Abstract
In the process of resolving fi nancing difficulties of small and medium enterprises (SMEs) in China, themeasurement of credit risk of SMEs is a very challenging problem. In this paper we develop a novel modelbased on the original KMV model with tunable parameter s to measure the credit risk of Chinese listed SMEs.By setting two credit warning lines to monitor the credit crisis of listed SMEs, we fi nd that the predictiveaccuracy of adjusted KMV model is stable to the change of default points in Chinese listed SMEs, which isdifferent from KMV Company's existing result. Our study shows that the credit risk of listed SMEs in China isrelatively high and tends to increase during the chosen period from the year 2004 to 2006. We also find thatthe asset size has signi ficant impact on credit risk and there are few credit riskfl uctuations before and afterthe split share structure reform
Keywords:Credit riskSmall and medium enterprises (SMEs)Early warningKMV modelDistance to default (DD)Asset sizeSplit share structure reform
Introduction
  Credit risk is the risk of loss due to a debtor's non-payment of aloan or other line of credit (either the principal or interest (coupon) orboth). Default occurs when a debtor has not ful filled his or her legalobligations according to the debt contract, or has violated a loancovenant (condition) of the debt contract, which might occur with alldebt obligations including bonds, mortgages, loans, and promissorynotes. Since financial innovation and derivatives grow rapidly incompetitive financial industry, credit risk measurement and manage-ment become essentially important.
  Although small and medium enterprises (SMEs) are the mostactive economic units in the national economy, the operational riskand credit guarantee risk are very high in SMEs due to their particularcharacteristics, which lead to a low credit rating in general. Theoperating performance of Chinese SMEs is poor in general, whichres ul ts in a high ope ra tio nal ris k a nd gu ar ant ee ris k to cre ditguarantee institutions [5,6]. The Financial System Survey Reportof C hines e SMEs i n 2 003 – 2 005 provid ed by Pe op le's Ba nk ofChina (including six major cities: Beijing, Xian, Dongguan, Taizhou,Wenzhou and Weihai), shows that 63.93% of the bank's gross badloans are caused by SMEs. Due to the lack of effective collateral andguarantees, the banks lending to SMEs are confronting much largerdefault loss. According to the credit rating for 350,041 SMEs made byIndustrial and Commercial Bank of China (ICBC China) in 2001, thereare only 16.31% of SMEs in grade A or higher, but 83.69% of SMEs ingrade BBB or lower by contrast. Credit rating is a main assessmenttool referred by credit guarantee, which are very cautious to theSMEs with low credit rating. Therefore, funding shortage is one of themajor problems for most SMEs which restrict their developments.Effective measurement of credit risk to SMEs has become a majorchallenge forfinancial institutions. With the rapid growth of SMEsPlate and the Growth Enterprise Market (GEM) coming up in China,the SMEs will have significant infl uence on Chinese economy as wellas the capital market. However, the growth of most SMEs suffersgr e at un c er ta in ty a n d un c on ti nu it y, in th a t t h ey u su a ll y h a veestablished for a very short period and have very limited manage-ment experiences. Due to the“growth illusion ”, a kind of credit risk ishardly perceived in the case of high-growth SMEs excessively relyingon debt financing [5]. Therefore, in this paper, we try to do someexploratory research on credit risk monitoring of Chinese listedSMEs.
  The rest of the paper is organized as follows. A literature reviewabout credit measurement and warning is provided in Section 2,followed by descriptions of the analytical models and methodologiesin Section 3. Then, the parameter estimation, results comparison andanalysis are discussed inSection 4. Section 5concludes the paper.
Literature review
  Before 1970s, the financial institutions focused on semi-quantitativeanalysis in credit measurement and management, which were mainlysubjective assessments of customer's credit by financial statementanalysis. Since 1970s, the western developed countries represented byU.S. developed a series of credit risk models on measurement andmanagement [3]. Thereby the combination of qualitative analysis andquantitative analysis in credit risk measurement infinancial institutionsis re aliz ed .
  Currently, many models are available for credit risk measurementand credit r ati ng [15,37] . I n the main t radit ional cr edit ri s kmeasurement models, the banker's expert system and rating methodare more subjective [29,30]. Furthermore, some statistical methodsare commonly used for credit risk prediction. It includes logisticregression analysis [20,24,33] , K nearest neighbor [13,28], multiplediscriminate analysis (MDA) [16] , Z-score model [1] and the improvedZETA credit risk model [26] . The general effort in credit ratingprediction using statistical methods was that a simple model with asmall list of financial variables was succinct and was easy to explain.However, the problem is that the multivariate normality assumptionsfor independent variables are frequently violated in financial datasets, which makes these methods theoretically invalid for finitesamples [15] . Recently, Arti ficial Intelligence (AI) techniques, partic-ularly the neural networks have been used to support credit ratingand bankruptcy predictions [2,7,18,34,35]. However, models obtainedin this machine learning method are usually very complicated andhard to explain, and they heavily rely on the samples and ex-perimental data.
  The modern credit risk measurement model includes four majorapproaches: CreditMetrics, Credit Portfolio View, CreditRisk+ andKMV model. The J.P. Morgan's CreditMetrics [8] and McKinsey's CreditPortfolio View [36] are directly related to the credit rating mechanism.However, because China's credit rating market is far from mature andlacks suf ficient credit data, the above two models (CreditMetrics andCredit Portfolio View) cannot be used in China. It is also very difficultto apply the CreditRisk+ model [31] developed by the Credit SuisseFinancial Products into Chinese credit market; that is because the keyrisk-driven parameter“default rate” of CreditRisk+ model is hard toestimate in present credit market of China. Moreover, the modelrequires the mutual debts to be independent [9]. The KMV modeldeveloped by the KMV Corporation is a structural model based on themodern corporatefinance theory and the option theory. It would bevery attractive to apply it to credit market of Chinese SMEs, where thefinancial data and credit information are insuf ficient, patchy or evendoesn't exist at all. The KMV model can use appearance informationfor measurement, such as thefluctuation of stock prices, credibility,macro-economic conditions, and sector's credit risk. It is a dynamicforward-looking approach.
