Márquez , Javier - An Introduction to credit scoring for small and medium size enterprises

8/6/2019 Mrquez , Javier - An Introduction to credit scoring for small and medium size enterprises

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An Introduction to Credit Scoring

For

Small and Medium Size Enterprises.

Javier Mrquez.1

February 2008

I. INTRODUCTION.

This paper is intend ed as a q uick primer on c red it scoring , and how itapp lies to the assessment of risk of sma ll and med ium size ente rprises (SMEs). It

is part o f a la rge r study on how c red it sc oring is c urrently be ing applied for this

purpose, and exploring the possibility of broadening the applicability of the

technique to enc om pass a w ider spec trum of SMEs. Thus, the a im has bee n to

provide the reader who wishes to understand what credit scoring is about but

do esnt wa nt to be come a spe c ialist, with enough informa tion o n c red it sc oring

fundamentals so as to feel comfortable with the subject in terms of its

mechanics, scientific foundations, applicability and the practical issues that

must be addressed for a successful application. It was deemed important to

specifically compare credit scoring with ratings, since they are often confused

and erroneously addressed as if they we re the sam e or a t least c lose

relatives. Essentially, the only thing they have in common, is that both are

systematic approaches to appraise the risk of an individual debtor;

methodologically however, they are extreme opposites.

Ratings live in the realm of big companies that issue or contract large

debt, and the evaluation of the risk of the debtor is done employing the

traditional techniques of fundamental analysisand experience. In contrast,

credit scoring is based on discriminant analysis; a statistical methodologydesigned to optimally classify a population (e.g. debtors) into clearly

distinguishable groups (e.g. good and bad). As such, it requires large

populations so that the statistical parameters estimated are reliable, and

provide a reasonable degree of certainty as to what group a particular

me mb er of the pop ulation b elong s. Thus, for single ob ligor risk measurem ent ,

1The a uthor wishes to tha nk Mr. Albe rto Jones of Mood ys , Vic tor Ma nuel Herrera of Standard

and Poo rs, and Guillermo Ma ss and Juan Ram on Bernal o f Banc o San ta nder-Serfn fo r their

ge nerous c ontributions to this effo rt. I wo uld p a rticula rly like to tha nk Augusto de la Torre w ho,

in spite of m y relucta nce , enco urag ed me to und ertake this project.

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the technique only makes sense for large populations of debtors with fairly

hom og eno us c ha rac teristics. Fina lly, whe rea s a rating is an o rd inal risk ind ica to r

in the sense tha t higher ra tings mea n less risk and lower rat ings imp ly more risk in

the opinion of whoever did the rating, credit scores are actual estimates of

default probabilities of debtors in a group, and their reliability depends on thesample in terms of size, the proportions of good and bad debtors it contains,

and the mathema tic al mod el used to d istinguish be twee n them.

Ratings however, are by far the most common reference on individual

c red it risk in the industry, for prac tica l and reg ulato ry reasons. Thus, no matte r

how individual credit risk is assessed, or how precise the technique used to

estimate a default probability, it will eventually have to be related to a rating;

either as a means to communicate in terms that are readily understood across

all levels of a lender organization and regulators, as a means to comply with

reg ula tion, or both.

Sec tion two g ives a b rief histo ry of ra tings and c red it sc oring . Besides

explaining how ea c h tec hnique c ate rs to d ifferent types of d eb tor pop ulations,

it is interesting to see that, contrary to popular belief, credit scoring is not a

recent fad, but dates back to over sixty years when consumer lenders were

overwhelmed in their capacity to process personal loan applications, and

something ha d to b e d one. In sec tion three, the ana tom y of c red it scoring is

explained: building scorecards, sample design, discriminant analysis and the

issues tha t must b e a ddressed in prac tice fo r suc c essful ap p lica tions. In the nextsec tion, we c ome full c irc le a nd show how , desp ite their d ifferenc es, sc ores c an

be mapped into ratings, establishing an indispensable link between the two

which, as already mentioned, is important both for practical and regulatory

purposes. In this sec tion, we a lso go into some d eta il on how it c an b e a pplied

in the Basel II frame wo rk. The paper conc ludes with a d isc ussion of the sta tus of

c red it scoring as it app lies to SME lend ing. It is see n why the too l is very useful at

the low end of the scale, and substantiate the claim that in this population the

use of credit scoring is widespread. However, it is also explained why the

technique becomes less and less applicable as one moves up the ladder, untilit bec om es d iffic ult or impossible to apply for the larger SMEs.

II. ABRIEF HISTORY OF THE SYSTEMATIC ASSESSMENT OFCREDITRISK:

CREDITRATINGS VS.CREDITSCORING.

The e ssenc e o f lend ing mo ney ha s be en und erstoo d from the ve ry

beg inning a nd it is unlikely to c hange ; namely, one needs to estab lish potential

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deb to rs c apac ity and willingness to p ay. Trad itiona lly, since the re is a rec orde d

histo ry o f c red it over 4000 yea rs ago 2 and of banking from the midd le a ges up

to the beg inning of the twentieth c entury, the assessme nt b y bankers of the risk

represented by potential debtors, in terms of their capacity and willingness to

pay had hard ly change d. There wa s a c ertain mystique surround ing the shrewdand exquisite banker with an infallible judgment who could, at a glance,

dete rmine the qua lity of a wo uld be c lient. Thus, any banker wo rth his salt wa s

supp osed to have a profound knowledg e o f his c lients and c ompe tition, which

allowed him to decide by trade, pure instinct and trusting in a bit of luck 3, who

he c ould lend money to, how muc h he c ould lend them, how muc h he c ould

charge, how he would be paid, and what collateral he could demand. Over

the last half of the last century to the present day, this perception of banking

has p rac tica lly disappea red a nd ove r the pa st twenty five years, there has

been a radica l cha nge in the wa y risk in genera l and c red it risk in particular, is

perceived, mea sured and ma nage d.

Basically, the change is a direct response to the dramatic increase in

complexity of the credit business, technology and financial knowledge.

Whereas well into the nineteenth century bankers generally dealt with a

relatively small client base (by todays standards), of elite customers who could

be dissected and evaluated on an individual basis, and a manageable

number of relatively large loans could be tailored to individual needs, by the

first q uarter of the twentieth c entury, the potential client b ase had expanded

enormously.

