E3 Journal of Business Managemen and Economics Vol. 3(3). pp. 7-37, March, 0 Available online hp://www.e3journals.org ISSN 4-748 E3 Journals 0 Full lengh research paper Finance, producion, manufacuring and logisics: VaR models for dynamic Impawn rae of seel in invenory financing He Juan *, Jiang Xianglin, Zhu Daoli 3, WangJian, Chen Lei 4 College of Traffic,Transporaion and Logisics, Souhwes Jiaoong Universiy, Chengdu 6003,China Insiue for Financial Sudies, Fudan Universiy, Shanghai 00433,China 3 School of Economics and Managemen, Tongji Universiy, Shanghai 0009, China 4 Deparmen of Credi Risk Managemen in Chengdu, Huaxia Bank 6000,China Acceped 4 February 0 This paper presens a framework of seing he impawn rae dynamically by dividing he impawn period ino differen risk windows. Besides, i proposes ha compared wih pledging loan of bonds and socks, he essence of invenory financing is o forecas he long-erm risk from shor-erm daa, and rade off beween he risk window and he erm of financial produc (impawn period). Based on he daase of spo seel (ϕhrb335), usually raded in he over-he-couner markes, his paper esablishes he model of VaR-GARCH(,)-GED, which can beer depic he feaure of he heeroskedasiciy, lepokurosis and fa-ails of he reurns, forecass VaR of seel during he differen risk windows in he impawn period hrough mehods of ou-of-sample. To improve he coverage of he model, his paper inroduces he coefficien K, and hen ges he impawn rae consisen wih he risk olerance of banks. The main resuls show ha he amended model may conrol he risk beer while reducing he efficiency loss compared wih exising mehods. I pus forward a dynamic impawn rae mode for banks. Keywords: finance; logisics; dynamic impawn rae; long-erm risk forecasing; invenory financing. INTRODUCTION Wih he rend ha indusry compeiion ransforms enerprises compeiion o supply chain compeiion, supply chain finance appears. Recenly, Euromoney magazine defines he supply chain finance as he mos popular opic in banking ransacion service over he pas few years, and assers ha he needs of he business will coninue o grow in nex several years. Supply chain finance is pricing and marke ransacion of capial and relevan service o mee he capial demand of supply chain producive organizaion(hu Y F, 009), and is also an innovaive service inegraing logisics and finance provided by logisic enerprises(chen X F, 005). Pu Corresponding auhor. E-mail: hejunlin93@63.com; 996449@qq.com anoher way, supply chain finance provides a sysemaic financial soluion o capial resricion problem. Compared wih mixed operaion in foreign developed counries, supply chain finance in China is pledged collaeral business paricipaed by commercial banks, core enerprises, SME (small & medium enerprises) and warehouse supervision enerprises and so on(feng, 007). Besides, differen from foreign developed fuures marke, invenory financing is mainly based on invenory in form of spo ransacions (such as maerial, producs, half-finished producs, ec.) raher han foreign popular righs pledge (receivable accoun, accouns payable and derivaives). In brief, he developmen of domesic supply chain finance is no only he business exension of radiional warehousing changing o modern logisics, and more imporan is ha is adapion o he presen marke under which i is so hard o finance for many SME while offering loans for banks. Tha is o say, i may
8 E3. J. Bus. Manage. Econ. commendably remi banking compeiion and financing dilemma of SME. Alhough supply chain finance marke has grea poenial in China, he worry abou is risk has resriced he prosperiy of invenory financing iself. According o Naional Income Accouns and Saisical Yearbook (People's Bank of China, 006), he curren invenory of all enerprises amouns o 5.94 rillion Yuan in China, 3.036 rillion Yuan of which are of small and medium enerprises, and 0.4 billion Yuan are of farmers. If he discoun rae of loans is 50%, hese financial asses can generae secured loans of abou.6 rillion Yuan, which equals o new loans of financial insiuions in one year. However, mos