  Previous studies confirm that the KMV model can be applied in thecredit market. McQuown [22] pointed out that the financial reportcould re fl ect the history of the company and the market price couldre flect the future development trend much better, yet the mostaccurate measurement of credit risk should use both information atthe same time. Kurbat and Korablev [19] tested the KMV model bylevel validation and calibration analysis. They proved that the KMVmodel was very effective using the datum of 1000 U.S. companies inthree years. Crosbie and Bohn [10] applied KMV model intofinancialcompanies and found that EDF value could accurately and sensitivelymonitor the credit changes before insolvency or when a credit eventhappened. The “New Basel Capital Accord” promoted Internal Ratings-Based (IRB) approach in credit risk management, where KMV was alsorecommended. It is clear that KMV model has been highly acceptedand used in the world.
  In recent years, Chinese scholars discussed the applicability ofKMV model in China. Du et al. [11] focused on qualitative analysis ofthe model and pointed out problems in using KMV. Wang [32]provided comparative study of KMV and other credit risk models. Heconsidered that the KMV model was more suitable for credit riskassessment of listed companies than other models. Recently, somescholars began to apply KMV model into credit risk identi fication inlisted companies. Cheng and Wu [6] (sample number is 15), Zhang etal.[40] (sample number is 60), Yang and Zhang[38] (sample numberis 144) and Ye et al. [39] (sample number is 22) adjusted theparameters of KMV model and found that the adjusted model couldtimely identify and forecast the credit risk of Chinese listedcompanies. Zheng [42] (sample number is 30) found that the EDFmodel did not send wrong messages to the listed companies withgood performance, but the asset value and equity value in high-risklisted companies were overvalued. Ma [21] applied KMV model intothe fi nancial distress warning of Chinese listed companies, and foundthat KMV model had more obvious advantages than the Logistic andFishe r model. Although previ ous work s prov ide theor etical andempirical proofs that the KMV model is a good guidance and referencefor quantitative credit risk management in China, the inference cannotbe made directly to Chinese market. Some existing works havediscussed the relationship between asset size and default. Moodycompany's study shows that the asset size is an important factora f fe c t in g d e fa u lt . T h e d e fa u l t pr ob a b il it y is v er y h ig h i n la rg ecompanies who are well-funded, solid and capable of market risksresistance [14] . While in small-sized listed companies, the defaultprobability is big due to the big volatility of stock price [41] . In thispaper, we will discuss how the default probability is affected byvarious risk factors in Chinese listed SMEs. Traditional KMV modelused to determine equity value volatility (σE) by simply adoptingstock price volatility, but the effects of equity changes (e.g., the sharesdistribution) and changes in net assets per share are not considered.This paper will adjust some parameters in KMV model and developimproved version of KMV model to meet the needs of Chinese listedSMEs' credit market. As a unique phenomenon in China, the splitshare structure reform will also be discussed
.3. Models
3.1. KMV modeling description
  KMV model developed by the KMV Company is based on theMerton Opti on Pricing Theory[23] .Itisasetofconceptualframeworks to estimate the default probability of a company. TheKMV m od el a ssu mes th a t the c om pa ny wi ll d ef aul t wh en th ecompany's asset value is less than liabilities. Fig. 1 reveals therelationship between equity value and asset value. According to thebasic idea of Merton model, the KMV model regards the company'sequity value as the call option, which considers asset value as theunderlying asset and the debt as the exercise price
  In Fig. 1 , L denotes the shareholders' initial investment in thecompany; D denotes the debts in default point. When the asset value( V) is more than the debts (D), shareholders will choose not to defaultand gain remaining profi ts after paying debts, which is consistent withan increasing equity value in Fig. 1, and it indicates the call option isex ec ut ed . Whi le , whe n th e ass et va lu e is le ss th an th e d eb ts ,shareholders will choose default by transferring the total assets tothe creditors, which is consistent with a constant equity value in Fig. 1,and it means the call option is not executed[4,10,17,25] .
  According to the above analysis, we can derive from the Black–Scholes option pricing formula that:E =VN d1ðÞ−De−r τNd2ðÞ=fV; σV; r ; D; τ ðÞ;ð1Þwhere E denotes the equity value,V denotes the asset value, D denotesthe default point, σvdenotes the asset value volatility, r denotes therisk free rate,τ denotes the debt maturity,N(⋅ ) denotes the standardnormal cumulative distribution function. In Eq. (1), d1and d2can becalculated as follows:d1 =ln V = D ðÞ+ r + σ2V= 2
τσVffiffiffiτp ; ð2Þd2 =ln V = D ðÞ+ r −σ2V= 2
τσVffiffiffiτp =d1−σVffiffiffiτp: ð3Þ
  There are two unknown parametersV and σvin Eq. (1) that need tobe solved. This can be achieved by introducing the relationshipbetween the equity value volatility ( σE) and the asset value volatility( σV) [14] (see Eq. (4)).σE =VN d1ðÞEσV=gV; σV; r ; D; τ ðÞ:ð4Þ
  After substituting Eqs. (1) and (2) into Eq. (4), we can derive thatσEis the function of V , σV, r , D and τ.