Although it is not the main subject of this paper, it is important to talk

about ratings since they are often confused with scores. As shall be seen later,

this does not mean however, that a relationship between ratings and credit

scores cannot be established. In fact, a correspondence can be established

and it ha s bec ome a nec essity fo r reg ula tory purposes, pa rticularly in the light

of the new Basel II accord, where capital charges due to risky assets can be

either ratings dependent in the standardized approach or PD driven, in the

Inte rna l Ra tings Based (IRB) approac h.

2.1. Rating s.

Large corporations, besides having access to banks, have been able to

place debt in public offerings in the market for centuries. As the number of

2Lew is reported in 1992, tha t a Bab ylonian stone tab let reads the insc rip tion: Two sheke ls of silver

have be en b orrowe d by Ma s-Sc ham ac h, the son o f Ad rad imeni, from the sun p riestess Ama t-

Sc hama c h, the d aughter of Warad Enlil. He will pa y the sun god dess interest. At the time of the

harvest he will pay ba c k the sum a nd the interest up on it.3No trad itiona l banker will ad mit grac efully to this luck c omp onent!

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participants grew, this led to an increasing demand by investors, of obtaining

reliab le info rma tion o n the solvenc y of the issuers. Thus, la rge firms, whic h have

always been given a special treatment, did not escape being labeled with

som e kind of indic ator of the risk they represented ; indeed , they w ere the first to

have suffered the onslaught! As early as the late eighteen hundreds and thebeginning of the twentieth century, the first rating agencies came into play on

the p rincip le of the investo r's right to know. In 1860 Henry Varnum Poor

pub lished his Histo ry of Railroads and Ca na ls of the United Sta tes and his

suc c ess led to the foundation o f Poo r s Pub lishing w ith the intention o f informing

investors on the financial soundness of issuers of publicly traded debt. In 1900,

John Moody and Co. published Moodys Manual of industrial and

Miscellaneous securities providing investors with financial information and

statistics on listed companies and issuers of debt. In 1906, the Standard Statistics

Bureau was formed to provide previously unavailable financial information on

U.S. companies and in 1916, they b eg an ra ting c orporate bo nds, with sove reign

debt ratings following shortly thereafter. Having sold his company in 1907,

Moody is back in the financial information business in 1909, with the idea of

offering investors research and analysis on publicly traded debt issues, starting

with railroads. Moodys investor services was created in 1914, and has been

publishing their Weekly Review of Financial conditions known today as

Moodys credit perspectives for nearly one hundred years, and claims to be

the first to devise the let te rs based rat ing system. The Sta nd ard Sta tistic s burea u

a lso expa nde d c onsistent ly to an eve r inc rea sing universe o f c om panies both in

the p rivate and pub lic sec to r and in 1941, Poo r's Pub lishing and Sta ndardSta tistics merge d to form the Standard & Poo r's Corpo ra tion we know tod ay.

Initial publications consisted of a brief analysis of financial ratios with certain

industry c om parisons and so on, and of c ourse, the rating. Anothe r ag enc y tha t

trac es its histo ry to the ea rly twent ieth c entury is Fitch (1913). Fitch a lso c laims

to be the first to devise the letters based rating system and has been

consistently gaining in international presence, specially after it acquired Duff &

Phelps in April of 20004. Tab le 2.1 com pares the let te ring systems used by the

d ifferent ra ting ag enc ies.

A rating is an indicatorof the creditworthiness of a debtor5. In Moodys

ow n wo rds:

A credit rating is an opinion of the credit quality of individual obligations

or of an issuers gene ral c red itworthiness, without respec t to ind ividua l

deb t ob ligations or othe r spec ific sec urities.

4It should b e p ointed o ut that the ab ove mentioned are not the only existing rating a ge ncies inthe world. We ha ve only mentioned those with the largest internationa l presenc e.

5Taken d irec tly from the rating a ge nc ys web sites.

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Speculative Grade

Invest-mentGrade

Associated Risk

Low

High

CCC

CaCCCC

CaaCCCCCC

BBBBaBBBB

BaaBBBBBB

AAA

AaAAAA

AaaAAAAAA

MoodysS&PFitch

MoreMore

RiskRisk

LessLess

RiskRisk

Tab le 2.1: Compa rison o f Rating Catego ries by Rating Ag enc y.

Other ra ting a genc ies have simila r definitions:

Standard & Poo rs:

A c red it rating is Sta nda rd & Poo r s op inion o f the g enera l

creditworthiness of an obligor, or the creditworthiness of an obligor with

respect to a particular debt security or other financial obligation, based

on releva nt risk fac tors. A ra ting does not c onstitute a rec om mendat ion to

purchase, sell, or hold a particular security. In addition, a rating does not

c om ment on the suita b ility of a n investment fo r a pa rticular investor .

Fitch:

Fitc h's c red it ratings p rovide an op inion o n the relative a b ility of an entity

to meet financial commitments, such as interest, preferred dividends,

repayment of principal, insurance claims or counterparty obligations.

Credit ratings are used by investors as indications of the likelihood of

receiving their money back in accordance with the terms on which they

invested.

Evidently, credit rating has come a long way since the first agenciesap pe ared a hundred years ag o. Not only have they expa nded the ir op erations

to cover the vast spectrum of firms and government agencies that publicly

issue debt, but they have consistently refined and systematized their methods.

There has a lso b een a para llel development by ba nks, whic h emp loy very

similar methods to evaluate the risk of their larger loans. In essence, and with

the peculiarities pertaining to each agency or bank, the risk assessment or

ra ting of a particular deb t issue o f a large deb tor, is a rrived at after a thoroug h

fund ame nta l ana lysis of the issuer and his ob liga tions in rela tion to the particular

issue. The q uantita tive a na lysis derived from historica l da ta and future

projections of financial statements under different business, market and

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economic scenarios, is contrasted with qualitative appreciations of particular

c ha rac te ristics of the issuer, and the env ironm ent . Thus, things like the qua lity o f

management and the business strategy of the issuer, along with the

c om petition a nd the reg ula tory req uirem ents it fa c es, whose c ont ribution to risk

are not e asily qua ntifiab le, are c arefully weighed be fore a rec omm endation orra ting is prop osed by the resea rc h te am responsible for the a na lysis. The final

rec om mendation or ra ting is assigne d , only a fter the findings, both quantitative

and qua litat ive, and the p rop osal of the resea rc h tea m have be en d iscussed in

a top level co mm ittee . Sc hem atica lly, the p roc ess is p resented in figure 2.1.

below. It is interesting to see all the things that are considered, and the

hierarchy assigned to each, in order to arrive at a rating and that qualitative

ana lysis is p lac ed a t the very top of the pyramid.

