A Comparative Study with Quantile Regression and Back Propagation Neural Network for Credit Rating

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1 Journal of Fnance and Economcs Volume 4, No. 2 (2016), ISSN E-ISSN X Publshed by Scence and Educaton Centre of North Amerca A Comparatve Study wth Quantle Regresson and Back Propagaton Neural Network for Credt Ratng Shn-Yun Wang 1*, He-Shun Syu 2 1 Department of Fnance, Natonal Dong Hwa Unversty, Hualen, Tawan 2 Chang Hwa Commercal Bank, Tape, Tawan *Correspondence: Shn-Yun Wang, Department of Fnance, Natonal Dong Hwa Unversty. 1, Secton 2, Unversty Rd. Shou-Feng, Hualen 974, Tawan. Tel: ; E-mal: gracew@mal.ndhu.edu.tw Receved: March 21, 2016 Accepted: Aprl 28, 2016 Onlne Publshed: July 28, 2016 DOI: /jfe.v4n2p46 Copyrght S.-Y. Wang & H.-S. Syu ** Abstract URL: In ths study, we use the quantle regresson and the back propagaton neural network to construct a credt ratng model for companes lsted n Tawan Stock Exchange and Over-The-Counter. The data we use s from 1997 to 2013 n Tawan. The data n the perod from 1997 to 2005 s n sample and the data n the perod from 2006 to 2013 s out of sample. TCRI establshed by TEJ s used as a dependent varable to analyze the relatonshp between 12 fnancal ratos and credt ratng. Our results show that the average forecastng correcton rate based on the propagaton neural network, whch s about 70%, s hgher than that based on the quantle regresson, whch s about 60%. However, nvestors and fnancal nsttuton are manly concerned about the companes facng bankruptcy so they are more nterested n whch companes bear hgher rsk. In ths case, the quantle regresson can provde hgher forecastng correcton rate for low-credt-rankng companes, whch s about 80%, than that provded by the back propagaton neural network, whch s about 55%. JEL Classfcatons: C52, C21 Keywords: credt ratng, quantle regresson, back propagaton neural network 1. Introducton It s mportant to forecast the bankruptcy among enterprses due to a lot of crss punchng the market. In 1997, many countres lke Indonesa, Thaland, and Korea etc. were facng serous ** Ths s an open access artcle dstrbuted under the terms of the Creatve Commons Attrbuton 4.0 Internatonal Lcense ( Lcensee: Scence and Educaton Centre of North Amerca How to cte ths paper: Wang, S. Y., & Syu, H. S. (2016). A comparatve study wth quantle regresson and back propagaton neural network for credt ratng. Journal of Fnance and Economcs, 4(2), ~ 46 ~

2 Journal of Fnance and Economcs Vol. 4, No. 2, 2016 bankruptcy and sufferng from great loss n the Asan economc crss. Before the dot-com bubble n 2000, a lot of nternet companes had been establshed even wthout clear busness model for revenue. Untl many companes could not pay the loan, the collapse of the bubbles happened. In 2008 fnancal crss, global market faced the extreme challenge because the poor qualty of the subprme mortgage whch obtans nvestment grade was sold to nvestors. One year later, the governments of Iceland and Greece had the overload debt and they could not repay for credtors. Above all events, many companes were default or bankruptcy so the credt ratng s mportant to measure whether the company s good or bad. A proper credt ratng model can reflect the default rsk of companes accurately. Hgh credt ratng score stands for low default rsk so the companes wth hgh credt ratng scores can hold better reputaton and are easer to get fnanced from the captal market. Due to nformaton asymmetry, t s more dffcult for a company wthout any credt ratng to rase fund n the market because nvestors can t get any nformaton about the company for nvestment decson makng. Therefore, credt ratng can not only decrease the nformaton asymmetry to nvestors but also lower the cost of fnancng for companes. Furthermore, credt ratng can also provde a