdependence: Credi spread correlaion beween and wihin U.S. and Canadian corporae bond markes, Norh American Journal of Economics & Finance, 41, hps://doi.org/ /j.najef Chordia, T., Roll, R., & Subrahmanyam, A. (003). Deerminans of Daily Flucuaions in Liquidiy and Trading Aciviy, Cuadernos De Economía, 003, 40(11), hps://doi.org/ /s Cochrane, J. H., & Piazzesi, M. (005). Bond Risk Premia, American Economic Review, 95(1), hps://doi.org/10.157/ Darbha, M., & Dufour, A. (014). The Term Srucure of Bond Marke Illiquidiy and Defaul Risk, Social Science Elecronic Publishing, 014. Heinke, V. G. (006). Credi spread volailiy, bond raings and he risk reducion effec of wachlisings, Inernaional Journal of Finance & Economics, 11(4), hps://doi.org/10.100/ijfe.75 Hou, X., Huang, D., Chen, Y., & Xu, K. (016). Analysis of he applicaion value of ypical facs in risk managemen of China's bond marke, Managemen Review, 8(09), Li, Y. (003). The credi risk of corporae bonds and he developmen of China's corporae bond marke, Journal of Renmin Universiy of China, (03), Liang, J., Zhao, Y., & Zhang, X. (016). Uiliy indifference valuaion of corporae bond wih credi raing migraion by srucure approach, Economic Modelling, 54, hps://doi.org/ /j.econmod Liu, S., & Zhao, X. (005). China: he risk and prevenion of Municipal Income Bonds, Managemen World, (03), Nischka, T. (018). Bond marke evidence of ime variaion in exposures o global risk facors and he role of US moneary policy, Journal of Inernaional Money & Finance, 83. hps://doi.org/ /j.jimonfin Pan, J., Xiao, Q. X., & School, B. (016). Pricing of Corporae Bond wih Sochasic Recovery Risk under he Hybrid Model, Sysems Engineering, 016. Prisker, M. (006). The hidden dangers of hisorical simulaion, Journal of Banking & Finance, 30(), hps://doi.org/ /j.jbankfin Schuknech, L., Von Hagen, J., & Wolswijk, G. (009). Governmen Risk Premiums in he Bond Marke: EMU and Canada, European Journal of Poliical Economy, 5(3), hps://doi.org/ /j.ejpoleco

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