  Thereby, we set a system of equations from Eqs. (1) and (4), whereV and σvare unknown parameters (see Eq. (5)).fV; σVðÞ− E =0gV; σVðÞ−σE=0ð5Þ
  Then we calculate the Jacobian Matrix of the functions. Accordingto the Newton-iterative method, which builds iteration throughTaylor expansion, we get Eq. (6).Vk +1 ðÞσk +1 ðÞV !=VkðÞσkðÞV !−∂f∂V∂f∂σV∂g∂V∂g∂σV0BBB@1CCCA−1fVkðÞ; σkV
−EgVkðÞ; σkðÞV
− σE0B@1CA; ð6Þwhere the appropriate initial values (V0, σV0) in Newton iteration areset by use of the trial-and-error method. We have tested nine groupsof values (V0,σV0): three values for initial asset size value V0andthree for initial volatility value σV0. Our sample size falls in the rangeof (1.0E+07, 1.0E+09), so we test three levels of values: 1.0E+07,1.0E+08 and 1.0E+09 for V0. The three levels of volatility values are0.1, 0.01 and 0.001. Computation in trial and error shows that theinitial value of (1.0E+09, 0.01) can achieve iteration convergence andthe convergence is fast. Based on this, we can calculate the values of Vand σV.
  WhenV and σVare given, the distance to default (DD) in indebtedcompanies can be calculated[10] . In KMV model, DD is de fined as:DD=V − DV σv: ð7Þ
  It is assumed that the asset value of the company follows thenormal distribution, thus the default distance re flects the standarddeviation from company's default. Then we can get the company'sexpected default frequency (EDF):EDF =N −DD ðÞ: ð8Þ
  However, the assumption that the asset value is subject to normaldistribution is questionable. The KMV Company tries to obtain theempirical value of EDF rather than the theoretical value from models.Fortunately, KMV Company has a huge historical database on defaultinformation of companies. They can count the number of defaultcompanies with same DD in a year. Then, the empirical value of EDF isthe ratio of the above counts to the total number of companies withthe same DD. While at present, there is no similar database in Chinesecredit market, which means no EDF statistics is available. So in thispaper, we take DD as the basis of credit evaluation. DD is a standardindex re flecting the company's credit quality, which can be com-pared for different companies and for different periods of time. Thegreater the value is, the more likely the company is to repay debts indue time, as a consequence the defaults will be less and the credit willbe better.
3.2. Parameter setting
  We discuss the calculation offi ve key parameters in this section.The first parameter is equality value (E ). Prior to China's split sharTable 2DD in three default points.Tim e 04/3 04/6 04/9 04/12 05/3 05/6 05/9 05/12 06/3 06/6 06/9 06/12DD mean D 0Non-ST 63.86 57.26 59.26 71.49 60.19 60.86 61.18 73.17 70.12 50.45 58.34 52.58ST 40.74 41.55 37.71 37.12 30.42 29.64 27.65 24.81 25.63 25.37 28.50 34.36Mean-difference 23.12 15.71 21.55 34.37 29.77 31.22 33.53 48.36 44.49 25.08 29.84 18.22D 1Non-ST 63.88 57.28 59.28 71.52 60.21 60.90 61.22 73.21 70.17 50.49 58.36 52.61ST 40.75 41.57 37.74 37.14 30.44 29.66 27.67 24.82 25.65 25.39 28.53 34.37Mean-difference 23.13 15.71 21.54 34.38 29.77 31.24 33.56 48.40 44.52 25.09 29.84 18.24D 2Non-ST 63.83 57.23 59.23 71.45 60.15 60.81 61.13 73.10 70.05 50.40 58.27 52.55ST 40.72 41.53 37.68 37.11 30.41 29.62 27.64 24.79 25.61 25.35 28.48 34.34Mean-difference 23.12 15.70 21.55 34.34 29.74 31.20 33.49 48.30 44.45 25.06 29.78 18.20Table 3T-test statistics.DD Levene's testfor equalityof varianc esT-test for equality of meansF Si gnificantlevelt df Sign ificantleve l(2 - t a i l e d )Mean-di ff er enceStand a rder rordifferenc eEqualvari ancesassu medD 00.006 0.937 10.977 22 0.000 29.605 2.697D 10.007 0.935 10.979 22 0.000 29.617 2.698D 20.006 0.938 10.973 22 0.000 29.577 2.695Table 4Wilcoxon test statistics.DD D0 D1 D2WilcoxonW 78.000 77.800 77.900Z − 4.157 − 4.156 − 4.157Significant level (2-tailed) 0.000 0.000 0.000structure reform, domestic A shares were divided into two classes:one type being freely bought and sold by normal investors (tradableshares) and the other that cannot be freely traded (non-tradableshares). This is a special phenomenon in Chinese securities marketaccording to the Code of Good Practice of Exercise of State-ownedCorporation Shares [41,43]. The value of non-tradable shares is hard tobe estimated and usually lower than the value of tradable shares. If theprice of per non-tradable share is simply represented by the price ofper tradable share, the company's equity value will be overestimated.Therefore, in this paper we follow the Code of Good Practice ofExercise of State-owned Corporation Shares set by Chinese regulators,and use net assets per share to represent the non-tradable sharesprice[43] . We can get:Equity Value =the Closing Price of Tradable Shares× the Number of Tradable S hares + Net Assets per Share× the Number of Non tradable Shares ;ð9Þwhere the number of non-tradable shares includes the limited sale ofshares in the split share structure reform. The second parameter isequity value volatility ( σE). We introduce a new way to calculate thisparameter. Not only the tradable shares price but also the equityc h a n ge s ( su c h a s eq u it y d on a ti on , d is tr ib u ti on a n d o ri en t a ti onrepurchase in the split share structure reform) and quarterly changesof net assets per share are all considered in the calculation ofσE. It caneffectively improve the accuracy in calculation of σE. A large numberof facts proved that GARCH (1, 1) model applies well to the Chinesestock market [27] . In this paper, after the equity value ( E) in eachtrading day has been calculated, we use GARCH toolbox in Matlab tocalculate equity value volatility.