QUALITATIVEQUALITATIVE

ANALYSISANALYSIS

ManagementManagement

StrategicStrategic ManagementManagement

FinancialFinancial FlexibilityFlexibility

QUANTITATIVE ANALYSISQUANTITATIVE ANALYSIS

Financial StatementsFinancial Statements

Previous OutstandingPrevious Outstanding

ProjectionsProjections

MARKET POSITIONSMARKET POSITIONS

SECTOR COMPETITIVE ENVIRONMENTSECTOR COMPETITIVE ENVIRONMENT

Global / DomesticGlobal / Domestic

REGULATORY ENVIRONMENTREGULATORY ENVIRONMENT

SECTORIAL ANALYSIS (I NDUSTRY)SECTORIAL A NALYSIS (I NDUSTRY)

MACROECONOMIC AND SOVEREIGN ANALYSISMACROECONOMIC AND SOVEREIGN ANALYSIS


QUALITATIVEQUALITATIVE

ANALYSISANALYSIS

ManagementManagement

StrategicStrategic ManagementManagement

FinancialFinancial FlexibilityFlexibility

QUANTITATIVE ANALYSISQUANTITATIVE ANALYSIS

Financial StatementsFinancial Statements

Previous OutstandingPrevious Outstanding

ProjectionsProjections

MARKET POSITIONSMARKET POSITIONS

SECTOR COMPETITIVE ENVIRONMENTSECTOR COMPETITIVE ENVIRONMENT


REGULATORY ENVIRONMENTREGULATORY ENVIRONMENT

SECTORIAL ANALYSIS (I NDUSTRY)SECTORIAL A NALYSIS (I NDUSTRY)

MACROECONOMIC AND SOVEREIGN ANALYSISMACROECONOMIC AND SOVEREIGN ANALYSIS


Figure 2.1. Standard Conside rations in the rating process.

(Courtesy of Mood ys Investo r Services.)

Although the general principles of fundamental analysis, as regards the

evaluation of the credit worthiness of a debtor are well established, the actual

methodologies of the rating agencies, and the internal rating systems used by

banks a re no t p ub lic ly d isc losed . In a ll ca ses they a re c onsidered an important

pa rt of the intellec tual property of the ba nks and the a genc ies and key fac tors

of their competitiveness in the industry. Indeed, both the rating agencies and

the b anks go to g rea t lengths in trying to c onvince the ma rket and the financ ial

autho rities tha t they d o it a s we ll as, or be tte r than the rest. There is an

important difference between the banks and the rating agencies however;

name ly, whereas banks a re unde r no ob liga tion to d isc lose their internal rat ings

to any one other than the financ ial authorities, disc losure of ratings is a t the very

hea rt o f the ra ting a genc ies business. This permits the ma rket a nd any

interested observer to see what the actual track record of the agencies is, and

how we ll the ra tings ac tua lly cap ture the risk in ra ted deb t issues.

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Data such as that of table 1.1 can be used to estimate default

probabilities by rating category. Figure 2.2 shows Moodys default probability

estimates by rating category over time. It is interesting to see that default

probabilities increase as ratings go down the scale, which is consistent with the

be havior ob served in the m ortality rate d ata shown ab ove6

.

Figure 2.2: Default Probability by Rating Categ ory(Courtesy of Moodys Investor Services.)

More recently, and specially after the Basel II initiative, banks who

havent already done so, are strongly urged to work towards using ratingsystems which, to each rating category, can explicitly associate a default

probability such as shown above, and an expected recovery rate in case of

defa ult. An exam ple o f rec ove ry rates is p resente d in tab le 2.3 be low .

Senio rity No. of Bond s Rec overy Rate

(Mean)

Standard

Deviation

Senior guaran tee d 89 57.94% 23.12%

Senior non gua rantee d 225 47.70% 26.60%

Senio r sub ord inated 186 35.09% 25.28%

Subo rd inated 218 31.58% 22.50%

Junior subordinated 34 20.81% 17.76%

Table 2.3: Rec overy Rates on Co rporate Bond s by Senio rity.(% o f fac e va lue of $100). Altman and Kishore(1997).

As seen above, the scrupulous recording of performance data by theagencies, has permitted the estimation of a wide variety of risk relatedmeasures. Simp ly to c onc lude this sec tion with ano ther rec om mendation of theBasel Committee, table 2.4 below shows a transition matrix, which provides

6 Although the numbers dont necessarily coincide due to differences in rating scales andmetho do logies of the d ifferent rating a ge ncies.

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the probability of migration of rated bonds from one rating category toanother.

Fina lly, it should b e fa irly ob vious tha t rating a la rge c orpora te loa n b y aba nk o

Rating AAA AA A BBB BB B CCC Default

r an agency, is a lengthy, labor intensive and costly affair, which is only

justified by the magnitude of the debt relative to the analytical effort (cost)involved, and the broad interest manifest by the investor community. As onegoes down the scale, doing such an in depth analysis becomes ever morecostly, to the point of becoming prohibitive, and some would argueunnec essary. This doe s not mea n tha t rating other types of loa ns is not done ;quite the c ontrary. Over the yea rs, ra ting systems for all sorts of loa ns(businesses,

AAA 94.30% 5.50% 0.10% 0.00% 0.00% 0.00%0.00% 0.00%

AA 0.70% 92.60% 6.40% 0.20% 0.10% 0.10% 0.00% 0.00%

A 0.00% 2.60% 92.10% 4.70% 0.30% 0.20% 0.00% 0.00%

BBB 0.00% 0.00% 5.50% 90.00% 2.80% 1.00% 0.10% 0.30%

BB 0.00% 0.00% 0.00% 6.80% 86.10% 6.30% 0.90% 0.00%

B 0.00% 0.00% 0.20% 1.60% 1.70% 93.70% 1.70% 1.10%

CCC 0.00% 0.00% 0.00% 0.00% 9.00% 2.80% 92.50% 4.60%

Table 2.4: Transition Ma trix.

Source :Altma n and Kao (1992), estima ted from d ata on b ond s issued be twe en 1971 and 1989,

consumer or personal loans) have been devised, where loan applicants

.2. Cred it Scoring.

