Forecasting Corporate Distress in the Asian and Pacific Region

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1 Frecasting Crprate Distress in the Asian and Pacific Regin Russ Mr, Wlfgang Härdle, Saeideh Aliakbari, Linda Hffmann The authrs are grateful fr the financial supprt, data access and ecellent research facilities prvided by the Risk Management Institute (RMI) f the Natinal University f Singapre (NUS) fr the study f crprate distress in Asia and the Pacific regin. We persnally thank Prf. Duan Jin-Chuan and Dr. Oliver Chen fr their inspiratin and valuable suggestins. We als wuld like t epress ur thanks t the staff f RMI NUS fr their patience and readiness t help in cnducting ur research. The wrk f R. A. Mr in develpment f the statistical algrithms was partially supprted by the German Academic Echange Service (DAAD). W. K. Härdle and L. Hffmann were als assisted by the Deutsche Frschungsgemeinschaft thrugh the SFB 9 Ecnmic Risk. Brunel University, Department f Ecnmics and Finance, Schl f Scial Sciences, Ubridge, Midd UB 3PH, United Kingdm and DIW Ecn, Mhrenstraße 5, 1117 Berlin, Germany; phne: Center fr Applied Statistics and Ecnmics, Humbldt-Universität zu Berlin, Spandauer Straße 1, 117 Berlin, Germany and Natinal Central University, Department f Finance, N. 3, Jhngda Rd., Jhngli City, Tayuan Cunty 31, Taiwan (R.O.C.); Brunel University, Department f Ecnmics and Finance, Schl f Scial Sciences, Ubridge, Midd UB 3PH, United Kingdm; Center fr Applied Statistics and Ecnmics, Humbldt-Universität zu Berlin, Spandauer Straße 1, 117 Berlin, Germany;

2 This study analyses credit default risk fr firms in the Asian and Pacific regin by applying tw methdlgies: a Supprt Vectr Machine (SVM) and a lgistic regressin (Lgit). Amng different financial ratis suggested as predictrs f default, leverage ratis and the cmpany size display a higher discriminating pwer cmpared t thers. An analysis f the dependencies between PD and financial ratis is prvided alng with a cmparisn with Eurpe (Germany). With respect t frecasting accuracy the SVM has a lwer mdel risk than the Lgit n average and displays a mre rbust perfrmance. This result hlds true acrss different years. Keywrds: Credit risk, Bankruptcy, Asian cmpanies, SVM JEL Classificatin: C1, G33, C5

3 1 Intrductin Althugh credit risk has always been a majr cncern fr investrs, in recent years high prfile inslvencies have attracted widespread attentin, first, after the dt-cm bubble and then in cnnectin with the subprime mrtgage crisis. In the Asian and Pacific regin, particularly the crisis f 199, caused a wave f inslvencies. The annuncement f the Basel III Capital Accrd in 1 after the adptin f Basel II in and Basel I in 199 indicates bth the cncern f banks and regulatrs abut prviding prtectin against credit risk and, at the same time, inadequacy f the eisting prtectin measures and methds fr measuring risk. As early as in the beginning f the XXth century Winakr & Smith (1935) prpsed the use f financial ratis fr seperating firms int slid stable and ptentially bankrupt nes. Ramser & Fster (1931) and Fitzpatrick (193) als applied financial ratis fr bankruptcy predictin. The systematic applicatin f statistics t bankruptcy analysis began with the wrks f Beaver (19) and Altman (19). They intrduced the univariate and multivariate discriminant analysis (DA), respectively. In 19 Altman presented a frmula fr predicting bankruptcy knwn as the linear Z-scre mdel (Altman, Haldeman & Narayanan, 1977). This frmula remains ppular fr frecasting default rates even tday due t its simplicity. The drawback f the Z-scre mdel is the assumptin f equal nrmal distributins fr bth failing and successful firms with the same cvariance matri. Later the fcus f research shifted twards the lgit and prbit mdels (Ohlsn(19), Martin (1977), Wigintn (19), Zavgren (193) and Zmijewski (19)). Other statistical methds which were intrduced at the same time, such as the gambler s ruin mdel (Wilc, 1971) and ptin pricing thery (Mertn, 197), were based n time series data. Later hazard r survival mdels (Glennn & Nigr, 5) and Frward Intensity Apprach (J. C. Duan & Wang, 1) used bth time series and crss-sectinal data. Anther type f mdels such as recursive partitining (Frydman, Altman & Ka, 195), neural netwrks(tam & Kiang, 199), rugh sets(dimitras, Slwinski, Susmaga & Zpunidis, 1999) and Supprt Vectr Machines(SVM)(Martens, Baesens, van Gestel & Vanthienen, ) were mstly applied t crss-sectinal data. One f the majr shrtcmings f many methdlgies is the fact that they ignre nn-mntnic dependence between sme financial ratis and the PD such as the lgistic regressin r are badly suited fr credit risk mdelling such as neural netwrks due t their multiple lcal equilibria. Fr further infrmatin please refer t Falkenstein, Bral & Carty (), Manning (), Fernandes (5) and Härdle, Mr & Schäfer (1). Fr instance, the prbability f default (PD) is nn- 3

