An approach to condition the transition matrix on credit. cycle: an empirical investigation of bank loans in Taiwan

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1 An approach o condiion he ransiion marix on credi cycle: an empirical invesigaion of bank loans in Taiwan Su-Lien Lu lous-lynn@mail.su.edu.w Deparmen of Finance, Naional Unied Universiy Kuo-Jung Lee leekj@pchome.com.w Deparmen of Financial Operaions, Shih Chien Univerisy Kaohsiung Campus Corresponding auhor: Assisan Professor, Deparmen of Finance, Naional Unied Universiy, No., Lien Da, Kung-Ching Li, Miao-Li, Taiwan 363, Republic of China. Tel: Fax: lous-lynn@nuu.edu.w

2 An approach o condiion he ransiion marix on credi cycle: an empirical invesigaion of bank loans in Taiwan Absrac This paper presens a formal mehodology for gauging he credi risk of financial insiuions. Alhough he proposed model is based on risk-neural probabiliy and Markov chain model, he model is more elaborae han previous researches. Firs, we provide a way o condiion he ransiion marix on credi cycle. Second, we assume ha he risk premium is ime-varian. Therefore, he defaul probabiliy and risk premium will be recursively endogenous. Third, we apply he mehodology o bank loans in Taiwan, which is never discussed in previous sudies. Furhermore, he procedure of he paper for assessing he credi risk of financial insiuions is easy o follow and implemen. On he whole, he credi risk modeling will be a crucial area for bank regulaors in he coming years. For providing an effecive credi risk review, we expec ha he paper is no only helping o assess he credi risk of financial insiuions, bu also helping o face he Basel Capial Accord. 2

3 . Inroducion Over a decade ago, he Basel Commiee on Banking Supervision ( he Commiee ) produced guidelines for deermining bank regulaory capial. The objecive of his accord was o level he global playing field for financial insiuions and proec all agains risk in he financial sysem. In 988, he Commiee issued he Inernaional Convergence of Capial Sandard (or Capial Accord of 988 ), which esablished regulaions regarding he amoun of capial ha banks should hold agains credi risk. Furhermore, he reamen of marke and operaional risk were incorporaed in 996 and 999, respecively. The final version of he Accord was published in 24 and will be implemened afer 26. The Commiee ried o srenghen capial requiremens given he differen risk exposures of financial insiuions and he wide range of differences in risk managemen sysems. The ne effec is ha will be able o use inernally based risk assessmen sysems in seing capial requiremens. For he credi risk, bank regulaors have o develop an effecive credi review process used o measure he credi risk of heir loans. Therefore, credi risk modeling will be a crucial area for bank regulaors in he coming years in order o provide an effecive credi risk review, no only helping o deec borrowers in difficuly, bu also helping o face he Basel Capial Accord. Recenly, a revoluion has been brewing in he way credi risk is boh measured and managed. Alhough he mos recen recession hi a differen imes in differen counries, mos saisics showed a significan increase in credi risk. In he pas, he Commiee approach has been described as a one size fi all. Now, he Commiee allows banks using inernal models raher han he alernaive regulaory ( sandardized ) model o assess heir credi risk. As a resul, mos new models and 3

4 echnologies have emerged applying o analysis credi risk, compared o previous mehods. Consequenly, accurae credi risk analysis becomes even more imporan oday. Alhough credi risk models have developed rapidly such as Jarrow, Lando and Turnbull (997), Kijima and Komoribayashi (998) and Wei (23), hey do no consider he credi risk of bank loans. They only apply Markov chain model o measure credi risk of bonds. On he oher hand, Lu (26) has applied Markov chain model o bank loans, he do no consider he dependence in ransiion marices, credi cycle, which is an imporan facor. Despie Wei (23) incorporae credi cycle ino ransiion marices, he assumes he risk premium is consan, ha is, ime-invarian. As a resul, his paper incorporae he credi risk and ime-varying risk premium ino Markov chain model ha is more elaborae han previous sudies. Furhermore, we esimae he credi risk of bank loans for hiry-one domesic banks in Taiwan. We expec ha he model no only provide an effecive credi risk review bu also help o face he Basel Capial Accord. The purpose of his paper is o provide an effecive model o measure he credi risk. The model is more elaborae han previous sudies such as Jarrow, Lando and Turnbull (997) and Wei (23) ha ignore he credi cycle and ime-varying risk premium. In his paper, we conribue o he lieraure in he following aspec. Firs, he model incorporaes well-documened empirical properies of ransiion marices such as heir dependence on credi cycle. This paper serves as one of he firs sudies o adop a condiional Markov chain model for assessing he credi risk of bank loans, which is never discussed in previous sudies. In addiion, we compare he difference beween he observed and fied ransiion marix. The observed ransiion marix is calculaed from original Markov chain model ha don consider credi cycle. On he 4

