Micro-Modelling Approaches for Credit Rating and Corporate Survival
Abstract
The essential issue of this book is the term credit, either in the context of credit markets, credit risk or credit rating. Credit markets’ existence is associated with credit risk, which refers to the risk of an economic loss from the failure of a counterparty to meet its contractual obligations. Due to credit risk, suppliers of credit need to assess the creditworthiness of prospective borrowers. Although modern approaches to credit risk analysis have been developed in recent decades, examining borrowers’ ability to repay their funds is one of the oldest lending activities. The main goal of this monograph is to apply and verify certain methods of credit risk modelling to real data from selected CEE countries. For the main purpose of this work, a micro approach is used to measure credit risk based on monitoring basic indicators and allowing creditors to take the necessary actions in time. The book aims at two partial financial and methodological objectives related to credit risk modelling in this context. Both of them are interconnected, and they complement each other throughout the book. In terms of financial application, this book’s principal objective is to analyse credit risk based on real data, assess its main factors, explore mutual relations, and draw conclusions related to risk assessment and market behaviour. The application is focused on two approaches of individual credit risk assessment within the areas of credit rating and corporate survival. The methodological purpose is the application and verification of rating and bankruptcy models. Rating models estimated using conventional approaches such as discriminant analysis or logistic regression are supplemented by an alternative survival analysis approach to determine the probability of rating downgrade over time. Survival analysis is subsequently used in the following empirical studies on corporate bankruptcy. We will investigate the relationship between the rating and corporate bankruptcy rates and estimate the rating assessment depending on the used model, input variables and the company's age. This book is intended for everyone interested in credit risk, particularly rating and corporate survival modelling, mainly for academia and students at all levels of study. This monograph aims to provide complex information on credit risk fundamentals, current trends and rating systems’ principles. However, the primary purpose is the practical application and estimating models using real corporate data. Thus, we can determine the main factors of rating assessment and corporate survival and demonstrate how these models can be developed through different statistical methods. The text is structured into three central parts: The theoretical background on credit risk and the credit rating industry, a description of econometric approaches used in the applications, and empirical studies on credit rating and corporate bankruptcy modelling. If the reader is particularly interested in estimating models and their comparison and interpretation, then it is suggested that they go directly to the practical application. However, reading the book step by step is recommended to understand the essence and main principles and use them in the application.
Full text
Se ies on Ad anced Economic Issues Facul y o Economics, VŠB-TUO
www.ek . sb.cz/saei [email p o ec ed]
ZDE ZAČÍNÁME POČÍTAT ČÍSLA STRÁNEK, ŘÍMSKÝM AŽ PO KONEC OBSAHU
PRÁZDNÁ STRÁNKA
Se ies on Ad anced Economic Issues
Facul y o Economics, VŠB-TUO
Ma ina No o ná
MICRO-MODELLING APPROACHES FOR
CREDIT RATING AND CORPORATE
SURVIVAL
Os a a, 2024
Ma ina No o ná
Depa men o Finance
Facul y o Economics
VŠB-Technical Uni e si y Os a a
17. Lis opadu2172/15
708 00 Os a a-Po uba, CZ
[email p o ec ed]
Re iews
Jiří Wi zany, P ague Uni e si y o Economics and Business
Lumí Kulhánek, VSB – Technical Uni e si y o Os a a
INFORMA
This publica ion is he ou pu o esea ch ac i i y by he esea ch eam o he p ojec No. SP
2019/132.
The ex should be ci ed as ollows: No o ná, M. (2024). Mic o-Modelling App oaches
o C edi Ra ing and Co po a e Su i al, SAEI, ol. 69. Os a a: VSB-TUO.
© VŠB-TUO 2024
P in ed in VSB-TUO
Co e design by EkF VSB-TUO
This wo k is licensed unde C ea i e Commons U eď e pů od 4.0 Meziná odní.
ISBN 978-80-248-4728-3 (p in )
ISBN 978-80-248-4729-0 (on-line)
DOI 10.31490/9788024847290
P e ace
The essen ial issue o his book is he e m c edi , ei he in he con ex o c edi
ma ke s, c edi isk o c edi a ing. C edi ma ke s’ exis ence is associa ed wi h
c edi isk, which e e s o he isk o an economic loss om he ailu e o a
coun e pa y o mee i s con ac ual obliga ions. Due o c edi isk, supplie s o
c edi need o assess he c edi wo hiness o p ospec i e bo owe s. Al hough
mode n app oaches o c edi isk analysis ha e been de eloped in ecen decades,
examining bo owe s’ abili y o epay hei unds is one o he oldes lending
ac i i ies.
The main goal o his monog aph is o apply and e i y ce ain me hods o
c edi isk modelling o eal da a om selec ed CEE coun ies. Fo he main
pu pose o his wo k, a mic o app oach is used o measu e c edi isk based on
moni o ing basic indica o s and allowing c edi o s o ake he necessa y ac ions in
ime. The book aims a wo pa ial inancial and me hodological objec i es ela ed
o c edi isk modelling in his con ex . Bo h o hem a e in e connec ed, and hey
complemen each o he h oughou he book.