4 mntnically dependent frm the net incme (NI) grwth. Negative r very slwly grwing NI may create prblems with paying cmpany debt bligatins. On the ther hand, high NI is likely t be nn-sustainable in the lng run causing high vlatility. Bth situatins can lead t a higher PD, what is in accrdance with the eisting literature (Mertn (197), Bharath & Shumway ()). The identificatin f the shape f the dependence, hwever, still remains a prblem. The nn-mntnic and nn-linear dependence between sme financial ratis and the PD has been addressed by intrducing nn-linear mdels such as recursive partitining, als knwn as classificatin and regressin trees (Frydman, Altman & Ka (195), Frydman, Altman & Ka (195)), neural netwrks (Tam & Kiang (199)), Primal Supprt Vectr Machines (PSVM) ((Friedman, )) and Supprt Vectr Machines (SVM) ((Martens, Baesens, van Gestel & Vanthienen, ), (Härdle, Mr & Schäfer, 1)). When classifying distressed vs. slvent cmpanies, the SVM allws adjustment f its cmpleity. The cmpeity can be then ptimised with respect t sme accuracy measure, fr eample the Accuracy Rati (AR), fr the data and predicting variables at hand. Figure 1 illustrates the classical trade-ff between the gd in-sample prefrmance and the generalisatin ability. In this eample by changing cmpleity f the classificatin methd between it pssible Fr mre details n the SVM please see Appendi A. In this study we use the Lgit and SVM appraches, bth in their crss-sectinal and dynamic setting, t analyse credit risk f firms in the Asian and Pacific regin and t establish the mst imprtant predictrs f default selected frm financial ratis. Data Descriptin The data used in this study were cllected and prepared by the Risk Management Institute (RMI) f the Natinal University f Singapre (NUS). The data cntain quarterly and annual cmpany reprts, default indicatrs and stck prices fr 5, listed firms frm the Asian and Pacific regin as well as the macrecnmic and selected financial data fr the cuntries in which the firms perate. The time cverage spans frm 19 t 1. The database als indicates the relevant industry f peratin fr each firm. In ur analysis we eclude cmpanies in the financial sectr, asset backed securities, funds and gvernement wned enterprises since the nature f these businesses is different frm nn-gvernmental manufacturing firms and service prviders. At the first stage the financial data are cnverted int financial ratis. These ratis are

5 e.g. Leverage X slvent 1 3 cmpanies A distressed cmpanies X 1 e.g. Prfitability Figure 1: A classificatin eample. The bundary between the classes f slvent and inslvent cmpanies can be either linear (1 r ) r nn-linear (3 and ). A mdel capable f prducing nn-linear bundaries can have lw (linear cases 1 and ), mderate (case 3) and high (case where verfitting is evident) cmpleities. By ptimising the cmpleity with respect t sme accuracy criterin, the ptimal bundary can be established (e.g. case 3). 5