banks did no make full use of abundan invenory resources. The pivoal poin is lack of risk managemen echniques abou invenory financing. Invenory financing, as one of main models of supply chain finance in China, make invenory as he pledge o srongly miigae credi risk of loans. During evaluaion of he loans, pledge invenory mus be evaluaed o find wheher i can mainain is capabiliy of guaranee for loan which is refleced by impawn rae (usually called loan-ovalue raio in oher lieraures). In commercial banks pracice, managemen approach from supply chain financing aciviies (The following simply defined as managemen approach ) provides he pledge loan based on he righs of commodiies or commodiies. The impawn rae shall no exceed he highes level of 70%, and he impawn period shall no exceed one year. Curren banking pracice sill rely on he experience o deermine he impawn rae, which would be far from consisen wih he risk olerance level of banks. Therefore, as a core issue, i is imporan o se impawn rae no only for he risk conrol of supply chain finance bu also for promoion of he developmen of he business. In recen years, he domesic and foreign scholars have made some beneficial exploraions on volailiy and risk managemen of collaeral pledged. Cossin and Huang (003) derive a general framework for collaeral risk conrol deerminaion in repurchase ransacions(cossin D, 003). In he domesic research, given ha he price of he pledged sock is flucuan randomly, Li Yi-xue, Feng Geng-zhong e al implemen risk esimaion sraegies of main body + deb and analyze loan-o-value raio decision of banks wih downside risk consrain when price disribuion of he sock a he end of he loan follows general disribuion and several special disribuions(li Y X, 007). These resuls have played posiive and pracical role in deeply undersanding and capuring he acual volailiy and risk level of pledged invenory marke. However, i is imporan o noe ha he quaniaive models above are mosly based on he mahemaical opimizaion mehod and ake he bank expeced revenue as he objecive funcion. To pu i simply, here are many heoreical modeling and cases based on individual samples while he empirical researches based on large number of samples are scarce. Wih he rapid developmen of modern financial risk managemen echnology, he domesic and overseas researchers have proposed risk managemen ools o manage invenory financing, and made considerable progress. As a main risk analysis and measuremen mehod, VaR (Value a Risk) raised by J. P. Morgan in he 90h of las cenury, has been widely used in he academics and pracice(jorion, 00). Alhough VaR could simply refer o he amoun of money ha asses are likely o lose over predefined period and a a given confidence level, i is difficul o measure he risk precisely. The main reason is ha he mos common parameric mehod of calculaing VaR no only depends on he disribuion of reurn of asses bu also he volailiy. Abundan empirical researches show ha he reurns of asse usually do no follow he independen normal disribuion in he efficien financial marke, bu feaures lepokurosis, fa-ails and volailiy clusering. Unforunaely, he exising researches srongly rely on he normal assumpion of reurns of asses, while aking lile accoun of he characerisics of fa ails and heeroscedasiciy. For insance, wheher using he VaR mehod o measure marke risk of socks(wang, 003), or sudying impawn rae of he sandard warehouse receip(li, 00), boh are based on he assumpion of he efficien financial marke where reurns obey independen normal disribuion. The mos popular model aking accoun of his phenomenon is he Auoregressive Condiional Heeroscedasiciy (ARCH) process, inroduced by Engle (98) and GARCH model exended by Bollerslev(986) (Bollerslev, 986; Engle, 98). Therefore, GARCH model is inroduced in he financial managemen field and hen widely used in financial pracice as one of main approaches o predicing volailiy. Ricardo(006) applies he GARCH heory o predicion of he volailiy of financial series accompanied wih oher heavy ails disribuions o esimae he maximum possible loss may be occurred. Gong Rui, Chen Zhong-chang (005), Liu Qing-fu e al (006)respecively describe he characerisics(fa-ails, volailiy clusering) of he financial ime series and consrucs he GARCH models for calculaing ime-varying value a risk based on he volailiy and disribuions of reurns of index of sock and copper fuures in China.