good reference of the company fnancal status to strengthen government s supervson and management. Ths study compares the quantle regresson wth the back propagaton networks (BPN) and tres to conclude the best method for credt ratng. Wth more accurate credt ratng, enterprses can adjust ther strategy accordngly and nvestors can also have more suffcent nformaton for ther nvestment polcy. Credt ratng receves affrmaton n the nternatonal communty. Moody and S&P (Standard & Poor) are famous n the global and ther ratng results are used extensvely. However, Bear Stearns rated as A by Moody and S&P went bankrupt durng 2008 fnancal crss so there s stll room to mprove extng ratng systems. If there s a more effectve ratng model to reflect the company fnancal status tmely, t could mprove market effcency as well as help the government to strengthen ts supervson and management. In these years, there are many methods establshed for credt ratng model, such as lnear probablty model, Dscrmnant analyss, Probt model, and Logt model. Recently, neural network whch can smulate artfcal ntellgence was also proposed. However, the proposed approaches usually provde averagng results only and can t provde further nformaton on extreme cases. Therefore, the credt ratng model based on these approaches can t provde suffcent nformaton to nvestors and may mslead them for rsk control. Ths study attempts to use quantle regresson approach whch was ntroduced by Koenker and Bassett (1978) to establsh credt ratng model because quantle regresson approach whch could provde observatons on all cases ncludng extreme ones n dfferent quantles s more robust to outlers and provdes another opton to measure credt rsk. In the past, most of studes conclude ther observatons based on the analyss on sngle major approach. However, even though there are already a lot of studes on credt ratng, t s stll dffcult for people to judge whch approach can provde more authentc results because there s no common sample pool and assumptons for the comparson across dfferent studes. Ths study compares two approaches, quantle regresson and BPN, for credt ratng and analyzes the potental mpacts when they are used for credt ratng. Hopefully, t could shed lght on whch approach s more relable for credt ratng. 2. Lterature Revew The earlest applcaton of ordnary least squares (OLS) to bond ratng model can be traced back to the study of Fsher (1959). Altman (1968) utlzed multple dscrmnant analyss (MDA) n Z-score. Altman selected, from 1946 to 1965, 33 bankruptcy frms as samples and another 33 fnancally healthy frms as matched samples. 22 accountng ratos were selected to extract lqudty, proftablty, leverage, solvency, and actvty by MDA. The results showed that Z = s the crtcal pont. Frms are n the safe zones when Z > and contrarly frms are n the dstress ~ 47 ~

3 Shn-Yun Wang & He-Shun Syu zones when Z < Besdes, the bankruptcy probablty of a company n the dstress zones s 95% n one year and 70% n two years. Therefore, the bankruptcy ratng accuracy descends wth tme. Meanwhle, Deakn (1972), Pnches and Mngo (1973), and Blum (1974) also utlzed MDA n the models but they chose dfferent accountng ratos n ther models. The common result was that the bankruptcy ratng for a company based on MDA has hgh accuracy n one year. Ohlson (1980) used 105 manufacturng frms whch confronted default from 1970 to 1976 and 2058 frms wth healthy fnance as samples. These studes utlzed logstc regresson analyss to establsh credt ratng model for bankruptcy predcton n recent three years. The results showed that the accuracy s 92.84% for three years predctng. Smlarly, Dambolena and Khoury (1980) used logt model to analyze the probablty of the falure. The results presented that the accuracy s 82.6% for predctng bankruptcy n fve years. Zmjewsk (1984) used probt model to construct