BANKRUPTCY PREDICTION BY USING SUPPORT VECTOR MACHINES AND GENETIC ALGORITHMS

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1 BANKRUPCY PREDICION BY USING SUPPOR VECOR MACHINES AND GENEIC ALGORIHMS SALEHI Mahd Ferdows Unversty of Mashhad, Iran ROSAMI Neda Islamc Azad Unversty Scence and Research Khorasan-e-Razav Branch Abstract: he orgnal purpose of ths study s comparng of Support Vector Machne and Genetc Algorthm and mpact of fnancal ratos on accuracy of bankruptcy predcton. In accordng to some lmtatons n tradtonal statstcal models, we used two models of Support Vector Machne and Genetc Algorthm. One of fndngs n ths research s mpact of fnancal ratos on accuracy of bankruptcy predctng and t shows that mproper selecton of fnancal ratos do not have hgh resolutons. Besdes, they can decreases accuracy of predcton and may wrong ntroduce results of the research. Moreover, Support Vector Machne was more powerful than Genetc Algorthm n year s t. However, t cannot be ntroduced whch of them s better. Identfyng of the most effectve fnancal ratos as predctor varables and create a more powerful models, whch can mprove accuracy of predcton and reduce bankruptcy rsk and ts heavy cost wll be decreased. hs research focuses on dentfyng the most effectve fnancal ratos and the most powerful model for predctng of bankruptcy. Key words: Bankruptcy predctng, Support Vector Machne, Genetc Algorthm, fnancal ratos 1. Introducton Bankruptcy and falure of company as unfavorable fnancal phenomena always be mportant. Snce md 20 th century, n accordng to growth of technology, wde envronmental changes and ncrease compettons have rased chance of falure and n other words, wth the advent of jont stock companes and ncrease demand of companes to fundng from outsde sources need to assess the fnancal stuaton of companes by nvestors and lenders n order to provde more confdence to nvest n the companes. Reasonable concerns of nvestors and ncome of ther captal and advantages and dsadvantages of bankruptcy predctng n companes, mcro economcs and others have led to wde research n dentfyng bankruptcy and methods Studes n Busness and Economcs

2 of ts predctng whch have been done n cross the globe. If we can predct bankruptcy and dentfyng chance of bankruptcy and then plannng and solve the problem, we wll troubleshoot and problem-solvng methods to prevent from waste of physcal and humanty sources. Moreover, ths model can be good leader for nvestors. In fact, predctng bankruptcy s one of methods, tools for predctng future stuaton of company and chance of bankruptcy can estmate by fnancal ratos, and these models due to rapd growth of technology and rse n economcal compettons are very mportant for researches and fnancal decson makers. By usng of ths model, credtors, nvestors and managers can be able to predct bankruptcy of companes n several pror and after year s occurrence. Followng, n accordng to fndngs of these models, we can do necessary actons for preventng losses. In fact, predctng models are separated n two or several levels by at least errors. hus, n process of predctng, we are followng a model whch can be able predct of bankrupt or non-bankrupt of a company based on a seres of fnancal data by classfed statstcs and machne learnng whch s called supervsed learnng (Premachandra et al, 2009). However, result of researchers ndcates that n between predctng bankruptcy models, average accuracy of artfcal ntellgence n predctng of bankruptcy s hgher than statstcal models. 2. Lterature revew here have been several models for Predctng bankruptcy. Beaver (1966) wth a sample of 158 companes, 30 fnancal ratos to be selected as the best ndcator of a company's fnancal health and t shows that ratos are as one of the best ndcators for fnancal health of companes and he beleved ratos are ference n healthy and falure companes. Altman (1968) by usng fve fnancal ratos va MDA model, he could propose that MDA model can evaluate bank loans, nternal control process and nvestment optons. Frydman et al, (1985) were the frst persons who used PRA model. Mn and Lee (2005) by Support Vector Machnes could desgn model for predctng companes, ther results show that Support Vector Machne had better performance compare wth other tradtonal statstcal models. Km and Kang (2012) n ther research show superorty of Support Vector Machne compare wth genetc algorthm. hey selected a sample nclude of 1200 Korean audtng companes and wth select of seven fnancal ratos (ncome to total assets rato, earnngs before nterest and taxes to nterest expense, retaned earnngs to total assets, cash return, total debt to total assets, Inventory to sales and total assets) showed that Support Vector Machne wth accuracy of 72.45% s more powerful compare wth the other models. Moreover, optmzed models wth Genetc Algorthm have hgher performance than the classfed ndvdual models Fnancal rato Bankruptcy predcton models are one of technques and tools to predct the future state of companes that evaluate bankruptcy by combnng group of rsk by Studes n Busness and Economcs

