Predicting probability of defaultof Indian corporate bonds: logisticand Z-score model approaches

Arindam BandyopadhyayNational Institute of Bank Management (NIBM), Kondhwe Khurd, Pune, India

Abstract

Purpose – This paper aims at developing an early warning signal model for predicting corporatedefault in emerging market economy like India. At the same time, it also aims to present methods fordirectly estimating corporate probability of default (PD) using financial as well as non-financialvariables.

Design/methodology/approach – Multiple Discriminate Analysis (MAD) is used for developingZ-score models for predicting corporate bond default in India. Logistic regression model is employed todirectly estimate the probability of default.

Findings – The new Z-score model developed in this paper depicted not only a high classificationpower on the estimated sample, but also exhibited a high predictive power in terms of its ability todetect bad firms in the holdout sample. The model clearly outperforms the other two contesting modelscomprising of Altman’s original and emerging market set of ratios respectively in the Indian context.In the logit analysis, the empirical results reveal that inclusion of financial and non-financialparameters would be useful in more accurately describing default risk.

Originality/value – Using the new Z-score model of this paper, banks, as well as investors inemerging market like India can get early warning signals about the firm’s solvency status and mightreassess the magnitude of the default premium they require on low-grade securities. The defaultprobability estimate (PD) from the logistic analysis would help banks for estimation of credit riskcapital (CRC) and setting corporate pricing on a risk adjusted return basis.

Keywords India, Bonds, Modelling, Emerging markets

Paper type Research paper

IntroductionCorporate liabilities have default risk. There is always a chance that a corporateborrower will not meet its contractual obligations and may renege from paying theprincipal and the interest due. Even for the typical high-grade borrower, this risk isthere even though it may be small, perhaps 1/10 of 1 percent per year. Although theserisks do not seem large, they are in fact highly significant. They can even increasequickly and with little warning. Further, the margins in corporate lending are verytight, and even small miscalculations of default risks can undermine the profitability oflending. But most importantly, many lenders are themselves borrowers, with highlevels of leverage. Unexpected realizations of default risk have destabilized,decapitalized, and destroyed many internationally active lending institutions.

Following the release of the recent Reserve Bank of India (RBI) draft guidelines(February 15, 2005) for the implementation of Basel II norms, the leading Indian banksare preparing to design appropriate internal credit risk models. The major motive is theincentive based approach for capital estimation for credit risk. In order to fetch theearly rewards of Basel II implementation, banks have to develop their own internal

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The Journal of Risk FinanceVol. 7 No. 3, 2006

pp. 255-272q Emerald Group Publishing Limited

1526-5943DOI 10.1108/15265940610664942

models for credit risk. Internal models offer an opportunity for a bank to measure andprice counter-party risk and systemize risks inherent in lending. Prediction of defaultprobability (PD) for each borrower or group of borrowers is the key input for theestimation of regulatory capital as well as economic capital for banks. It is also equallyimportant for the banking industry and financial institutions to discriminate the goodborrowers (non-defaulting) from the bad borrowers (defaulting). This will not only helpthem in taking lending decisions but also practicing better pricing strategies to coveragainst the counter party risk. While, internationally, considerable research has beenmade to predict corporate default, very few attempts have been done for EmergingMarket like India.

The purpose of this paper is to build a robust framework that enables banks andfinancial institutions in emerging market economy like India to classify a firm in thedefault or non-default category based on the information of its financial variables. Thiskind of model can serve as a useful tool for quick evaluation of the corporate riskprofile. Second, it can also be used to track the firms to check for their default statusover time. As a result such model can help banks to get an early warning signal aboutthe default status of its corporate clients. In this paper, we estimate an MDA model topredict corporate default using a balanced panel data of 104 Indian corporations for theperiod of 1998 to 2003. The financial ratios and other basic information are collectedfrom the Centre for Monitoring Indian Economy (CMIE) Prowess database. Thisdatabase is similar to the Compustat database in the USA. However, as we havementioned earlier, it is not enough to know a qualitative differentiation ofcounter-parties for properly evaluating credit risk. One has to go one step furtherand differentiate quantitatively between different counter-parties. Accordingly, wealso estimate probability of default (PD) of each firm for the same corporate portfoliothrough logistic regression. Here we also explore the role of non-financial factors inpredicting default. For this purpose, we empirically examine whether the combined useof financial and non-financial factors lead to more accurate PD estimates.

The rest of the paper is structured as follows. In the next section we discuss aboutthe data, definitions and construction of variables and hypotheses. The third sectionportrays the corporate bond default rates across different rating grades in India as wellas industry wise default rates. In the fourth section, we demonstrate the developmentof the Z-score model for Indian corporations, main results, and the model validation.The fifth section presents the results and methodology of logistic analysis to predictcorporate bond defaults. Here we also compare the significance of financial andnon-financial parameters in describing default risk. We have also tested the predictivepower of logistic model. The sixth section discusses the main conclusions.

