Modeling an Accounting-Based Rating System for Austrian Firms

Furthermore, as Sobehart, Keenan, and Stein 2000a point out in one com-of Moody’s studies, the relationship between financial variables and default riskvaries substantially between large

Rating System for Austrian Firms

Erstgutachter: o.Univ.Prof Dr Josef Zechner

Zweitgutachter: o.Univ.Prof Dr Engelbert Dockner

Wien, im Juni 2002

1 Introduction 6

I Parameter Selection 11

II Choice of Input Variables 11

III Model-Type Selection 13

IV Default Definition 15

V Time Horizon 16

3 The Data Set 18 4 Methodology 25 I Selection of Candidate Variables 25

II Test of Linearity Assumption 33

III Univariate Logit Models 40

IV Derivation of the Default Prediction Models 43

5 Three Rating Models for Austria 46 6 Rating Models Based on Sector Information 56 I Choice of the Appropriate Sector Information 58

II Univariate Regression Results 59

III Multivariate Regression Results 60

7 A Rating Model for Germany 67 I The German Data 68

II The Rating Model for German firms 71

2

8 Testing for Rating Accuracy 78

I The Receiver Operating Characteristic 80

II Interpretation of the Area Under the ROC Curve 87

III Confidence Intervals for the Area ˆA 88

IV Connection between ROC and CAP Curves 91

V Applying the Concept of ROC Curves to the Austrian Rating Models 93

9 Conclusion 96 A 100 I The Data Set with Loan-Restructuring as Default Criterion 100

II The Data Set with 90-Days-Past-Due as Default Criterion 103

B 106 I Program Code for the Implementation of the adjusted Hodrick-Prescott Filter in STATA 7.0 106

C 109 I Correlations between Accounting Ratios of the Same Credit Risk Factor Group 109

D 114 I Correlations between Firm-Based and Sector-Based Accounting Ratios 114

4

I would like to thank my supervisors Josef Zechner and Engelbert Docknerand my coauthors Bernd Engelmann and Dirk Tasche for their intellectual sup-port In addition, Helmut Elsinger, Sylvia Fr¨uhwirth-Schnatter, Alfred Lehar,David Meyer, Otto Randl, Michaela Schaffhauser-Linzatti and Alex Stomperhave made valuable comments I also thank participants of the doctoral sem-inars at the University of Vienna and at the European Financial ManagementAssociation 2001 in Lugano and participants of the conference of the AustrianWorking Group on Banking and Finance 2001 in Vienna Besides, I gratefullyacknowledge financial support from the Austrian National Bank ( ¨ONB) underthe Jubil¨aumsfond grant number 8652 and the contribution of three Austriancommercial banks, the Austrian Institute of Small Business Research, the Aus-trian National Bank, and the German Central Bank for providing the necessarydata for this thesis.

5

In January 2001 the Basel Committee on Banking Supervision released the ond version of its proposal for a new capital adequacy framework In this releasethe Committee announced that an internal ratings-based approach could form thebasis for setting capital charges for banks with respect to credit risk in the nearfuture For this reason it is one main purpose of this work to develop a simpleand therefore practicable but efficient credit quality rating model applicable tothe Austrian market that could be used by Austrian banks as a benchmark whenadjusting their internal rating models

sec-Essentially, there are three main possible model inputs: accounting variables,market-based variables such as market equity value and so-called soft facts such

as the firm’s competitive position or management skills As in Austria the ket capitalization is very low, for most companies market-based variables are notobservable, which also implies that models based on the option pricing approachoriginally proposed by Merton are not optimal for an application to Austria Be-sides, due to the inherent subjectivity of candidate variables and data unavailabil-

mar-6

ity, soft facts were excluded from the model, too, leaving accounting variables asthe main input to the statistical analysis based on logistic regressions However,

as in the literature also some other factors such as the size or the legal form ofthe companies are reported to be helpful in predicting default, these variables areadditionally included into the model building process

Besides, in contrast to similar studies that can be found in the literature, thiswork extends the study beyond the analysis of accounting variables in comparingthem to the respective median values in the appropriate sector or branch As

it is common habit to evaluate the performance of a company by comparing

it to similar firms operating in the same industry, this approach could also beused in estimating default-prediction-models The hypothesis would be that theworse a firm does compared to the typical firm of a sector, the higher its defaultprobability should be For example lower net profits per assets than that of themean or median firm should increase the default probability, while a lower debtratio should decrease it