3 fnancal ratos. n the most models of bankruptcy have used of accountng nformaton that s used often n the form of fnancal ratos. he role of accountng nformaton derved from the ference between the company's fnancal was one of the controversal ssues n the healthy and unhealthy companes n recent decades. Altman (1968) argued that fnancal ratos of bankrupt companes to non-bankrupt fnancal ratos are sgnfcantly ferent. Chen (2011) n ther emprcal study that ncluded 42 fnancal, 33 fnancal ratos, 8 non-fnancal ratos and used one of the combnaton of macroeconomc ndcators to get the result, fnancal ratos are more effectvely n antcpatng of bankrupt. Hossary (2006) beleved that 79% of research n the feld of bankruptcy predcton used fnancal ratos as predctng varable. Gahlon (1988) showed that related nformaton about cash flows, ncludng varatons n cash flows from operatons and cash coverage rato ndex, are sutable for predctng bankruptcy. Blum (1974), Deaken (1972), Mensah (1983) argued that the current cash to total debt as a crucal predctor Support vector machnes Support Vector Machne s statstcal learnng algorthms and t s lookng for optmal screen separator by the vectors supportng and ths way they can solve classfed problems (Yoon, 2010), Support Vector Machne s so smple that t can be analyzed by mathematcs. Recently, Support Vector Machne has frequent applcatons such as credt ratngs and predctng tme seres. Support Vector Machne usng a lnear model to classfy of nonlnear boundary through a nonlnear mappng nto a hgh dmensonal feature space to perform lnear model created n the new space. Nonlnear decson boundares n the new space wll create an enormous page. hus, Support Vector Machne s an algorthm that s a certan knd of lnear model and fnd that the maxmum margn of the enormous page. Maxmum of the enormous page can lead to maxmum separaton n among the classes. Moreover, the nearest educatonal data to the maxmum margn of the enormous page refers to the support vectors. Support vectors can determne the boundary amongst classes and the rest of the tranng data s not necessary to specfy the bnary class boundares (Mn & Lee, 2005). Studes conducted by ths method have been shown that, Support Vector Machne In terms of performance s better than other methods such as bankruptcy predcton ANN- CBR-MDA (Rav Kumar& Rav, 2007). Vapnk proposed the support vector machnes (Vapnk, 1995). he support vector machnes (Support Vector Machnes) [1] have been hghly concerned n recent years. Based on the structured rsk mnmzaton (SRM) prncple, Support Vector Machnes seek to mnmze an upper bound of the generalzaton error nstead of the emprcal error as n other neural networks. Addtonally, the Support Vector Machnes models generate the regress functon by applyng a set of hgh dmensonal lnear functons. he Support Vector Machne regresson functon s formulated as follows (Pa and Ln, 2005): Studes n Busness and Economcs