With the growth of the middle class in the eighteen hundreds, money

lender

rate d b y S&P.

provide information through a questionnaire of some sort, which is then

processed by a credit analyst, who rates and decides to grant or reject the

loan, based on experience and intuition. Initially the information required was

purely judgmental, and depended heavily on analysts personal opinions of

what determined capacity and willingness to pay. It quickly became evident

that in many cases, there were rating inconsistencies due to differences of

opinion between analysts. Furthermore, the number of applications kept

grow ing, to the point that a na lysts we re overwhelmed , and som ething e lse was

nee ded . This b rings us to the main sub jec t.

2

s realized there was a rapidly growing market in smaller loans with the

added attraction of diversification and the ensuing protection in large

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numbers. This g ives rise to the c rea tion o f the first c om me rcial banks, pa wn

brokers and even mail order services7; a ll c a tering to c onsumer cred it. The

process really takes off in the 1920s with the possibility of the public at large to

buy auto mob iles. This howeve r req uired a rad ic a l c hang e in the wa y of do ing

business; namely, there was a need to standardize products and systematizethe loan originat ion a nd m anage ment p roc ess. In tod ays environm ent, this has

bec om e a n imp erative. Sinc e the typ ica l deb tor is lost in the a nonymity of the

grea t m ass of individuals tha t owe banks or othe r consumer cred itors mo ney, it

is prohibitive to carry out an evaluation of the risk they represent based solely

on secrets of the trade, intuition, pure experience or even a rating process as

previously described; some kind of automatic classification of the quality of

deb tors has be c om e a nec essity.

Cred it sc oring is the first fo rma l approa ch to the p rob lem o f assessing the

credit

Shortly a fter the wa r, with the adve nt of automa tic c alculators that

eventu

risk of a single debtor in a scientific and automated way, in direct

respo nse to the need of p roc essing la rge volumes of app lica tions for relatively

small loans. During the nineteen thirties some mail order companies already

overwhelmed with demand, devised scoring systems in an attempt to

overcome the inconsistencies detected in the credit granting decisions of

d ifferent ana lysts. Thus, ob servable at tributes of g oo d or ba d deb to rs we re

identified, measured and numerically graded accordingly, to produce a final

score as a simple sum of the individual components. In many cases the score

was associated with a rating. When credit analytical talent and expertise

became scarce during WWII, companies engaged in consumer credit on ala rge sc a le, asked experience d ana lysts to write down the rules which led them

to d ec ide whethe r or not they would g ive som eone c red it. The result was a

hybrid assortment of different kinds of scoring systems and a variety of

c ond itions which experienc e ha d taug ht should be met , if a loan wa s to ha ve a

rea sonable c hanc e o f pe rforming8.

ally led to full fledged computers, the processes described became

sub jec t to a utom ation. The sc ientific bac kground to m od ern credit scoring is

provided by the pioneering work of R. A. Fisher(1936) who devised a statistical

technique called discriminant analysis, to differentiate groups in a population

through measurable attributes, when the common characteristics of the

7Mail order services began as clubs in Yorkshire in the 1800s, and were restricted to small segments of

the population for very special purposes.

8Note that this is very similar to an expert system.

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members of the group are unobservable 9. In 1941 D. Durand recognized that

the same approach could be used to distinguish between good and bad

loans. Mating automation with statistical discriminant analysis was a natural

route for credit scoring to follow, eliminating the largely subjective rules of

thumb adhered to by analysts, regardless of their validity10

. Ob viously, the routeto success was heavily mined, since establishing creditworthiness of a debtor

using an automated process based on discriminant analysis was viewed as a

frontal attack on conventional banking wisdom, painstakingly acquired

throug h several millennia. The most famo us anec dote is tha t of E. F. Wond erlic,

president of Household Finance Corp. (HFC) in the early 1940s. Wonderlic was

well versed in statistics through his training in psychology, and tried to

implement credit scoring in HFC. His frustration at the rejection of the technique

is evident in his 1948 report where, after proving that credit scoring actually

worked, in a way that any audience technically qualified in statistical

techniques would have readily accepted, he pleaded: These figures from

actual results should prove conclusively to the most skeptical that the Credit

Guide Score is a too l11 which is consistently able to point out the degree of risk

in any personal loan, provided, of course, that it is correctly scored. Tha t his

c onc ern wa s we ll founde d wa s c orrob orated when it wa s later discovered that

ma ny ana lysts approved loa ns first, and then filled in the sc orecard to show a

passing score.

Perseverance prevailed however, and more systems were developed.

Initially, both the variables selected and the scores assigned were mainly judgmental, but the systematic application of the methods contributed with

uniformity of scoring criteria providing the credit origination process with sorely

needed c onsistenc y and p red ic tab ility. The ec onomics of p roc essing the

exponential growth in personal loan applications, along with increasingly

refined statistical techniques with the ensuing improvement of the predictive

power of the models, and the constant advances in available computing

power, which inexorably reduced application processing time, ultimately

forced the a c c ep ta nce o f sta tistica lly ba sed , automa ted sc oring system s. The

introduction of credit cards in the 1960s provided further impulse for the

extensive use of credit scoring in banks, retailers, and any large consumer

lend er. Curiously, the issua nc e in the U. S. of the Equa l Credit Op portunity Ac ts

9 Fisher was concerned with the problem of differentiating between two varieties of Iris by the size of the

plants and the origins of skulls by their physical measurements.

10 As previously mentioned, hybrid systems where scoring interacts with expert rules is the domain of

artificial intelligence. See for example Cuena, et. al. (1990).

11 The Credit Guide Score was the manual distributed through HFC indicating how credit applications

should be scored.

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and its amendments in 1975-76 ensured the complete acceptance of credit

scoring. It became illegal to reject a loan on the basis of gender, religion, or

rac e, unless it wa s em pirica lly derived and sta tistica lly based . Thus, the

imp artiality in the a ssessment o f would b e d eb tors is ge nerally ac c ep ted as one

of credit scorings main virtues, and leave it to statistics to decide whether aparticular cha rac te ristic is riskier tha n another.

This has not gone unc ontested howe ver. In several countries d ifferent

types of activists have lobbied intensively to forbid the use of variables relative

to gender, race and creed arguing they could produce discriminatory results,

despite evidence to the contrary. In 1976 for example, Chandler and Ewert

showed that if gender were allowed to be a scoring variable, more women

than me n would have a c c ess to c red it12. Many c onsumers a lso o bjec t to c red it

scoring, feeling demeaned by being treated impersonally as just a number or

ano ther memb er of the g roup , and helpless to p lea their c ase w hen rejecte d.