(Gong R, 005; Liu Q F, 006) The lieraures above mosly esimae marke risk of sock index, bonds and fuures of commodiies based on he GARCH models, which have relaively robus risk conrol measures, such as price limis, daily selemen and margins rules ec. Besides, he liquidiy is good, and he selemen ime is shor. Hence, mos of curren research based on he GARCH models focuses on shor-erm risk wihin wo weeks especially daily risk. Compared wih bonds, socks and fuures, spo commodiies raded in he OTC (over he couner marke) have rare risk measures. Moreover, he liquidiy is disproporional o risk rae. The low liquidiy and
Juan e al. 9 ineviably relaively long selemen ime of spo pledged collaeral causes high risks in invenory financing. The key poin of invenory financing is o forecas long-erm risk, in oher words, o predic value a risk of N laer based on pas samples. Pu anoher way, he essenial of seing impawn rae dynamically is o resolve wo problems: one is how o rade off beween risk holding horizon and he erm of financial producs; he oher is o rade off beween daa frequency and forecas frequency, ha is o say how o predic he long-erm (muli-periods) risk based on hisorical samples. As he bigges producer and consumer of seel in he world, seel is always imporan raw maerials of pillar indusries of China such as real esae, auomobile, equipmen manufacuring, e al. Besides, wih he characerisics of beer liquidiy, easy sorage and nonperishable, seel has been as an ideal pledge. In he laer half of 008, wih he impac of he inernaional financial crisis, he price of seel had a sharp diving, which had caused price risk of invenory financing o increase dramaically. So seing appropriae impawn rae dynamically based on VaR mehod can conrol he price risk of invenory and improve he efficiency of financing quanificaionally. Providing ha subsanial lieraure above, combined wih exising research of impawn rae of invenory financing, his paper does some work as follows: () Differen from he exising research saically seing impawn rae in he erm of produc (i.e. impawn period), his paper, aking accoun comprehensively of macroeconomic environmen, he credi level of counerpary, he liquidiy of pledged invenory and he risk preference of banks, firs proposes a dynamic model seing dynamic impawn rae by dividing he impawn period ino differen risk windows o rade off he dilemma of risk holding period and he produc erm a he operaional level. () In order o beer depic he feaures of heeroscedasiciy, lepokurosis and fa-ails, i inroduces Generalized Error Disribuion, hen builds VaR-GARCH (,)-GED model raher han he Risk Merics based on normal assumpion, and hen proposes he formula of long-erm VaR o deal wih he problem beween daa frequency and forecas frequency. (3) as far as he predicaion of volailiy concerned, he predicion ou of sample is more pracical (Whie, 000), so, his paper predicaes volailiies of differen impawn period ou of samples. (4) Since i s impossible for any model o precisely forecas risk, his paper ses he parameer K o improve risk coverage. (5) The Hi sequences will be esablished based on failure rae in back esing o ensure reliabiliy of he research. The res of he paper is organized as follows. Secion se up models, including VaR-GARCH model for longer-erm risk forecasing and dynamic impawn rae model. Secion 3 is he empirical analysis, including he sample selecion, he daa characerisic descripion and he deailed resul analysis. Secion 4 is model evaluaion. And he final secion concludes. Model assumpion Given ha he price of pledged invenory, like financial asses, flucuaes, his paper adops he inernaional common pracice under which banks have o have ools and mehods o imely evaluae