fnancal dstress predcton model. Dutta and Sheckhar (1988) appled neural network for bond ratng and the accuracy s 83.3%. Surkan and Sngleton (1990) used BPN n credt ratng and the accuracy s 88%. Addtonally, these studes also showed BPN has better predcton accuracy than MDA. Km, Westroffer and Redmond (1993) used lnear model, MDA, logt model, and neural network to develop ratng model and found that neural network s the most accuracy among all models. Chaveesuk, Srvaree-Ratana and Smth (1999) used logt model, BPN, and support vector machnes to establsh ratng model and found that these models have great accuracy. Huang, Chen, Hsu, Chen and Wu (2003) used Support vector machnes and BPN to research the ratng of US and Tawan frms and results showed that the accuracy s approxmately 80%. Nemann, Schmdt and Neukrchen (2008) ndcated that fnancal data s not normal dstrbuton. Unless the data s processed by Box and Cox, t can t be used n statstcal models approprately. Quantle regresson was ntroduced by Koenker and Bassett (1978). The advantage s that t does not defne samples as normal dstrbuton. When the dstrbuton of samples s not a normal dstrbuton, the results of quantle regresson could reasonably explan the margn effects n the dfferent quantles. Kordas (2002) used Bnary quantle regresson to model frm s credt. The sample of ths study ncluded 300 defaults and 800 non-defaults. The results showed that bnary quantle regresson s better than probt model. Whttaker, Whtehead and Somers (2005) also used quantle regresson to model consumer credt scorng. In recent years, quantle regresson s used extensvely n the research ncluded stock market, labor market, and medcal feld, but few credt ratng researches used quantle regresson. Ths study attempts to use quantle regresson to establsh credt ratng model and choose approprate fnancal varables accordng to related researches to evaluate company s credt. The purpose s to use quantle regresson to analyze the tals effectvely and accurately. Based on the works n above lteratures, we choose quantle regresson and BPN for comparson to dstngush whch model s better and can provde more nformaton to the market. 3. Methodology The data ncludes lsted and OTC companes ssued by Tawan Economc Journal (TEJ). Because of the specalty, fnancal ndustry companes are not ncluded. The research perod s from 1997 to Tawan Corporate Credt Rsk Index (TCRI) ssued by TEJ s from 1 to 9. The dependent varable, TCRI, s assgned as 3, 2 and 1, respectvely f Tawan TCRI score s from 1 to 3, from 4 to 5 and from 6 to Independent Varables Accordng to Altman (1968), Ohlson (1980), Huang et al. (2003), and Nemann et al. (2008), ths study uses some fnancal ratos to estmate credt ratng. There are nne varables n the model such as sales over total asset (STA), days-account recevable turnover (TDCP), account recevable turnover (ART), workng captal over total asset (WCTA), quck rato (QR), earnngs before nterest ~ 48 ~

4 Journal of Fnance and Economcs Vol. 4, No. 2, 2016 and tax over total asset (EBITTA), nventory turnover (IT), equty over total lablty (ETL), and natural logarthm of total assets (LNTA). They could estmate proftablty, return on equty, actvty, lqudty, solvency, and leverage Quantle Regresson Quantle regresson, whch s superor to ordnary least squares (OLS), was proposed by Koenker and Bassett n Especally for analyss of fnancal data, whch has fat-tal dstrbuton, quantle regresson could be used to observe the margn effect of ndependent varables affectng the dependent varables n each quantle. Snce OLS uses normal dstrbuton, whch may not be true n every case, to descrbe the average margn effect, there s lmtaton to use t for credt ratng, especally for extreme value measurng. Quantle regresson s based on condtonal quantle functon; t could obtan the slope of the endogenous varables