In e ms o inancial applica ion, his book’s p incipal objec i e is o analyse
c edi isk based on eal da a, assess i s main ac o s, explo e mu ual ela ions, and
d aw conclusions ela ed o isk assessmen and ma ke beha iou . The applica ion
is ocused on wo app oaches o indi idual c edi isk assessmen wi hin he a eas
o c edi a ing and co po a e su i al.
The me hodological pu pose is he applica ion and e i ica ion o a ing and
bank up cy models. Ra ing models es ima ed using con en ional app oaches such
as disc iminan analysis o logis ic eg ession a e supplemen ed by an al e na i e
su i al analysis app oach o de e mine he p obabili y o a ing downg ade o e
ime. Su i al analysis is subsequen ly used in he ollowing empi ical s udies on
co po a e bank up cy. We will in es iga e he ela ionship be ween he a ing and
co po a e bank up cy a es and es ima e he a ing assessmen depending on he
used model, inpu a iables and he company's age.
This book is in ended o e e yone in e es ed in c edi isk, pa icula ly a ing
and co po a e su i al modelling, mainly o academia and s uden s a all le els
o s udy. This monog aph aims o p o ide complex in o ma ion on c edi isk
undamen als, cu en ends and a ing sys ems’ p inciples. Howe e , he p ima y
pu pose is he p ac ical applica ion and es ima ing models using eal co po a e
da a. Thus, we can de e mine he main ac o s o a ing assessmen and co po a e
VI P e ace
su i al and demons a e how hese models can be de eloped h ough di e en
s a is ical me hods.
The ex is s uc u ed in o h ee cen al pa s: The heo e ical backg ound on
c edi isk and he c edi a ing indus y, a desc ip ion o econome ic app oaches
used in he applica ions, and empi ical s udies on c edi a ing and co po a e
bank up cy modelling. I he eade is pa icula ly in e es ed in es ima ing models
and hei compa ison and in e p e a ion, hen i is sugges ed ha hey go di ec ly
o he p ac ical applica ion. Howe e , eading he book s ep by s ep is
ecommended o unde s and he essence and main p inciples and use hem in he
applica ion.
Ma ina No o ná, Os a a, Ap il 2024
B ie Con en s
P e ace ..................................................................................................... V
B ie Con en s ...................................................................................... VII
Con en s .................................................................................................. IX
Lis o Abb e ia ions ............................................................................. XI
Chap e 1 In oduc ion ........................................................................... 1
Chap e 2 The Essen ials o C edi Ra ing Assessmen ....................... 5
2.1 Role o C edi Ma ke s ................................................................. 6
2.2 Classi ica ion o C edi Risk ......................................................... 7
2.3 Fac o s o C edi Risk ................................................................. 11
2.4 C edi Risk Analysis.................................................................... 14
2.5 Obligo -Le el C edi Risk .......................................................... 18
2.6 Issue-Speci ic C edi Risk ........................................................... 24
2.7 Fundamen als o Ra ing Assessmen ......................................... 32
2.8 Desc ip ion o C edi Ra ing P ocess ........................................ 37
2.9 Cu en Issues in Ra ing Indus y ............................................. 41
2.10 Chap e Summa y ....................................................................... 46
Chap e 3 App oaches o C edi Ra ing and Co po a e Bank up cy
Modelling ..................................................................................... 47
3.1 In oduc ion and Resea ch Backg ound ................................... 47
3.2 Disc iminan Analysis ................................................................. 54
3.3 Logis ic Reg ession Analysis ...................................................... 62
3.4 Su i al Analysis ......................................................................... 74
3.5 Chap e Summa y ....................................................................... 90
VIII B ie Con en s
Chap e 4 The E ec o Selec ed Fac o s on Ra ing and i s Dynamics
....................................................................................................... 93
4.1 Co po a e C edi Ra ing Assessmen Models ........................... 94
4.2 Modelling o Ra ing Downg ades Based on Mul iple Failu e-
Time Da a ................................................................................... 109
4.3 Chap e Summa y ..................................................................... 118
Chap e 5 Rela ionship Be ween Ra ing and Co po a e Bank up cy
Ra es ........................................................................................... 121
5.1 Associa ion Be ween Ra ing and Co po a e De aul s ............ 122
5.2 Modelling o Co po a e Su i al Based on Kaplan-Meie
Es ima es .................................................................................... 126
5.3 The Rela ionship Be ween Bank up cy Ra es and Ra ing
Assessmen ................................................................................. 133
5.4 Chap e Summa y ..................................................................... 139
Chap e 6 Su i al Models wi h Ca ego ical Va iables .................. 141
6.1 Applica ion o he Cox P opo ional Haza ds Model ............ 141
6.2 Pa ame ic Models .................................................................... 147
6.3 Chap e Summa y ..................................................................... 152
Chap e 7 The Use o Financial Pe o mance Indica o s in Su i al
Analysis ...................................................................................... 155
7.1 Es ima ion o Su i al Models ................................................. 155
7.2 Cumula i e Bank up cy Ra es and Ra ings o Speci ic
Pa ame e s ................................................................................. 167
7.3 Chap e Summa y ..................................................................... 173
Chap e 8 Conclusion .......................................................................... 177
Appendix .............................................................................................. 181
Lis o Figu es ...................................................................................... 205
Lis o Tables ........................................................................................ 207
Re e ences ............................................................................................ 211
Index ..................................................................................................... 223
In oduc ion 3
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
is essen ial o unde s and how a ing agencies p o ide a ing assessmen s. Thus,
he main p inciples o a ing sys ems and he c edi a ing p ocess a e desc ibed in
he second chap e .