  The third parameter is default point ( D). KMV Company found thatthe companies generally do not default when their assets value is upto the book value of total liabilities [10] . When the company defaults,the asset value is generally between the current liabilities and thebook value of total liabilities, which can be described to:D =CL + k × LL ; 1 ≥k ≥ 0; ð10Þwhere D denotes default point, CL denotes current liabilities, and LLdenotes long-term liabilities. By doing a great deal of observations tothe default companies, KMV Company found that the most frequentdefault point is at k = 0.5, and the predictive accuracy of model issensitive to the changes of default point[10,17]. But this default pointis an experiential value based on American companies, which may notbe suitable for the listed SMEs in China. The default point must be setby considering the debt structure of a company and the creditsituation of a country. Thus, obviously we face a big hurdle indetermining the default point of Chinese listed SMEs. Previous studieson default point setting are generally similar to the KMV Company's[27,40]. None of the existing research discussed default points andcredit risk of SMEs yet. In this paper, we fi rst set three scenarios:k = 0.5 (D0), k =0 (D1), and k =1 (D2), and then compare theeffectiveness of credit risk model in Chinese listed SMEs in these threescenarios.
  The fourth and fifth parameters are liability maturity (τ) and riskfree rate ( r ). Beca use of the limited availability of d ata andinformation, the calculation time is set for one year to predict thecredit risk in next year. While the setting time is consistent with otherexisting studies, it would be helpful to examine the results. For therisk free rate, we adopt one-year time deposit rate published by thePeople's Bank of China (see Table 1).
Parameter and model effectiveness
4.1. Sampling and data preprocessing
  The data window is from 2004 to 2006. We select samples fromlisted SMEs in China under the following steps: a ) the companiesshould be listed in Shanghai and Shenzhen Stock Exchange beforeDecember 31, 2005 and only issued A shares, which ensures theanalyzing time being more than one year. b) The tradable shares of thecompany are less than 50 million in the period of 2004 to 2006, and byDecember 31, 2003, the main income or the total assets are less than500 million RMB and the number of employees is less than 2000people, which meet the SME Standard in China. c ) There is no missingata. After the first screening, there are 80 samples that matched. Theraw datum are quarterly datum from 2004 to 2006, including netassets per share, current liability, long-term liability, the closing stockprice of each trading day, the tradable shares and the non-tradableshares. The entire datum is from Wind Database and DragoninfoFinancial Information References System (DFIRS).
  We execute the Newton-iterative algorithm of KMV model inMatlab software to calculate V, σVand then DD. The default points areset at D0, D1, and D2respectively. But for one sample we cannot getresult from the iteration due to its negative equity value, which cannotbe executed in GARCH toolbox in Matlab. Finally, we get 79 sets ofresults on V, σVand DD for 12 quarters from 2004 to 2006. Theeffect ive sample s includ e 20 ST&*ST co mpanies and 59 non-STcompanies. ST companies are those being special treated because ofnegative net pro fits in consecutive years. *ST companies are thosesuffering from losses for three consecutive years.
4.2. Model validity verification and comparison in differentdefault points
  It is generally held that the ST&*ST companies are in financialcrisis. They may have higher credit risks than the general ones. Wedivide the total samples into two groups: Group1 including 20 ST&*STcompanies and Group 2 with 59 non-ST companies.
  Firstly, we compare the means of DD in two groups from March,2004 to December, 2006. The statistics of DD at three default pointsare shown in Tabl e 2 . The res ults in dicate tha t DD in non -STcompanies are all larger than those in ST companies, which reflectsthe fact that default risk in non-ST companies is much smaller. Itmeans the DD results yielded from KMV model are valid. Then weconduct a test for two-independent samples to verify the signi ficantdifference in DD between non-ST and ST companies (see Tables 3and 4). The T -test and Wilcoxon test statistics show that the DD of twogroups have significant difference at the level of α = 5% at threedefa ult point s, and the ir res pecti ve popu lations have the samedistribution. It indicates that adjusted KMV model can effectivelydiscriminate the default risk in listed SMEs.
  The mean-difference of DD between non-ST and ST companiesgradually increases from 2004 to 2005 and decreases in 2006, and thetrends of the DD difference at the three points are almost overlapped(see Fig. 2 ), which means the DD differences in non-ST and STcompanies are stable to the changes of default point.
  In order to further verify and compare the validity of KMV model inrisk identi fication, we introduce the Receiver Operating CharacteristicCurves (ROC). ROC is used for analyzing the accuracy of classificationcriteria, which is particularly effective in comparing the accuracywhen a variety of classifications exist [12] . Many Chinese scholarshave also used ROC in the study of KMV model [27,40].
  In this paper,we take the case in June 30, 2005 as an example to describe theprinciple of ROC curve. Fig. 3 shows the number of ST and non-STcompanies in different DD intervals. Table 5 shows the cumulativenumber of ST and non-ST companies when DD is lower than thecritical point.In this paper, the sensitivity is de fined as the proportion that STcompanies are exactly judged to special treatment (ST), the specificityTable 7The area under ROC curve in 12 time points.04/3 04/6 04/9 04/12 05/3 05/6 05/9 05/12 06/3 06/6 06/9 06/12 Mean Standard DeviationD 00.869 0.755 0.873 0.840 0.869 0.889 0.911 0.923 0.902 0.752 0.838 0.815 0.853 0.056D 10.871 0.753 0.874 0.840 0.869 0.889 0.914 0.927 0.903 0.752 0.836 0.815 0.8536 0.057D 20.869 0.752 0.873 0.840 0.869 0.888 0.911 0.923 0.900 0.754 0.838 0.815 0.8527 0.056is defined as the proportion that non-ST companies are exactly judgedto be outside of ST, the false rate is de fined as the proportion that non-ST companies are falsely judged to ST and the false rate is just equal to(1− specificity). As shown in Table 6, when DD ≤ 30 is viewed as thejudgment criterion of ST, the corresponding sensitivity and specifi cityare 0.40 and 0.00 respectively. When DD ≤ 50 is viewed as thejudgment criterion of ST, the sensitivity and specificity values are 0.90and 0.36 respectively. When DD ≤ 70 is viewed as the judgmentcriterion of ST, the values are up to 1.00 and 0.75. Then we can getthe ROC curve presented in false rate (1− specificity) ( X-axis) andsensitivity ( Y-axis) (see Fig. 4 as an example). It shows the rela-tionship between the false judgment rate of non-ST and the truejudgment rate of ST in different critical points of DD.