Literature surveyIn theory, corporate insolvency is indicated either by fall in the asset value or due toliquidity shortage (i.e. falls in the ability to raise capital to finance project). Therefore,we should expect that the ratios that reflect the cash flow structure and movement ofmarket value of firm’s asset to be different among defaulted and solvent firms (Wilcox,1971; Scott, 1981). Several later studies incorporated these theoretically determinedfinancial characteristics in the explanation of corporate default. For example, Caseyand Bartczak (1985), Gentry et al. (1985) and Aziz et al. (1988) used cash flow variablesin their model in predicting corporate failure. Opler and Titman (1994) and Asquith

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et al. (1994) report that default is primarily caused by firm-specific idiosyncraticfactors. On the other hand, researchers like Lang and Stulz (1992) and Denis and Denis(1994) argue for a systematic nature of bankruptcy risk. Kranhnen and Weber (2001)presented a normative set of generally accepted rating principles that point out thenecessity of links among industry risk, business risk, financial risk, management risk,facility risk, and probability of default. Grunert et al. (2005) analyzed credit file datafrom four major German banks and found empirical evidence that the combined use offinancial and non-financial factors leads to a more accurate prediction of future defaultevents than the single use of each of these factors. Other studies look at the relationbetween default and the stock market. KMV Corporation of Moody (1993) using Blackand Scholes (1973) approach made an attempt to predict default in an option pricingcontext; i.e. to model when the option to default has more value than the option tocontinue.

Because of the lack of a unifying theory, there has been an explosion of differentempirical methods used to predict business failure in different markets. Statisticalmodels can help banks to predict default probability to get an early warning signalabout the default status of the corporate clients. Excellent reviews of the plethora ofstudies can be found in Dimitras et al. (1996) and Mossman et al. (1998). The firstapproach to predicting corporate failure has been to apply a statistical classificationtechnique called MDA to a sample containing both failed and non-failed firms. Studieslike Beaver (1966) and Altman (1968) pioneered this approach. Beaver (1966, 1968) didunivariate analysis of a number of bankruptcy predictors and set the stage formultivariate attempts by him and others. He found that a number of indicators coulddiscriminate between matched samples of failed and non-failed firms for as long as fiveyears prior to failure. He also developed a Z-score model by using multivariate analysisin 1968. In the same year, Altman developed his classic multivariate insolvencyprediction model (MDA) for publicly traded manufacturing firms in the USA. Theinitial sample in his study is composed of 66 corporations with 33 firms in each of thetwo groups distressed and solvent. The indicator variable Z-score forecasts theprobability of a firm entering bankruptcy within a two-year period (the cut-off score isbelow 1.81). In the original Z-score formula for predicting bankruptcy Altman (1968)employed working capital/total assets ratio, retained earnings/total assets ratio,earning before interest and taxes/total assets ratio, market value of equity/book valueof total debt ratio, and sales/total assets ratio as predictor of financial health of acompany.

In Altman et al. (1977) constructed a second-generation model with severalenhancements to the original Z-score approach. The new model, which was calledZETA, was effective in classifying bankrupt companies up to five years prior to failureon a sample of corporations consisting of manufacturers and retailers. The ZETAmodel tests included non-linear (e.g., quadratic) as well as linear discriminate models.The non-linear model was more accurate in the original test sample results but lessaccurate and reliable in holdout or out-of-sample forecasting. Subsequently, in Altmanet al. (1995) modified his Z-score model to emerging market corporations, especiallyMexican firms that had issued Eurobonds denominated in US dollars. In this enhancedZ-score model, he dropped sales/total assets and used book value of equity for thefourth and final variable to make it more suitable for the private firms.

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Several researchers influenced by the work of Altman (1968) on the application ofdiscriminant analysis, explored ways to develop more reliable financial distressprediction models. Subsequently, new analytical techniques like logit or probit models(Martin, 1977; Ohlson, 1980; Zavgren, 1985; Lennox, 1999; Westgaard and Wijst, 2001;Grunert et al., 2005), multidimensional scaling (Mar Molinero and Ezzamel, 1991),artificial neural networks (Tam, 1991; Wilson and Sharda, 1994/1995), multinomiallogit (Johnsen and Melicher, 1994), multicriteria decision aid methodology (Zopounidisand Dimitras, 1998), etc. have been introduced to predict corporate failure in differentmarkets.

As one can see from the collective literature discussed above, a very large number ofempirical bankruptcy prediction models do multiple discriminant analysis (MDA)pioneered by the seminal works of Altman (1968, 1995) based on the accounting data.However, these models, though worked successfully, are very much country specificand may not fit well with the Indian condition. The ratios as well as the weights ofMDA would differ across countries and regions (as one can see the Altman’s original1968 model for US manufacturing firms is different from that of Emerging Marketmodel of 1995 based on Mexican data). Further, Z-score model only gives predictionabout the qualitative differentiation of counterparties. If banks are interested todirectly estimate the probability of default (PD), MDA analysis is not applicable since itdoes not produce such probabilities.

One possible solution for banks, which intends to estimate PD directly, is the use oflimited dependent logit model (similar to Amemiya, 1981; Maddala, 1983). Unlike thediscriminant model, the logistic model has the flexibility to incorporate both thefinancial as well as non-financial factors in predicting default. While the financialratios capture the firm specific information, the non-financial factors help to evaluatethe link of the firm with macroeconomic factors and the capability of the firm to churnout cash flow in the required numbers.