5 oher hand, we incorporae he credi cycle wih he fied ransiion marix. The empirical resuls show ha if we ignore he credi cycle, hen esimaed resuls will be disored and no rue. Second, he model exends he previous framework by relaxing he risk premium as ime-varying parameer. Third, he esimaed procedures are easy o follow and implemen. The model can apply o value he credi risk of oher financial insiuions. On he whole, we expec ha he model proposed in he paper will be helpful for Taiwan s financial insiuions. This paper is organized as follows. Secion provides moivaion. In Secion 2 reviews lieraure concerning models of credi risk. Secion 3 presens he formal mehodology of his paper. Secion 4 describes he sample daa used in his paper. Secion 5 shows he main empirical resuls. Finally, secion 6 includes a discussion of our findings and a conclusion. 2. Lieraure Review Over he las years, credi risk modeling and credi derivaives valuaion have received remendous aenion worldwide. These credi risk models can be grouped ino wo main caegories: he srucural-form model and he reduced-form model. One imporan difference beween hese wo caegories of models is he implici assumpion hey make abou managerial decisions regarding capial srucural. The srucural-form model is also called he asse value model for assessing in credi risk, ypically of a corporaion s deb. I was based on he principle of pricing opion in Black and Scholes (973) and more deailed model developed by Meron (974). Furhermore, he basic Meron model has subsequenly been exended by removing 5

6 one or more of Meron s assumpions. For insance, Black and Cox (976) and Kim, Ramaswamy and Sundaresan (989) sugges ha capial srucure is explicily considered and defaul occurs if he value of oal asses is lower han he value of liabiliies. Brennan and Schwarz (978) and Longsaff and Schwarz (995) invesigae sochasic ineres rae correlaed wih he firm process. Leland (994) endogenizes he bankrupcy while accouning for axes and bankrupcy coss. Consequenly, srucural-form models rely on he balance shee of he borrower and he bankrupcy code in order o derive he probabiliy of defaul. Alhough hese exensions of Meron s original framework, hese models sill suffer some drawbacks. Firs, since he firm s value is no a radable asse, nor i is easily observable, he parameers of he srucural-form model are difficul o esimae consisenly. Second, he inclusion of some fricions like ax shields and liquidaion coss would break he las rule. Third, corporae bonds undergo credi downgrades before hey acually defaul, bu srucural-form models canno incorporae hese credi-raing changes. Reduced-form models aemp o overcome hese shorcomings of srucural-form models, such as Jarrow and Turnbull (995), Duffie and Singleon (997), Jarrow, Lando and Trunbull (997) and Lando (998). Unlike srucural-form models, reduced-form model make no assumpions a all abou he capial srucure of he borrowers. The calibraion of his probabiliy of defaul is made wih respec o raings agencies daa. The original Jarrow and Trunbull (995) model, which was perhaps he firs reduced-form model o experience widespread commercial accepance, was worked ou hrough he use of marices of hisorical ransiion probabiliies from original raings and recovery values a each erminal sae. In conras, reduced-form models can exrac credi risks from acual marke daa and are no dependen on asse value and leverage. Therefore, parameers ha are relaed o he firm s value need no 6

7 be esimaed in order o implemen hem. Jarrow, Lando and Turnbull s (997) model maches he Commiee s opinion reasonably well and represens a major sep forward in credi risk modeling. The model of Jarrow, Lando and Turnbull (997) is based on he risk-neural probabiliy valuaion model, also called he Maringale approach o pricing of securiies, which derives a risk premium for he dynamic credi raing process from he Markov chain process and hen esimaes he defaul probabiliy by ransiion marix. Bu, hey ignore some condiions such as credi cycle, which is an empirical properie of ransiion marix. From a credi risk modeling perspecive, variaion in ransiion marices aribue o credi cycle is poenially very imporan. For Belkin, Suchower and Fores (998), hey employ a parameer o measure he credi cycle, meaning he values of defaul raes and of end-of-period risk raings no prediced by he iniial mix of credi grades. As well-known, raings changes plays a crucial role in many credi risk models and he disribuion of raing changes vary across ime. The Basel Commiee on Banking Supervision also emphasizes he imporance of he credi cycle, which may improve he accurae assessmens of credi risk. Therefore, if ignore such dependence, hen i may lead o inaccurae assessmens of credi risk. There are some known researches which explicily link he impac of he dependence of ransiion marices, such as Belkin, Suchower and Fores (998) and Kim (999). Wilson (997) has shown ha ransiion probabiliies change over ime as he sae of he economy evolves and ha hese changes drive correlaions beween changes in he credi qualiy of differen obligors. Belkin, Suchower and Fores (998) employ a parameer o measure he credi cycle and propose a mehod of calculaing ransiion marices condiional on he credi cycle. Kim (999) builds a credi cycle 7