Va ious egula ions s imula e he o mal quan i ica ion o c edi isk and he
use o c edi po olio models in inancial ins i u ions. Thus, many issues mus be
conside ed when selec ing he app op ia e app oach o c edi isk modelling. Fo
example, suppose he c edi isk analys e alua es c edi isk as a disc e e e en
and concen a es me ely on a po en ial de aul e en . In ha case, he undamen al-
based models p o ide a sui able way o assessing c edi isk. On he o he hand,
s uc u al and di e en quan i a i e app oaches should be applied i he modelle
analyses he dynamics o he deb alue and he associa ed c edi sp ead o e he
whole ime in e al o ma u i y. Th oughou his book, and especially he
applica ion pa , c edi isk is conside ed a disc e e e en , such as a po en ial
de aul o bank up cy e en ep esen ed by a ing g ade o he p obabili y o
su i al. In such cases, he main ask is o assess he c edi isk o a pa icula issue
o issue , ypically h ough c edi isk models de eloped o disc imina e be ween
lowe and highe c edi isk. Such models a e usually based on he s a is ical
analysis o pas cha ac e is ics o deb o s o issue s, mainly quan i a i e a iables
such as co po a e inancial a ios. Since hese models a e ocused on e alua ing
indi idual subjec s, mos ly based on da a om inancial s a emen s, hey a e also
e e ed o as mic o models o undamen al-based models. In he applica ion pa ,
a en ion is paid o he p ocedu e and de elopmen o such models and hei use
and in e p e a ion.
The econome ic app oaches selec ed based on he ecen s udies and used in
he applica ion pa a e desc ibed in Chap e 3. Fi s ly, we p o ide some esea ch
e iew, a summa y o app oaches used in he ch onological con ex , and he main
indings o selec ed s udies in his sec ion. Following, we will ind he possible
ex ension o he cu en esea ch and emphasize he con ibu ion o his wo k in
he con ex o he applica ion pa , which is ocused on CEE coun ies and he use
o su i al analysis. Nex , he selec ed me hods used in he applica ion pa a e
desc ibed. Fi s , disc iminan and logis ic eg ession analyses a e desc ibed and
used in Chap e 4 o es ima e a ing models. Then, he p inciples o su i al
analysis a e explained, and selec ed su i al models a e desc ibed, ocusing on he
Kaplan-Meie es ima es, he Cox p opo ional haza ds and he Weibull model.
These app oaches a e hen used in Chap e s 5, 6 and 7.
The i s applica ion s udy in Chap e 4 is ocused on c edi a ing modelling.
Fi s ly, selec ed me hods a e used o es ima e a ing models based on da a om
CEE coun ies. Then, based on he main indings, we de e mine he main
accoun ing-based a iables o he c edi a ing o non- inancial companies om
selec ed CEE coun ies ep esen ing economies wi h a sho e his o y and adi ion
o capi al ma ke s. The analysis is based on a co po a e a ing e alua ion known
as MORE Ra ing. This s udy's me hodological objec i e is o compa e models
de eloped by di e en app oaches, such as disc iminan and logis ic eg ession
analysis and sugges a mo e sui able me hod o a ing modelling. Finally, his pa
4 Chap e 1
2024 Ma ina No o ná
is ollowed by he modelling o a ing downg ade employing su i al analysis
me hods. The e o e, we can compa e he main indings and iden i y he key
in luen ial a iables on a ing assessmen and he haza d o a ing de e io a ion
based on wo di e en app oaches.
The aim o Chap e 5 is o assess he ela ionship be ween he a ing and
co po a e bank up cy a es. This s udy is based exclusi ely on da a om Czech
companies and hus complemen s he main indings om CEE coun ies. In his
sec ion, we compa e published de aul a es wi h es ima ed bank up cy a es.