value of pledged invenory before pracicing invenory financing. Therefore, he models are se up based on he following assumpions. Logisics enerprises and banks closely cooperae wih each oher; The impawn rae varies during impawn period wih he varying macroeconomic environmen, credi level of counerpary, liquidiy of pledged invenory and he risk preference of banks; Considering he erm of invenory financing is less han one year, so he ineres rae is assumed as consan. Model se-up Allowing for he characerisics of heeroscedasiciy, lepokurosis and fa-ail, VaR-GARCH(,)-GED model is used o esimae he volailiy of reurn rae of pledged invenory; furhermore he long-erm price risk, which indicaes he maximum possible loss over a predefined ime horizon a cerain level of confidence esablished previously, will be calculaed based on VaR(value a risk). The risk-free value of pledged invenory, which can be obained by subracing he VaR, is also he amoun of loan. The seps of his model are organized as follows: Yield rae of pledged invenory: R = ln P ln P () R Where is defined as he logarihmic reurn, price a ime. Volailiy of yield rae of pledged invenory P is he In financial lieraure, he volailiy of financial asses is he sandard deviaion of reurn rae. Similarly, he volailiy of pledged invenory is he sandard deviaion of is reurn in his paper. Recen subsanial empirical sudies indicae ha financial asses are characerized of volailiy clusering, which conribue o he heeroscedasiciy of reurns. Accordingly, GARCH model is inroduced o depic his rai above. Besides, curren research shows ha GARCH (,) model migh describe mos of he ime-varying variance of financial series. Therefore, we use he GARCH (,) o forecas he volailiy of invenory, and esablish he condiional mean equaion and condiional variance equaion as follows:
30 E3. J. Bus. Manage. Econ. R = µ + σ z, z i. i. d., E( z ) = 0, Var( z )= σ = + ε + β σ 0 µ Where is he condiional mean, allowing for ha he mos of log-reurns of financial asses are independen or low-order serial correlaions, which is basic idea in curren research of volailiy of financial asses(see(tsay, µ 0 005)). Thus, o assume previously = ε σ z. is sochasic disurbing erm, also called residuals. In his z σ formula, is he Innovaions; is he condiion variance a, 0 is consan; is he ARCH parameer, β is he GARCH parameer, > 0 and 0, > 0, β > 0. z In he curren pracice, he Innovaion is usually assumed o follow normal disribuion. However, i usually feaures faer ails in pracice. The suden disribuion was firsly inroduced by (Bollerslev, 987), while (Nelson, 99) suggesed he so-called Generalized Error Disribuion (GED) for beer approximaing he fa-ails of he innovaions. Consequenly, his paper z assume follows GED. The densiy funcion of GED is, v v f ( x, v) = exp ( / ) ( x / γ + v ) Γ (/ v) (4) Where γ γ when v =, ( / v) / = [ Γ(/ v) / Γ (3/ v)] ; z follows normal disribuion; for v < z disribuion of has faer ails han normal disribuion. VaR and impawn rae, he Taking ino accoun of boh he volailiy of pledged invenory price and he ime horizon from risk idenificaion o risk reamen, he calculaion of VaR in invenory financing is a process of long-erm risk forecasing, raher han daily ones, which no only mee he demand of emerging business (supply chain finance e al) bu also he regulaions of Basel Accord Ⅱ or even he laes version Basel Accord Ⅲ ha banks mus repor longer erm VaR o supervision insiuions. Unforunaely, as menioned in he inroducion, curren researches are mainly concerned wih shor-erm risk, while ignoring long-erm risk measuremen. The besknown mehod in pracice is square-roo rule wih formula () (3) as VaR( T ) = VaR()* T. Alhough such scaling is widely used, i is valid only when he reurn follows he independen normal disribuion wih a zero rend. However, he reurn ypically feaures lepokuric and fa ails, so he scaling is no longer valid when applied o evaluaion of long-erm risk in invenory financing. Considering all above, in order o obain more precise VaR, (Dowd, 004) proposed he revision of square-roo rule. VaR