  We can use the area under ROC curve to measure the accuracy ofKMV model in distinguishing ST and non-ST companies. When thearea is in the range of (0.90, 1.00), the accuracy of the model isexcellent. When the area is in the range of (0.80, 0.90), the accuracy isgood. When the area is in the range of (0.70, 0.80), the accuracy is fair.When the area is in the range of (0.60, 0.70), the accuracy is poor.When the area is in the range of (0.50, 0.60), the accuracy is poor andthe model fails.
  Table 7 shows the area under ROC curve at three default pointsfrom March 2004 to December 2006. The average areas at threedefault points are 0.8530, 0.8536 and 0.8527 respectively. It indicatesthat the KMV model can accurately dis tinguish ST and non-STcompanies at three default points. The statistics show that theaccuracy atD1( D = Current Liabilities) is a little better than at othertwo points. But the paired samples T -test shows no significantdifference at the three points. It means the predictive accuracy of KMVmodel is stable. Combining with the results in Fig. 2, we can concludethat the predictive accuracy of KMV model is stable to the changes ofdefault point in Chinese listed SMEs, which is different from the resultof KMV Company that the prediction accuracy of KMV model issensitive to the changes of default points.
4.3. Credit risk and warning of Chinese listed SMEs
  In this section, we will discuss the situation of credit risk in Chineselisted SMEs and try to set the credit risk warning lines. To facilitate thecomparison with previous studies, we choose default point at D 0forthe following analysis.
  The following analysis is based on three groups of samples. Group1 includes 20 ST&*ST companies and group 2 includes the rest 59 non-ST companie s i n Se c t i on 4 . 2. G ro u p 3 in c lu d e s 2 0 b lu e c h i p scompanies selected from non-ST companies, which have the bestperformance and the most average earnings per share (fully diluted)Table 8A DD comparison with previous studies.Sample Time E calculation: whether consider σ Eestimation: whether consider DD interv al withlargest ST frequencySourceTrad able shares pricing Non-tradable shares pricing Equity changes Net assets per share80 listed SMEs 2004 –2006 Yes Yes Yes Yes b 30 This paper15 A shares 2000 Yes No No No b 2 [6]30 A shares 1998 –2001 Yes No No No b 4 [40]22 A shares 2000 –2003 Yes Yes No Yes b 8 [39]60 A shares 1999 –2002 Yes Yes No Yes b 4 [42]852 A shares 2002 Yes No No No b 3 [21]Table 9ST frequ ency in 2004 – 2006.ST frequency ≤ 30 30 –40 40– 50 50– 60 60– 70 70– 80 80–90 N 90200403 1 0.7 0.357 0.182 0.2 0 0.143 0200406 1 0.421 0.235 0.1 0.5 0 0.333 0200409 1 0.454 0.235 0.15 0.125 0 0 0200412 0.9 0.571 0.125 0.3 0.071 0 0.167 0.067200503 0.917 0.444 0.091 0.111 0.083 0.167 0 0200506 1 0.538 0.167 0.083 0.077 0 0 0200509 1 0.3 0.143 0.067 0.077 0 0 0200512 1 0.5 0.333 0.071 0.083 0 0 0200603 1 0.636 0 0.2 0 0 0 0200606 0.769 0.176 0.158 0.056 0.25 0 0 0200609 0.636 0.636 0.091 0.059 0.091 0 0 0200612 0.667 1 0.167 0 0.5 03-year average 0.907 0.531 0.175 0.115 0.171 0.014 0.058 0.006in three years among the total samples. Group 3 is set as the referencegroup. Fig. 5 demonstrates a comparison of default distances (DD)among the three groups. We find that DD in non-ST companies andblue chips are much bigger than in ST companies, which means it ismuch likely to default in ST companies than in non-ST and blue onesin Chine se l iste d SMEs. And DD differ ence s bet wee n no n-S Tcompanies and blue chips are very small, the DD trends of twogroups are almost overlapping from 2004 to 2006. The DD trends in STcompanies seem much smoother than those in other two groups,which means the DD of ST companies has small changes in threeyears. It can be concluded that ST companies keeps high default riskfo r se ve ra l ye a rs , es pe c ia ll y in 1 – 2 ye a rs be fo re or aft er be in gidenti fied as ST. Combining with Figs. 5 and 2 ,we find that the DDdifference between ST and non-ST companies is more and moreobvious from 2004 to 2005 due to the improving credit in non-STcompanies and the declining credit in ST companies. In 2006, thedifference began to slow down, where the credit in non-ST companiesdecreases a lot but increase slightly in ST companies.
  Fig. 6 describes the default distance statistics of listed SMEs. Wefind that the credit in three years is stable. In general, DDfluctuateswithin the range from 50 to 60 and shows a slight decrease in 2006.The mean and standard deviation of DD change in the same directionwith a correlation coefficient of 0.831, which shows a resonance. Thisis mainly due to some companies' sudden credit improvement inshort time, which brings a quick growth of DD and enlarges thedifference between DD and the total average value of DD. It iscoincident that DD changes a little in the first three quarters andincreases a lot in the last quarter both in 2004 and 2005, whichindicates that some fi nancial information of the Chinese listed SMEsdisclosed to public may be fabricated. DD in ST companies is gettingsmaller from 2004 to 2005 and has a slow recovery in 2006. It meansthe credit of ST companies is poor in the fi rst two years, the closer tobe ST, the bigger the default risk is. In 2006, with the help ofrecapitalization, asset injection, recover arrears and financial subsi-dies, some ST companies get the chance to get rid of defi cits, and thecredit tends to get better. The ST label may be removed as expected.