n dfferent quantles when gven the exogenous varables. Due to dstrbuton-agnostc assumpton n resdual term, quantle regresson s more robust. The method of quantle regresson s ntroduced as follows. Gven th quantle ( (0,1) ), there s a lnear relatonshp between condtonal quantle of y and x, where =1,,n, y s the credt ratng and x represents exogenous varable ncludng company s fnancal varable. Quantle regresson could be wrtten as: y = x β + u (1) φ φ Under the assumpton of equaton (1), Quant ( y x ) = nf { y : F ( y x) } = x β (2) Quant( u x) = 0, where Quant φ y x ) means the condtonal quantle of y n th quantle, gven ( Furthermore, we could estmate β ˆ whle vares from 0 to 1. Besdes, there s a specal case, medan regresson when s 0.5. n ~ 49 ~ x. Mn ρ( y x β), (3) where ρ ( y x β ) s an ABS (absolute value) functon and could be defned as ρ ( u) = u f u 0 or ρ ( u) = ( 1) u f u < 0 (4) ˆ β mn ˆ β (1 ) ˆ = + β y x y x (5) u 0 u< 0 If = 0.5, equaton (5) could be rewrtten as ˆ mn 0.5 ˆ β = y x β, whch s LAD (Least u absolute devaton) estmator. Ths regresson s called medan regresson whch s a specal case n 0.5 quantle. The basc concept of quantle regresson gves estmators dfferent weght n dfferent quantle. Therefore, when there are extreme values whch exst n the tal, quantle regresson model s more robust than OLS. Ths study wll use quantle regresson to examne the relatonshp between credt ratng and fnancal varables. From the above descrpton, t s obvous that the quantle regresson consders the condtonal probablty dstrbuton of explaned varables. In order to use quantle regresson to analyze data, the dependent varables must be ordered. When the varable of credt ratng s ordered from low to hgh, low quantle stands for poor credt and hgh quantle stands for preferred credt.

5 Shn-Yun Wang & He-Shun Syu 3.3. Neural Network Neural network s a knd of model whch equps the structure of the bologcal neural network. NN uses a bulk of artfcal neuron to calculate. In most of cases, NN could change nternal structure based on the external nformaton. NN s not a lnear statstc model and usually used to model the complex relatonshp between nput and output. Due to the weakness of dependng hstorcal fnancal data for credt ratng, the outcomes must be modfed by artfcal concept. Hence, NN model could mtate people s consderaton for credt ratng model development Base Model In the sample NN model, bologcal neuron obtans the nformaton from outsde and the nformaton s handled by neural nucleus. The processng procedure gves the messages dfferent weghts based on ther mportance. When transferrng through the functon of artfcal neuron, we can get the output n equaton (6). n y = f( w x u) (6) w:weght; u:bas; f:transfer functon. = Basc Structure The basc structure of NN equps mult-layer structure and multlayer feedforward network, whch s composed by nput layer, hdden layer, and output layer, s the most popular one. Dfferent layers are connected wth each other. Input layer s responsble for ganng a bulk of non-lnear messages. Output layer produces outcomes by transferrng, analyzng, and weghtng data. Hdden layer whch connects many neurons n each layer les between nput layer and output layer. There could be more than one hdden layers but accordng to Zhang, Patuwo and Hu (1998), sngle hdden layer s already suffcent to descrbe complex lnear relatonshp of the data n the model. In ths study, multlayer feedforward network s appled wth sngle hdden layer and there are research varables and fnancal varables n the nput layer. In the hdden layer, dfferent weghts are appled to the varables whch have no relatonshp wth each other. Fnally, the output layer presents the outcome Back Propagaton Neural Network (BPN) BPN, a knd of multlayer feedforward network, can enhance the predcton accuracy through the process of supervsed learnng. Supervsed