T P T F T ( ) = [ exp( µ + σ )] P Where is defined as he iniial value of uni pledged invenory (for simpliciy, his paper denoes he uni price F as he iniial value). denoes he lef quanile a cerain he level of confidence. Compares o he square roo rule, his modified model has made much improvemen and is able o avoid he predicaion of day-o-day volailiy. However, i sill relies on he square roo rule more or less. In order o improve he deficiency of wo approach above, Philippe Jorion (00), Ruey S. Tsay(005), (Andersen, 006) and Ricardo.A(006) argue ha he condiional variance of he long ime horizon equals o he sum of daily condiional variances under he efficien marke hypohesis ha he reurn is independen. T µ : + T = R + i i= σ : + T = σ + σ + L+ σ + + + T ( + β ) T = TVL + ( σ V ) + L ( + β) σ β σ i = VL + ( + ) ( V ) + i + L Where. Hence, he formula (5) can be modified in he following way, VaR( T) = P exp ( µ [ : + T ] + F σ[ : + T ] ) (8) In banking pracice, i is necessary o se he appropriae risk window (risk holding horizon) o measure risk. Furhermore, i faciliaes o conrol marke risk (i.e. price risk) of invenory financing o se impawn rae dynamically. As is well known, risk window and confidence level are he wo key parameers when VaR is applied o forecas he possible maximum loss. As regards he risk windowt, i is always defined as selemen ime, which is consisen wih he maximumt ideally since in banking pracice, mos of asses are moneary asses of good liquidiy and herefore hese (6) (5) (7)
Juan e al. 3 P S K S V Figure. The design of mechanism of impawn rae T Margin call, Replenishmen areas are mainly concerned wih daily VaR. However, as for he pledged invenory, heoreically, we should consider comprehensively he liquidiy of supply chain financial marke, he sample size and pledged asse posiion adjusmen o adjus i. In Pracice, according o heir personal risk preferences, banks are concerned wih no only he liquidiy of pledged invenory, bu also credi level of counerpary and some financial indicaors such as level of solvency, profiabiliy. In addiion, according o he recommendaion of inernal model of marke risk measuremen of commercial bank which was issued by China Banking Regulaory Commission, he level of confidence is se as 99%. Afer deermining he risk window and confidence level based on heory analysis as well as banking pracice, we can calculae he VaR during he risk window, and obain he risk-free value which is he amoun of loan as menioned above. The raio beween he risk-free value and curren price of pledged invenory is he impawn rae. P VaR ω = 00% P Sk = 00% P Where ω is defined as impawn rae. Obviously, Sk denoes he risk-free value. Alhough he VaR-GARCH (,)-GED model can porray he lepokuric and fa ailed and volailiy clusering of reurn o a cerain exen, i is possible ha he risk would be underesimaed. Accordingly, he liquidiy, he credi level of counerpary and he cos of replenishmen and closed posiion are considered comprehensively, and hen he warning level is brough o conrol he risk of bank in his paper. (9) As can be seen from Figure., during he risk window T, when he price of seel falls below he warning level, margin call or replenishmen will be done ill he value of seel regresses above he warning line. Closed posiion will be done if companies refuse o do hem in ime. Based on his, we se he correcion facor K =. ~.(which references he guidelines of sock collaeral issued by China Securiies Regulaory Commission, 004). In banking pracice, banks should ake ino accoun comprehensively ha macroeconomic environmen, he credi level of counerpary, he liquidiy of pledged invenory and he risk preference of hemselves o se K reasonably, which also helps o remi he adverse selecion and moral hazard o some exen. In he empirical analysis followed, his paper assumes K =., and he modified model will be: P VaR ω = 00% P K S K = K 00% P SV = 00% P S Where V is defined as he amoun of pledged loan. Numerical experimens Sample selecing (0) In his secion, in order o evaluae he models, we ake he seel rebar (ϕhrb335) as sample, which is widely used in he indusries of real esae and infrasrucure indusries. The daa se is obained from XiBen new line sock and ShangHai fuures exchange for he period of Sepember 5h, 005 o December 3h, 009. The daa from Sepember 5h, 005 o December 3h, 009 end o be as he sample used o esimae he parameers; he res will be as es sample. Then we carry on a series of simulaed pledge wih he saring dae of impawn conrac as January h, 009. The impawn period is se o be he maximum. Obviously, i is imporan o rade off he impawn period and risk holding period. Generally speaking, he longer risk holding period is, he more radical banks end o be; he shorer holding period is, he more conservaive banks end o be. In banking pracice, risk holding period can be aemp o se respecively as: week, weeks, monh,, 3, 4, 5, 6, 7, 8, 9, 0,,. Descripive saisics of log-reurn of seel rebar price As shown in Figure, he log-reurns series show
3 E3. J. Bus. Manage. Econ.. R.08.04.00 -.04 -.08 06M0 06M07 07M0 07M07 08M0 08M07 Figure. The linear graph of log-reurn of seel rebar in Shanghai Table. Descripion of basic feaures of log-reurns Mean S.D Skewness Kurosis J-B D-W 0.0009 0.009.038 4.976 57887.78(0.0000).955 Table. The resuls of ADF es of log-reurns -Saisic Prob.* Augmened Dickey-Fuller es saisic -3.8975 0.0000 Tes criical % level -3.437695 values: 5% level -.86467 0% level -.56849 Table 3. The resuls of ARCH effec es Heeroskedasiciy Tes: ARCH F-saisic 3.55798 Prob. F(5,855) 0.0000 Obs*R-squared 34.44 Prob. Chi-Square(5) 0.0000 significan volailiy clusering which indicaes ha ARCH effec possibly exiss in log-reurns. Table provides summary saisics as well as he Jarque Bera saisic for esing normaliy. In almos all cases, he null hypohesis of normaliy is rejeced a any level of significance, as here is evidence of significan excess kurosis and posiive skewness. D-W value is close o, so he log-reurns may be as independen. Only when he ime series is saionary, can we esablish he GARCH model. Therefore, i is necessary o carry on Augmened Dickey-Fuller es (i.e. ADF uni roo es). As shown in Table, in all cases, he null hypohesis is rejeced a any level of significance (%, 5%, 0%), so he ime series of daily log-reurn is saionary. As shown in Table 3, he value is significan, which indicaes ha he ARCH effec exiss in he residuals of daily log-reurns. Empirical resuls As menioned in Table 4, all he parameers of GARCH(,)-GED are significan. In addiional, he value of AIC and SC is reasonable. Consequenly, i is z accepable o assume follows GED o depic he lepokurosis and fa-ail of log-reurns. The condiional mean and condiional variance can be rewrien as follows: R = ε () σ = 3.40E 06 + 0.5ε + 0.745σ From equaion (), i can be obained ha: ()
Juan e al. 33 Table 4.The parameer esimaion of GARCH(,) GED 0 β v AIC/ SC GARCH(, )-GED 3.40E-06 (0.0000) 0.5 (0.0000) 0.745 (0.0000) 0.853 (0.0000) -8.495-8.3965 + β = 0.86 <, which denoes ha he ime series of daily log-reurn is saionary. The long-erm variance can be calculaed hrough he following he formula: 0 V = L.374E 05 β =. Addiionally, he parameer v is 0.853 obained by Eviews. The corresponding quanile on lef is -.87when he confidence level is 99%. Combining wih he equaions (7), (8) and (0), he empirical resuls can be shown in able 5. Model evaluaion Back esing of long-erm risk In order o es he accuracy of he VaR-GARCH (,)- GED model considering volailiy clusering and heavy ails, we sill have o es he risk coverage level (See Table 6) of VaR. Since he price risk is an inherenly unobservable variable,we have o monior VaR forecass by checking no only wheher our forecass are realized, bu wheher hey are consisen wih subsequenly realized reurns given he confidence level. In he exising back esing mehods of VaR, he mos widely applied are failure rae mehod (see (Kupiec, 995)) and inernal back-esing model of Basel accord. Boh he wo mehods are applied o examine he excepions ha he acual loss is beyond he daily VaR. For insance, when he ime horizon is year, he confidence