8 index and his mehod is similar o ha of Belkin, Suchower and Fores (998). Nickell, Perraudin and Varooo (2) quanify he dependence of ransiion marices on he indusry, domicile of he obligor, and on he sage of he business cycle by employing ordered probi models. Alhough hey aemp o incorporae credi cycle in ransiion marices, hey don consider he risk premium. Furhermore, Wei (23) propose muli-facor, Markov chain model ha consider he credi cycle and risk premium on ransiion marix. Wei (23) allows he ransiion marix o evolve according o credi cycle. Alhough his model is more general han previous sudies, he assumes ha he risk premium is kep consan over ime. According o Kijima and Komoribayashi (998) and Lu (26), hey propose a procedure o esimae he risk premium, which is no ime-invarian bu is acually always ime-varian. As a resul, here are wo imporan facors, he credi cycle and risk premium, for assessing credi risk. The paper relaxes assumpions of previous researches by incorporaing he credi cycle and ime-varian risk premium ino Markov chain model for assessing he credi risk of bank loans, which is more elaborae han previous sudies. Consequenly, we expec ha he paper can improve he accuracy of assessmen of credi risk and helpful for Taiwan s banking indusry. 3. Model Specificaion 3. Observed ransiion marix Credi raings of firms are published in a imely manner by raing agencies, such as Sandard & Poor s or Moody. They provide invesors wih invaluable informaion o assess firms abiliies o mee heir deb obligaions. If a company s credi qualiy 8

9 has improved or deerioraed significanly over ime, such a review will promp he agency o raise or lower i raing. Since he marke considers companies wih high raings o be less risk han hose wih low raings, credi raings change from ime o ime o indicae firms credi risk raings. In recen years, i has become common o use a Markov chain model o describe he dynamics of firm credi raings, as in Jarrow and Turnbull (995) and Jarrow, Lando and Turnbull (997). To be more specific, le x represen he credi raing a ime of a bank s borrower. We assume ha x = {x, =,,2,...} is a ime-homogeneous Markov chain on he sae space S={, 2,, C, C+}, where sae represens he highes credi class; and sae 2 he second highes,, sae C he lowes credi class; and sae C+ designaes defaul. I is usually assumed for he sake of simpliciy ha he defaul sae C+ is absorbing. Furhermore, le ( x = jx i) f ij = P + =, i, j S, =,,2, denoe he probabiliy of sae i ransiing o sae j hrough he acual probabiliy measure. Tha is, f ij and P represen he one-sep ransiion probabiliy and acual probabiliy measure, respecively. Then, he discree ime and he regime-swiching of credi class i ransiing o credi class j can be represened by a ime-homogeneous ransiion marix as following, is called observed ransiion marix f f F = M f 2 C f f f 2 22 M C2 L L O L L f f f C 2C M CC f f f,c + 2,C+ M C,C+ A (C = Ο ( C) C) D (C ) ( ) () C where f ij > i, j and f = i. The submarix is defined on j= ij (CA C) non-absorbing saes Ŝ = {, 2,..., C}. The componens of submarix A denoe he regime-swiching of credi classes for he bank s borrower, however i excludes 9

10 defaul sae C+. D is he column vecor wih componens, which represen (C ) f i,c+ he ransiion probabiliy of banks borrower for any credi class, i.e., i=, 2,,C, swiching o defaul class, i.e., j=c+. We assume for he sake of simpliciy ha bankrupcy (sae C+) is an absorbing sae, so ha Ο ( C) is he zero column vecor giving a ransiion probabiliy from he defaul sae a iniial ime unil final ime. Once he process eners he defaul sae, i would never reurn o credi class sae, so ha fc +,C + =. In such a case, we would say ha defaul sae C+ is an absorbing sae. 3.2 Fied ransiion marix For considering he credi cycle, here are some procedures o calculae he fied ransiion marix. The firs sep is o devise a mapping hrough which he ransiion probabiliy can be ranslaed ino credi scores. The paper employs he normal disribuion which is easy o calculae. Since he summaion of each row in a ransiion marix is always equal o. We can inver he cumulaive normal disribuion funcion saring from he defaul funcion as Belkin, Suchower and Fores (998), Kim (999) and Wei (23). Therefore, he ransiion marix as equaion () can be convering as follow y y Y = M y 2 22 C,2 y y y 3 23 M C,3 y y y 4 24 M C,4 L L O L y y y C 2C M C,C (2) Equaion (2) is ( C C) because of no need o cover he row for he absorbing sae, defaul sae. If we conver equaion (2) ino a probabiliy ransiion, hen we also ge a ransiion marix as equaion (). As in Belkin, Suchower and Fores (998), we