Sample data characteristics, variable definitions, and hypothesesThe information on defaulted and solvent firms is collected from CRISIL’s annualratings of long-term bonds issued by 542 companies from 1998 until 2004. Thesecompanies are then matched by their asset size, year, and industry affiliation.Following these criteria in a random selection, we finally got a sample of 52 solventfirms and 52 defaulted firms. The defaulted group is a class of manufacturers whoselong-term bonds have been defaulted between 1998 and 2003[1]. The solvent firms arechosen on a stratified random basis drawn from CRISIL rating database. The meanasset size of the firms in the solvent group (Rs. 948.51 Crore) is slightly greater thanthat of the defaulted group (Rs. 818.62 Crore), but matching exact asset size of the twogroups is not always necessary[2]. The financial information of these 104 companiesover the period of 1998 to 2003 is obtained from the CMIE Prowess database. Inaddition to the accounting data, information on ISO certification is obtained from theQ-Prod’s directory. In order to test the predictive accuracy of our estimated sample, aholdout sample of another 50 (25 solvent and 25 defaulted) companies is being createdfor the years 2003 and 2004. Our estimated sample of 104 firms have been classifiedinto 11 industry categories based on their major economic activities after matchingthem with the National Industrial Classification (NIC) codes (see Table I).

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As we discussed in the introductory section, the variables to be included in bankruptcyprediction models should be able to relate the properties of the cash flow incombination with the debt obligations and the movement in the asset value of the firm.While MDA technique can successfully draw the best combination of key ratios from alarge set of financial ratios, the logistic model can capture more firm specificidiosyncratic factors and also can relate the firm to the macro economic conditions. Weinitially started with many financial ratios and finally arrive at five key ratios (in ourMDA model) that best discriminate between our sample of good and bad firms. Inorder to pick up the best ratios, we looked at:

. F and Wilk’s Lambda statistics to check the statistical significance of eachindividual ratio, including determination of relative magnitude of eachindependent variable (i.e. standardized values of their coefficients).

. Within sample discriminatory power of these ratios’ best combinations.

. Chi-square statistic as check for the overall significance of various discriminantfunctions and finally.

. Our own analytical judgment.

The final profile of ratios is as follows:. WK_TA: working capital over total assets is a measure of the net liquid assets of

the firm relative to the total capitalization. Working capital is defined as thedifference between current assets and current liabilities. Hence the ratio is aproxy for the short-term liquidity condition of the firm.

. CASHPROF_TA: cash profit over total assets is a measure of cash flow of thefirm. Cash profit is obtained by adding the non-cash charges such as depreciationand amortization to the profit after tax (or net profit).

. SOLVR: solvency ratio judges the long-term solvency of a firm. Higher thesolvency ratio better is the ability of the firm to meet key term obligations andlower will be the probability of default. The solvency ratio is computed bydividing the firm’s total assets (net of revaluation reserves, advance tax andmiscellaneous expenses not written off) by its total borrowings plus currentliabilities and provisions minus advance payment of tax.

Industry dummy Industry type Number of firms

IND1 Food products/sugar/tea/tobacco/beverages 4IND2 Paper 3IND3 Textile 9IND4 Chemical 27IND5 Machine/electrical/computers 14IND6 Metal/non-metal 23IND7 Auto/parts 6IND8 Power 2IND9 Diversified 5IND10 Service 9IND11 Other manufacturing 2Total 104

Table I.Industry categories of

sample companies

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. OPPROF_TA: operating profit over total assets is a measure of the trueproductivity of the firm’s assets. It measures the firm’s earning capability. Thehigher is the ratio, the better for the company.

. SALES_TA: the capital turnover ratio is a standard financial ratio (also used byAltman in his original 1968 model) illustrating the sales generating ability of thefirm’s assets. It is the ratio of total sales to total assets. This ratio gives anindication as to how efficiently a company is utilizing its assets. Higher is thisratio, the better for the company.

In the logit analysis, we have included another financial variable: MVE_BVL – theequity market value over the book value of the liabilities proxy for the firm’s assetvalues. It also measures the solidity of the firm. In calculating book value of totalliabilities, total net worth of the firm is subtracted from the total liability of the firm.Hence, the BVL gives the book value of total outside liabilities of the firm.

All the six ratios represent either value or income of the firms with respect to totalassets. They are all hypothesized to be either positively related to solvency ornegatively related to the firm’s default probabilities.

Following non-financial variables are taken from the existing literature aboutcorporate solvency:

. Age of the firm. Age of the company since incorporation. A relatively young firmwill probably show a low retained earnings/total assets (RE/TA) ratio because ithas not had time to build up its cumulative profits (Altman, 2000). Therefore, itmay be argued that the young firm is somewhat discriminated against in thisanalysis, and its chance of being classified as bankrupt is relatively higher thanthat of another older firm, ceteris paribus. But, this is precisely the situation inthe real world. The incidence of failure is much higher in a firm’s earlier years[40-50 percent of all firms that fail do so in the first five years of their existence(Dun and Bradstreet, annual statistics)]. The age effect is thus clear: young firmsare more likely to default. We take natural log of the number of years of the firmsince incorporation as measure of firm age.

. Group ownership. Studies covering various countries have found that firmsassociated with top business groups have greater stability in the cash flows andshow better productivity as well as risk sharing than unaffiliated firms(Gangopadhyay et al., 2001). Together with the existence of mutual debtguarantees through group affiliation, firms may reduce the possibility offinancial distress. Some studies delineating the effect of Indian business groupaffiliation on firm sales have observed that top 50 business group firms have abetter reputation advantage in the product market and are likely to export more.They are also on average spend more advertising, marketing, distribution andresearch and development (R&D), and thus have larger amount of intangibleassets (Bandyopadhyay and Das, 2005). Accordingly, we can hypothesize thattop 50 business group firms are safer firms than their non-top 50 groupcounterparts.