6 gruped int seven categries: prfitability, leverage, liquidity, activity, cst structure, dynamics and size, characterising cmpany perfrmance frm different sides. A summary statistics f the indicatrs is presented in tables. Financial reprts in the database are released quarterly, semi annually and annually, hwever, the beginning f a financial year and, hence, reprting dates fr cmpanies are different and spread thrughut the year. T reflect this situatin we inde each financial reprt by a unique time ID number accrding t the year and mnth f the reprt in rder t have the fianacial infrmatin n regular mnthly basis fr all firms. Since the reprting date almst invariably falls n the last day f a mnth, this encding gives us the precise time f a default event. After assigning the reprt time ID number t each bservatin, distressed firms are defined based n the default infrmatin in the database. Each mnthly reprt f a firm receives the default indicatr y = 1 if the firm files a credit event reprt within a perid with a ne year lng perid starting after ne year after the date f the financial reprt (distressed bservatins). Fr the rest f the bservatins (slvent bservatins) the default indicatir is y = 1. In this study we call this hrizn specificatin design 1. This hrizn is cnsidered t analyse the effects f the default n the lng term debt which has maturity f ver ne year. Additinally, t see the effects f the shrt term debt n PD, we analyse distress fr a different hrizn, when the default indicatr y = 1 is assigned t thse bservatins recrding a credit event reprt filing within the tw year perid frm the date f the financial reprt (distressed bservatins) and fr the rest (slvent bservatins) the default indicatir is y = 1. This hrizn specificatin is called design. A brad range f credit events is applied t identify distressed firms and assign the default indicatir (y = 1), including filings under Chapter 11, Chapter 15, Chapter 7, restructuring, liquidatin, being sued by creditrs and failing in cupn and principle payments. Overall, the bankruptcy events cded frm 1 t 1 and 3 t 333 in the database are included t define distressed bservatins. In the dataset with the hrizn under the design specificatin, there are 311, bservatins frm which 7,9 (.39%) bservatins are indicated as distressed and 3,33 (97.1%) as slvent. The distributin f slvent and distressed bservatins amng cuntries varies substantially. Fr instance, fr Australia and Hng Kng, there are respectively nly (.3%) and 19 (.3%) f distressed bservatins ut f 19 and 5,5 bservatins whereas fr China there are,1 (7.%) distressed bservatins ut f 57,91 bservatins (see table 1).

7 Hrizn: Design 1 Hrizn: Design Cuntry Distressed Slvent Distressed Slvent firms firms firms firms Australia 3 (.1 % ) 1 (.3 % ) 13 China 1 (. % ) 37 1 (7. % ) Hng Kng 1 (.1 % ) (.3 % ) 555 India (.17 % ) 1 (.51 % ) 775 Indnesia (. % ) (1.1 % ) 1 Japan 1 (.17 % ) (.3 % ) 713 Malaysia 35 (1.17 % ) (3.1 % ) 3173 Philippines 113 (1.9 % ) (.1 % ) 15 Singapre 3 (. % ) (1. % ) 75 Suth Krea 99 (. % ) 9 3 (. % ) 5153 Taiwan (1. % ) 39 (.7 % ) 39 Thailand (1.19 % ) 17 (.77 % ) 17 Table 1: Distributin f distressed and slvent firms acrss cuntries..1 Variable Descriptin The cmpnents f the financial ratis which are estimated frm data are eplained belw and the summary statistics fr them fr distressed and slvent firms are prvided in tables and 3. Prfitability Ratis 1. NI/TA : return n assets; net incme / ttal assets.. NI/S : net prfit margin; net incme / sales. 3. OI/TA: perating return n assets; perating incme / ttal assets.. OI/S : perating prfit margin; perating incme / sales. 5. EBIT/TA: grss return n assets; earnings befre interest and taes / ttal assets.. EBIT/S : grss prfit margin; earnings befre interest and taes / sales. Leverage Ratis 1. OK/TA : wn capital rati; wn capital / ttal assets.. CL/TA : current debt rati; current liabilities / ttal assets. 3. TD/TA : bank debt rati; the rati f ttal bank debt / ttal assets. Liquidity Ratis 1. STD/D : fractin f debt which is shrt term debt (liquidity).. CASH/TA : cash and cash equivalents / ttal assets. 3. CASH/CL : cash rati; the rati f cash and cash equivalents / current liabilities. 7