11 decompose Y of ime- ino wo facors: Y 2 = αl + α ε (3) where L is sysemaic componen ha shared by all borrowers, meaning credi cycle. The credi cycle will be posiive in good year, which imply ha for each iniial credi raing, a lower han average defaul rae and higher han average rae of upgrades o downgrades. On he oher hand, he credi cycle will be negaive in bad year. In any year, he observed ransiion marix as above will deviae from he norm, ha is L =. The ε is non-sysemaic, idiosyncraic facor ha unique o a borrower. We also assume ha L and ε are uni normal variable and muually independen. The coefficien α is an unknown coefficien, which represens he correlaion beween Y and credi cycle, L. We find he coefficien of each row of equaion (2) o minimum he weigh, mean-squared discrepancies beween he observed ransiion probabiliies and observed ransiion probabiliies. We define P (i, j) Φ(y = i, j+ ) Φ(y i, j ) (4) y αˆ i, j+ L y αˆ i, j L P (y = Φ Φ i, j+, yi, j L ) (5) 2 2 αˆ αˆ where Φ( ) represens he sandard normal cumulaive disribuion funcion and equaion (4) and (5) represen he observed and fied ransiion probabiliy of sae i ransfer o j observed in ime-, respecively. The leas square problem akes he form as Belkin, Suchower and Fores (998) min n [ P (i, j) P (y, y L )],i i, j+ i, j L i j P(yi, j+, yi, j L )[ P (yi, j+, yi, j L )] 2 (6) where n,i is he number of borrowers from iniial sae i ransfer o sae j. In

12 addiion, he weighing facor is P (y i, j n,i +, yi, j,l )[ P (y i, j+, y i, j. Therefore, we,l )] can ge fied ransiion probabiliy via equaion (6). Then, we consruc he fied ransiion marix as follow m m M = M m 2 C m m m M 2 22 C2 L L O L L m m m M CC C 2C m m m,c+ 2,C+ M C,C+ (7) 3.3 Risk premium and defaul probabiliy In addiion, he paper uses he risk-neural probabiliy approach o assess he credi risk of bank loans. Alhough a radiional risk-neural probabiliy approach is used o assess he defaul probabiliy of corporae deb, he mehods and models for assessing he credi risk on bank loans and bonds are similar. Accordingly, we conclude ha a risk-neural probabiliy approach also can apply o bank loans. For he pricing of he defaulable borrower, we need o consider he corresponding sochasic process x~ = {x ~, =,, 2, L} of credi raing under he risk-neural probabiliy measure. For valuaion purposes, he fied ransiion marix needs o be ransformed ino a risk-neural fied ransiion marix under he equivalen maringale measure where we le M ~ denoe such a marix. Alhough he ransiion marix under he new measure need no be Markovian, i is an absorbing Markov Firs, in essence, boh loans and bonds are conracs ha promise fixed paymens of principle and ineres in he fuure. Second, loans and bonds sand ahead he claims of a firm s equiy holders if he firm goes ino defaul. Third, here are covenans on aciviies he borrower may underake while he loans or bonds are ousanding, including limis on he ype and amoun of new deb, invesmens, and asse sales ha can enhance he probabiliy of repaymen. For any given cash flow, he higher dividend payou o sockholders, he less are available for repaymen o bondholders and lenders. Finally, he rae of loans are similar o bond yields, usually reflecing risk premiums ha vary wih he perceived qualiy of he borrowers and he collaeral or securiy backing of he deb. 2