What’s more, historically credit risk models were developed using the fault criterion bankruptcy, as this information was relatively easily observable.However, the Basle Committee on Banking Supervision (2001a) defined default

de-as any credit loss event de-associated with any obligation of the obligor, includingdistressed restructuring involving the forgiveness or postponement of principal,interest, or fees and delay in payment of the obligor of more than 90 days Ac-cording to the current proposal for the new capital accord banks will have to usethis tight definition of default for estimating internal rating-based models Now

an important question is whether “old” rating models that use only bankruptcy asdefault criterion are therefore outdated, or whether there is a possibility to adjustthem in such a way that they perform just as well as models that were developed

using a more complex default definition One of the main aims of this thesis is

to answer this question, and therefore rating models using the default definitions

of bankruptcy, loan restructuring and 90 days past due will be estimated andcompared

The data necessary for this analysis was provided by three major Austriancommercial banks, the Austrian National Bank and the Austrian Institute ofSmall Business Research By combining these data pools a unique data set oncredit risk analysis for the Austrian market was constructed However, althoughthe data was carefully inspected and harmonized, it is still advantageous to cross-check the chosen methodology by applying it to a second, more homogeneousdata set Therefore the analysis is repeated with the similar, but larger and homo-geneous data pool of German firms gathered by the German Central Bank, wheredefault is defined as hard insolvency As the economies in Germany and Aus-tria are comparable in many aspects, similar results of the rating model buildingprocess for the German data set as for the Austrian one would further strengthenthe Austrian model

Finally, the performance of the estimated models has to be evaluated ever, testing the accuracy of internal rating models by statistical methods is still

How-an open question in the literature, even though Basel II further increases theneed of banks and regulators for statistical validation procedures The validationtechniques currently used in practice are the concepts of Cumulative AccuracyProfiles and Accuracy Ratios, which deliver a single number to judge upon thequality of internal rating models However, the reliability of such judgements isquestionable if no confidence interval can be stated in addition to the AccuracyRatio Therefore, by using the concept of Receiver Operating Characteristics andthe U-test of Mann-Whitney, in the last chapter of this thesis confidence inter-

vals for the area under the Receiver Operating Characteristic Curve are derived

in an analytical and consequently simple way Besides, a relationship betweenthis area and the Accuracy Ratio is proven, which demonstrates that the conceptsderived for Receiver Operating Characteristic Curves can be applied to Cumu-lative Accuracy Profiles, too Hence different rating models can be compared

by using confidence intervals instead of single numbers, which allows a sounddecision-making about the superiority of one model, as will be demonstrated bycomparing the performance of the models developed in this thesis

The remainder of this work is composed as follows: In Chapter 2 the modelbuilding strategy is chosen, while Chapter 3 describes the data and Chapter 4 de-tails the applied methodology The derived Austrian rating models are depicted

in Chapter 5 and Chapter 6 examines the estimation results when the accountingratios are compared to the respective median values in the appropriate branch.Chapter 7 presents the German rating model Finally the power of the developedmodels is tested in Chapter 8 Chapter 9 concludes

Model Selection

As already mentioned in the introduction it is the aim of this study to develop asimple and therefore practicable but yet efficient model to derive a credit qualityrating for Austrian firms from certain firm characteristics To do this, the firststep is to decide on the following five important questions:

1 Which parameters shall be estimated?

2 Which input variables are used?

3 Which type of model shall be estimated?

4 How is default defined?

5 Which time horizon is chosen?

In the following sections these questions will be answered for the work at hand

10

I Parameter Selection

When we try to predict credit risk, we actually are interested to predict the tential loss that we might incur So the credit quality of a borrower does notonly depend on the default probability, the most popular credit risk parameter,but also on the exposure-at-default, the outstanding and unsecured credit amount

po-at the event of default, and the loss-given-default, which usually is defined as apercentage of the exposure-at-default However, historically most studies con-centrated on the prediction of the default probability, just as this study will dodue to data unavailability for the exposure-at-default and the loss-given-default

II Choice of Input Variables

As already mentioned earlier, there are essentially three main possible modelinput categories: accounting variables, market-based variables such as marketequity value and so-called soft facts such as the firm’s competitive position ormanagement skills Historically banks used to rely on the expertise of creditadvisors who looked at a combination of accounting and qualitative variables tocome up with an assessment of the client firm’s credit risk, but especially largerbanks switched to quantitative models during the last decades

One of the first researchers who tried to formalize the dependence betweenaccounting variables and credit quality was Edward I Altman (1968) who de-veloped the famous Z-Score model and showed that for a rather small sample

of observations financially distressed firms can be separated from the non-failedfirms in the year before the declaration of bankruptcy at an in-sample accuracy

rate of better than 90% using linear discriminant analysis Later on more ticated models using linear regressions, logit or probit models and lately neuralnetworks were estimated to improve the out-of-sample accuracy rate and to come

sophis-up with true default probabilities (see f ex Lo (1986) and Altman, Agarwal,and Varetto (1994)) Yet all the studies mentioned above have in common thatthey only look at accounting variables In contrast to this in the year 1993 KMVpublished a model where market variables were used to calculate the credit risk

of traded firms As KMV’s studies assert, this model based on the option pricingapproach originally proposed by Merton (1974) does generally better in predict-ing corporate distress than accounting-based models Besides, they came up withthe idea to separate stock corporations of one sector and region and to regresstheir default probabilities derived from the market-value based model on ac-counting variables and then use those results to estimate the credit risk of similarbut small, non-traded companies (see Nyberg, Sellers, and Zhang (2001))