The issue is rea lly one o f imp ersona l versus impartial which g ives rise to a

lively, endless and largely unsettled discussion, since deciding which variables

are po litic ally co rrec t and which a re not, and if and when p ersona l attention

is warranted for some cases, pertains more to the realms of ethics or business

practice and is therefore highly subjective 13. The va riab les ac tua lly used in

sc orec ards for co nsumer loa ns a re no sec ret, and anybo dy who has filled in an

application for a credit card, mortgage or car loan knows what they are:

Besides name and address, the relevant variables refer to education,

employment, how many years in the job, number of dependants, salary andother sources of income (investments etc.), properties and possessions (houses,

c ars etc .), othe r deb ts, ba nk and persona l refe renc es and so on. This

information is usually complemented with payment history data obtained from

the public registries.

Tod ay, it is lite ra lly prohib itive, both fo r considerations of financ ial risk

assessment and in terms of required manpower, to engage in consumer

lend ing ac tivities in any othe r wa y. To the c hag rin of d ie-hard trad itional

analysts, by 1963 default rates in consumer loans screened with credit scoring

techniques, had dropped by 50% or more.14 This suc c ess invariab ly led money

lenders to try credit scoring in other types of loans, e.g. personal, car or

mortgage loans. A case which is of particular interest, is the parallel effort by E.

Altman (1968) who first proposed a scoring technique to predict the risk of

12Among other things, the main reason is that in low income groups with part time employment, women

are generally better than men at repaying their debts.

13See for example Churchill and Nevin (1979), Capon (1982) and Saunders (1985) for arguments on both

sides of the table.

14See Meyers and Forgy(1963) and Churchill et. al.(1977).

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c om panies going b ankrup t. The d isc ussion of Altman s z-sc ore method will help

to illustrate the c onc ep t, be fore go ing into c red it sc oring in a m ore rigorous wa y

in the next sec tion.

2.3. A c lassica l exa mp le o f Credit Scoring: Altma ns Z-Score.

As previously mentioned, as soon as it became accepted as a useful

tool to asses the creditworthiness of a debtor for consumer loans, the search for

other applications was on. In particular, Edward Altman (1968) pioneered the

application of discriminant analysis to the prediction of corporate bankruptcy

with what he called the Z-Sc ore. Using accounting data on healthy and

bankrupt companies, Altman calculated the financial ratios used by

ac c ounta nts and ana lysts to assess the solvenc y of b usiness firms, and ob ta ined

the following discriminant function to distinguish healthy companies from

those with a high probab ility of ba nkruptc y:

54321 998.420.107.3847.717.0 XXXXXZScoreZ ++++==

The va riab les tha t be st d isc riminate d b etw een hea lthy and ba nkrupt

c ompa nies were:

X1 = Working Capita l / Tota l assets.

X2= Reta ined Earnings / Tota l assets.

X3= EBITT

15 / Tota l assets.

X4= Ma rket Va lue o f Sha res / Tota l assets.

X5= Sa les / Tota l assets.

Altma n s sta tistica l stud y show ed tha t the Z-Sc ore w as Norma lly

distributed for both groups and the respective means of the distributions was

4.14 for hea lthy co mpanies and 0.15 for those tha t were b ankrup t. Thus, by

ob taining the Z-Score for a pa rtic ular comp any one c an d ec ide which group

it is more likely to belong (healthy or bankrupt) by performing the

c orrespond ing sta tistica l tests of hypothesis. This c om me nt und erlines one of the

main characteristics of all statistical techniques, and discriminant analysis is no

exception; namely, that absolute certainty as to what group a company

belongs to is impossible. One can only place a company16 in one group or the

other with a certain probability or confidence level. This mea ns tha t m ista kes

c an and will be m ade; but this is true o f any method . The imp ortant thing he re is

15Earnings before Interest and Taxes.16Obviously this refers to companies outside the sample that was used to estimate the model.

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that in discriminant analysis, as opposed to more traditional techniques, the

actual probability of making a mistake and the associated costs can be

estimated.

Figure 2.3 illustrates the conc ep t. Spea king in genera l terms, disc riminantana lysis identifies a d istribution of Sc ores for goo d deb to rs and a nother for

bad debtors. Notice that the shaded area is ambiguous, in the sense that

there are small probabilities of comparable orders of magnitude, that debtors

with sc ores in this reg ion can belong to one g roup or the o the r. This points out to

the well known type one and type two errors in statistics, which in the

language of credit scoring means: 1)Placing the debtor in the healthy group

when it rea lly belong s in the b ad one (Type I error); or 2) Plac ing the d eb to r in

the bad group when it is ac tua lly goo d (Type II error). In the first c ase, a loa n

would be granted and some money would be lost if and when the default

oc c urs. In the sec ond c ase the loa n would be rejecte d and the c orrespo nding

profit fo reg one . Thus, when a score fa lls in the fuzzy a rea , in the dec ision o f

which group to place the debtor, there are two elements which must be

c onside red ; name ly, the p rob ab ilities of the de bto r belonging to o ne g roup or

the other, and the c osts assoc iated w ith misc lassific a tion.

BankruptBankrupt GroupGroup Healthy Group

ZZ--scorescore0.15 4.14

Type I and II Errors

Number

Numberofoffirms

firms

((Frequen

cy

Frequen

cy))

BankruptBankrupt GroupGroup Healthy Group

ZZ--scorescore0.15 4.14

Type I and II Errors

Number

Numberofoffirms

firms

((Frequen

cy

Frequen

cy))

Figure 2.3 The d isc riminating d istributions in

Altma ns Z-Score a nd type I a nd II errors.

The exam ple ac c entua tes the simp lic ity and p rac tica lity of cred it

scoring. As a weighted sum of the values of certain attributes of a debtor,

which are obtained directly from loan application formats, internal data and

public registries, once the data is captured, the processing is fully automatic.