Based on he compa ison, we p opose he p ocedu e o a ing es ima ion using
bank up cy a es and a e age sp eads. Nex , he Cox p opo ional haza d and he
Weibull model a e used in Chap e 6 o assess he impac o indus y, legal o m
and company size on he su i al p obabili y, ollowed by e alua ing he in luence
o inancial a iables on he su i al p obabili y in Chap e 7. Bo h s udies
iden i y he e ec o selec ed a iables on co po a e su i al, whe he ca ego ical
o quan i a i e. In addi ion, cumula i e bank up cy a es a e es ima ed using he
models and con e ed o a a ing assessmen . A signi ican ad an age o his
app oach is using he ime a iable in su i al models, which allows us o
de e mine he a ing no only depending on inancial pe o mance o o he
cha ac e is ics bu also on he company's age. Thus, his p ocedu e ep esen s a
dynamic app oach o modelling and p edic ing indi idual a ings.
Finally, he main indings and o e all sugges ions a e summa ized in he
conclusion in Chap e 8.
This book used wo s a is ical so wa e packages o da a analysis: IBM SPSS
So wa e and S a a s a is ics. All models a e es ima ed based on unique co po a e
da a om he MORE Ra ing and co po a e da a on Czech companies om he
Magnusweb da abase.
Chap e 2
The Essen ials o C edi Ra ing
Assessmen
The c ucial issue in his monog aph is he e m c edi , which e e s o c edi
ma ke s, c edi isk, o c edi a ing. This chap e p o ides an in oduc ion o c edi
and c edi ma ke s c i ical ole; howe e , he p ima y a en ion will be paid o he
explana ion o c edi isk, i s measu emen and analysis.
This monog aph is ocused on wo a eas o applica ion: c edi a ing and
co po a e su i al modelling. Bo h opics a e associa ed wi h c edi isk; howe e ,
he assessmen uses di e en me hods and da a and is conduc ed om di e en
pe spec i es. Ne e heless, bo h app oaches a e used o ob ain mo e in o ma ion
abou co po a e c edi isk and a e no mu ually exclusi e. On he con a y, i is
app op ia e o use bo h ways o analyse he c edi isk and i s dynamic in ce ain
cases.
This sec ion aims o p o ide an in oduc ion and a li e a u e e iew o c edi
a ing and co po a e su i al modelling. Fi s , he emphasis will be on he pu pose
and goals o modelling, some ecen esea ch, and a summa y o he app oaches
used. Then, we g adually ocus on he heo e ical backg ound and he cu en s a e
o c edi a ing modelling. Finally, a en ion will be paid o he o e iew o he
co po a e su i al p oblem.
The s uc u e o he monog aph’s emaining pa co esponds wi h he
pa icula objec i es o his wo k, as hey a e men ioned in he in oduc ion. Fi s ,
a li e a u e e iew will p o ide he p inciples and pu pose o a ing and su i al
models (Chap e 2). Then, he s a is ical me hods used in he applica ion will be
desc ibed (Chap e 3). The main pa is he applica ion, in which he es ima ed
models, p ocedu es and main esul s will be p esen ed (Chap e s 4–7). Finally, he
main indings o he a ing and bank up cy analysis will be compa ed and used o
d aw his monog aph's main conclusions and ecommenda ions.
6 Chap e 2
2024 Ma ina No o ná
2.1 Role o C edi Ma ke s
C edi ma ke s a e ma ke s o c edi ha can be desc ibed as ansac ions be ween
he c edi o ( he lende ) and he deb o ( he bo owe ). The c edi o supplies
money o non-mone a y asse s such as goods, se ices o secu i ies o he deb o
in e u n o a p omise o u u e paymen , which ypically includes he amoun o
in e es (Joseph, 2013). The c edi o s gene ally ha e no igh o owne ship, and
he in e es ep esen s compensa ion o unde aken isk.
The economic ole o c edi lies in he ac ha bo owe s wi h insu icien
esou ces can ge unds om lende s, usually h ough inancial in e media ies.
Thus, when used e ec i ely, c edi enables he economic g ow h o bo owe s,
inc easing household consump ion and business in es men . C edi is used by
businesses, indi iduals, and go e nmen s, and ypically, i leads o economic
g ow h (Joseph, 2013). In inancial ma ke s, c edi is supplied by inancial
ins i u ions such as comme cial banks in loans. I can be p o ided by in es o s
who pu chase bonds issued by de ici uni s. Deb holde s a e known as c edi o s
o lende s, and hey ypically g an loans o hold bonds. Con e sely, he use o
c edi by de ici uni s o bo owe s can be conside ed a p ima y sou ce o deb
inancing. While bonds a e ypically aded, loans a e no assumed o be adable
in deb ma ke s (De Se igny and Renaul , 2004).