4 y = w (x) + b, he tranng algorthms of Support Vector Machnes try to fnd the optmal separatng hyperplane by maxmzng the margn between the hyperplane and the data and thus mnmzng the upper bound of the generalzaton error. Delverng promsng results makes, the Support Vector Machnes extensvely applcable n many nformatonprocessng tasks, ncludng data classfcaton, pattern recognton and functon estmaton. Support Vector Machnes are ordnarly used as bnary classfers that separate the data space nto two areas. he separatng hyperplane s not explctly gven. A small number of data ponts, called support vectors, represent t. However, the real data are often lnearly nseparable n the nput space. o overcome ths, data are mapped nto a hgh dmensonal feature space, n whch the data are sparse and possbly more separable. In practce, the mappng s also not explctly gven. Instead, a kernel functon s ncorporated to smplfy the computaton of the nner product value of the transformed data n the feature space. hat s, choosng a kernel functon mples defnng the mappng from the nput space to the feature space (Wu and Wang, 2012) Genetc algorthm Genetc algorthm, whch s known as evolutonary approach, ntroduced for the frst tme by Holland (1975). Genetc algorthm s one of search algorthms and t s based on the genetc lvng creatures. Followng, codng should be done and t s the most common format the chromosomes n genetc algorthms. Each decson varable n Format of bnary form and then get together and make ths varable chromosome and also a ftness functon must be devsed solutons to each encrypted value of the run to select parents for reproducton. Combnaton and mutaton operators are used to produce new offsprng. hs process s repeated several tmes and produce the next generaton populaton and crowd converged standards wll be revewed and f the process s termnated. Fundamentally genetc algorthms are a class of search technques that use smple forms of the bologcal processes of selecton nhertance varaton Strctly speakng they are not optmzaton methods per se, but can be used to form the core of a class of robust and _exble methods known as genetc algorthm based optmzers. Genetc Algorthms are a famly of computatonal models nspred by evoluton. hese algorthms encode a potental soluton to a spece problem on a smple chromosomelke data structure and apply recombnaton operators to these structures as to preserve crtcal nformaton. Genetc algorthms are often vewed as functon optmzer, although the ranges of problems to whch genetc algorthms have been appled are qute broad. An mplementaton of genetc algorthm begns wth a populaton of (typcally random) chromosomes. One then evaluates these structures and allocated reproductve opportuntes n such a way that these chromosomes, whch represent a better soluton to the target problem, are gven more chances to `reproduce' than those chromosomes that are poorer solutons. he 'goodness' of a soluton s typcally wth respect to the current populaton (erela, 2003). Studes n Busness and Economcs

5 3. Research methodology he populaton of the study s lsted companes n the ehran Stock Exchange and the sample ncluded 158 companes from the communty who were selected based on artcle 141 of the Commercal Code ehran bankrupt each year and each ndustry wll also choose a non-bankrupt. Note that the model Support Vector Machne and genetc algorthm per year the -1 and -2 were also fnancal nformaton relatng to the year the fnancal statements of the Company the samples were extracted. H 1 : Support Vector Machne s stronger n accuracy of bankruptcy predcton than Genetc Algorthm. One of the best ways for cross-valdaton s parttonng a sample of data nto tranng set, and testng set. In ths research, k-fold cross valdaton method was appled; whch the sample s randomly parttoned nto k subsamples. Of these k subsamples, one subsample s used as the valdaton data for testng the model, and k 1 sub-sample are used as tranng data. In tranng phase, the tranng data set apples to the Support Vector Machne algorthm, and then Support Vector Machne calculates Lagrange multplers and afterwards the weghts and bas. Now the data that has not been appled to Support Vector Machne are appled and the error rate s computed. K ( x, x ) j = exp x Maxmze Subject x 2 σ j 2 2 to n = 1 n = 1 1 λ 2 o λ C n λ y = o n = 1 j= 1 λ λ y j y, = 1,..., n j K ( x, x ) ; hat s called Gaussan kernel functon Potental varables he predctve varables of the study are dvded nto two parts. he frst part of the frst phase of the ndependent varables s a set of 56 fnancal ratos of lqudty, proftablty, operatng and fnancal leverage, whch s through the study of research conducted n the feld of bankruptcy. he second stage ncludes 9 varables out of 56 prmary varables whch have features the ablty to separate and remove varables whch cannot separate healthy and unhealthy companes. herefore, three varables lke returns of assets, fxed assets turnover rato and rato of equty to captal. able 1 shows the results of varables. Further, Fgure 1 shows the method of varable selecton. j Studes n Busness and Economcs

6 Return on nvestment Asset returns Percent return on nvestment Captal Workng rato able 1. Independent Varables Workng Captal to Sales Workng Captal to otal Assets Workng captal to total labltes Proft to gross proft Operatng proft to sales Fxed assets to equty Current Assets to Sale Net proft on sale Useful measure of loan Sale to nventory otal labltes to equty Inventory to sale Rato of current assets Rato of nventory to captal workng he total fnancal cost of debt Debt cost to Gross Proft Cash to total debt Cash to total assets Operatng cash flow to debt Operatng cash to equty Operatng cash flow to assets Operatng cash to sale Operatng proft to equty Accumulated earnngs to total assets Sale to recevable accountng Operaton proft to nterest expense Gross profts to total debt Captal Workng to equty Gross proft to total ncome Sze Net Income to otal Debt Operatng proft to total assets otal debt to equty Equty to total assets Equty to captal Workng captal to long-term debt Sales to otal Assets Collecton perod Debt to equty rato Cash adequacy rato Lablty rato Cash rato Debt coverage rato Workng Captal Debt to Captal Quck rato Cash turnover rato he fnancal burden of loans Inventory turnover Fxed assets turnover Accounts recevable to total debt Current labltes to total assets Studes n Busness and Economcs