8 . QA/CL : quick rati; quick assets (current assets inventries) / current liabilities. 5. CA/CL : current rati; the rati f current assets / current liabilities.. WC/TA : wrking capital (current assets minus current liabilities) / ttal assets. 7. CL/TL : current liabilities / ttal liabilities. Activity Ratis 1. TA/S : asset turnver; ttal assets / sales.. INV/S : inventry turnver; inventries / sales. 3. AR/S : accunt receivable turnver; accunt receivables / sales.. AP/CS : accunt payable turnver; accunt payables / cst f sales. Cst Structure Ratis 1. INT/D : average cst f debt; the rati f interest payments t debt.. EBIT/INT paid : interest cverage rati; the rati f earnings befre interest and taes t interest paid. Dynamic Ratis 1. Sales-Grwth : ne year grwth in sales.. NI-Grwth : ne year grwth in incme. Size 1. lg(ta) : cmpany size; lgarithm f ttal assets.. lg(s) : lgarithm f ttal sales.. Summary Statistics In this sectin summary statistics f the financial ratis fr distressed and slvent cmpanies are prvided. They are reprted fr Design 1 (table ) and Design (table 3) hrizn designs, pled acrss cuntries. The first five clumns in each table summarize the estimates fr distressed cmpanies and the net five clumns reprt the estimates fr slvent cmpanies. q.5 and q.95 are 5% and 95% quantiles. N is the number f bservatins fr which the rati can be cmputed based n the available data and IQR represents the interquartile range fr each rati.

9 19-1 Distressed Firms Slvent Firms Variable N q.5 Med IQR q.95 N q.5 Med IQR q.95 Prfitability NI/TA NI/S OI/TA OI/S EBIT/TA EBIT/S Leverage OK/TA CL/TA TD/TA Liquidity STD/D CASH/TA CASH/CL QA/CL CA/CL WC/TA CL/TL Activity TA/S INV/S AR/S AP/CS Cst Structure INT/D EBIT/INT Dynamics Sales-Grwth NI-Grwth lg(ta) lg(s) Table : Summary statistics fr distressed firms (the left five clumns) and slvent firms (the right five clumns) acrss cuntries. Hrizn: Design 1. N indicates the number f bservatins which cntain the variable. q.5 and q.95 are respectively 5% and 95% quantiles. IQR is the interquartile range. Size 9

10 19-1 Distressed Firms Slvent Firms Variable N q.5 Med IQR q.95 N q.5 Med IQR q.95 Prfitability NI/TA NI/S OI/TA OI/S EBIT/TA EBIT/S Leverage OK/TA CL/TA TD/TA Liquidity STD/D CASH/TA CASH/CL QA/CL CA/CL WC/TA CL/TL Activity TA/S INV/S AR/S AP/CS Cst Structure INT/D EBIT/INT Dynamics Sales-Grwth NI-Grwth lg(ta) lg(s) Table 3: Summary statistics fr distressed firms (the left five clumns) and slvent firms (the right five clumns) acrss cuntries. Hrizn: Design. N indicates the number f bservatins which cntain the variable. q.5 and q.95 are respectively 5% and 95% quantiles. IQR is the interquartile range. Size 1