level is 99%, he excepions of less han 7 are acceped in he failure rae mehod, while only less 4 imes may be acceped by Basel II inernal green ligh area. Bu boh of hese mehods are no suiable for back esing of long-erm risk in invenory financing business. Based on research above, he Hi funcion is esablished o es he accuracy of long erm price risk predicing. Pu anoher way, we have o observe he excepions ha he expeced price of invenory (risk-free value) is higher han he acual price. Hi =, P < P VaR 0, + i orelse (3) S = P VaR Where k, which denoes he expeced price (risk-free value, he warning level is called in his paper), f is he observed number of excepions in he sample. f / N is close o saisically, if he bias is oo large, he model could no predic he price risk correcly. If he frequency of price of pledged invenory puncures he warning level S K, and he cos of replenishmen is oo high, he risk migh be underesimaed, so i is necessary o es wheher he price series P puncure he loan value S V which is correced by he parameer K. The funcion can be seen as follows: Hi, p + i< SV = 0, orelse (4) The main resuls show ha he model of VaR- GARCH(,)-GED may predic he risk perfecly in mos risk windows. Unforunaely, he failure raes are.3% and 3.5% in he risk windows of 3 and 4 respecively, which are far beyond % corresponding o 99% confidence level. However, he risk coverage level (See Table 6) has been improved remarkably via K, which plays an imporan role as capial cushion. Tesing beween he impawn rae and lowes value of he seel rebar As menioned in previous research, he impawn rae reflecs he risk expecaion of banks abou pledged collaeral. Thus, he impawn rae obained by an effecive model should be in posiive correlaion wih he lowes value in he erm of saisics, alhough i is unable o reflec for he specific one due o various random facors. Pu simply, he closer he coefficien of correlaion is o, he beer he model performs. Table7 and Table 8 presen he lowes price of seel rebar under differen risk windows and corresponding impawn rae during ime horizon, he coefficien of correlaion are respecively 0.999999, which is close o. This shows ha he correced model is efficien.
34 E3. J. Bus. Manage. Econ. Table 5. The empirical resuls of differen risk windows of impawn period Risk window week weeks monh 3 4 5 6 7 8 9 0 Size N 5 3 43 65 87 08 30 53 74 96 8 39 6 P 3580 3580 3580 3580 3580 3580 3580 3580 3580 3580 3580 3580 3580 3580 P +T 3700 3700 3800 3330 340 3350 3490 3800 450 3630 3480 3480 3590 3740 VaR 06 65 8 309 377 433 480 53 564 599 63 664 69 7 S K 3474 345 335 37 303 347 300 3057 306 98 948 96 888 859 S V 358 304 3047 973 9 860 88 779 74 70 680 65 66 599 ω 0.88 0.87 0.85 0.83 0.8 0.80 0.79 0.78 0.77 0.76 0.75 0.74 0.73 0.73 Table 6. The resuls of esing risk coverage level of model Risk window week weeks monh 3 4 5 6 7 8 9 0 Size N 5 3 43 65 87 08 30 53 74 96 8 39 6 S K 3474 345 335 37 303 347 300 3057 306 98 948 96 888 859 f 0 0 0 0 8 3 0 0 0 0 0 0 0 0 f /N 0 0 0 0.3% 3.5% 0 0 0 0 0 0 0 0 S V 358 304 3047 973 9 860 88 779 74 70 680 65 66 599 f 0 0 0 0 0 0 0 0 0 0 0 0 0 0 f /N 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Table 7. The impawn rae and lowes value under differen risk windows during impawn period Risk window week weeks monh 3 4 5 6 7 8 9 0 P L,T 3580 3580 3580 3330 340 340 340 340 340 340 340 340 340 340 ω 0.88 0.87 0.85 0.83 0.8 0.80 0.79 0.78 0.77 0.76 0.75 0.74 0.73 0.73
Juan e al. 35 Table 8. The correlaion merics of ω and P L,T ω PL,T ω.000000 0.999999 PL,T 0.999999.000000 The analysis of efficiency of model As menioned in he inroducion, he value of impawn rae is almos lower han 70% based on experience mehod in banking pracice. This mehod may conrol risk while causing higher efficiency loss. In he following ex, we will compare he model of he impawn rae wih he mehod of experience, and hen inroduce wo indicaors: efficiency loss, risk rae. To faciliae he processing, we selec he upper limi (70%) of impawn rae in he mehod based on banks experience. P + T SV = 00% P (5) SV = 