  Table 8shows a DD comparison with previous literatures. We findthat the DD in this paper is bigger than in previous studies. This ismainly due to a certain model parameter setting, where we take theequity changes (especially in duced by the split share structu rereform) and the change of net assets per share into consideration toestimate the value of σE. As a result, the equity volatility is much lessthan previous studies. Because the parameters are adjusted, we canhardly compare our results with existing works based on largecompanies. However, we can set credit early-warning lines by DD tomonitor credit crisis in listed SMEs.
  We divide DD into 8 intervals. The frequencies of ST companies in8 intervals in three years are shown inTable 9. Fig. 7 illustrates theaccumulative DD at the end of 2005 and Fig. 8 illustrates the averagefrequency line of ST in three years. We can conclude that the smallerthe DD is, the larger the ST frequency is, which once again verifies thevalidity of KMV model on credit rating of listed SMEs. By studyingstatistics of three years, we find ST frequency is the largest whenTable 10DD in different asset sizes.Size range (100 million yuan) The average DD in 3 yearsSmall-sized 0.42–3 43.262Medium-sized 3.86–5 55.589Large-sized 6 –13.5 57.984DD∈ ( −∞, 30). So DD = 40 is set for the second grade of credit early-warning line and DD = 30 is set for the fi rst grade of credit early-warning line. We can draw a curve for real-time DD changes. Byobserving DD in September and December in 2006, including threelisted companies under temporary suspension, there are 25 compa-nies (31.6% of total samples) below the second grade warning and 15companies (18.99% of total samples) below thefirst grade warning.That means half of the listed SMEs below the second grade warningwill be in credit crisis in 2007. And 90% of the listed SMEs below thefirst grade warning will be in credit crisis in 2007, the credit situationshould be alerted, and some remedy measures should be taken assoon as possible. Thus we find, the credit risk of listed SMEs in China islarge and the credit situation is not optimistic.
4.4. Asset size and credit risk
  The previous result shows that the credit risk of Chinese listedSMEs is very big. Comparing the ST frequency line based on 852medium and large companies in china[21] with the ST frequency linein Fig. 8,we find that the default probability in listed SMEs is muchbigger than in medium and large companies in China. However,whether credit risk is related to the asset size needs a furtherdiscussion. We sort all the samples in descending order according totheir 3-year average total assets. The top 20 ranked companies aredefined as the large-sized group, the last 20 ranked companies aredefined as the small-sized group, and the rest 19 companies in themiddle is defined as the medium-sized group. The relationships ofassets and DD in three groups are shown in Table 10 . Fig. 9 shows thetime series of DD in these three groups. Table 10 and Fig. 9 indicatethat DD in small-sized SMEs is much lower than in medium and large-sized SMEs in general, and the DD trends in medium-sized group andin large-sized group are almost the same, but the former is a littlesmaller than the latter. That means the probability of default is thelargest in small-sized listed SMEs and is much lower in medium andlarge-sized ones, and the differences between medium and large-sized companies are very small. It can be concluded that the small-sized companies with total assets less than 300 million have apparentweaker risk resistance.
  Table 11 provides the correlation coefficient of DD and total assetsin three years. In the first half of 2004, the total assets and DD isweakly negative correlated. In the latter half of 2004, the correlationturns to be weak positive. It turns to be significantly positive from thebeginning of 2005, which indicates the default distance is small insmall-sized SMEs, and the probability of default is very large. Astime goes, the effects of asset size on credit risk are more and moreobvious.
4.5. Split share structure reform and credit risk
  In this section, we use Fisher test to compare the variances ofcredit risk in listed SMEs before and after the split share structurereform. The split share structure reform starts in the middle of2005 and has a great impact on the Chinese stock market. Underthe reform, non-tradable shareholders negotiated a compensa-tion plan with tradable shareholders in order to make their sharestradable.
  There are 52 listed SMEs under reform or that have finishedshares reform by 2007. Among them, there are only 3 ST companiescarrying out the reform, and the majority of reformed companiesare non-ST companies (see Table 12). The schedule of reform inlisted SMEs is shown in Table 13. We can see that the reformaccelerate from the end of 2005 to 2006 and reach the peak in thesecond quarter of 2006, but in the last quarter of 2006, the reformssuddenly reducedTable 11Correlation coefficient of DD and total assets.Tim e 04/3 04/6 04/9 04/12 05/3 05/6 05/9 05/12 06/3 06/6 06/9 06/12Pear son correlation coefficient − 0.030 − 0.024 0.096 0.154 0.203 0.329* 0.303* 0.411* 0.396* 0.421* 0.377* 0.234P value (two-tail) 0.820 0.848 0.405 0.181 0.080 0.003 0.007 0.000 0.000 0.000 0.001 0.349Total assets (100 million) 4.796 4.715 5.017 4.656 4.719 4.758 4.851 4.607 4.689 4.802 4.949 5.899
  However, whether the reform would affect the credit risk of listedSMEs is still unknown. In this paper, we collect two types of DD andσEbefore and after shares reform to compare the variances of credit risk.Fisher test can be used to judge whether the shares reform hasimpacts on credit risk. We divide the credit risk (DD value) into twoclasses with the boundary of the date starting shares reform: pre-shares reform refers to the period from the beginning of 2004 to theinitial date of reform, and post-shares reform refers to the period fromthe initial date of reform to the beginning of 2007. The tests of equalityof group means show that both DD means and σEmeans before andafter reform are not significant in statistics at α-level of 5% (seeTable 14 ), which means for both σEand DD, there is no signi ficantdiffer ences before and after shares ref orm. The va lidity tes t ofdiscri minant functi on shows that the dis criminant effect is notsignificant (see Table 15), which means the credit risk before andafter the reform cannot be discriminated effectively. We can concludethat there is no obvious difference in credit risk before and after sharesreform, and the reform has few impacts on credit risk.