learnng revses the target value by adjustng the weghts repeatedly untl the bas s close to zero. Although the predcton accuracy of BPN s hgh, there are some shortcomngs. Its learnng process could take a long tme to converge, e.g. hundreds or thousands cycles. In addton, there are no clear rules to determne the number of appled neurons n hdden layer and how to set the learnng speed. So far the best way s try-and-error to fnd the best settng for the outcome Predcaton Accuracy Calculaton In order to calculate the predcton accuracy, classfcaton of the predcton values, t, s needed. A cut-off score, t c, s used for the classfcaton n ths study. When t > tc, the predcton value s assgned to a group. Contrarly, the predcton value s assgned to another group. The determnaton of t c s shown n equaton (7). ( nt 21+ nt 12) tc = (7) ( n1 + n2) The cut-off score consders the dfferent sample number n each group and assgn each group dfferent weghts to reduce the error of category. Fnally, ths study uses the confuson table to present the outcomes. Confuson table s manly used for the predcton accurate rate calculaton. ~ 50 ~

6 Journal of Fnance and Economcs Vol. 4, No. 2, Emprcal Results Ths part ncludes descrptve statstcs, analytcal results of quantle regresson, and analytcal results of BPN. Frst, the descrptve statstcs are used to demonstrate the tendency dfference between n-sample perod (1997~2005) and out-of-sample perod (2006~2013). Second, the results of quantle regresson are analyzed to verfy whether the tendency of the dependent and ndependent varables matches the ntuton. Then how we establsh BPN and ts basc structure s descrbed. Fnally, a confuson table s used for the predcton accuracy comparson between quantle regresson and BPN Descrptve Statstcs In-sample ncludes lsted and OTC companes n Tawan from 1997 to Out-of-sample ncludes lsted and OTC companes n Tawan from 2006 to On the other hand, fnancal and nsurance ndustres are more specfc, so ths study excludes them. Total sample of n-sample are On the other hand, Total sample of out-of-sample are Table 1. The descrptve statstcs of n-sample perod Samples Average Medan Mnmum Maxmum STDEV. RETA ROE EPS STA TDCP ART WCTA QR EBITTA IT ETL LNTA Table 2. The descrptve statstcs of out-of-sample perod Samples Average Medan Mnmum Maxmum STDEV. RETA ROE EPS STA TDCP ART WCTA QR EBITTA IT ETL LNTA ~ 51 ~

7 Shn-Yun Wang & He-Shun Syu From table 1 and table 2, we can observe that TDCP (days-account recevable turnover), ART (account recevable turnover), QR (quck rato) and IT (nventory turnover) have large varaton between n-sample perod and out-of-sample perod. ART and IT have a rght-skewed tendency whle the retaned earnngs of companes and ROE have a decreasng tendency. When companes have hgher WCTA (workng captal over total asset) and QR (quck rato), companes are more conservatve. In addton, the leverage and ETL (equty over total lablty) have a rsng tendency. Ths means that companes has lower debt and rases equty n fnance Analytcal Results of Quantle Regresson Table 3. The result of quantle regresson const ** ** ** ** ** ** ** ** RETA ** ** ** ** ** ** ** * ROE ** ** ** ** * * EPS ** ** ** ** ** ** ** ** ** STA ** ** ** ** ** ** ** ** ** TDCP * * ** ** ** ** ** ** ART WCTA * ** ** ** ** * * ** * QR ** ** ** ** * ** ** ** * EBITTA ** ** ** * ** ** IT ETL ** ** ** ** ** ** ** ** ** LNTA ** ** ** ** ** ** ** ** ** Ths table descrbes the result of quantle regresson ncludng fnancal varables aganst TCRI. Ths study dvdes 9 quantles, φ s from 0.1 to 0.9. ** 5% sgnfcance level *1% sgnfcance level. ~ 52 ~