. ISO Quality Certification (ISOD). This dummy is taken as a product marketsignal about the firm that it maintains a quality management system and isconcerned with customer expectations and satisfactions. It has been empirically

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observed that ISO certified firms are successful in the product market(Bandyopadhyay and Das, 2005). Therefore we assume that possessing an ISOcertificate by a firm would reduce its chance of default.

. Control variables-industry characteristics. The industry factors affect the firms’performance and therefore affect default as well. There are incidents of clusteredincidents of default. In order to capture the industry specific effects, our samplefirms have been classified into 11 industry dummies depending on its majoreconomic activity.

Bond default rates in IndiaTable II presents an average one-year transition matrix of 542 corporate bond ratingsfrom 1995-1996 to 2004-2005. The transition probabilities captured in the matrixquantify the likelihood that a company will change from one rating grade to anotherwithin a year. The one-year average stressed probability of default (PD) of variousrating notches are reported in the last column[3]. One can see that as the credit qualityworsens (i.e. decline in the rating grades), the probability of default increases. Further,the PD jumps sharply as soon as we move from Investment Grade Bonds toNon-Investment Bond Grades (say from 5.17 percent for BBB to 28.93 percent for BB).We also observe that rating stability declines as the credit quality worsens. The higherrisk in the bottom grades (mainly non-investment grades) calls for developing acorporate default predictor model that would better capture the firm’s characteristicsand could give an early warning signal of corporate distress. In Table III, we get anidea about corporate bond default rates by major industry groups. As expected, thedefault rate varies across different industries especially in the non-investmentcategory. The high default rates are found in Chemical, Food Products and Tobaccoand Beverages, Machine and Electrical, Metal and Non-Metal sectors, and Paper andTextile sectors.

Development of the Z-score model for Indian corporationsGiven the sample of 104 equal mutually exclusive classes of solvent and defaultedfirms over the period of 1998 to 2003, we estimate the multivariate linear discriminantfunction to obtain a Z-score that will help to predict bankruptcy for new firms. Thesolvent set of firms is matched with the defaulted set by asset size, industry, and yearof data. Several combinations of the variables were tried in order to estimate the best

Year 2Year 1 AAA (%) AA (%) A (%) BBB (%) BB (%) B (%) C (%) D (%)

AAA 97.08 2.92 0.00 0.00 0.00 0.00 0.00 0.00AA 2.54 87.57 7.93 1.05 0.60 0.15 0.00 0.15A 0.00 4.35 79.97 9.14 3.48 0.44 0.73 1.89BBB 0.00 0.74 5.90 67.53 14.76 2.21 3.69 5.17BB 0.00 0.83 0.00 1.65 57.02 4.13 7.44 28.93B 0.00 0.00 0.00 7.41 0.00 55.56 7.41 29.63C 0.00 0.00 0.00 2.33 0.00 0.00 51.16 46.51D 0.00 0.00 0.31 0.31 0.92 0.00 0.00 98.46

Table II.Average one year

transition matrix (years1995-1996 to 2004-2005)

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distress classification function in a stepwise regression method. The essentialassumption is that variance-covariance matrices of the two groups are statisticallyidentical[4]. The weights of the discriminant function are the difference of the meanvectors of the explanatory variables for the solvent and defaulted groups. In the MDAmodel our purpose is two folds: The first one is to look for predictors (financial ratios)that lead to lowest misclassification rates within the sample and the second one is toget improved prediction accuracy in an un-estimated holdout sample.

The discriminant analysis model involves linear combinations of the followingform:

Z ¼ b0 þ b1X1 þ b2X2 þ b3X3 þ . . .þ bkXk

where D ¼ discriminant score, bs ¼ discriminant coefficients or weights, and Xs ¼predictors or independent variables. The coefficients, or weights (b), are estimated sothat groups differ as much as possible on the values of the discriminant function. Thisoccurs when the ratio of between-group sum of squares to within-group of sum ofsquares for the discriminant scores is at a maximum. Any other linear combination ofthe predictors will result in a smaller ratio. The test statistics used for carrying out thisanalysis is F and Wilk’s Lambda. Intuitively, a small Lambda signifies that a smallproportion of the total variance of the constituent variables is being accounted for bywithin groups’ dispersions while a larger proportion of the total variance is explainedby the squared deviation of the between group means from their pooled mean. Thiswould be translating to a high value of the F-statistic, which means a greater chancefor the null of equal means to be rejected.