The p opo ion o loans and bonds on he o al amoun o deb inancing can
di e in a ious coun ies, depending on adi ion, legal en i onmen (e.g.,
p ope y igh s sys em), mac oeconomic condi ions o he de elopmen o capi al
ma ke s. The p opo ion o hese wo ways o inancing in he Czech Republic can
be seen in Figu e 2-1. In his g aph, he o al loans include sho - e m (less han
one yea ), medium- e m (1 – 5 yea s) and long- e m loans (mo e han i e yea s)
o clien s p o ided in CZK, and o al bonds consis o all bonds issued in CZK,
including go e nmen and co po a e bonds. As can be seen, he amoun o loans
exceeds he numbe o bonds du ing he whole pe iod. F om 2012 o 2019, we can
see ela i ely s able de elopmen , wi h he sha e o loans being a ound 56% on
o al deb inancing and he p opo ion o bonds mo ing abou 44%. Howe e ,
since 2019, we ha e seen ha he pe cen age sha e o bonds has isen, mainly due
o inc eased go e nmen bond issuance du ing he COVID-19 pandemic.
While he a io o bo h ypes o inancing emains ela i ely s able, excep in
he pos -pandemic pe iod, annual changes a e somewha ola ile. Bond issuance
ose by 21.2% om 2011 o 2012, mainly due o an inc ease in co po a e bonds
by 40.4%. The dec ease in he bonds issued in 2017 is p ima ily due o he decline
in go e nmen bond issuance, wi h he opposi e end since 2019 (see Figu e 2-2).
The Essen ials o C edi Ra ing Assessmen 7
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Figu e 2–1 P opo ion o loans and bonds in he Czech Republic (end o he yea )
Sou ce: Czech Na ional Bank (ARAD, 28. 9. 2022), au ho
In mos ad anced economies, banking in e media ion has educed o e he pas
yea s due o he inc easing b ead h o c edi ma ke s, and he end owa d
ma ke -based inance seems o be e y s ong (De Se igny and Renaul , 2004).
Howe e , banks as in e media ies s ill ul il a c ucial ole in h ee p ima y
unc ions: liquidi y, isk and in o ma ion in e media ion.
Figu e 2–2 Annual change o loans and bond issues in he Czech Republic (in %)
Sou ce: Czech Na ional Bank (28. 9. 2022), Czech S a is ical O ice (28. 9. 2022), au ho
2.2 Classi ica ion o C edi Risk
Risk can gene ally be de ined as he ola ili y o e u ns leading o unexpec ed
losses, as de ined by C ouhy e al. (2014). Se e al isk ac o s can in luence his
ola ili y o e u ns, including:
• Ma ke isk ha changes in ma ke p ices and a es will nega i ely a ec
a secu i y o po olio alue.
• C edi isk o an economic loss om a coun e pa y's ailu e o ul il hei
con ac ual obliga ions.
0%
20%
40%
60%
80%
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
Bonds Loans
-5%
0%
5%
10%
15%
20%
25%
30%
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
Bond Issues Loans o clien s GDP
8 Chap e 2
2024 Ma ina No o ná
• Liquidi y isk includes he isk ha a i m canno aise he necessa y cash
( unding isk) o a ansac ion will no be execu ed ( ading isk).
• Ope a ional isk e e s o po en ial losses om ope a ional ailu es
(managemen , con ols, aud, human ac o s). I is closely ela ed o legal
and egula o y isk o epu a ion isk.
• Business isk e e s o unce ain y abou he demand o p oduc s, p ices,
and p oduc ion cos s.
• S a egic isk is he isk o signi ican in es men s wi h high unce ain y
abou success and p o i abili y.
The exis ence o c edi and c edi ma ke s is associa ed wi h c edi isk. In he
ex , c edi isk e e s o he isk o economic loss om a coun e pa y's ailu e o
mee i s con ac ual obliga ions, such as in e es paymen s o p incipal epaymen .
Howe e , c edi isk in ol es he possibili y o non-paymen on a u u e
commi men and du ing a ansac ion. This ype o isk is called se lemen isk. I
a ises om exchanging p incipals in di e en cu encies o paymen s in di e en
ime zones du ing a sho window, ypically a day. T adi ionally, c edi isk is
conside ed a p e-se lemen isk, which a ises du ing he obliga ion’s li e (Jo ion,
2011). O e all, c edi isk can be decomposed in o he ollowing ou ca ego ies:
• De aul isk e e s o he deb o ’s capaci y o e usal o mee deb
obliga ions such as in e es o p incipal paymen s by mo e han a
easonable elie pe iod om he due da e (usually 60 days in he banking
indus y).
• Bank up cy isk can be conside ed he isk o aking o e a de aul ing
bo owe ’s asse s o coun e pa y. In his case, deb holde s a e aking o e
he con ol o he company om he sha eholde s.
• Downg ade isk is he isk ha he c edi wo hiness o he bo owe o
coun e pa y migh de e io a e in he u u e when a signi ican de e io a ion
can be seen as he de aul .