Conclusions and further consideration
  In this paper, we propose a new method to improve the accuracy ofσEin KMV model. The KMV model with tuned parameters is capable ofidentifying and predicting the credit risk of listed SMEs. Throughmul ti ple t ests, the v al idity of t he mode l is ve rifi ed wi th t h eexperimental results, which are very consistent with the reality. Wefind that the predictive accuracy of adjusted KMV model is stable tothe changes of default point in Chinese listed SMEs, which is differentto the KMV Company's results where datum come from westerncountries. Along with the improvement of information disclosure andChinese equity market, the default distance calculated by KMV modelwill be much closer to the true value, and the model will be muchmore effective to identify the credit risk of listed SMEs.
  In general, the credit of Chinese listed SMEs is poor and stable from2004 to 2006, with DD ranging from 50 to 60. The ST Company ismuch likely to default than the non-ST companies and blue chips. Thecredit of ST companies is poorest in the first two years and tends toimprove in 2006. The closer to the date being identi fied as ST, thehigher the default risk is. Fortunately, Some ST companies have thepossibility to get rid of de ficits with the help of recapitalization, assetinjection, recover arrears and fi nancial subsidies, and the ST labelmight befinally removed.
  We set two credit warning lines for Chinese listed SMEs. TheDD = 40 is set for the second grade warning, and the DD = 30 is set forthe first grade warning. Results show that there are big credit risks inChinese listed SMEs. Half of listed SMEs below the second gradewarning will be in credit crisis in the next year and the creditcondition must be attended closely. 90% of listed SMEs below the fi rstgrade warning will be in credit crisis in the near future, the creditcondition must be alerted and some remedy measures should betaken as soon as possible. The credit warning lines can assist thesecurities regulatory institutions in monitoring the credit crisis oflisted SMEs and they just play the role of the EDF value, which iscon fidential inside KMV Company. In the future, we can also build amapping relation between DD and EDF by gathering years of defaultdatum.
  Wefind that the asset size has significant impact on credit risk. Theprobability of default is the biggest among small-sized listed SMEs andmuch lower in medium and large-sized ones. The default differencesbetw een medi um a nd la rge -si zed c ompan ies ar e ti ny. The ris kresistance in small business with total assets less than 300 million isthe po ore st . As se ts si ze a nd de fau lt ri sk ar e wea kl y po si ti vel ycorrelated in the first half of 2004 and weakly negatively correlatedin the latter half of 2004. When going into 2005, they show asignificant negative correlation. As time goes, the impacts of asset sizeon credit risk will become more and more obvious.
  The credit risk does not change very much before and after thesplit share structure reform, which brings few impacts on credit risk inthe test period. However, the observation after reform is not longenough, the lagged effects of equity changes on credit risk may not befound in a short period of time.
  Future works would be done in building the most optimumfunction of two volatilities ( σEand σV) for listed SMEs. More datashould be collected to verify the results produced by our modelTable 12Split share structure reform progress sheet.Reform progre ss Under the way or have fi nished No reformNon-ST (59) 49 10ST (20) 3 17Total 52 27Table 13Split share structure reform schedule in listed SMEs.Refor mschedu le3rdseasonin 20054thseasonin 20051stseasonin 20062ndseason 2in 20063rdseasonin 20064thseasonin 2006TotalUnde r the wayor havefinished2 12 6 19 12 1 52Table 14Tests of equality of group means.Wilks' lambda F df1 df2 Significant levelDD 0.979 2.194 1 102 0.142σE0.975 2.587 1 102 0.111Table 11Correlation coefficient of DD and total assets.Tim e 04/3 04/6 04/9 04/12 05/3 05/6 05/9 05/12 06/3 06/6 06/9 06/12Pear son correlation coefficient − 0.030 − 0.024 0.096 0.154 0.203 0.329* 0.303* 0.411* 0.396* 0.421* 0.377* 0.234P value (two-tail) 0.820 0.848 0.405 0.181 0.080 0.003 0.007 0.000 0.000 0.000 0.001 0.349Total assets (100 million) 4.796 4.715 5.017 4.656 4.719 4.758 4.851 4.607 4.689 4.802 4.949 5.899Note: “* ” indicates that it is signi ficant at the level of 1%.Table 15Wilks' lambda .Test of function(s) Wilks' lambda Chi-squar e df Significant level1 0.974 2.695 2 0.260
Acknowledgements
  This work was partially supported by the National Natural ScienceFoundation of China (Grants No. 70921001, No. 70631004). Theauthors are also grateful to the referees for their helpful commentsand valuable suggestions for improving the earlier version of thepaper.