Results of the discriminant analysisBased on the above methodology, three reduced form single equation of the originaldiscriminant equations and their summary results are reported in Table IV. Model 1 isthe rework of Altman’s original 1968 Z-score model. It comprises of variables that havebeen used by Altman for analyzing corporate default chance in US market. Thecoefficients of the variables have been re-estimated using the above data. Model 2comprises of a set of four variables and is the revised form of Altman’s Emerging

Figures in percentIndustry IG NIG ALL

Auto/parts 1.79 16.67 2.87Chemical 0.88 32.00 3.98Diverse 3.70 18.75 7.14Food products/sugar/tea/tobacco/beverages 1.37 55.56 7.41Machine/electrical/computers 2.75 37.14 7.51Metal/non-metal 3.11 35.48 6.60Other manufacturing 0.00 0.00 0.00Paper 0.00 33.33 5.66Power 0.00 0.00 0.00Service 0.22 27.78 1.25Textile 1.52 40.00 5.44

Table III.Industry wide averagePD for IG and NIG andpooled, 1995-1996:2004-2005

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Market Score Model (1995). Model 3 of Table V is ours. This new Z-score modelcomprises of five ratios. Two of these ratios are same to those in Model 1 namelyworking capital to total assets (WK_TA) and sales over total assets (SALES_TA).Three new variables are cash profits to total assets (CASHPROF_TA), solvency ratio(SOLVR), and operating profit over total assets (OPPROF_TA). The discussion on theexpected signs of these ratios has already been done in variable definitions section.

Although Model 1 and Model 2 exhibit a reasonable high degree of classificationpower, Model 3 (which is ours) has the best ability to classify the current sample ofgood and bad firms. However, the robustness of Model 3 needs to be established by aset of diagnostic tests.

The first set of tests pertains to checking the difference of the means of the twogroups, both individually and also as a whole for the entire function. From Table VI,the magnitude of the Wilk’s Lamda and F-statistic of the individual variables (used inModel 3) suggests that given the data, the likelihood of the means of the solvent anddefaulted groups to be equal is highly unlikely. Hence, the null hypothesis of theequality of means with respect the same variance co-variance matrix for both the

Percent of correctclassification

(within sample)Model Linear discriminant equation Good Bad

Model 1: re-worked Altman(1968)

Z ¼ 2 1.689 þ 2.436WK_TA þ8.158RE_ TA þ 3.73PBIT_TAþ 0.037MVE_BVL þ 1.602

SALES_TA

84 82

Model 2: re-workedemerging market (1995)

Z ¼ 2 1.096 þ 2.893WK_TA þ1.197RE_TA þ 11.711PBIT _TAþ 0.042MVE_BVL

88.2 75.9

Model 3: new Z-score model Z ¼ 2 3.337 þ 0.736WK_TAþ 6.95CASHPROF _TAþ 0.864SOLVR þ7.554OPPROF_TA þ1.544SALES_TA

85.2 91Table IV.

Three alternativediscriminant models for

Indian firms

Solvent(DEF ¼ 0)

Defaulted(DEF ¼ 1) Wilk’s Lambda for F-stat. for difference

Mean Std dev. Mean Std dev. difference in mean in mean

WK_TA 0.192 0.145 20.068 0.33 0.796 153.3 *

CASHPROF_TA 0.099 0.073 20.027 0.092 0.633 347.33 *

SOLVR 2.32 1.304 1.27 0.37 0.763 185.26 *

OPPROF_TA 0.093 0.075 20.032 0.084 0.622 363.56 *

SALES_TA 1.06 0.6 0.57 0.33 0.796 152.81 *

Notes: Total number of observations: 624. F-statistic and Wilk’s Lambda are used for discriminatingthe solvent group from the defaulted group. The higher value of F and lower value of Wilk’s Lambdaindicate greater chance for the null of equal means of the two groups to be rejected. * denotessignificant at 1 percent or better

Table V.Group statistics

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groups is rejected at 1 per cent or better level of significance. The result also fits wellfor the discriminant function as a whole. The overall chi-square of the discriminantfunction is 388.8 with degrees of freedom 5 (with probability. x2 ¼ 0:00) indicating avery high overall significance of the model. Many other variables are also being tested;however the variables used in the third model have the best combination with highestlevel of discriminatory power.

The Z-score obtained in Model 3 may however suffer from the misclassification cost.Misclassification may arise due to type I and type II errors. Type I error occurs whenthe model incorrectly classifies a “bad” firm as “good”. Type II error arises when themodel identifies a “good” firm as “bad”. Obviously, type I error is more costly for bankthan the type II error. Therefore, it is necessary to estimate posterior probabilities to seta benchmark to make a correct decision about the firm’s default status. For this, weestimate two separate Fisher’s discriminant equations and for a firm:

Z solvent¼ ¼ 26:812 2 1:72ðWK_TAÞ þ 3:52ðCASHPROF_TAÞ þ 3:016ðSOLVRÞ

24:757ðOPPROF_TAÞ þ 5:354ðSALES_TAÞ

Zdefaulted ¼ 23:475 2 2:456ðWK_TAÞ2 3:43ðCASHPROF_TAÞ þ 2:152ðSOLVRÞ

212:311ðOPPROF_TAÞ þ 3:81ðSALES_TAÞ

Using the above two equations, we obtain two scores for the same firm. In the nextstep, the final Z-score obtained in Model 3 denotes a reduced form representation of theabove two discriminant equations (i.e. the difference between solvent and defaultedscore):

Z ¼ Zsolvent 2 Zdefault

or:

Z ¼ 23:337 þ 0:736ðWK_TAÞ þ 6:95ðCASHPROF_TAÞ þ 0:864ðSOLVRÞ

þ7:554ðOPPROF_TAÞ þ 1:544ðSALES_TAÞ

Accordingly we predict a firm as solvent (or non-defaulting) if the final Z-scoreobtained is positive (as for him, Prob. (solvent) . Prob. (defaulted)). Similarly, the firmwith a negative Z-score is classified as one liable to default within a year horizon.