• Se lemen isk e e s o he isk due o he exchange o cash lows when
a ansac ion is se led. I can be caused by coun e pa y de aul , liquidi y
cons ain s, o ope a ional issues (C ouhy e al., 2014).
Due o all ypes o c edi isk, supplie s mus assess hei c edi wo hiness
be o e g an ing c edi o p ospec i e bo owe s (Joseph, 2013). In addi ion, since
adi ional banks ypically hold he loan un il ma u i y, hey analyze he iskiness
o he bo owe s’ ac i i ies bo h be o e and a e he loan is made because hey
ace he isk ha he bo owe ’s c edi quali y could de e io a e du ing he li e o
he loan.
Some lende s, such as banks, use inancial inno a ions in a ious s a egies o
educe c edi isk and inc ease e u ns. These inno a ions p ima ily in ol e
secu i iza ion, syndica ion o loans, p op ie a y ading and in es men in non-
adi ional asse s, o inc eased use o inancial de i a i es (Saunde s and Allen,
2010; S owell, 2010):
The Essen ials o C edi Ra ing Assessmen 9
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
• Secu i iza ion ep esen s an inno a i e way o lende s o aise unds in
he capi al ma ke by selling hei asse s’ u u e ecei able cash lows, such
as mo gage, s uden o c edi ca d loans. The loans and o he asse s a e
packaged and sold as asse -backed secu i ies. This p ocess ans e s c edi
isk o in es o s, while banks can ee up capi al o o he lending and
in es men ac i i ies.
• Loan syndica ion is ano he way how banks can educe isk exposu es.
Fi s ly, a bank o igina es a loan and hen sells pa s o he loan o ou side
in es o s. The ou side in es o s include o he banks, hedge unds, mu ual
unds, insu ance companies and o he in es o s. Banks’ p op ie a y
in es men ac i i ies in ol e non-clien - ela ed in es men s in secu i ies o
o he asse s o hei accoun s; o example, banks es ablish hedge unds,
p i a e equi y, o en u e capi al unds. These subsidia ies a e hen
in ol ed in in es men ac i i ies ha a e conside ed oo isky o banks.
• The use o inancial de i a i es co e s he use o c edi de aul swaps
designed o ans e he c edi isk on a po olio o banks o nonbanks,
ypically insu ance and einsu ance companies.
As we can see in he p e ious ex , lende s such as banks can educe c edi isk
in di e en ways. These inno a i e ac i i ies also sligh ly change he adi ional
iew as an ins i u ion ha issues sho - e m deposi s and o e s long- e m loans.
E en hough hese inno a i e s a egies ha e been inc easing in ecen yea s,
banks s ill ace a subs an ial c edi isk esul ing om hei adi ional ac i i ies.
Fo his eason, hey pay conside able a en ion o c edi isk measu emen and
managemen . No only do banks ace c edi isk om hei ope a ions, bu also
pe sons placing deposi s wi h banks o in es o s pu chasing co po a e bonds.
We al eady de ined c edi isk as he p obabili y o loss due o he ailu e o
coun e pa y's unwillingness o mee con ac ual obliga ions. Acco ding o Joseph
(2013), c edi isk gene ally exis s whene e a p oduc o se ice is ob ained
wi hou paying o i . A single bo owe (obligo ) exposu e is known as i m-c edi
isk, while c edi exposu e o a g oup o bo owe s is called a po olio-c edi isk.
C edi isk is he p oduc o a ious e en s and ac o s, such as domes ic,
in e na ional o company-speci ic issues. As we can see om he scheme in Figu e
2-3, some o he causes a e mo e con ollable han o he s.
10 Chap e 2
2024 Ma ina No o ná
Figu e 2–3 Majo sou ces o c edi isk
Sou ce: Joseph (2013), p. 16
Uncon ollable isks a e called sys ema ic isks, and hey a e associa ed wi h
ex e nal o ces ha a ec all businesses and households in he coun y. Fo
ins ance, he equency o de aul s o bank up cies ypically inc eases du ing he
economic ecession, causing c edi losses o he lende s (Joseph, 2013). Figu e 2-
4 shows he numbe o co po a e de aul s o companies a ed by S anda d &
Poo ’s om 1981 o 2015. The bank up cy numbe inc eased du ing each o h ee
pe iods o economic down u n: The ecession o he ea ly 1990s ha came a e
he Black Monday o Oc obe 1987, he i s 2000s ecession, and he g ea
ecession o 2008.
Figu e 2–4 To al numbe o co po a e de aul s (1981–2015)
Sou ce: S&P Global Ra ings (2015), au ho
Unsys ema ic isk can be conside ed con ollable because hese isks do no
a ec he en i e economy o all businesses o households. On he o he hand, hese
isks a e mainly indus y o company-speci ic. Lende s migh educe unsys ema ic
isk h ough di e si ica ion o ex ending c edi o a ious cus ome s.