7 Fgure 1. Algorthm Genetc By comparng two models of Support Vector Machne and Genetc Algorthm and calculate error I and error II by followng equtaton of 2, 3 and 4: Correct Rate = Number of rue Predcton otal Number of Samples *** Error 1 = *** *** *** Error 2 = If correct rate closer to 100 and error I and error II closer to zero, predcton algorthm become closer to the realty. Error I s number of falure predctons of bankrupt companes and error II s number of number of falure predcton of non-bankrupt companes to total non-bankrupt companes and cost of these errors are ferent sgnfcantly. Cost of false classfed as healthy company when company goes toward bankrupt (error I) s hghly more than when a healthy company dentfed as falure company (error II). hus, n bankruptcy models should be a balance between the types of forecast error. Results of the algorthms mplemented n the frst year, Year s t and t-1 show n able 2. ( 2) ( 3) Studes n Busness and Economcs

8 year t-1 able 2. Results of the algorthms before deletng the outlers algorthm SVM GA SVM GA Accuracy of the predcton ype I error ype II error t-2 SVM GA Although n the frst stage, the accuracy of the predcton of both models s not satsfyng, but genetc algorthm compared to Support Vector Machne has hgher accuracy of predcton and smaller type II error n three years t, t-1 and t-2. However, type I error s not consstent wth these two results, so we compare the two models by usng -test (because the output of the algorthms are normal). he results are presented n able 3. able 3. Results of the -test n year t t Error E Results of -test n year s t and t-2 show that of accuracy of predcton s less than.05 but type I error s not consstent wth accuracy of predcton and type II error. In year s t-1 sgnfcance level of accuracy of predcton s more than 0.05 so the hypothess s not sgnfcant. he results are presented n ables 4 and 5. able 4. Results of -test n year t-1 t Error E able 5. Results of the -test n year t-2 t Error E Studes n Busness and Economcs

9 In second stage, Genetc Algorthm and Support Vector Machne models are desgned and compared based on the 9 varables selected among 56 ntal ndependent varables from the frst stage. Increasng accuracy of predcton, decreasng errors of Support Vector Machne and Genetc Algorthm and algnng these crterons are observed n ths stage compared to the frst stage, whch able 6 shows the results of ths stage. able 6. Results of the algorthms after deletng the outlers year algorthm Accuracy of predcton ype I error ype II error SVM GA SVM GA SVM GA In year s t and t-1, accuracy of predcton of Support Vector Machne s more than genetc algorthm, and ts type I and II errors are less. Consderng the algnment of the results, we can conclude that n year s t and t-1, Support Vector Machne model s more powerful than genetc algorthm. However, n year t-2 accuracy of predcton and type I error of genetc algorthm s hgher. ables 7, 8 and 9 demonstrate the results of ths stage. able7. Results of -test n year s t Error E Error able 8. Results of -test n year t E Studes n Busness and Economcs