Model 1: re-workedAltman (1968) (%)

Model 2: re-worked emergingmarket (1995) (%)

Model 3: new Z-scoremodel (%)

Defaulted no.correct (Type I)

80 84 92

Solvent no. correct(Type II)

88 84 96

Table VI.Classification power ofthe model for the holdoutdample of 25 corporationsfor the year 2004

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Z-score model validationIn order to judge the correct prediction power of the discriminant function, the modelneeds to be tested with a sample that has not been used for estimation. The holdoutsample validation perhaps constitutes one of the best tests to validate the discriminantfunction. Further, the model should also be able to predict the default much before theoccurrence of the incident. Since we are using a balanced panel data over the period1998 to 2003, the Z-score model should be able to capture the dynamics of defaultincidents.

Holdout sample validationTable VI shows that when the Model 3 tested on a holdout sample of 50 companies (25defaulted and 25 solvent) for the period 2004, it can correctly classify 92 percent of thedefaulted firms and 96 percent of the solvent firms. However, both the type I and typeII error rates are much higher in case of Model 1 (20 percent and 12 percentrespectively) and Model 2 (16 percent each). Therefore, Model 3 has the best holdoutsample predictive accuracy.

Prediction power back in timeHaving enough confirmed the predictive power of our new Z-score model; we nowcheck its long run predictive ability. The question we try to answer is: how far into thefuture the model predicts accurately? Accordingly, we examine the overalleffectiveness of the third model for a longer period of time prior to the occurrence ofactual default. This has important strategic meaning for the banks, because thecorporation may default on bank loan much before its bond instrument publicly ratedas D. Therefore, earlier the model can identify signs of stress, lesser are the costsinvolved in taking the required steps.

To test the long run accuracy of our Z-score model, we have created holdout sampleof another 37 defaulted Indian corporations and collected their financial data. Thesecorporations got D ratings from CRISIL between the years 1996-2005. Next, weexamine the prediction power of our model back in time from 0, 1, 2, 3, 4, 5, 6 yearsprior to default. As can be seen from the Table VII that the predictive ability of themodel to identify defaulting firm falls from 88 percent one year prior to default to 45percent as one goes back six years prior to the occurrence of default. We also compare

Year prior to default

Model 1: re-workedAltman (1968)

(%)

Model 2: re-workedemerging market (1995)

(%)

Model 3: newZ-score model

(%)

0 79 79 881 59 73 882 55 50 683 – – 574 – – 565 – – 456 – – 45

Notes: Using a holdout sample of 37 Indian corporate bonds defaulted between the year 1996-2005.Also using 0 as the cutoff score

Table VII.Relative comparison of

classification andpredictive accuracy of

three discriminantmodels: early warning

signal (time dimension)

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the long run predictive power of our model with Model 1 and Model 2. Our model (i.e.Model 3) clearly out performs the other two models even if one goes back two yearsprior to default (with 68 percent accuracy). Moreover, the type I accuracy rate of Model3 is pretty high (88 percent) on data from one financial statement prior to default onoutstanding bonds.

Testing the power of the model on distressed firm’s sampleFinally, we examine 148 distressed manufacturing firms who reported bankrupted byBoard for Industrial and Financial Reconstruction (BIFR) of India in year 2004. AsTable VIII shows, our Z-score model is still robust and can also forecast corporatefailure up to five years prior to distress. The accuracy rate is very high until two yearsprior to distress (87 percent). We also compare the predictive accuracy power of ourmodel with Model 1 and Model 2. It is evident from Table VIII that our model performsmuch better than the other two previous models.

Logit model: estimation procedureWe have done Logistic regression analysis to investigate the relationship betweenbinary or ordinal response probability and explanatory variables. The method fitslinear logistic regression model for binary or ordinal response data by the method ofmaximum likelihood. Like discriminant analysis, this technique weights theindependent variables and assigns a Z-score in a form of failure probability to eachcompany in a sample. Discriminant analysis and logit analysis have differentassumptions concerning the relationships between the independent variables. Whilelinear discriminant analysis is based on linear combination of independent variables,logit analysis uses the logistic cumulative probability function in predicting default.

The logit equation we have estimated takes the following form:

PD ¼ FðZ Þ

¼ 11þe2Z ¼ 1=1 þ e2ðb0þb1X1þb2X2þb3X3þ...þbkXÞ

where F(Z) is the cumulative logistic distribution.

Year prior to failure

Model 1: re-workedAltman (1968)

(%)

Model 2: re-worked emergingmarket (1995)

(%)

Model 3: newZ-score model

(%)

0 94 95 971 95.3 95.3 96.32 82.5 85 873 73 73 784 62 68 73.35 55 56 68.1

Notes: Using a holdout sample of 148 Indian Manufacturing Firms reported bankrupted by Board forIndustrial and Financial Reconstruction (BIFR) of India in the year 2004. Also using 0 as the cut-offscore

Table VIII.Relative comparison ofbankruptcy predictionpower of threediscriminant models:early warning signal(time dimension)

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We have applied Maximum Likelihood Estimation (MLE) procedure for estimation ofthe parameters.