Due to those facts at first sight one might deduce that one should use amarket-value based model when developing a rating model for Austrian firms,however, as already mentioned above, in Austria there are almost no tradedcompanies According to the Austrian Federal Economic Chamber in the year

2000 stock corporations accounted for only about 0.5% of all Austrian panies Furthermore, as Sobehart, Keenan, and Stein (2000a) point out in one

com-of Moody’s studies, the relationship between financial variables and default riskvaries substantially between large public and usually much smaller private firms,implying that default models based on traded firm data and applied to privatefirms will likely misrepresent actual credit risk Therefore it is preferable to relyexclusively on the credit quality information contained in accounting variableswhen fitting a rating model to the Austrian market I also considered the possi-

bility to include soft facts into the analysis, but due to the inherent subjectivity

of candidate variables and data unavailability, soft facts were excluded from themodel, too Instead the importance of some other factors for default prediction,i.e the size and the legal form of the companies as well as the sector in whichthey are operating, was tested, too

Besides, in contrast to similar studies that can be found in the literature, thiswork extends the study above the analysis of accounting variables in comparingthem to the respective median values in the appropriate sector or branch As

it is common habit to evaluate the performance of a company by comparing

it to similar firms operating in the same industry, this approach could also beused in estimating default-prediction-models The hypothesis would be that theworse a firm does compared to the typical firm of a sector, the higher its defaultprobability should be For example lower net profits per assets than that of themedian firm should increase the default probability, while a lower debt ratioshould decrease it

Finally, one could try to incorporate macro-economic factors like the grossnational product, the level of unemployment or interest rates into the analysis tocapture the influence of the business cycle However, these influences can not bestudied with the data set at hand for reasons that will be depicted in Chapter 3

III Model-Type Selection

In principal, three main model categories exit:

 Judgements of experts (credit advisors)

 Theoretical models (option pricing approach)

However, as already evident from the arguments in Section II, the choice ofthe model-type and the selection of the input variables have to be adapted toeach other The option pricing model, for example, can only be used if market-based data is available, which for the majority of Austrian companies is not thecase Therefore this model is not appropriate Excluding the informal, rathersubjective expert-judgements from the model-type list, only statistical modelsare left Within this group of models, on the one hand logit and probit models,that generally lead to similar estimation results, and on the other hand neural net-works are the state of the art.2 Although there is some evidence in the literaturethat artificial neural networks are able to outperform probit or logit regressions inachieving higher prediction accuracy ratios, as for example in Charitou and Char-alambous (1996), I decided in favor of the latter mainly because of two reasons.Firstly, there are also studies as the one of Barniv, Agarwal, and Leach (1997)finding that differences in performance between those two classes of modelsare either non-existing or marginal, and secondly the chosen approach allows

to check easily whether the empirical dependence between the potential input

1 For a comprehensive review of the literature on the various statistical methods that have been used to construct default prediction models see for example Dimitras, Zanakis, and Zopoundis (1996).

2 A nice introduction (in German language) to neural networks and their applications, tages, and limitations can be found in F¨user (1995).

advan-variables and default risk is economically meaningful, as will be demonstrated

in Chapter 4

IV Default Definition

Historically credit risk models were developed using the default criterion ruptcy, as this information was relatively easily observable But of course banksalso incur losses before the event of bankruptcy, for example when they movepayments back in time without compensation in hopes that at a later point intime the troubled borrower will be able to repay his debts Therefore the BasleCommittee on Banking Supervision (2001a) defined the following reference def-inition of default:

bank-A default is considered to have occurred with regard to a particular obligorwhen one or more of the following events has taken place:

 it is determined that the obligor is unlikely to pay its debt obligations cipal, interest, or fees) in full;

(prin- a credit loss event associated with any obligation of the obligor, such as

a charge-off, specific provision, or distressed restructuring involving theforgiveness or postponement of principal, interest, or fees;

 the obligor is past due more than 90 days on any credit obligation; or

 the obligor has filed for bankruptcy or similar protection from creditors.According to the current proposal for the New Capital Accord banks willhave to use the above regulatory reference definition of default in estimatinginternal rating-based models Now an important question is whether “old” rating

models that use only bankruptcy as default definition are therefore outdated, orwhether there is a possibility to adjust them in such a way that they perform just

as well as models that were developed using a finer default criterion One of themain aims of this thesis is to answer this question, and therefore rating modelsusing the default definitions of bankruptcy, loan restructuring and 90 days pastdue will be estimated and compared