8 Journal of Fnance and Economcs Vol. 4, No. 2, 2016 Table 3 shows the analytcal results of quantle regresson usng 6490 samples from 1997 to 2005 for nne quantle values wth = 0.1, 0.2,, 0.9. The results show that most of the varables have a postve effect on the credt ratng at 5% sgnfcance level and t s consstent wth our expectaton. However, the ROE have a negatve effect on credt ratng for 0.1 and 0.2 quantle at 1% sgnfcance level. Ths means that the market would request hgher return when companes bear hgher credt rsk. In addton, although ART and IT are not sgnfcant for each quantle at 5% sgnfcance level, the regresson results show that they have a postve effect on credt ratng and t s also consstent wth our expectaton. quantle quantle quantle quantle ~ 53 ~

9 Shn-Yun Wang & He-Shun Syu quantle quantle quantle Fgure 1. The graph of quantles and the ntercept of varables (contd.) From Fgure 1, we could observe that the regresson coeffcent of ROE ncreases from negatve to postve wth the quantle value from 0.1 to 0.9. Ths means that ROE has a negatve effect on credt ratng when the credt ratng s poor and ROE has a postve effect on credt ratng when the credt ratng s good. Although the regresson coeffcent of ROE s negatve n 0.3 and 0.9 quantle, t s not sgnfcant. For ART, the graph shows that the regresson coeffcent ncreases wth the quantle value from 0.1 to 0.9. Ths means that the margnal effect of ART on credt ratng grows wth ART. For the scale of enterprse, the regresson coeffcent of LNTA grows larger and larger wth the quantle value from 0.1 to 0.9. Ths means that the margnal effect of the enterprse scale on credt ratng grows wth the enterprse scale Analytcal Results of Back Propagaton Neural Network Due to the learnng process, BPN would modfy the parameters of the model based on new nput data contnuously to acheve the best modelng accuracy. Hence, when establshng BPN model, we need to set ntal values for the parameters and then try-and-error for the best condton. In ths study, there are 12 varables n the nput layer and there s sngle hdden layer wth 10 neurons. In the output layer, credt ratng s used. Bayes rule method s appled n the tranng functon to ~ 54 ~

10 Journal of Fnance and Economcs Vol. 4, No. 2, 2016 enhance the generalzaton ablty of the network as well as shorten the learnng tme. Batch gradent descent wth momentum algorthm s appled n the learnng functon so that t could response the local gradent change and the latest modelng error tendency. Table 4 compares the analytc results of quantle regresson and BPN. It shows that quantle regresson has better predcton accuracy n the group of Y = 1 n the quantle 0.1 and 0.2. The accuracy s 97.46% and 89.49% for the n-sample data, and 93.23% and 78.62% for the out-of-sample data. Although the total accuracy s low n the quantle 0.1 and 0.2, quantle regresson has better capablty to predct whch company s a bad company n ths range. In the quantle from 0.3 to 0.7, the accuracy s good n the group of Y = 2. The best accuracy of 97.07% and 94.90% s acheved n the quantle 0.5 and 0.4 for n-sample data and out-of-sample data, respectvely. The total accuracy s from 58% to 62% for n-sample data and from 61% to 66% for out-of-sample data. In the quantle 0.8 and 0.9, quantle regresson has better predcton ablty n the group of Y = 3 wth the accuracy of 65.85% and 88.24% for the n-sample data and 87.85% and 97.91% for the out-of-sample data. Ths means quantle regresson has better capablty to predct whch company s good company. Fnally, BPN has better predcton accuracy n the group of Y = 2 wth the accuracy of 93.84% for n-sample data and 93.2% for out-of-sample data. Although ts predcton accuracy s low n the groups of Y = 1 and Y = 3, the total accuracy s the best wth 71.2% for n-sample data and 75.02% for out-of-sample data. model Table 4. The quantle regresson compares wth BPN TCRI Sample Y = 1 Y = 2 = 3 ~ 55 ~ Y Total 0.1 In-sample 97.46% 20.11% 0.60% 37.15% Out-of-sample 93.23% 32.30% 1.69% 43.53% 0.2 In-sample 89.49% 55.64% 2.23% 53.81% Out-of-sample 78.62% 72.57% 5.52% 