In the logit regression, our purpose is to evaluate the role of balance sheet variablesas well as the non-financial variables in predicting corporate bond default and to arriveat an estimate of probability of default for a firm using them.

Before we discuss our results, let us first look at the descriptive statistics of thevariables used in the logistic regressions. Table IX, gives us some descriptive statisticsabout the sample of firms used in the logistic analysis. It is evident from the descriptivestatistics table that all the financial ratios for solvent group of firms on average lookrelatively better than their defaulted counterparts. As far as the non-financial parametersare concerned, the greater percentage of solvent firms possess ISO certificate than thedefaulted firm. Similarly, defaulted firms are on average younger than the defaultedfirms. The solvent firms also mostly belong to the top 50 business groups than thedefaulted ones. The difference is also statistically significant as evident from thet-statistics reported in column 8[5]. Furthermore, standard deviations of financial ratiosare very high for defaulted companies in comparison to the solvent firms.

Results of the logit modelWe define the dependent variable by coding an indicator binary variable with a 1(default) or a 0 (non-default). The same balanced panel data set of 104 companies (52defaulted firms and 52 solvent firms) over the period 1998 to 2003 has been used to runthe logit model. In a stepwise logistic regression method, we finally obtain three sets ofmodels. In Model 1 and 2, we test financial as well as non-financial parameters thathave been discussed earlier in the variable definition section. Model 3 only explains therole of financial factors on the probability of default by a firm. The results aresummarized in columns 2, 3, and 4 of Table X.

Model 3 (Table X) shows that the financial ratios (SOLVR, CASHPROF_TA,WK_TA, SALES_TA and MVE_BVL) are negatively significant (5 percent orbetter) on default probability. The results of Model 3 are consistent with ourtheoretical expectation, which is discussed in the data and variable section. InModel 1 and Model 2, we test the explanatory power of both the financial as wellas non-financial parameters. The financial ratios have the same expected signs aswe have found in Model 1 and 2. As far as non-financial parameters areconcerned, the age parameter LN(AGE) is negatively significant, implying that

Mean Std. dev.Mean

DEF ¼ 0 Std. dev.Mean

DEF ¼ 1 Std. dev.t-statistics

for difference

SOLVR 1.78 1.08 2.32 1.304 1.27 0.371 13.61 * * *

CASHPROF_TA 0.036 0.105 0.1 0.07 20.03 0.09 19.1 * * *

WK_TA 0.06 0.29 0.19 0.17 20.07 0.33 12.17 * * *

SALES_TA 0.81 0.55 1.04 0.61 0.57 0.33 11.81 * * *

MVE_BVL 1.303 4.65 2.63 6.58 0.155 0.35 6.53 * * *

ISOD 0.57 0.49 0.69 0.46 0.46 0.50 5.99 * * *

Dtop50grp 0.37 0.48 0.46 0.50 0.29 0.45 4.53 * * *

LN(AGE) 3.22 0.78 3.46 0.77 2.99 0.73 7.78 * * *

No. of observations 624 312 312

Table IX.Descriptive statistics forlogit model: comparison

between defaulted groupand solvent group

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younger firms are more risky than the older firms. It is more likely that maturedfirms have established a reputation with credit institutes and private investors thatalleviates the asymmetric information problems because an extended period ofscrutiny would permit a better understanding of the economic viability of the firm.In the case of a liquidity crunch, an older firm could rely on such a relationship toobtain additional lines of credit or favorable grace periods and can avoid acorporate default event. On the other hand, young firms have less time to solidifya relationship with its creditors and private investors hence increasing the chanceof financial distress during a credit crunch.

Similarly, the likelihood of default is less if the firm belongs to the top 50 businessgroup. Likewise, the ISO dummy (ISOD) has negative influence on the probability ofdefault (DEF), indicating that the firms that maintain a quality management system haveless chance of default. The industry dummies are significantly different from zerosuggesting that we cannot reject the presence of industry effects on firm’s default status.

Now, let’s compare the diagnostic tests of these models. As reported in the lower panelof Table X, Pseudo R 2 is highest (0.70) in Model 1 in comparison to Model 2 (0.66) andModel 3 (0.57)[6]. The chi-square statistics is also highest in case of Model 1. We alsochecked the predictive power of the logistic models by using ROC graphs in Figure 1 and

Variables Model 1 Model 2 Model 3

DEF Coefficients Coefficients CoefficientsSOLVR 21.23 * * * 21.47 * * * 21.78 * * *

CASHPROF_TA 212.91 * * * 213.49 * * * 211.74 * * *

WK_TA 210.35 * * * 29.02 * * * 24.54 * * *

SALES_TA 21.67 * * * 21.79 * * * 21.32 * * *

MVE_BVL 21.74 * * * 21.56 * * * 21.33 * * *

ISOD 21.27 * * * 21.88 * * * –Dtop50grp – 20.805 * * * –LN(AGE) 21.66 * * – –IND1 21.114 Dropped –IND2 Dropped Dropped –IND3 0.45 2.37 * * –IND4 1.27 2.69 * * * –IND5 2.48 * * 3.51 * * * –IND6 0.86 2.92 * * * –IND7 0.46 2.08 –IND8 Dropped Dropped –IND9 1.49 1.57 –IND10 23.52 * * * 21.89 –IND11 Dropped Dropped –Intercept 11.46 * * * 5.24 * * * 5.5 * * *