00% P + T P T (6) Where + is defined as he price a period-end of risk window; < shows ha he risk is under conrol. As can be seen from Table 9, Table 0 and Figure3, he wo indicaors are in negaive correlaion, which is consisen wih he facs in pracice. Addiionally, he risk rae of he wo mehods is less han. Thus, he risk is under conrol. Bu he efficiency loss is grea in he experience-based mehod, even if we ake he upper limi (70%) of impawn rae. Alhough he model in his paper has a cerain degree efficiency loss, i has been grealy improved compared wih he mehod based on experience in comparable shor risk windows. CONCLUSIONS In response o he longer-erm risk holding periods due o he insufficien liquidiy of pledged invenory, his paper iniially esablishes he model of VaR-GARCH(,)-GED o forecas he long-erm price risk, which beer depic he characerisics of volailiy clusering, lepokurosis and fa-ails, subsequenly obain he analyical formula of VaR which is used o measure he risk of differen risk holding periods, and finally se dynamic impawn rae by dividing he impawn period ino differen risk windows, aking accoun of macroeconomic environmen, he credi level of counerpary, he liquidiy of pledged invenory and he risk preference of banks. The conclusions are arrived as follows: The ime series of reurn of rebar price in Shanghai, have significan characerisics of, faails, volailiy clusering. I is imporan o noe ha, he model may be able o predic he longerm risk in mos cases; however, he failure rae of risk window boh in 3 and 4 are far beyond he confidence level, which shows ha he model is no able o predic he long-erm risk perfecly, alhough allowing for he characerisics of fa-ails and volailiy clusering. Consequenly, he revision has o be done considering comprehensively macroeconomic environmen and he volailiy of pledged invenory, when banks and supervision insiuions use he maure and sound VaR models o forecas risk. Based on his, he correced parameer K was inroduced ino his paper. The resuls show ha, he risk coverage level has been improved remarkably via K, which plays an imporan role as capial cushion. In addiion, banks could ge he upper bound of K via sress ess, for insance, in response o he exreme case, sress es migh be carried on regarding o he price plunge of seel in 008. There is a significan posiive correlaion beween he impawn raes obained from model and he lowes price in he fuure risk window. This model could reflec reasonably he risk expecaion of banks abou pledged seel. Moreover, compared wih he empirical mehod widely used in banking, he model could conrol risk, while having he higher financing efficiency. Therefore, i may beer improve he aracion of invenory financing by reducing he adverse selecion and moral hazard o some exen. I is imporan o keep in mind ha o simplify he operaion in pracice, his paper mainly discusses he predicion of ime-varying volailiy of reurns based on VaR-GARCH(,)-GED model while unforunaely ignoring he auocorrelaion of logreurns due o he insufficien liquidiy of pledged invenory, which may be he criical facor resuling in he failure rae of far beyond % in he 3 risk window. Thus, i remains for fuure research o improve he accuracy of longer-erm price risk predicion of pledged invenory accompanied wih he auocorrelaion of log-reurns. All hese research could provide quaniaive basis for decision making which may faciliae o release he risk and improve he reurns for banks.
36 E3. J. Bus. Manage. Econ. Table 9. Analysis of efficiency and risk based on experience of impawn period Risk window week weeks monh 3 4 5 6 7 8 9 0 33% 33% 36% 3% % 4% 7% 36% 49% 3% 7% 7% 30% 34% 68% 68% 66% 75% 77% 75% 7% 66% 59% 69% 7% 7% 70% 67% Table 0. Analysis of efficiency and risk of VaR-GARCH(,)-GED model Risk window week weeks monh 3 4 5 6 7 8 9 0 5% 7% % 0% 9% 4% 9% 9% 4% 6% % 3% 7% 3% 85% 84% 80% 89% 90% 85% 8% 73% 65% 75% 77% 76% 73% 69% Figure 3. Comparison beween VaR-GARCH(,)-GED mode and experience mehod during impawn period
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