Both the relevant attributes and their weights are obtained by statistical

techniques, using criteria that seek to differentiate as muc h as possib le, the

sc ores of hea lthy d eb tors from those tha t a re not. Thus, the c umb ersom e part o f

imp lementing c red it sc oring is the e stimation of the mo del and its ca lib ra tion to

ensure its p red ict ive capab ility. This proc ess is done d irec tly with ea c h particularba nks da ta and mode ls should b e reca librated pe riod ic ally to ensure tha t the

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model adapts to economic conditions and the dynamics of the market. All of

this is explained in the next section, and the main techniques of discriminant

ana lysis a re p resented in som e d eta il in append ix A .

III. The Anatom y of Cred it Scoring Tec hniques.

In this sec tion we d isc uss the wha t and how of c red it sc oring. We

begin by describing the scorecard , followed by a discussion of its principal

elements and the relevant practical issues; namely, the applicants

characteristics and attributes, accept/reject cut-offs, the definition of good

and bad deb tors, sam ple d esign a nd so o n. The sec tion ends with a b rief

description of d isc riminant analysis, which is the main statistical tool used forbuilding scorecards17.

3.1. The Mec hanics of Cred it Sc oring.

As illustrated by the previous example, credit scoring is an eminently

pragmatic and empirical approach to the problem of risk assessment of

individual debtors. The e mp hasis is on p red ict ing d efa ults, not on e xplaining

why they do or do nt oc c ur. The b asic e lements of c red it sc oring a re: 1) A set of

categories of information called Cha rac teristics or Variab les with theircorresponding attributes, which qualify and/or quantify how each

c harac teristic app lies to an individual deb tor, 2) The po ints assoc ia ted to a

particular attribute as it pertains to an applicant and 3) A threshold or cut-off

value.

In credit scoring terms, characteristics refer to the questions asked,

whereas attributes are the specific answers to these questions, whether they be

provided by the applicants or obtained from other sources, such as internal

bank da ta or public reg istries. The wo rds charac teristic and va riab le are

synonymous18, a lthough the first is desc rip tive of the type o f information

comprised in each category, while the latter emphasizes the random nature of

the information within a particular category. For example, a typical

Characteristic or Variable considered in consumer loans is, Residentia l Sta tus.

Note however, tha t the ac tua l numb er of at tributes (possible a llowed a nswe rs

to a question) pertaining to this category can vary widely from one creditor to

ano ther. Wherea s one might b e ha pp y with only two (dichotomous) attributes

17A mo re d eta iled presenta tion will be found in App end ix A.

18 Characteristic would be the word used by the credit analyst using the model, whereas variab le wo uld be the wo rd used by the statistician do ing the estimation and c alibration.

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like owner-renting, another might require more specifics such as: owner with no

mo rtgage , owner with a mo rtg ag e, rent unfurnished , rent furnished or living with

parents. Assuming for the mo ment tha t a ttributes are sc ored with integers from

naught to five, where higher is be tter, in the first c ase ow ner m ight me rit a five

while renting might merit a two. In the second case, five could be the scoreof owner no-mortga ge , four for owner with mortga ge and so o n do wn the

line to a zero for living with parents .

This little examp le illustrate s the typ ica l sc oring struc ture used in prac tice;

namely: Although, as was the case for Altmans z-score, characteristics with

single attributes scored with continuous values can be used, current practice

favors a finite number of attributes (at least two) associated with each

c harac teristic and in ge neral, the po ints assoc iated to e ac h a ttribute are two

digit numbers. Attributes associated to each characteristic are intended to be

comprehensive and mutually exclusive; i.e. only one in each characteristic is

pe rtinent to a n ap plic ant, and no question c an g o unanswered . In the nam e o f

practicality, parsimony is the name of the game; the less characteristics,

attributes and scores you can get away with, without sacrificing the predictive

capability of the model, the better. In principle, characteristics and attributes

are d ete rmined solely on the b asis of their pred ic tive c apac ity. As such, save for

legal restrictions such as those mentioned in the previous section, anything

goes: regardless of whether or not a characteristic conforms to intuition or

conventional wisdom, If it aids prediction it is included, and discarded

otherwise.

In its simplest form, the typical scoring sequence of an application, is to

score each characteristic with the points of the pertinent attribute, and add

over all the characteristics to obtain a total score. Now the third element

c om es into p lay: The to ta l sc ore is c om pared to the threshold o r c ut-off value

and, if it exceeds the threshold, the loan is granted; it is rejected otherwise.

3.2. The Scorec ard.

The sc oreca rd is the orga nizer of the mec hanica l proced ure of c red it

scoring described in the preceding section, and is best explained with an

example. Consider a simple scoring exercise in a small regional bank for a loan

to a small local business, and assume that only six characteristics are required

to asses the risk of app lic ants in this c red it ca tegory; namely: The Age o f the

Applicant, Years of the Business, Liquidity Ratio, Debt to Net Worth, Previous

Experience with the Bank, and Maximum Delinquency Ever from the Public

Reg istry. Tab le 2.1 shows how c ha rac te ristics, attributes and points are

orga nized in the correspond ing Score Card . Notice tha t charac teristics 3 & 5are directly related with the capacity to pay, 2 & 4 directly address the

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willingness to pay, and the first two are behavioral and indirect indicators of

c apa c ity/ willingness, as d icta ted by experienc e. The ta b le shows the a ttributes

that correspond to each characteristic and their associated points.

The sc oring p roc ess is straight forwa rd . For example, consider a 43 yearold entrepreneur whos been in business for 8 years. His financials show a

liquidity ratio of 62% and a Debt to Net worth of 37%. Finally, His previous

experience with the bank shows no past due payments over 30 days and the

information from the public registry confirms this, showing maximum

delinquency ever to be thirty days. Referring to the scorecard presented in

ta b le 3.1, this app licants score is 12.5 :

SCORE = 2.0 + 1.5 + 1.0 + 3.5 + 2.0 + 2.5 = 12.5

Notic e tha t in the last row o f ea c h panel is a line lab eled NEUTRAL , which is

the c ut off referenc e for ea c h cha rac teristic; i.e. 1.5 for Age of Ap p lica nt , 1.0

for Years of Business and so on . The Neut ral att ribute serves several purpo ses;

first and foremost, the sum of their points (1.5 + 1.0 + 2.0 + 1.0 + 2.0 + 3.0 = 10.5) is

the o verall accept/reject threshold. Since h is sc ore (12.5) exceed s the thresho ld

(10.5), our 43 year old entrepreneur will be granted his loan. Notice that this is

the case, despite the fact that his points in two of the characteristics were

below the neutral value; namely (1.0 < 2.0) in Liquidity Ratio and (2.5 < 3.0) in

Ma ximum Delinquenc y Ever. Thus, the sec ond rea son tha t the Neut ra l

attribute is important is that it allows the analyst who oversees the automatic

scoring process, to detect where the weaknesses of the applicant lie, and

override the systems assessment (one way or the other) if warranted 19.