11 Hrizn: Design 1 Hrizn: Design Cuntry Distressed Slvent Distressed Slvent firms firms firms firms Australia (. % ) (. % ) China 3 (1.3 % ) 3 39 (.1 % ) 7 Hng Kng 3 (.19 % ) 15 7 (. % ) 15 India (. % ) 15 (. % ) 15 Indnesia (.5 % ) (1.19 % ) 511 Japan 1 (.1 % ) (.35 % ) 37 Malaysia 7 (1.1 % ) (3.1 % ) 51 Philippines 39 (. % ) 17 1 (. % ) 7 Singapre 9 (.53 % ) (1.7 % ) 55 Suth Krea 77 (.1 % ) (.37 % ) 35 Taiwan 77 (.35 % ) 5 (1. % ) 197 Thailand 11 (1.7 % ) (.7 % ) 151 Table : Distributin f distressed and slvent firms acrss cuntries after remving variables with mst missing values. These variables are : INT/D, EBIT/INT, AP/CS, STD/D, Sales-Grwth and NI-Grwth. As we can see frm table 3, the lwest number f available bservatis belng t variables: INT/D, EBIT/INT, AP/CS, STD/D, Sales-Grwth and NI-Grwth. Table presents the distributin f distressed and slvent firms after remving these variables with mst missing values. After remving them and cleaning missing values the ttal number f distressed bservatins in the data set increases frm 1,1 t,. 3 Univariate Analysis f the Predictrs f Default The analysis f financial ratis and their individual pwer as predictrs f default can be cncisely dne by estimating univariate dependence f PD frm each variable. Since the range f each predictr can change significantly, we represent all predictrs with their percentiles. Univariately estimated PDs are reprted in figures. They were btained as k nearest neighbr estimates (k-nn) with Gaussian weights: PD(q) = n i=1 I(y i = 1)e (q q i ) σ n i=1 e (q q i ) σ, (3.1) where q 1 is a percentile f a cmpany fr which PD is estimated, q i is the percentile f cmpany i f the data set and the smthing parameter σ is set t.. I(y i = 1) is the distress indicatr which equals 1 if y i = 1 when cmpany i is defined as distressed and therwise. 11

12 1 Univariate PD (Prfitability Ratis) NI/TA OI/TA EBIT/TA 1 Univariate PD (Prfitability Ratis) NI/TA OI/TA EBIT/TA Univariate PD (Prfitability Ratis) 1 NI/S OI/S EBIT/S Univariate PD (Prfitability Ratis) 1 NI/S OI/S EBIT/S Figure : Univariate prbabilities f default fr Prfitability Ratis pled ver cuntries and years. Hrizn: Design 1 (left panel), Hrizn: Design (right panel). The variables differ substantially in their predictive pwer. Fr instance, variables EBIT/TA, CL/TA and lg(s) indicate strng predictive pwer and als traditinally appear in the literature as strng indicatrs. In cntrast sme variables such as STD/D, AR/S and Sales-Grwth shw less discriminating pwer. Anther imprtant bservatin frm the plts is that sme predictrs, many f which with high discriminating pwer, such as CL/TA, OK/TA, CA/CL, EBIT/INTpaid, lg(ta), INT/D and CL/TL have a nn-mntnic dependence with PD. We analyse the relatinship between each predictr f default with PD and their predictive pwer n data pled ver cuntries. The results are presented fr the tw hrizn designs, Design 1 and Design. 1

13 1 Univariate PD (Leverage Ratis) OK/TA CL/TA TD/TA 1 Univariate PD (Leverage Ratis) OK/TA CL/TA TD/TA Figure 3: Univariate prbabilities f default fr Leverage Ratis pled ver cuntries and years. Hrizn: Design 1 (left panel), Hrizn: Design (right panel). 1 Univariate PD (Liquidity Ratis) STD/D CASH/TA CASH/CL 1 Univariate PD (Liquidity Ratis) STD/D CASH/TA CASH/CL Univariate PD (Liquidity Ratis) 1 QA/CL CA/CL WC/TA CL/TL Univariate PD (Liquidity Ratis) 1 QA/CL CA/CL WC/TA CL/TL Figure : Univariate prbabilities f default fr Liquidity Ratis pled ver cuntries and years. Hrizn: Design 1 (left panel), Hrizn: Design (right panel). 13