V Time Horizon

As the Basle Committee on Banking Supervision (1999a) illustrates for mostbanks it is common habit to use a credit risk modeling horizon of one year Thereason for this approach is that one year is considered to reflect best the typicalinterval over which

a) new capital could be raised;

b) loss mitigation action could be taken to eliminate risk from the portfolio;c) new obligor information can be revealed;

d) default data may be published;

e) internal budgeting, capital planning and accounting statements are pared; and

pre-f) credits are normally reviewed for renewal

But also longer time horizons could be of interest, especially when decisionsabout the allocation of new loans have to be made To derive default probabilitiesfor such longer time horizons, say 5 years, two methods are possible: firstly,one could calculated the 5-year default probability from the estimated one-year

value, however, this calculated value might be misleading as the relationshipbetween default probabilities and accounting variables could be changing whenaltering the time horizon Secondly, a new model for the longer horizon might

be estimated, but usually here data unavailability imposes severe restrictions Asdisplayed in Chapter 3 and Appendix A, about two thirds of the largest data setused for this study and almost all observations of the two smaller data sets arelost when default should be estimated based on accounting statements prepared

5 years before the event of default - therefore this study sticks to the convention

of adopting a one-year time horizon, the method also currently proposed by theBasle Committee on Banking Supervision (2001b)

The Data Set

As illustrated in Chapter 2, in this study accounting variables are the main input

to the credit quality rating model building process based on logistic regressions.The necessary data for the statistical analysis was supplied by three major com-mercial Austrian banks, the Austrian National Bank and the Austrian Institutefor Small Business Research The original data set consisted of about 230.000firm-year observations spanning the time period 1975 to 2000 However, due

to obvious mistakes in the balance sheets and gain and loss accounts, such asassets being different from liabilities or negative sales, the data set had to be re-duced to 199.000 observations Besides, certain firm types were excluded, i.e.all public firms including large international corporations, as they do not repre-sent the typical Austrian company, and rather small single owner firms with aturnover of less than 5m ATS, whose credit quality often depends as much onthe finances of a key individual as on the firm itself After also eliminating fi-nancial statements covering a period of less than twelve months and checkingfor observations that were twice or more often in the data set almost 160.000

18

firm-years were left Finally those observations were dropped, where the defaultinformation was missing or dubious By using varying default definitions, threedifferent data sets were constructed The biggest data set defines the defaultevent as the bankruptcy of the borrower within one year after the preparation

of the balance sheet and consists of over 1.000 defaults and 123.000 firm-yearobservations spanning the time period 1987 to 1999 The second data set, which

is less than half as large as the first one, uses the first event of loan restructuring(for example forgiveness or postponement of principal, interest, or fees withoutcompensation) or bankruptcy as default criterion, while the third one includes al-most 17.000 firm-year observations with about 1.600 defaults and uses 90 dayspast due as well as restructuring and bankruptcy as default event The differentdata sets are summarized in Table 3.1

Table 3.1

Data set characteristics using different default definitions

This table displays the number of observed balance sheets, distinct firms and defaults as well

as the covered time period for three data sets that were built according to the default definition

of bankruptcy, rescheduling, and delay in payment (arising within one year after the reference point-in-time of the accounting statement) The finer the default criterion is, the higher is the number of observed defaults, but the lower is the number of total firm-year observations as some banks only record bankruptcy as default criterion.

default definition bankruptcy restructuring 90 days past due

firm-years 124,479 48,115 16,797

companies 35,703 14,602 6,062

defaults 1,024 1,459 1,604

time-period 1987-1999 1992-1999 1992-1999

Each observation consists of the balance sheet and the gain and loss account

of a particular firm for a particular year, the firm’s legal form, the sector in which

it is operating according to the ¨ONACE-classification 1, the median values forselected accounting ratios for the appropriate branch and year, and the informa-tion whether default occurred within one year after the accounting statement wasprepared.

The composition of the data for the largest data set (bankruptcy) is illustrated

in Table 3.2 as well as in Figure 3.1 to Figure 3.4 The corresponding graphsfor the other two data sets, that depict similar patterns as the figures for thebankruptcy data, are shown in Appendix A

Table 3.2

Number of observations and defaults per year for the bankruptcy data set

This table shows the total number of the observed balance sheets and defaults per year The last column displays the yearly default frequency according to the bankruptcy data set, that varies substantially due to the varying data contribution of different banks.