Ob viously, this only happens when the score s p roximity to the threshold c asts a

doubt on the verdict from the mechanical procedure. Although in most

insta nc es of c onsume r lend ing the rule is app lied b lind ly, in the case o f SMEs,

this grey area is in the order of 10% around the overall accept/reject

threshold. In ma ny cases, there a re even a utom at ic overrides p rog ram me d into

the system; in other words, if a score falls in the grey area, another set of tests

are performed automatically which either narrow down the grey area or

ultimately decide the issue mechanically. In countries like the U.K.20 lenders areencouraged to give rejected applicants the right to appeal, anticipating

mistakes such as typographical errors or incorrectly captured data.

Furthermore, a rejected applicant may consider that there is relevant

information outside that contemplated in the application form, and therefore

merits a persona l revision tha t c an help his c ase a nd c hange the dec ision.

19 Normally, in the best case he would have to have authorization from his supervisor. If theap plication is for a relatively large loan, he wo uld have to g o through a c om mittee.

20 The U.K. Guid e to Cred it Sc oring (2000).

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Another important property of the Neutral attribute is that it honors its

name; that is, scoring a characteristic with the Neutral attributes points, does

not incline the b a lanc e one w ay or the othe r. This is bec ause in this c ase, the

points a re p ic ked so tha t they a re p red iction neutral; neither a id ing o r hurting

the app lica nts c ause, when a c harac te ristic is scored so. This is useful when forsom e reason o r othe r, the answe r provided by the a pp licant is amb iguo us. (e.g.

marking more than one attribute etc.), the default choice is the Neutral

attribute.

1. AGE OF APPLICANT(Owner)

2. YEARS OF THE BUSINESS(Company)

ATTRIBUTES POINTS ATTRIBUTES POINTS

Less than 30 years 0.0 Less than 2 years 0.030 years 34 years 0.5 2 years 3 years 11 months 0.535 years 39 years 1.5 4 years 4 years 11 months 1.040 years 49 years 2.0 5 years 9 years 11 months 1.550 years 59 years 2.5 10 years or more 2.560 years or more 2.0 No Answer 0.0No Answer 0.0 NEUTRAL 1.0

NEUTRAL 1.5

3. LIQUIDITY RATIO(Company)

4. PREVIOUS EXPERIENCE WITH THE BANK(Company)


Less than .25 0.0 New client, Less than 6 months 1.0

.25 - .74 1.0 More than 30 past due 0.0

.75 - .99 1.5 No past due payments over 30 days 2.01.00 1.24 2.0 No past due payments 2.01.25 1.74 3.0 No enquiries 1.01.75 or more 3.5 NEUTRAL 1.0

Cannot be calculated 0.0NEUTRAL 2.0

5. DEBT / NET WORTH(Company)

6. MAXIMUM DELINQUENCY EVER(Company and/or Owner)

(Public Registry)


Less than .25 4.0 No investigation (Q) 3.0.25 - .49 3.5 No record (R) 3.0.50 - .74 3.0 No Trade Lines (N) 2.5.75 - .99 2.5 No Usable Trade Line (I) 2.51.00 1.24 2.0 Charge Off 0.51.25 1.74 1.5 120 + Days Delinquent (1) 1.01.75 2.99 1.0 90 Days Delinquent (2) 1.53.00 or more 0.5 60 Days Delinquent (3) 2.0Cannot be calculated 0.5 30 Days Delinquent (4) 2.5NEUTRAL 2.0 Unknown Delinquency (5) 3.0

Current and Never Delinquent (7) 4.5Too new to Rate(8) 3.0All other (9) 3.0

NEUTRAL 3.0

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Table 3.1: Simple Sc orec ard Example.21

21 This is a sample of six c ha rac teristics from a n ac tua l SME sc orec ard used in a Mexican Bank.The p oints have be en c hang ed in com plianc e with the ba nks req uest.

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As to the sources of information, the example clearly shows how the

data in the form filled by the applicant is complemented with data from the

banks own records, and external sources; in this example, the Public Registry.

But there may be others. Information such as regional, economic and financialindicators for the industry where the applicant performs his activity, may have

predictive capacity as to the applicants expected performance, and should

be included in the sc orec ard.

3.3. Prac tica l co nside rations in building scorec ards.

Befo re g et ting into spec ific estima tion method s, som e p relimina ries a re in

order about sample design, the definitions of good and bad applicants

and c ut-off va lues. This is bec ause the a va ilab ility of da ta as we ll as the

decisions on the classification criteria of good and bad, and the type of

accept/reject rules dictated by business objectives and culture, will condition

the e stima tion m ethod ology c hosen a nd its rea c h.

3.3.1. Sam ple de sign a nd Rejec t inference.

As regards the sample, besides the obvious fact that it should be

random , rep resenta tive of individua ls tha t a re likely to app ly for a loa n the so

called through the door population and enough to guarantee statistical

significance, it is important to point out that there is an inherent bias in all creditsc oring metho do log ies; name ly, that the d ata on g ood and ba d risks be longs

mo stly to deb tors who se a pplic a tions we re a c c ep ted . This means tha t only the

probability of an accepted debtor going bad can be estimated, but the

inferred proba bility that a rejected ap plicant wa s in fac t g ood, is biased .