61.37% 0.3 In-sample 56.76% 86.14% 6.62% 61.66% Out-of-sample 52.91% 90.82% 16.34% 65.83% 0.4 In-sample 26.06% 96.62% 11.01% 59.66% Out-of-sample 35.52% 94.90% 23.49% 63.63% 0.5 In-sample 16.51% 97.07% 17.93% 58.72% Out-of-sample 22.73% 94.09% 35.41% 62.74% 0.6 In-sample 12.89% 96.30% 28.13% 59.45% Out-of-sample 17.28% 91.70% 49.13% 62.59% 0.7 In-sample 10.45% 94.02% 40.70% 61.78% Out-of-sample 13.50% 85.85% 64.83% 61.47% 0.8 In-sample 4.97% 87.68% 65.85% 60.62% Out-of-sample 9.36% 72.21% 87.85% 57.55% 0.9 In-sample 1.64% 70.27% 88.24% 55.29% Out-of-sample 4.86% 48.47% 97.91% 45.73% BPN In-sample 58.00% 93.84% 31.80% 71.20% Out-of-sample 54.44% 93.20% 55.35% 75.02% Note: Ths table presents the accuracy of quantle regresson and BPN wth three groups

11 5. Concluson Shn-Yun Wang & He-Shun Syu Ths study uses fnancal varables to establsh credt ratng model and compares quantle regresson wth BPN. The data ncludes lsted and OTC companes n Tawan from 1997 to 2013 but companes n fnance and nsurance ndustry are excluded due to the specalty. TCRI, presented n TEJ, s the credt ratng varable as dependent varable. Accordng to the references, 12 fnancal varables are chosen as ndependent varables to construct credt ratng model n ths study. The predcton accuracy of quantle regresson, 93.23% and 78.62% for out-of-sample data, s better than BPN for companes wth poor credt ratng, Y = 1, n the quantle 0.1 and 0.2. In addton, the accuracy of quantle regresson, 87.85% and 97.91% for out-of-sample data, s better than BPN for companes wth good credt ratng, Y = 3, n the quantle 0.8 and 0.9. However, the total accuracy of BPN s better than quantle regresson and has the best predcton accuracy for the medan credt group of Y = 2 among three credt groups. In the quantle from 0.3 to 0.7, quantle regresson has smlar credt predcton capablty to BPN wth good accuracy for the group of Y = 2 and they both have worse credt predcton capablty for the group of Y = 1 and Y = 3 among three credt groups. BPN has about 70% total accuracy whch s hgher than the total accuracy, 60%, of quantle regresson. Hence, BPN s better than quantle regresson n total accuracy. However, nvestors sometmes care more about hgh-rsk companes rather than low-rsk companes because they may suffer from great nvestment loss due to hgh-rsk companes. Therefore, the man purpose of credt ratng s to dentfy hgh-rsk companes to prevent nvestors from great loss and provde gudance to the government for supervson polcy adjustment. In ths case, quantle regresson s a better credt ratng model than BPN even though the total accuracy could be sacrfced. References [1] Altman, E. I. (1968). Fnancal ratos, dscrmnate analyss and the predcton of corporate bankruptcy. Journal of Fnance, 23(4), do: /j tb00843.x [2] Blum, M. (1974). Falng company dscrmnant analyss. Journal of Accountng Research, 12(1), do: / [3] Chaveesuk, R., Srvaree-Ratana, C., & Smth, A. E. (1999). Alternatve neural network approaches to corporate bond ratng. Journal of Engneerng Valuaton and Cost Analyss, 2(2), [4] Dambolena, I. G., & Khoury, S. J. (1980). Rato stablty and corporate falure. Journal of Fnance, 35(4), do: /j tb03517.x [5] Deakn, E. B. (1972). A dscrmnant analyss of predctors of busness falure. Journal of Accountng Research, 10(1), do: / [6] Dutta, S., & Shekhar, S. (1988). Bond ratng: A non-conservatve applcaton of neural networks. Proceedngs of IEEE Internatonal Conference on Neural Networks, 2, do: /icnn [7] Fsher, L. (1959). Determnants of rsk premums on corporate bonds. Journal of Poltcal Economy, 67(3), [8] Huang, Z., Chen, H., Hsu, C. J., Chen, W. H., & Wu, S. (2003). Credt ratng analyss wth support vector machnes and neural networks: A market comparatve study. Decson Support Systems, 37(4), do: /s (03) ~ 56 ~

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