References
[1] E.I. Altman, R.G. Haldeman, P. Narayanan, Zeta analysis: a new model to identifybankruptcy risk of co rporations, Journal of Banking and Finance 7 (1) (1977)29–54.[2] E.I. Altman, G. Marco, F. Varetto, Corporate distress diagnosis: comparisons usinglinear discri minant analysis and neural networks (The Italian Experience), Journalof Banking and Finance 18 (3) (1994) 505–529.[3] E.I. Altman, A. Saunders , Credit risk measurement: developments over the last20 years, Journal of Banking & Finance 21 (1998) 1721–1742.[4] J.B. Caouette, E.I. Altman, P. Narayanan, Manag ing Credit Risk: the Next GreatFinancial Challenge, John Wiley & Sons, Inc, New York, 1998.[5] X. Chen, W. Han, J. She, The credit risk, company quality and growth illusion,Economic Theory and Business Management 12 (2006) 62 –67.[6] P. Cheng, C. Wu, New method to analyze credit status of the listed companies,Systems Engineering Theory, Methodol ogy and Applications 11 (2) (2002) 89 –93.[7] P.K. Coats, L.F. Fant, Recognizing financial distress patterns using a neural networktool, Financial Management 22 (3) (1993) 142 – 155.[8] Credit Metrics, Technic al Do cument, J.P. Morgan & Co., New York, April 1997.[ 9] C re d i t S u i ss e Fi n a n c i a l P r od u c ts , C r e d i tR i sk + : a C r ed i t Ri s k Ma n ag em e n tFramework, London, 1, 1997.[10] P.J. Crosbie, J.R. Bohn, Modeling default risk, White Paper, Moody's KMV, RevisedDecember, 2003.[11] H.W. Du, W. Yang, Applyi ng KMV model in China: issues in empirical studies,Studies of International Finance 11 (2004) 22 – 27.[12] J.P. Egan, Signal Detection Theory and ROC Anal ysis, Academic Press, New York,1975.[13] W.E. Henley, D.J. Hand, Construction of a k -nearest-neighbour credit-scoringsystem, IMA Journal of Management Mathematics 8 (4) (1997) 305– 321.[14] J. Hull, Options, Futures, and Other Derivative Securiti es, 3rd EditionPrentice Hall,New Jersey , 1997.[15] Z. Huang, H. Chen, C.J. Hsu, W.H. Chen, S. Wu, Credit rating analysis with su pportvector machines and neural networks: a marke t comparative study, DecisionSupport System 37 (2004) 543– 558.[16] H.Y. Izan, Corporate distress in Australia, Journal of Banking and Finance 8 (2)(1984) 303–320.[17] S. Kealhof er, J. Bohn, Portfolio management of default risk, White Paper, Moody'sKMV. San Francisco, Revised May 31, 2001.[18] C.L. Kun, H. Ingoo, K. Youngsig , Hybrid neural network models for bankruptcypredictions, Decision Support Systems 18 (1) (1996) 63 – 72.[19] M. Kurbat, I. Korablev, Methodology for testing the level of the EDF™ creditmeasure, White Paper, Moody's KMV, Revised August 08, 2002.[20] D. Martin, Early warning of bank failure: a logit regression approach, Journal ofBanking and Finance 1 (3) (1977) 249 – 276.[21] R. Ma, Testing KMV on the financial distress of listed companies in China,Application of Sta tistics and Management 25 (5) (2006) 593 –601.[22] J.A. McQuown, A Comment on Market vs. Accounting-Based Measures of Defa ultRisk, KMV Corporat ion, LLC, San Franc isco, September, 1993.[23] R.C. Merton, On the pricing of corporate debt: the risk structur e of interest rates,Journal of Finance 29 (1974) 449– 470.[24] J.A. Ohlson, Financial ratios and the probabilistic prediction of bankruptcy, Journalof Accountin g Research 18 (1) (1980) 109–130.[25] A. Saunders, L. Allen, Credit Risk Measurement: New Approaches to Value at Riskand Other Paradigms, John Wiley & Sons, New York, March, 2002.[26] J. Scott, The probability of bankruptcy: a comparison of empirical predictions andtheoretical models, Journal of Bankin g and Finance 5 (3) (1981) 317 –344.[ 27 ] X . Sh i , R. Re n , Em p i ri c al te st s of co n si st en c y bet we en ma r ke t- ba se d an daccounting based credit models, Systems Engineering —Theory & Practice 10(2005) 12 – 20.[28] K.S. Shin, I. Han, A case-based approach using inductive indexing for corporatebond rating, Decision Support Systems 32 (2001) 41 –52.[29] L.D. Smith, E.C. Lawrence, Forecasting issues on a liquida ting long-term loanportfolio, Journal of Banking and Finance 19 (6) (1995) 959–985.[30] R.A. Sommerville, R.J. Taf fler, Banker judgment versus formal forecasting models:the case of country risk assessm ent, Journal of Bankin g and Finance 19 (2) (1995)281 – 297.[31] C. Suisse, CreditRisk+: a Credit Risk Management Framework, Credit SuisseFinancial Products London, 1, 1997.[32] Q. Wang, J. Chen, The study of credit risk model and pricing method, ModernFinance and Economics: Journal of Tianjin University of Finance and Economics 22(4) (2002) 14–16.[33] R.C. West, A factor-analytic approach to bank condition, Journal of Banking andFinance 9 (2) (1985) 253 – 266.[34] D. West, Neural network credit scoring models, Computer & Operations Research27 (11–12) (2000) 1131 – 1152.[35] R.L. Wilson, S.R. Sharda, Bankruptcy prediction using neural networks, DecisionSupport Systems 11 (5) (1994) 545– 557.[36] D. Wu, D.L. Olson, Enterprise risk managemen t: small business scorecard analysis,Production Planning & Con trol 120 (4) (2009) 362–369.[37] D. Wu, D.L. Olson, Enterprise risk management: coping with model risk in a largebank, Journal of Operational Research Society 61 (2) (2010) 179– 190.[38] X. Yang, Y. Zhang, An empirical study on credit risk management of China's listedcompanies, China Soft Science 1 (2004) 43 – 47.[39] Q. Ye, N. Jing, L. Xu, Research on credit risk measureme nt based on the CapitalMarket Theory, Economist 2 (2005) 112– 117.[40] L. Zhang, Z. Yang, S. Chen, An application of KMV model in credit risk evaluation ofpublic companies, System Engineering 22 (11) (2004) 84–89.[41] S. Zhang, A comparison of the market value of listed companies under theexamining and approving system, Financial Theory and Practice (7) (2006).[42] M. Zheng, Empirical research of credit risk for the public company using EDFmodel, Journal of Industrial Engineering and Engineering Management 19 (3)(2005) 151– 154.[43] Chinese Stock Supervisory Committee, Code of Good Practice of Exercise of State-Owned Corporation Shares, 1997, p. 62.