C edi isk
Sys ema ic isk
Socio-Poli ical
Risks Economic Risks
O he
Exogenous Risks
Unsys ema ic
isk
Business Risks Financial Risks
0
50
100
150
200
250
300
To al de aul s
Yea
The Essen ials o C edi Ra ing Assessmen 11
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
2.3 Fac o s o C edi Risk
The p incipal p oblem in c edi isk measu emen is o quan i y he isk o losses
due o coun e pa y de aul . As Jo ion (2011) sugges s, he dis ibu ion o c edi
isk can be conside ed a compound p ocess d i en by he ollowing h ee
a iables:
• De aul ,
• loss gi en de aul ,
• c edi exposu e.
De aul is he p incipal issue in c edi isk measu emen , so i is essen ial o
pay some a en ion o i s explana ion. The de ini ion o de aul o an obligo
ypically includes he ollowing cha ac e is ics:
• Days pas due c i e ion o de aul iden i ica ion,
• indica ions o unlikeness o pay,
• condi ions o a e u n o non-de aul ed s a us.
Due o he absence o speci ic ules and o he aspec s o he applica ion,
a ious app oaches ha e been adop ed ac oss ins i u ions and ju isdic ions. Based
on he Eu opean Banking Au ho i y (EBA, 2016), ins i u ions use di e ing
p ac ices ega ding de aul . As s a ed in he epo
1
, speci ic ules adop ed in mos
ju isdic ions usually ocus on coun ing days pas due and applying he ma e ial
h eshold. On he o he hand, pa icula ules on di e en aspec s o he de ini ion
o de aul a e much less common. To ha monize a consis en use o de aul
meaning, he EBA sugges s guidelines o inc ease compa abili y o isk es ima es
and own unds equi emen s, especially when using in e nal a ing-based o IRB
models. Fo example, in he Czech Republic, he de aul subjec is egula ed by
he Ac on Bank up cy and Se lemen , known as he Insol ency Ac
2
. This Ac
aims o con ol he esolu ion o he deb o ’s insol ency and imminen bank up cy
and he deb o ’s discha ge o deb s. Acco ding o his Ac , a deb o is insol en i
hey ha e se e al c edi o s, ou s anding inancial liabili ies o e due o mo e han
30 days, and canno ul il such liabili ies. While insol ency is a speci ic legal e m
meaning ha a deb o canno pay hei deb s, de aul gene ally means ha a deb o
has no ye paid a deb as equi ed.
We can conside de aul as a disc e e s a e o he coun e pa y wi h some
p obabili y o de aul (PD). The de e mina ion o he likelihood o de aul is he
c ucial issue in he c edi isk managemen app oach and can be achie ed h ough
a ious me hods (De Lau en is, 2010):
• The obse a ion o his o ical de aul equencies and alloca ion o di e en
c edi classes (ex-pos ),
• he use o ma hema ical and s a is ical ools o expec he p obabili y (ex-
pos ),
1
The guidelines will apply om 1 Janua y 2021
2
Ac No. 182/2006 on Bank up cy and Se lemen
12 Chap e 2
2024 Ma ina No o ná
• he combina ion o judgmen al and mechanical app oaches o he app oach
based on ma ke p ices.
The p obabili y o de aul can be conside ed he de aul isk measu e wi hin a
speci ied ime ho izon, usually one yea . Al e na i ely, when exposu es a e mo e
han one yea , he assessmen is ypically based on cumula i e p obabili ies (De
Lau en is e al., 2010).
The ypical echnique o assess he c edi wo hiness o e ail and comme cial
loans’ coun e pa y is sco ing models (De Se igny and Renaul , 2004). Al hough
he c edi sco ing me hod was explo ed and in oduced by Al man (1968) se e al
decades ago, i is s ill a opical heme o esea che s and p ac i ione s. Today,
di e en and mo e sophis ica ed me hods, such as nonpa ame ic echniques o
machine lea ning me hods, can be applied in c edi isk managemen . Ano he
app oach o assessing de aul isk is based on i m- alue-based o s uc u al
models ha desc ibe he de aul p ocess as he explici ou come o he i m alue’s
de e io a ion. Based on his app oach, co po a e secu i ies a e conside ed
con ingen claims o op ions on he issuing i m’s alue. This me hod was
in oduced by Me on (1974) as he i s example o an applica ion o op ion
p icing me hodology o p ice co po a e secu i ies. C edi sco ing models can be
applied o any bo owe , whe eas s uc u al models can be p ima ily used o he
la ges companies lis ed on s ock exchanges (De Se igny and Renaul , 2004).
Loss gi en de aul (LGD) is he second key a iable in a c edi isk analysis,
and i can be conside ed he ac ional loss due o de aul , p o ided ha de aul is
gi en in his case. The complemen o one is called eco e y a e; o example, i
a ac ional eco e y a e is 30%, 70% o he exposu e is LGD. The eco e y a e
is exp essed as a pe cen age o he pa amoun eco e ed on de aul ed deb s and
e e s o he amoun o money eco e ed. LGD can be de ined as
1i
LGD =−
(2.1)
whe e i is he eco e y a e (Jo ion, 2011).