14 1 Univariate PD (Activity Ratis) TA/S INV/S AR/S AP/CS 1 Univariate PD (Activity Ratis) TA/S INV/S AR/S AP/CS Figure 5: Univariate prbabilities f default fr Activity Ratis pled ver cuntries and years. Hrizn: Design 1 (left panel), Hrizn: Design (right panel). 1 Univariate PD (Cst Structure Ratis) INT/D EBIT/INTpaid 1 Univariate PD (Cst Structure Ratis) INT/D EBIT/INTpaid Figure : Univariate prbabilities f default fr Cst Structure Ratis pled ver cuntries and years. Hrizn: Design 1 (left panel), Hrizn: Design (right panel). 1

15 1 Univariate PD (Dynamic Ratis) SALES GROWTH NI GROWTH 1 Univariate PD (Dynamic Ratis) SALES GROWTH NI GROWTH Figure 7: Univariate prbabilities f default fr Dynamic Ratis pled ver cuntries and years. Hrizn: Design 1 (left panel), Hrizn: Design (right panel). 1 Univariate PD (Size Ratis) LOG TA LOG S 1 Univariate PD (Size Ratis) LOG TA LOG S Figure : Univariate prbabilities f default fr Cmpany Size pled ver cuntries and years. Hrizn: Design 1 (left panel), Hrizn: Design (right panel). 15

16 Cmparisn f the PD between Asian and German Cmpanies In this sectin we cmpare the results f the PD univariate analysis fr Asian firms (hrizn: Design 1) pled acrss all cuntries with the analysis f the same r very clse financial ratis fr German firms. The dataset fr German cmpanies was kindly prvided fr ur analysis by the Deutsche Bundesbank and cvers the years cntaining arund 5, balance sheets and incme statements frm which, belng t bankrupt firms. Sme f the financial ratis that are used by the Deutsche Bundesbank fr cmpany rating are the same as cnstructed fr Asian cmpanies, while thers are specific fr Germany. We reprt the cmparisn f the cmmn financial ratis in figures The graphs fr Germany reprt the cumulative default rate with the hrizn f default f three years and abve, whereas the hrizn f default fr RMI data lies between ne and tw years. The pssibilty f registering default within a much brader range f hrizns eplains the higher PD fr German data. Fr mre infrmatin see (Härdle, Mr & Schäfer, 1). German cmpanies in cntrast t Asian nes are primarily private (nn-traded) and are f a smaller size. Mrever, the sample f firms in the Bundesbank database is epected t be biased. These are the firms wh vluntarily applied fr rating in rder t receive refinancing frm cmmercial banks and are mstly self-selected slvent cmpanies. Despite many similarities, the dependence f PD frm the individual financial ratis can display certain differences between German and Asian cmpanies which can be attributed t a mre hmgeneus sample fr Germany, disparity in cmpany registratin frms and sizes and the self-selected nature f the German sample. These differences are mstly prclaimed if the dependence fr the cmpanies frm ne f the regins has a U shape. 5 Variable Selectin and Rating Mdel Cmparisn The criterin fr cmparing different mdels is a rbust accuracy measure, the median Accuracy Rati (AR) estimated n btstrapped subsamples. AR is the rati f tw areas (i) between the cumulative default curves fr the mdel being evaluated and the mdel with the zer predictive pwer and (ii) between the cumulative default curves fr the ideal mdel and the mdel with the zer predictive pwer (figure 1). AR is used 1