year observations in % defaults in % default ratio in %

Eu-In Table 3.2 the number of observations and defaults per years is depicted It

is noticeable that the ratio of defaults to total observations is rather volatile Itvaries much more than could be explained purely by macro-economic changes.The reason for this pattern lies in the composition of the data set Not all bankswere able to deliver data for the whole period of 1987 to 1999, and while somebanks were reluctant to make all their observations of good clientele availablebut delivered all their defaults, others did not record their defaults for the entireperiod The consequence is that macro-economic influences can not be studiedwith this data set, what - anyway - would be beyond the scope of this thesis.Besides, it is important to guarantee that the accounting schemes of the involvedbanks are (made) comparable, because we can not easily control for the influ-ence of different banks as - due to the above mentioned circumstances - theydelivered data with rather in-homogeneous default frequencies Therefore onlymajor positions of the balance sheets and gain and loss accounts could be used.The comparability of those items was proven when they formed the basis forthe search of observations that were reported by more than one bank and severalthousands of those double counts could be excluded from the data set

Figure 3.1 groups the companies according to the number of consecutivefinancial statement observations that are available for them For about 7,000firms only one balance sheet belongs to the bankruptcy data set, while for the resttwo to eight observations exist These multiple observations will be importantfor the evaluation of the extent to which trends in financial ratios help predictdefaults

Figure 3.1 Obligor Counts by Number of Observed Yearly Observations

This figure shows the number of borrowers that have either one or multiple financial statement observations for different lengths of time Multiple observations are important for the evaluation

of the extent to which trends in financial ratios help predict defaults.

develop-Figure 3.2 Distribution of Financial Statements by Legal Form

This figure displays the distribution of the legal form The test sample differs slightly from the estimation sample as its percentage of limited liability companies is a few percentages higher.

Development Sample

81% Limited Liability Companies 14% Limited Partnerships 4% Single Owner Companies 2% General Partnerships

Validation Sample

86% Limited Liability Companies 9% Limited Partnerships 2% Single Owner Companies 2% General Partnerships

Figure 3.3 Distribution of Financial Statements by Sales Class

This graph shows the distribution of the accounting statements grouped according to sales classes for the observations in the estimation and the test sample Differences between those two samples according to this criterion are only marginal.

Development Sample

35% 5-20m ATS 40% 20-100m ATS 20% 100-500m ATS 3% 500-1000m ATS 2% >1000m ATS

Validation Sample

36% 5-20m ATS 38% 20-100m ATS 19% 100-500m ATS 4% 500-1000m ATS 3% >1000m ATS

Figure 3.4 Distribution of Financial Statements by Industry Segments

This figure shows that the distribution of firms by industry differs between the development and the validation sample as there are more service companies in the test sample This provides a further element of out-of-universe testing.

Development Sample

25% Service 33% Trade 29% Manufacturing 12% Construction 1% Agriculture

Validation Sample

34% Service 30% Trade 25% Manufacturing 10% Construction 1% Agriculture

For reasons described in Chapter 2, the credit risk rating model for Austrian panies shall be developed by estimating a logit regression and using accountingvariables as the main input to it The exact methodology, consisting of the selec-tion of candidate variables, the testing of the linearity assumption inherent in thelogit model, the estimation of univariate regressions and the construction of thefinal model, will be explained in the following chapter

com-I Selection of Candidate Variables

To derive a credit quality model, in a first step candidate variables for the finalmodel have to be selected As there is a huge number of possible candidate ratiosand according to Chen and Shimerda (1981) in the literature out of much morethan 100 financial items almost 50% were found useful in at least one empiricalstudy, the selection strategy described below was chosen

25

In a first step all potential candidate variables that could be derived from theavailable data set were defined and calculated Already at that early stage somevariables cited in the literature had to be dropped, either because of data unavail-ability or because of interpretation problems An example for the first reason

of exclusion is the productivity ratio “Net Sales / Number of Employees” tioned in Crouhy, Galai, and Mark (2001), as in the current data set the number

men-of employees for a particular firm is not available Interpretation problems wouldarise if for example the profitability ratio “Net Income / Equity” was considered,

as - in contrast to most Anglo-American studies of large public firms - the equity

of the observed companies sometimes is negative Usually we would expect thatthe higher the return on equity, the lower the default probability is However,

if equity can be negative, a firm with a highly negative net income and a smallnegative equity value would generate a huge positive return-on-equity-ratio andwould therefore wrongly obtain a prediction of low default probability To elimi-nate those problems all accounting ratios were excluded from the analysis wherethe variable in the denominator could be negative

Then, in a second step the accounting ratios were classified according to theten categories leverage, debt coverage, liquidity, activity, productivity, turnover,profitability, firm size, growth rates and leverage development, which representthe most obvious and most cited credit risk factors Table 4.1 lists all accountingratios that were chosen for further examination according to this scheme

Table 4.1

Promising Accounting Ratios

In this table all accounting ratios that are examined in this thesis are listed and grouped according

to ten popular credit risk factors Besides, in the fourth column the expected dependence between accounting ratio and default probability is depicted, where + symbolizes that an increase in the ratio leads to an increase in the default probability and - symbolizes a decrease in the default probability given an increase in the ratio Finally, column five lists some current studies in which the respective accounting ratios are used, too.