13 chain, which may no be ime-homogeneous. Thus he fied ransiion marix under he risk-neural probabiliy measure is given by M ~ (, + ) m ~ (, + ) L m ~ C (, + ) m ~,C+ (, + ) m ~ 2(, + ) L m ~ 2C (, + ) m ~ 2,C+ (, + ) = M O M M m ~ C(, + ) L m ~ CC (, + ) m ~ C,C+ (, + ) L A ~ (, + ) D ~ (, + ) (C C) (C ) = ~ Ο ( C) ( ) (8) ~ + P{x ~ jx ~ +, i, j S. m ~ and ~ ij P represen he risk-neural where (, ) = = i} m ~ ij = fied ransiion probabiliy and risk-neural probabiliy measure. The condiions for equaion () mus be saisfied here, ogeher wih he equivalence condiion ha m ~ ij (, + ) > if and only if m ij >. Noe ha he risk premium plays a crucial role for assessing he credi risk. The zero risk rae (risk-free rae) and risky rae (loan s rae) can capure he credi risk of he bank loans for every raing class wih he risk-neural probabiliy measure. Firs, le V (,T) be he ime- price of a risk-free bond mauring a ime T, and (,T) V i be is higher risk, ha is, risky counerpar for he raing class, i. However, a loan does no lose all ineres and principal when he borrower defauls. Realisically, we assume ha a bank will receive some parial repaymen even if he borrower goes ino bankrupcy. Le δ be he proporions of he loan s principle and ineres, which is collecable on defaul, where in general δ will be referred o as he recovery rae. If here is no collaeral or asse backing, hen δ =. On he conrary, he recovery rae is < δ. As shown by Jarrow, Lando and Turnbull (997), i can be assumed ha 3

14 m ~ i, j (, + ) = λ () m, i, j S, and λ ) = λ (), for j i and heir procedure for ij ij ij ( i risk premium as V (,) V (,) i λ i() = (9) ( δ)v (,)m i,c+ In equaion (9), i is apparen ha a zero or near-zero defaul probabiliy, i.e., m i,c +, would cause he risk premium esimae o explode and i is also implied ha he credi raing process (including defaul sae) of every borrower is independen, which is inappropriae and irraional for bank loans. However, if he borrower defauls, hen we should never esimae he defaul probabiliy in he fuure. As a resul, we modify he assumpion ha every borrower s credi raing class is independen only before enering defaul sae. We redefine he risk premium as C V (,) V (,) m ~ i δ l i() = ij (,), i=,2,,c and =,,T () m ( δ)v (,) i,c+ j= A ~ (, + ) = A ~ (, )A ~ (, + ) where m ~ (, ) are he componens of he inverse marix A ~ (, ) and ij () A ~ (, ) will be inverible. Noe ha he m i,c + is he ransiion probabiliy of fied ransiion marix by procedure as above. The denominaor of equaion () is no ha, bu ha m ), which can avoid he problem in equaion (9). For equaion (), A ~ (, ( i,c+ + ) = Λ() A and Λ () is he ( C C) diagonal marix m i,c + wih diagonal componens being he risk premium adjused o l j (), j Ŝ. In paricular, he risk premium of = is V (,) δv i(,) l i() =, for i=,2,,c (2) m ( δ)v (,) i,c+ Therefore, we can esimae risk premium by a recursive mehod for all loan periods, 4

15 =,,, T. On he whole, we also find ha risk-neural ransiion marix varies over ime o accompany he changes in he risk premium by equaion () and (2). Then, we assume he indicaor funcion o be, if I { τ > T} ( no defaul before ime T) { = δ, if τ ( defaul before ime T) I} (3) Since he Markov processes and he ineres rae are independen under he equivalen maringale measure, he value of he loan is equal o = V = V (,T) (,T) { E ~ [ { }] E ~ [ { }]} { Q ~ τ> T + δ τ T [ Q ~ T i i τ > + δ { ( ) Q ~ τ i δ + δ ( τ > T) } V (,T) = V (,T) i ( ) ( > T) ]} (4) where Q ~ i ( τ T > ) is he probabiliy under he risk-neural probabiliy measure ha he loan wih raing i will no be in defaul before ime T. I is clear ha V (,T) V (,T) Q ~ i i δ ( τ > T) = ( δ)v (,T) C = m ~ j= ij (,T) = m ~ i,c+ (,T) (5) which holds for ime T, including he curren ime, =. Similarly, he defaul probabiliy occurs before ime T as V (,T) V (,T) Q ~ i i ( τ T) =, for i=,.,c and T=,2, (6) ( δ)v (,T) Consequenly, we can esimae he defaul probabiliy of bank loans under risk-neural probabiliy measure ha incorporae wih credi cycle and ime-varying risk premium. 5