The stud y of rejec ts22 is only justified to the degree that it somehow

improves the accept/reject criteria; either because it distinguishes better

between good and bad, and/or is more in tune with the lenders business

ob jec tives; for example, by improving p rofitab ility. The only wa y to study thebehavior of rejects is to buy data; i.e. carry out an experiment where

applicants that would be rejected are in fact accepted. Because of the

implied costs, the studies conducted for the sake of acquiring information on

rejects are partial, in the sense that lenders are only willing to carry out such

experime nts on as small a samp le of rejec ts as possible. The tec hniques va ry

depending on how fast one wishes to acquire data on rejects and how much

the orga niza tion is willing to spend . Thus, if spee d is of the essenc e , the best

method is to accept all applications for a limited time, until a statistically

22 The inclusion of rejec ts in the samp le wa s first p rop osed by Reic hert, Cho and Wagner(1983).

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representative sample of rejects is obtained. If the decision is to reduce costs

and spread them over time, what is generally done is to accept a random

numb er of rejec ts (e.g. eve ry tenth rejec t) until a go od samp le is ob ta ined . This

last scheme can be mixed with a scheme where all applicants with scores not

too far below the rejection threshold (say 5 to 10%) are a c c ep ted , and be lowthat, ac cep t a random number.23

Apart from this, the determination of sample size, and the proportion of

goods and bads that should be put in the sample, are estimated

according to standard statistical techniques. It is also standard practice to set

aside a control sample containing good and bad loans on which to back

test the model. Although the more the merrier, one must strike a balance

between available data, the size of the sample and its relevance in terms of

how w ell the da ta represents the c urrent market situat ion. This me ans tha t

information should be as recent as possible -12 to 24 months old - and that

there should be enough data to ensure statistical significance of the results.

According to Lewis (1992) sample sizes of 3000 where the proportion of goods

to bads is a round 50-50 is a good p lac e to sta rt; Sidd iqi (2006) says tha t a

samp le o f 2000 ea ch of go od s and ba ds is adeq uate. If rejec t study is desired ,

then an additional 2000 rejects should be considered in the sample. An

imp ortant p rac tica l conside ra tion is tha t typ ic a lly, the pop ulat ion is strongly one

sided sinc e the go od s outnum ber the b ads in ra tios of a t least twenty to o ne, so

that ac tually having sam ples with equa l numbers of g ood s and ba ds, may b e

difficult to obtain. In this case put in all the bads you can get, and enoughgoods so as to minimize statistical error.

Other issues on sample selection have to do with things like

seg menta tion, augm enta tion, ad justments and so on. The nee d fo r

segmentation arises from the fact that applicants in different regions, income

categories or lines of business, may behave differently to the same

c harac teristics and a ttributes, so tha t the we ights which c lassify them into go od

or ba d a re d ifferent. Augmenta tion has to d o w ith the fea sib ility and de sirability

of augmenting the sample as new data is received. Adjustment has to dowith over sampling when there is apriori knowledge on the goods/bads ratio

of the through the door population, and the differences with the available

data 24.

23 See for exam p le Thom as et. a l. Ch. 8. and Sidd iqi Ch. 6.24 There are many other technical considerations that must be addressed which cannot be

disc ussed here d ue to limita tions of spa c e. The read er who w ishes to e xpa nd o n the subjec t isenc ourag ed to c onsult the spe c ialized bib liog raphy e.g. Thom as et. al. Ch. 8 and Sidd iqi Ch.6.

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3.3.2. The definition o f ba d .

Notice that the selection of the sample requires in all cases that the

good debtors can be distinguished from the bad which must be defined25

.Again, pragmatism, in the sense that the classification rule resulting from the

definition is easy to interpret and the performance of the accounts can be

trac ked over time, is essent ial. The d efinition m ust a lso c onform to p rod uc t

c harac teristics and business c ulture and ob jec tives, so tha t d efinitions can

vary widely from one creditor to another. For example, whereas a very

common rule is to classify any debtor delinquent in three consecutive

payments as bad, there are creditors that favor distinguishing between

different levels of delinquency as they are related to pricing and profitability.

For example, an account that is consistently thirty days overdue, but never rolls

over to two or three, can be very profitable if properly priced. Other definitions

c an a lso ta ke into a c c ount the d olla r va lue o f losses in case o f delinque nc y.

Notice that the definition adopted will have a direct impact on the

sample selection and size, for the reasons previously explained. In general, the

tighter the definition (e.g . write-off or 120 days delinquent ), the ha rder it

will be to get the required number of bad accounts for the sample, whereas

the op posite is true in looser definitions (e.g . 30 da ys in arrea rs ). This points

out the trade off between the precision in the definition of bad, and the data

c ount required for a g ood sta tistica l fit, and lea ds to the next top ic .

3.3.3. The c ut-o ff value .

Determining the accept/reject threshold is basically a balancing act

between data availability which is a structural constraint, and the business

priorities of the lender in terms of number of accounts that leads to the

ac hievement o f the o b jec tives of the firm. Thus, if lowering the c ut-off means

inc rea sing the numb er of a c c ounts and mo re p rofits in sp ite of highe r costs, and

profits a re the p rime o b jec tive, it should be done . Howeve r, there are ca seswhere profits dont even enter the equation. For example, the objective may

be to simp ly red uc e losses to a c erta in proportion of a sset va lue; or increa se the

approval rate to gain market share while maintaining costs at a certain level;

define a cut-off that improves the overall turn around and reduce

organizationalcosts or simply maximize the predictive power of the model. All

of these c riteria are c urrently used to dete rmine the threshold.

25By co nvention, go od is everything tha t isnt ba d .

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Cut-off parameters are obtained directly from the statistical estimation

procedure used to fit the model to the sample data, and minimally, should

correspond to expected accept and reject rates in line with company

objectives. A rigorous analysis however, demands the examination of other

metrics where the impact of the accept/reject rates are associated to thecorresponding expected ratio of goods to bads of the accepted accounts,

and the impact of the rule on profitability, revenues and costs, should be

c arefully a ssessed .

The simp lest c ut-o ff rule w as illustrated in sec tion 3.2, and it is c a lled a

hard low side cut-off because it leaves no room for overriding the

mec hanica l ac cep t/ reject d ec ision. As mentioned in that sec tion, bec ause we

are dealing with uncertainty, the most common rule is to define a gray area

around the hard c ut-off of 5 to 10% where a pp lic a tions whose sc ores lie in this

interval, are referred to autom at ic ove rride tests and / or ma nual sc rutiny for the

final dec ision. Som e orga niza tions use mo re c om plex c ut-off rules, assoc iating

scores to different credit limits. For example, suppose that Tmin=T0 ,, T1, T2,

.Tn=Tmaxare the finite numb er n of thresholds or cut-offs defined by a lend er

to determine credit limits Li dep end ing on a pp lica nts sc ores. Then , the rule

c ould go along the follow ing lines26:

niTScoreifL

TTifL

Tif

LimitCredit iii ,...2,1;Score

Score0

maxmax

1

min

=

>

Márquez , Javier - An Introduction to credit scoring for small and medium size enterprises

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Transcript of Márquez , Javier - An Introduction to credit scoring for small and medium size enterprises