Accounting Ratio Credit Risk Factor Hypothesis Literature

12 Cash Flow / (Liab.-Advances)* Debt Coverage - b

13 Current Assets / Current Liabilities Liquidity - a, c, d, e, f

15 Working Capital / Assets Liquidity - a, b, d, e

25 Working Capital / Current Liabilities Liquidity - d

31 Accounts Receivable / Operating Income Activity + c

33 Accounts Receivable / Liabilities* Activity

-a Falkenstein, Boral, and Carty (2000) b Khandani, Lozano, and Carty (2001)

c Lettmayr (2001) d Chen and Shimerda (1981)

e Kahya and Theodossiou (1999) f Crouhy, Galai, and Mark (2001)

CPI Consumer Price Index 1986

* assets, equity and liabilities adjusted for intangible assets and cash

Table 4.1 continued Promising Accounting Ratios

In this table all accounting ratios that are examined in this thesis are listed and grouped according

to ten popular credit risk factors Besides, in the fourth column the expected dependence between accounting ratio and default probability is depicted, where + symbolizes that an increase in the ratio leads to an increase in the default probability and - symbolizes a decrease in the default probability given an increase in the ratio Finally, column five lists some current studies in which the respective accounting ratios are used, too.

Accounting Ratio Credit Risk Factor Hypothesis Literature

34 Accounts Receivable / Material Costs Activity + a

39 Operating Income / Personnel Costs Productivity - c

40 (Net Sales-Material Costs)/Personnel Costs Productivity - c

41 Material Costs / Operating Income Productivity + c, f

48 (EBIT+Interest Income)/Operating Income Profitability - c

49 (EBIT + Interest Income) / Assets Profitability - c

50 Ordinary Business Income / Assets Profitability - c

51 Ordinary Business Income / Assets* Profitability - b

52 (Ord.Bus.Income+Interest+Depr.) / Assets* Profitability - b

53 Ord Business Income / Operating Income Profitability - a, c

58 Retained Earnings / Assets Profitability - a, d, e

62 Net Sales / Last Net Sales Growth Rates -/+ a, b

63 Operating Income / Last Op Income Growth Rates -/+ a

64 (Liab./Assets) / (Last Liab./Assets) Leverage Change + a

65 (Bankdebt/Assets)/(Last Bankdebt/Assets) Leverage Change + a a Falkenstein, Boral, and Carty (2000) b Khandani, Lozano, and Carty (2001)

c Lettmayr (2001) d Chen and Shimerda (1981)

e Kahya and Theodossiou (1999) f Crouhy, Galai, and Mark (2001)

CPI Consumer Price Index 1986

* assets, equity and liabilities adjusted for intangible assets and cash

The credit risk factor group leverage contains ten accounting ratios Those suring the debt proportion of the assets of the firm should have a positive re-lationship with default, those measuring the equity ratio a negative one In theliterature leverage ratios are usually calculated by just using the respective items

mea-of the balance sheet, however, Baetge and Jerschensky (1996) and Khandani,Lozano, and Carty (2001) suggested to adjust the equity ratio in the followingway to counter creative accounting practices:

 Subtract intangible assets from equity and assets as the value of these assetsgenerally is considerable lower than the accounting value in the case ofdefault;

 Subtract cash and equivalents from assets (and debt) as one course of tion for a firm wishing to improve its reported liquidity is to raise a short-term loan at the end of the accounting period and hold it in cash

ac-Therefore also such adjusted accounting ratios are considered in the study athand and are marked with a star in Table 4.1 whenever either assets, equity, debt

or several of those items are adjusted for a certain accounting ratio

Debt Coverage

Debt coverage either measures the earnings before interest and taxes to interestexpenses or the cash flow to liabilities ratio Here liabilities were adjusted bysubtracting advances from customers in order to account for industry specifici-ties (e.g construction), where advances traditionally play an important role infinancing

Liquidity is a common variable in most credit decisions and can be measured by

a huge variety of accounting ratios The most popular ratio is the current ratio,calculated as current assets divided by current liabilities In general the hypoth-esis is that the higher liquidity, i.e the higher cash and other liquid positions orthe lower short-term liabilities, the lower is the probability of default However,for the four liquidity ratios that are scaled by sales instead of assets or liabilities,another effect has to be taken into account As discussed below, the larger theturnover of a firm the lower is its default probability, implying that the smallerthe reciprocal of turnover the more creditworthy a company is Therefore wehave the effect that - as for example a large “Working Capital / Net Sales” ratiocan be caused by good liquidity or by small sales - the overall influence of anincrease in these ratios on the default probability is unclear Nevertheless thoseratios were often used in older studies, and as they were found to be useful forthe credit risk analysis in Tamari (1966), Deakin (1972) and Edmister (1972)they were also selected for further examination in the work at hand

Activity Ratios

Activity ratios are accounting ratios that reflect some aspects of the firm that haveless straightforward relations to credit risk than other variables, but that never-theless capture important information Most of the ratios considered in this studyeither display the ability of the firm’s customers to pay their bills, measures byaccounts receivable, or they evaluate the company’s own payment habit in look-ing at accounts payable For example a firm that suffers from liquidity problemswould have higher accounts payable than a healthy one Therefore the defaultprobability should increase with these ratios The only exception is “AccountsReceivable / Liabilities”, as here an increasing ratio means that a larger fraction

of the firms own debt can be repaid by outstanding claims For activity ratiosthat use inventory in the numerator again a positive relationship to the defaultprobability is expected, as a growing inventory reveals higher storage costs aswell as non-liquidity.