16 4. Daa In Taiwan, here are wo raing agencies, he Taiwan Raing and he Taiwan Economic Journal. The sample daa come from wo daabases of he Taiwan Economic Journal (TEJ), including he Taiwan Corporae Risk Index (TCRI) and long and shor-erm bank loans. The sample period is beween 997 and 23. The TCRI is a complee hisory of shor and long-erm raing assignmens for Taiwan s corporaions. The definiions of he raings caegories of TCRI for long-erm credi are similar o Sandard & Poor s and Moody. TEJ applies a numerical class from o 9 and D for each raing classificaion. The caegories are defined in erms of defaul risk and he likelihood of paymen for each individual borrower. Obligaion raed number are generally considered as being he lowes in erms of defaul risk, which is similar o he invesmen grade for Sandard & Poor s and Moody. Obligaion raed number 9 are he mos risky and he raing class D denoes he defaul borrower. Therefore, he raing caegories used by TEJ, Sandard & Poor s and Moody are quie similar, hough differences of opinion can lead in some cases o differen raings for specific deb obligaions. On he oher hand, since he borrowers obligaion raed numbers are no consisen in every year, we combine he number ~4 as a new raing class, denoed as. Similarly, we combine number 5~6 and 7~9 as wo new raing classes, denoed as 2 and 3, respecively. Thus, here are four raing classes,, 2, 3 and D. The long and shor-erm bank loan daabase is record all debs of corporaions in Taiwan, including lender names, borrower names, rae of deb, and deb issuance daes, ec. For he viewpoin of banks, we can analyze he credi raing class of borrowers o invesigae he credi risk of bank loans. On he oher hand, he risk-free rae is published by he Cenral Bank in Taiwan. 6

17 We ake he governmen bond s yield as a proxy for he risk-free rae. The yields of governmen bonds for various mauriies hose published by he Cenral Bank in Taiwan. Since he mauriy of bank loans and governmen bonds are differen, we have o adjus he yields of governmen bonds, so we inerpolae he yield of governmen bond whose mauriy is closes and ake i as he risk-free rae. Finally, he recovery rae plays an imporan role for making lending decisions ha serves as securiy for bank loans. In general, banks will se a recovery rae according o kinds, liquidiy, and value of collaeral before lending. Fons (987) assumed a consan recovery rae of.4 according o he hisoric level. Longsaff and Schwarz (995) and Briys and de Varenne (997) also assumed a consan recovery rae. Cary and Lieberman (996) assessed he recovery rae on a small sample of defauled bank loans and found ha i averaged over 7%. Copeland and Jones (2) assumed ha he recovery rae is equal o zero in all sample years. On he oher hand, Lu and Kuo (25) suggesed aking he recovery rae as he exogenous variable from. o.9. According o previous sudies, here is no clearly definiion of he recovery rae and he daa on recoveries on defauled loans is clearly incomplee. Consequenly, we assume he recovery rae as exogenous variables from. o.9 in his paper following he assumpion of Lu and Kuo (25). In conclusion, we analyze defaul risk for a leas a one-year horizon and herefore exclude observaions for shor-erm loans and incomplee daa. We also exclude loans ha have an overly low rae because hey are likely o have resuled from aggressive accouning poliics and will bias he esimaed resuls. Since he daa wihou posing collaeral are insufficien for gauging credi risk, we do no consider hese loans. 2 Tha is, we analyze he credi risk of mid-and long-erm loans wih 2 In general, a bank exposes iself o higher risks if i lends wihou collaeral. As a resul, banks always 7

18 posing collaeral for hiry-one domesic banks in Taiwan. 5. Empirical Resuls In his paper, we esimae he credi risk of hiry-one domesic banks in Taiwan. 3 We compare differences of he credi risk beween observed and fied ransiion marix. There are four seps. Firs, we calculae he observed ransiion marix by equaion (). We show he average observed ransiion marix of hiry-one banks from 998 o 23 in Table. There is an ineresing phenomenon in Table. The defaul probabiliy is higher in high raing class,, han ha in low raing class, 2. The phenomenon may be due o credi cycle and risk-neural probabiliy measure. Therefore, we esimae credi cycle and risk premium in furher seps. Iniial Raing Table. Observed ransiion marix, Raing a he end of year 2 3 D reques borrowers o pos collaeral. 3 The hiry-one domesic banks include:() Bank of Taiwan; (2) Bank of Overseas Chinese; (3) Bowa Bnak; (4) Cenral Trus of China; (5) Chang Hwa Commercial Bank; (6) Chaio Tung Bank; (7) Chinarus Commercial Bank; (8) Chinfon Commercial Bank; (9) Cosmos Bank, Taiwan; () EnTie Commercial Bank; () E. Sun Commercial Bank; (2) Far Easern Inernaional Bank; (3) Firs Commercial Bank; (4) Fubon Commercial Bank; (5) Fuhwa Commercial Bank; (6) Grand Commercial Bank; (7) Hua Nan Commercial Bank; (8) Hsinchu Inernaional Bank; (9) Jih Sun Inernaional Bank; (2) Land Bank of Taiwan; (2) Taipei Inernaional Bank; (22) Taiwan Cooperaive Bank; (23) Taipei Bank; (24) Taishin Inernaional Bank; (25) Ta Chong Bank; (26) The Chinese Bank; (27) The Expor-Impor Bank of he Republic of China; (28) The Farmers Bank of China; (29) The Inernaional Commercial Bank of China; (3) The Shanghai Commercial and Saving Bank; (3) Unied World Chinese Commercial Bank. 8