17 Univariate PD (Prfitability) EBIT/S OI/S EBIT/TA 1 Univariate PD (Prfitability, DE) EBIT/S (K1) OI/S (K) EBIT/TA (K3) Figure 9: Univariate prbabilities f default fr Prfitability Ratis pled ver cuntries and years fr Asia (hrizn: Design 1, left panel) and Germany (right panel). Univariate PD (Leverage) OK/TA 1 Univariate PD (Leverage, DE) OK/TA (K) Figure 1: Univariate prbabilities f default fr Leverage Ratis pled ver cuntries and years fr Asia (hrizn: Design 1, left panel) and Germany (right panel). 17

18 Univariate PD (Liquidity) CASH/TA 1 Univariate PD (Liquidity, DE) LiquidAssets/TA (K1) Figure 11: Univariate prbabilities f default fr Liquidity Ratis pled ver cuntries and years fr Asia (hrizn: Design 1, left panel) and Germany (right panel). Univariate PD (Activity) INV/S AR/S 1 Univariate PD (Activity, DE) INV/S (K31) AR/S (K) Figure 1: Univariate prbabilities f default fr Activity Ratis pled ver cuntries and years fr Asia (hrizn: Design 1, left panel) and Germany (right panel). 1

19 Univariate PD (Cst Structure) EBIT/INTpaid 1 Univariate PD (Cst Structure, DE) EBIT/INTpaid (K9) Figure 13: Univariate prbabilities f default fr Cst Structure Ratis pled ver cuntries and years fr Asia (hrizn: Design 1, left panel) and Germany (right panel). Univariate PD (Dynamics) NI GROWTH 1 Univariate PD (Dynamics, DE) NIG (K1) Figure 1: Univariate prbabilities f default fr Dynamic Ratis pled ver cuntries and years in Asia (hrizn: Design 1, left panel) and Germany (right panel). 19

20 Univariate PD (Size) lg TA 1 Univariate PD (Size, DE) lg(ta) (K33) Figure 15: Univariate prbabilities f default fr Cmpany Size pled ver cuntries and years in Asia (hrizn: Design 1, left panel) and Germany (right panel). since it is nt sensitive t a mntnic transfrmatin f a scre in cntrast t ther accuracy measures such as hit rate r α and β errrs. The btstrap prcedure (Efrn & Tibshirani, 1993) fr mdel cmparisn starts with the selectin f tw nn-verlapping randm subsamples f 1 bservatins (5 nndefaulting and 5 defaulting firms) frm the riginal data set. One f thse subsamples is used as a training set and the ther ne as a testing set. A classificatin mdel (SVM r Lgit) is trained n the frmer and its AR is estimated n the latter. The prcedure is repeated 1 times creating a set f 1 estimates f AR frm which the median is cmputed and used fr the cmparisn f mdels. The mdel with the highest median AR is preferred. All data were first cleaned frm utliers by capping them: if < q inf () then = q inf () and if > q sup () then = q sup (). Here q inf () = Median() 1.5IQR() and q sup () = Median()+1.5IQR(). Secndly, all data were standardised as new = ( median())/σ(). This was dne t avid an ecessive influence f the variables with a higher dispersin. These transfrmatins are rutinely applied t the data prir t analysis. Variable selectin was perfrmed using the frward selectin prcedure which starts with univariate mdels. At step ne the first variable is selected that prduces the mst accurate univariate mdel as judged by its median AR estimated by btsrapping. At step tw, in additin t this variable, the secnd variable frm the remaining is chsen which has the highest meadian AR amng all alternatives. At step three a trivariate mdel is selected, etc. The variables selected by Lgit and SVM fr pled data are presented in table 5. After a certain step fur the accuracy f bth the Lgit and SVM