Productivity

Here the costs for generating the company’s sales are measured by looking at thetwo big cost categories personal and material expenses The higher the costs, theworse the firm is off

Turnover

As for example illustrated in Coenenberg (1993), asset turnover reflects the ciency with which the available capital is used According to Lettmayr (2001) ahigh “Sales / Assets” ratio is a prerequisite to obtain high returns with relativelylow investment and has a positive effect on the liquidity of the firm, thereforereducing the default probability

effi-Profitability

Profitability can be expressed in a variety of accounting ratios that either measureprofit relative to assets or relative to sales As higher profitability should raise afirm’s equity value and also implies a longer way of revenues to fall or costs torise before losses incur, a company’s creditworthyness is positively related to itsprofitability

Size

According to Falkenstein, Boral, and Carty (2000) sales or total assets are almostindistinguishable as reflections of size risk Both items are divided by the con-

sumer price index to correct for inflation Usually smaller firms are less fied and have less depth in management, which implies greater susceptibility toidiosyncratic shocks Therefore larger companies should default less frequentlythan smaller firms.

in Section 4 II

Change of Leverage

Lenders are often more interested in where the firm is going than where it hasbeen For that purpose, trends are often analyzed The most important trendvariables are probably the change in profits and the change in liabilities How-ever, former studies such as the one of Falkenstein, Boral, and Carty (2000) findthat ratio levels in general do better in discriminating between good and default-ing firms than their corresponding growth ratios Nevertheless the impact of achange in liabilities shall be examined in thesis However, profit growth ratioswill not be explored as they suffer from the problem of possible negative values

in the denominator discussed above

II Test of Linearity Assumption

After having selected the candidate accounting ratios, the next step is to checkwhether the underlying assumptions of the logit model apply to the data.1 Thelogit model can be written as

To test for this linearity assumption, the variables are divided into about 50

groups that all contain the same number of observations, and within each groupthe historical default rate respectively the empirical log odd is calculated Finally

a linear regression of the log odd on the mean values of the variable intervals isestimated

What I find is that for most accounting ratios the linearity assumption isindeed valid As an example the relationship between the variable “Current Lia-bilities / Total Assets” and the empirical log odd for the bankruptcy criterion aswell as the estimated linear regression is depicted in Figure 4.1 The fit of theregression is as high as 82.02%

However, for some accounting ratios the functional dependence between thelog odd and the variable is nonlinear In most of these cases the relationship is

1 For a good introduction to logit regressions see Hosmer and Lemenshow (1989).

Figure 4.1 Linearity Test for the “Current Liabilities / Total Assets” Ratio for

the Bankruptcy Data Set

This figure shows the relationship between the variable “Current Liabilities / Total Assets” and the empirical log odd for the bankruptcy criterion, which is derived by dividing the accounting ratio into about 50 groups and calculating the historical default rate respectively the empirical log odd within each group Finally a linear regression of the log odd on the mean values of the variable intervals is estimated and depicted, too We can see that for the “Current Liabilities / Total Assets” ratio the linearity assumption is valid.

R2: 8202

Bankruptcy Data SetCurrent Liabilities / Total Assets

-6

-5

-4

still monotone, as for example for “Bank Debt / (Assets-Bank Debt)” depicted

in Figure 4.2 Therefore there is no need to adjust these ratios at that stage of themodel building process, as one will get significant coefficients in univariate logitregressions, the next step for identifying the most influential variables, anyway

But there are also two accounting ratios, i.e “Sales Growth” and ing Income Growth”, that show non-monotone behavior just as was expected.The easiest way would be to exclude those two variables from further analysis,

“Operat-Figure 4.2 Linearity Test for the “Bank Debt / (Assets-Bank Debt)” Ratio for

the Bankruptcy Data Set

This figure shows the relationship between the variable “Bank Debt / (Assets-Bank Debt)” and the empirical log odd for the bankruptcy criterion, which is derived by dividing the accounting ratio into about 50 groups and calculating the empirical log odd within each group Then a linear regression of the log odd on the mean values of the variable intervals is estimated and depicted, too We can see that for the “Bank Debt / (Assets-Bank Debt)” ratio the linearity assumption is not valid, but nevertheless the graph displays a monotone relationship between the variable and the default probability.