Number of Obs. 518 518 558LR x2 statistics 492.93 (14) 469.47 (14) 437.69 (5)Prob.. x2 0.00 0.00 0.00Pseudo R 2 0.70 0.66 0.57

Notes: The dependent variable DEF is a default dummy; DEF=1, if the company’s long term bond isdefaulted in any year between the year 1998 to 2003 and DEF =0, if there is no default. The model 1and model 2 use all financial and non-financial factors. Model 3 uses only financial parameters. * * *

denotes significant at 5 percent or better; * * denotes significant at 5-10 percent

Table X.Logit model: prediction ofdefault events withdifferent factor types

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calculate the area under the ROC curve based on the model estimates by logit[7]. One canclearly see from Figure 1 that Model 1 has the highest within sample prediction power of97.2 percent in comparison to Model 2 and Model 3. Further, we have performed achi-squared test to summarize the predictive accuracy of these three models into asummary statistic. The chi-squared test yielded a significance probability of 0.001suggesting that there is a significant difference in the areas under the three ROC curves.Hence, it is evident from our results that inclusion of non-financial factors along with thefinancial factors improves the default-forecasting ability of the model. The results ofModel 1 indicate a strong relationship between default and the financial and non-financialvariables. The Model 1 can be directly used for finding PDs in credit-risk models[8].

Predictive power of the logistic modelOne may again argue that model performance may be driven by type I and type II errorrates. Consequently, Model 1 has been tested in the same holdout sample that we used inMDA analysis. The 2003 and 2004 holdout sample consists of equal number of 25 cases ofsolvent and 25 cases of defaulted firms. As evident from the results reported in Table XI,model 1 clearly shows good capacity to discriminate between defaulted and solvent firms.

Figure 1.Comparison of ROC

curves for three models

Predicted group

Original group Defaulted Solvent TotalDefaulted 47 3 50

(94%) (6%) (100%)Solvent 8 42 50

(16%) (84%) (100%)

Table XI.Classification power ofthe logistic Model 1 for

the holdout sample of theyears 2003 and 2004

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ConclusionsUsing a sample of 104 listed corporations from CRISIL, we have developed a Z-scoremodel for Indian firms that can accurately predict bond default one year in advance.The model not only has a high classification power within sample (91 percent), but alsoexhibited a high predictive power in terms of its ability to detect bad firms in thetwo-holdout samples (with 92 percent and 88 percent accuracy rates). Moreover, themodel also can predict corporate bankruptcy in two years prior to financial distresswith an accuracy rate of 97 percent and 96.3 percent respectively. The new Z-scoremodel of this paper outperforms the other two contesting models comprising ofAltman, 1968 and emerging market score 1995 set of ratios respectively. Using ourZ-score model, banks as well as investors can get early warning signals about the firmand might reassess the magnitude of the default premium they require on low-gradesecurities.

In the logit analysis, we link the firm’s performance with the macro economicenvironment. The logit results show that PD is a decreasing function of cash profitover total assets, working capital to assets, total sales relative to total assets, solidity,solvency ratio, firm age, ISO certification and top 50 group affiliation. Further, industryaffiliation of a firm is also an important factor for explaining its default status and alsoneeds to be taken into account. From our empirical analysis we find that inclusion ofboth financial and non-financial factors leads to more accurate default prediction thanthe single use of accounting ratios.

Notes

1. CRISIL defines default as a credit event where the underlying corporate has missedpayments (a single day’s delay or a shortfall of even a single rupee) on a rated instrument interms of the promised repayment schedule. CRISIL’s rating does not factor in any postdefault recovery.

2. A paired t-test on the mean asset difference between the two groups had shown statisticallyinsignificant results.

3. The probability of default (PD) per rating grade counts the average percentage of bond inthis rating grade in the course of one year.

4. It is empirically observed fact that the linear discriminant model has a higher holdoutsample predictive power compared to the quadratic discriminant model (Altman, 1993).Moreover, the former is more amenable for interpretation compared to the latter.

5. A Wilcoxon rank-sum test showed that all the financial and non-financial parameters aresignificantly better for solvent group (at 1 percent or better level) than the defaulted group.

6. Pseudo R 2 is a likelihood ratio index, which is analogous to the R 2 in a conventionalregression model. Here Pseudo R2 ¼ 12 Lmax=L0 , where L0 is the initial value of likelihoodfunction and Lmax is the highest value.

7. Receiver Operating Characteristic Curve (ROC) quantifies the accuracy of diagnostic tests todiscriminate between defaulted firms and solvent firms using each value of the logit score asa possible cutoff point. The analysis uses the ROC curves of the sensitivity (percentage oftrue defaulted outcomes correctly specified) vs. 1-specificity (percentage of false defaultedoutcomes correctly specified) of the diagnostic test. This calculates the area under the ROCcurve based on the model estimated by logistic regression predictions. The greater the areaunder the ROC curve, the better the predictive power of the model. Therefore, a steeper curvefrom the diagonal line indicates a more powerful model.

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8. From Table results of Model 1, one can estimate the probability of default (PD) by using thefollowing equation: PDi ¼

11þexpð2ziÞ

, zi ¼ aþ bXi , where a is the intercept and b representsthe parameters that may explain default incidents.

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Corresponding authorArindam Bandyopadhyay can be contacted at: arindam@nibmindia.org

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