21 Mdel being evaluated 1 1 Cumulative default rate Mdel with zer predictive pwer A Cumulative default rate Mdel with zer predictive pwer B Perfect mdel number f all cmpanies number f successful cmpanies number f bankrupt cmpanies Number f cmpanies, rdered by their scre Number f cmpanies, rdered by their scre Figure 1: Accuracy Rati (AR) is the rati f tw areas A and B. mdels des nt eperience any significant imprvements, what is evident frm very high p-values. The SVM was always applied with R = r d/ and C = (c/n)(/d), where r and c were chsen based n the values reprted as perfrming well fr cmpany rating (Lacerda & Mr (), Härdle, Mr & Schäfer (1)). These tw parameters f the SVM used in ur study were r =.5 and c = 1 fr a lw cmpleity SVM with high generalisatin ability, which is epected t perfrm well n a brad range f data sets. The perfrmance f the SVM can be ptentially further increased by ptimising r and c fr the studied data. The transfrmatins fr cmputing R and C figuring in the SVM frmulatin (see Appendi A) were applied t keep the SVM invariant f the data dimensin d and the number f bservatins in the training set n. As the table 5 indicates bth mdels cnsidered Lgit and SVM have selected the first three variables identically: TD/TA, lg(s), CL/TA. The frth variable selected by the SVM is TA/S, while lg(ta) was selected by Lgit. These variables frm the basis fr ur mdel cmparisn. Frecasting Accuracy Figure 17 represents the time series f Accuracy Ratis (AR) fr pled data and a separate cuntry with the highest number f distressed bservatins, China. The training set data are cllected frm the year indicated in the plts alng the hrizntal ais. The testing set data are cllected fr the year T +, where T is the training set year. The 1

22 Lgit SVM (R =.5,C = 1) Step Variable Med.AR p ma p Variable Med.AR p ma p 1 TD/TA 57.5 TD/TA 57.5 lg(s) 9. lg(s) CL/TA 71.1 CL/TA lg(ta) 73. TA/S WC/TA RV Table 5: Variables selected at each step by the frward selectin prcedure fr Lgit and SVM fr the pled data. Fr cmputing the median AR fr each cmbinatin f variables and the distributins f AR required fr the tests, 1 btstrapped subsamples were used. The cnfidence level p ma is reprted fr the test with H : the mdel is nt significantly different frm the fur-variable mdel which was selected; p crrespnds t the H : a mdel is nt significantly different cmpared t a previus reduced mdel which has ne variable less. Median AR, p ma and p are reprted in percentage pints. used default hrizn specificatin is Design. This arrangement guarantees that there are n verlapping bservatins in the data sets and frecasting is made ut-f-sample. The parameters f the SVM are r =.5 and c = 1. The variables are the same nes selected by varibale selectin prcedure. Fr SVM these variables are: TD/TA, lg(s), CL/TA and TA/S and fr Lgit: TD/TA, lg(s), CL/TA and lg(ta). As it is evident frm figure 17, SVM usually utperfrms Lgit in frecasting crprate distress. The difference in AR can be as high as 7.5%, as it is the case fr China in 5. On the ther hand there are much fewer years when the SVM underperfrmed cmpared t the Lgit. The maimum difference in this case is nly.%. Fr the pled data in seven years ut f eight the SVM has a higher perfrmance than the Lgit, althugh the differences in this case are mre mderate than fr China. The similar cnclusin abut a higher predictive pwer f the SVM can be reached frm analysing figure 1. It reprts the distributin f the differences in AR between the SVM and Lgit estimated n 1 btstrapped subsamples f the data pled acrss cuntries and years. Althugh the average imprvement is mderate, arund.5%, the SVM can achieve a much higher relative imprvement fr etreme scenaris. This is evident frm a lnger right tail f the prbability density functin. In ther wrds, the SVM has a lwer mdel misspecificatin risk cmpared with Lgit, bth n average and in the etreme cases. T illustrate the perfrmance f the SVM and Lgit we will cnsider a tw dimensinal case (figures 19 and ). The lines crrespnd t the isquants with the PD equal t the average PD fr the data. Hwever small the differences may be, they are sufficient t

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