19 Then, we esimae fied ransiion probabiliies ha consider credi cycle by equaion (6) and consruc fied ransiion marix. Thus, we lis average fied ransiion marix from 998 o 23 in Table 2. For Table and 2, we find ha credi cycle have significan effec on ransiion marix. The credi cycle can explain he special phenomenon in able. The defaul probabiliy is higher in raing class 2 han ha in, which is more reasonable and reliable. The defaul probabiliy will be overesimaed and underesimaed of less risk raing class o higher risk raing class. On he oher hand, he defaul probabiliy will underesimae in observed ransiion marix, especially for a paricular raing class, 3. Furhermore, we esimae he ime-varying risk premium and incorporae ino fied ransiion marix o ge defaul probabiliy under risk-neural probabiliy measure. On he oher hand, he coefficien α is he correlaion beween Y and credi cycle L in equaion (3). The esimaed value of α is.934 in Table 2. Iniial Raing Table 2. Fied ransiion marix, Raing a he end of year 2 3 D αˆ.934 Third, we esimae he ime-varying risk premium o ransform fied ransiion marix ino risk-neural fied ransiion marix via equaion () and (2). Therefore, we lis average risk premium in Table 3. The fied ransiion marix under risk-neural probabiliy measure is shown in Table 4. 9

20 Table 3. Average risk premium Mauriy (Years) Raing Table 4. Fied ransiion marix under risk-neural probabiliy measure, Iniial Raing Raing a he end of year 2 3 D Finally, we assess he average defaul probabiliy of 3 banks by equaion (6) and able 5 and figure show he empirical resuls. In 2 and 2, we find ha defaul probabiliies are higher han oher years, which may be accompanied by a change in he business cycle in Taiwan and explained below. Table 5. Defaul probabiliy Year Defaul probabiliy

21 defaul probabil Figure. Average defaul probabiliy year One conribuions of he paper is incorporaing he credi cycle and ime-varying risk premium ino ransiion marix, which is never discussed in previous sudies. Broadly speaking, he credi cycle means he values of defaul raes and of end-of-period risk raings no prediced, using observed ransiion marix, by he iniial mix of credi grades. In good years, credi cycle will be posiive and negaive in bad years. Figure 2 represens he hisorical movemen of credi cycle ha describes pas credi condiions no eviden in he observed ransiion marices. On he oher hand, figure 3 shows he oal scores of monioring indicaors of Taiwan 4 from 998 o 23. The cyclical hrough occurs in 2-2 ha is he period of economic recession of Taiwan. According he model seing, he credi cycle will be posiive in good years and negaive in band years. For figure 2 and 3, we find ha credi cycle drops below zero while Taiwan s business cycle from peak o rough in 2-2. From Table 5 and figure, we find ha defaul probabiliies in 2-2 are higher han oher years. On he whole, he relaive high proporion borrowers ogeher wih 2-2 credi slump accouns for a high number of defaul ha may be due o he business cycle. 4 The oal scores of monioring indicaors of Taiwan is composed of moneary aggregaes Mb, direc and indirec finance, bank clearing, remiance, sock price index, manufacuring new order index, expors, indusrial producion index, manufacuring invenory o sale raio, nonagriculural employmen, expor price index, and manufacuring oupu price index. 2

22 Tha is, he credi risk in 2-2 is higher han oher years. On he oher hand, credi cycle has sayed posiive and credi condiions have remained benign and he defaul probabiliies are low during oher periods. Consequenly, he model for esimaing he defaul probabiliy is accurae and reliable Figure 2. Credi cycle from 998 o year Figure 3. Toal scores of monioring indicaors // 998/5/ 998/9/ 999// 999/5/ 999/9/ 2// 2/5/ 2/9/ 2// 2/5/ 2/9/ 22// 22/5/ 22/9/ 23// 23/5/ 23/9/ year/monh 22