R2: 636

Bankruptcy Data SetBank Debt / (Assets - Bank Debt)

Figure 4.3 shows the resulting relationship between the ratio “Sales Growth”and the log odd for the bankruptcy data set.2 Now the accounting ratios aretransformed to log odds according to these smoothed relationships and in anyfurther analysis the transformed log odd values replace the original ratios asinput variables.

Besides, this test for the appropriateness of the linearity assumption also lows for a first check whether the univariate dependence between the consideredaccounting ratios and the default probability is as expected As can be seen in

al-2 As the Hodrick-Prescott filter was not implemented in Stata 7.0, the statistical software package used for all calculations, a program had to be developed to execute the filter The program code is displayed in Appendix B.

Figure 4.3 Smoothed relationship between “Sales Growth” and the empirical

log odd for the default criterion bankruptcy

This figure shows the smoothed relationship between the variable “Sales Growth” and the log odd for the bankruptcy data set In any further analysis the transformed log odd values are used

as input variable instead of the corresponding accounting ratio.

Bankruptcy Data Set

of those variables show a positive empirical relationship to default and the othertwo a negative one

Another important result already derived at this early stage of the modelbuilding process is the fact that the functional dependence between log odd andinput variable is the same for all three default definitions for all examined vari-ables So if the relationship between log odd and accounting variable is linear

for the default criterion bankruptcy, it is also linear for the criteria loan turing and 90 days past due This can be interpreted as a first hint that perhapsmodels that were developed by using a certain default definition also do wellwhen used to predict default based on other default criteria This possibility will

restruc-be examined in detail in Chapter 5

One example for the equality of the functional dependence between variablesand default probability for all three data sets is depicted in Figure 4.4 Here thelinearity assumption is valid Further examples for non-linear but monotone andnon-monotone behavior are displayed in Figure 4.5 The functional relationshipsbetween accounting ratios and log odds for all variables are recorded in Table 5.1

in the next chapter

Figure 4.4 Functional Dependence between “EBIT / Total Assets” and the

De-fault Probability for all Three Data Sets

This figure shows that the functional dependence between the log odds and the “EBIT/Assets” ratio is the same for all three default definitions.

R2: 7728

Log Odd Values Fitted Values

Log Odd Values Fitted Values

-5 -4 -3 -2

R2: 8861

EBIT / Total Assets Log Odd Values Fitted Values

Figure 4.5 Functional Dependence between “Bank Debt / (Assets - BankDebt)”

and “Sales Growth” and the Default Probability for all Three Data Sets

This figure shows that the functional dependence between the log odds and the “Bank Debt / (Assets - Bank Debt)” ratio respectively “Sales Growth” is the same for all three default defini- tions.

R2: 636

Bankruptcy Data Set

Bank Debt / (Assets - Bank Debt) Log Odd Values Fitted Values

Rescheduling Data Set

Bank Debt / (Assets - Bank Debt) Log Odd Values Fitted Values

-5 -4 -3 -2

R2: 5917

Delay-in-Payment Data Set

Bank Debt / (Assets - Bank Debt) Log Odd Values Fitted Values

Bankruptcy Data Set

Sales Growth Smoothed Values Original Values

-5.5 -5 -4.5 -4

Smoothed Values Original Values

Smoothed Values Original Values

-3 -2.5 -2 -1.5

III Univariate Logit Models

After verifying that the underlying assumptions of a logistic regression are valid,the next step is to estimate univariate logit models to find the most powerfulvariables per credit risk factor group Here the data sets are divided into a de-velopment sample and a test sample in the way illustrated in Chapter 3 Theunivariate models are estimated by using exclusively the data of the develop-ment samples However, before we can do so we have to decide which type oflogit model should be estimated

Actually, the data sets at hand are longitudinal or panel data sets as they veal information about different firms for different points in time According

re-to M´aty´as and Sevestre (1996) panel data sets offer a certain number of tages over traditional pure cross section or pure time series data sets that should

advan-be exploited whenever possible Amongst other arguments they mention thatpanel data sets may alleviate the problem of multicollinearity as the explanatoryvariables are less likely to be highly correlated if they vary in two dimensions.Besides, it is sometimes argued that cross section data would reflect long-runbehaviour, while time series data should emphasize short-run effects By com-bining these two sorts of information, a distinctive feature of panel data sets,

a more general and comprehensive dynamic structure could be formulated andestimated, M´aty´as and Sevestre (1996) conclude

Although these arguments are convincing, the problem with the data setsused in the study at hand is that they are incomplete panel data sets Not allfirms are covered for the whole observation period, on the contrary, as depicted

in Chapter 3 and Appendix A for a non-negligible number of companies onlyone accounting statements was gathered at all What’s more, also trend variables