10 able 9. Results of -test I year t-2 Error E In year t absolute value of t statstc for accuracy of predcton and type I error s more than correspondng value n t-student (t=1.73) and accordng to algnng of type II error wth accuracy of predcton and type I error and also ths fact that sgnfcance level for all three crterons s less than.05, wth the confdence of 95 % we can say that Support Vector Machne s more powerful than Genetc Algorthm. However, n years t-1 and t-2 sgnfcance level of accuracy of predcton s more than Conclusons In ths research, we try to compare the two models the Support Vector Machne And genetc algorthm. he compare dd based on mportance of fnancal ratos n bankruptcy predcton n two pre-electon the Effectve ratos and after the electon was conducted and the results ndcate that the n the frst stage n year s t and t-2 Algorthm Genetc has the hghest accuracy and lowest type II error. However, type I error s not algned wth the other crtera cannot make a decson whch of them s better and t can be sad as result of avalable ratos whch cannot separate healthy and falure company. Although, n year s t-1 the genetc algorthm wth the accuracy of 84.15%, hgher than expected Support Vector Machne and sgnfcance level s greater than 0.5 the research hypothess rejected. In the second stage of the selecton - effectve ratos and remove of fnancal ratos that were unable to separate the two groups leads to mprove accuracy and declne errors sgnfcantly, moreover results of models become algned and makng decson about bankruptcy predcton models become easer. In fact, remove of neffectve observatons n the second stage can mprove accuracy of predcton wth 94.30% and t s obvous that Support Vector Machne has better performance compare wth genetc algorthm and the hypothess s confrmed. Furthermore, our results are consstng of research by Km and Kang (2012). Although, the hypothess s rejected n year s t-1 and t-2 but evaluatng crtera become algned together and makng t easer to choose a robust model. Due to the hgh accuracy, predcton wth Support Vector Machne s proposed that genetc algorthm or Support Vector Machne combne wth other models lke honeybee colones and t s better to use of market prce and compare t wth the results of ths research. Moreover, t s proposed that nvestgate, s there any ference between varable methods lead to the selecton of the ferent ndependent varables. Studes n Busness and Economcs

11 5. References Altman, E. I, (1968).Fnancal ratos, dscrmnate analyss and the predcton of corporate bankruptcy, the Journal of Fnance, 23(4), Beaver,W, H.(1966), Fnancal ratos as predctors of falure. Journal of Accountng Research, 4, Emprcal Research n Accountng: selected studes, (supplement), Blum, M. (1974). Falng Company Dscrmnant Analyss. Journal of Accountng Research, 12(1), Chen,M.Y.,(2011). Bankruptcy predcton n frms wth statstcal and ntellgent technques and a comparson of evolutonary computaton approaches. Computers and Mathematcs wth Applcatons, 62, Deakn, E. (1972). A Dscrmnant Analyss of predctors of Busness Falure. Journal of Accountng Research, 10(1), Frydman, H., Altman, E., Kao, D. (1985). Introducng Recursve Parttonng for Fnancal Classfcaton: the case of Fnancal Dstress. Journal of Fnance, 40(1), Gahlon,J.M.,Vgehand.R.L.,(1988).Early Warnng of Bankruptcy Usng flow Analyss. he Journal of commercal Bank Lendng.pp:4-15. Holand,J.A.,(1975),"Adaptaton n natural and artfcal systems", Ann Arbor, MI: unversty of Mchgan press. Hossar,G.,(2006). A Rato-Based Mult-Level Modelng Approach for Sgnalng corporate collapse: A study of Australan corporatons. Swnburne unversty of echnology. Australa, A thess for the degree of Doctor of phlosophy. Km, M.J., Kang, D. K., (2012).classfers selecton n ensembles usng genetc algorthms for bankruptcy predcton. Expert systems wth Applcatons,39, Mensah, Y.M. (1983). he Dfferental Bankruptcy predctve Ablty of specfc predcton Models: A Methodologcal study. Journal of Accountng Research, 22(1), Mn,Y, H., Lee, Y.C.(2005). Bankruptcy predcton usng support vector machne wth optmal choce of kernel functon parameters. Expert systems wth applcatons, 28, Pa, P, F., Ln, C, S (2005), A hybrd ARIMA and support vector machnes model n stock prce forecastng, the nternatonal journal of management scence, vol. 33: Premachandra,I.M.,Bhabra,G.S.,Sueyosh,.,(2009), "DEA as A ool For Bankruptcy Assessment: A comparatve study wth logstc Regresson echnque",european Journal of operatonal Research 193,pp: Rav Kumar, P. Rav, V. (2007). Bankruptcy predcton n banks and frms va statstcal and ntellgent technques. European Journal of operatonal Research, 0, relea, I, C ) 2003) the partcle swarm optmzaton algorthm: convergence analyss and parameter selecton, Informaton Processng Letters 85" Vapnk V (1995), the nature of statstc learnng theory. New York: Sprnger. Wu, K, P., Wang, S, D (2012), Choosng the kernel parameters for support vector machnes by the nter-cluster dstance n the feature space, Pattern Recognton, Vol. 42, pp Yoon, J.S., Kwon, Y.S. (2010). A practcal approach to bankruptcy predcton For small busnesses: substtutng the unavalable fnancal data for credt card sales nformaton. Expert systems wth Applcatons, 37, Studes n Busness and Economcs