23 6. Conclusion I is imporan o noe ha he model depends largely on he borrower s credi raings and he risk-free erm srucure of he ineres rae, which are forward looking and reflec he curren posiion. They are a imely and reliable measure of credi qualiy. Therefore, accurae and imely informaion from he borrower s credi raing daa provides a coninuous credi monioring process in his paper. This paper have highlighed some raher grea differences beween he previous researches such as Jarrow, Lando and Turnbull (997), Kijima nad Komoribayashi (998), Wei (23) and Lu (26), ec. This paper focuses on providing a formal model o assess he credi risk of bank loans for hiry-one domesic banks in Taiwan. The proposed model conribues o he lieraure in following aspecs. Firs, he model incorporae he credi cycle ino he ransiion marix, called fied ransiion marix. In addiion, we compare differences beween he observed and fied ransiion marix. The empirical resul shows ha he observed ransiion marix will overesimae and underesimae he defaul probabiliy of less risk raing class and risky raing class, respecively. Second, we relax he assumpion of risk premium as a ime-varying parameer ha is assumed as a consan parameer in Jarrow, Lando and Turnbull (997) and Wei (23). Finally, he procedure is easy o follow and implemen. We recommend ha he mehod also can apply o assess he credi risk of oher financial insiuions, such as a bills finance company. On he whole, we expec ha he paper can help banks esimae heir credi risk more carefully and are also an effecive ool for any financial insiuions credi review process. 23

24 Reference Basel Commiee on Banking Supervision, 24, Inernaional convergence of capial measuremen and capial sandards: a revised framework, Bank for Inernaional Selemen. Belkin, B., Suchower, S. and Fores Jr., L., 998, A one-parameer represenaion of credi risk and ransiion marices, CrediMerics Monior, Third Quarer. Black, F. and Scholes, M., 973, The pricing of opions and corporae liabiliies, Journal of Poliical Economy, 8, Black, F. and Cox, J.C., 976, Valuing corporae securiies: some effecs of bond indenure provisions, Journal of Finance, 3, Brennan, M. and Schwarz, E., 978, Corporae income axes, valuaion, and he problem of opimal capial srucure, Journal of Business, 5, 3-4. Briys, E. and de Varenne, F., 997, Valuing risky fixed rae deb: an exension, Journal of Financial and Quaniaive Analysis, 32, Cary, L. and Fons, J., 993, Measuring changes in corporae credi qualiy, Moody s Special Repor, Novermber. Copeland, L. and S. A. Jones, 2, Defaul probabiliies of European sovereign deb: marke-based esimaes, Applied Economics Leers, 8, Duffie, D. and Singleon, K.J., 997, An economeric model of he erm srucure of ineres-rae swap yields, Journal of Finance, 52, Fons, J., 987, The defaul premium and corporae bond experience, Journal of Finance, XLII, Jarrow, R. A. and Turnbull, S.M., 995, Pricing derivaives on financial securiies subjec o credi risk, Journal of Finance, 5, Jarrow, R.A., Lando, D. and Turnbull, S.M., 997, A Markov model for he erm 24

25 srucure of credi risk spreads, Review of Financial Sudies,, Kim, I.J., Ramaswamy, K. and Sundaresan, S., 989, The valuaion of corporae fixed income securiies, Working Paper, Universiy of Pennsylvania. Kijima, M. and Komoribayashi, K., 998, A Markov chain model for valuing credi risk derivaives, Journal of Derivaives, 6, Lando, D., 998, On Cox processes and credi risky securiies, Review of Derivaives Research, 2, Leland, H. E., 994, Corporae deb value, bond covenans and opimal capial Srucure, Journal of Finance, 49, Longsaff, F.A. and Schwarz, E.S., 995, A simple approach o valuing risky fixed and floaing rae deb, Journal of Finance, 5, Lu, S.L. and Kuo, C.J., 25, How o gauge he credi risk of guaranee issues in Taiwanese bills finance company: an empirical invesigaion using a marke-based approach, Applied Financial Economics, 5, Lu, S.L., 26, The defaul probabiliy of bank loans in Taiwan: an empirical invesigaion by Markov chain model, Asia Pacific Managemen Review, forhcoming. Meron, R.C., 974, On he pricing of corporae deb: he risk srucure of ineres raes, Journal of Finance, 29, Nickell, P., Perraudin, W. and Varooo, S., 2, Sabiliy of raing ransiions, Journal of Banking and Finance, 24, Wei, J.Z., 23, A muli-facor, credi migraion model for sovereign and corporae debs, Journal of Inernaional Money and Finance, 22, Wilson, T., 997, Credi risk modeling: A new approach. Unpublished mimeo, McKinsey Inc., New York. 25

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