The main di e ence be ween he p obabili y o de aul (PD) and loss gi en
de aul (LGD) is ha a dis ibu ion be e ep esen s LGD han a single igu e. As
De Se igny and Renaul (2004) sugges , unce ain y abou eco e y depends on
quan i iable ac o s and mo e uzzy ac o s such as deb o s o c edi o s’ ba gaining
powe .
Fo example, he e is a clea link be ween senio i y and he eco e y le el, as
shown in Table 2-1. The able shows he deb eco e ies o companies a ed by
Moody’s du ing 1985 – 2016. We can see ha eco e ies co ela e wi h hei
p io i y o claim in he capi al s uc u e in mos cases, whe e claims wi h highe
p io i y ha e highe a e age eco e y a es. The e a e small di e ences in
eco e y a es be ween Eu ope and he es o he wo ld; howe e , i mus be no ed
ha hese esul s, pa icula ly Eu opean eco e ies, a e based on a ela i ely small
sample o loans and bonds.
The Essen ials o C edi Ra ing Assessmen 19
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
de e mine he p obabili y o de aul , usually based on hei expe ience. Gene ally,
he main ac o s a ec ing an indi idual c edi isk a e ela ed o he bo owe 's
pe sonal and economic posi ion, which banks ha e used o many yea s. Fo
example, Chapman (1940) speci ies wo ypes o aspec s ela ed o c edi isk in
pe sonal lending:
• Pe sonal cha ac e is ics such as age, sex, amily s a us, and
• occupa ional and economic posi ion, o example, income and bo owe 's
ne wo h.
The abili y o pay is p ima ily de e mined by he applican ’s employmen and
he indus y in which hey a e engaged. These ac o s a e ela ed o bo owe s'
income, asse s such as eal es a e, au omobiles, secu i ies, and deb s, such as
mo gages, c edi ca ds, and o he pe sonal loans ha can be used o iden i y he
inancial capaci y. In many coun ies, he c edi his o y o a bo owe ’s
esponsible epaymen o deb s is eco ded and used by lende s as an essen ial
aspec o de e mine indi idual c edi wo hiness o an indi idual’s abili y o epay
a deb . The impo ance o each o he o me ac o s can di e o di e en banks,
and i is usually subjec o hei assessmen . In assessing he c edi quali y o a loan
applican , lende s look a a ious measu es. The s a ing poin is he applican ’s
c edi sco e, a nume ical g ade o he bo owe 's c edi his o y (Fabozzi, 2013).
The well-known and widely used c edi sco e sys em by lende s in he Uni ed
S a es is he FICO Sco e, de eloped by Fai Isaac Co po a ion and i s in oduced
in 1989. This sys em is used o assess he c edi isk o indi idual bo owe s and
de e mine whe he o ex end c edi . This assessmen is based on accoun paymen
his o y, he cu en le el o indeb edness, ypes o c edi used, leng hs o c edi
his o y o new c edi accoun s (Fai Isaac Co po a ion, 2017). FICO sco es ange
om 300-850, wi h indus y-speci ic sco es om 250-900, whe e he highe he
sco e, he lowe he c edi isk. The basic scheme o FICO sco es and hei
de ini ions a e in he able below (Table 2-2). Acco ding o ecen da a, Ame ican
consume s' a e age FICO sco e eached 699 in la e 2016 (Ka imzad, 2015).
Table 2–2 FICO C edi Sco es
FICO Sco es
De ini ion
800 +
Excellen , an excep ional bo owe
749-799
Good, a e y dependable bo owe
670-739
A e age, a good sco e bo owe
580-669
Fai , below he a e age bo owe
579 and lowe
Poo , a e y isky bo owe
Sou ce: Ka imzad (2015), au ho
The sys em o FICO Sco es is based on he ollowing i e ca ego ies:
• Paymen his o y e e s o a bo owe 's his o ical abili y o pay hei
paymen on ime; his ca ego y ep esen s he mos c i ical ac o in he
20 Chap e 2
2024 Ma ina No o ná
c edi assessmen . C edi his o y usually includes c edi ca ds, e ail
accoun s, ins almen loans, o mo gage loans.
• Amoun s owed show he amoun s owed on speci ic accoun s, including
c edi ca d balances, ins almen loans, and o he e ol ing c edi accoun s.
• Leng h o c edi his o y posi i ely a ec s he c edi sco e; he longe he
eco d, he highe he sco e.
• C edi mix is ano he c ucial de e minan o he sco e, especially he o al
numbe and ypes o bo owe s' accoun s.
• The new c edi ca ego y sugges s ha opening se e al c edi accoun s in
a sho pe iod ep esen s a g ea e isk, especially o people wi h a b ie
c edi his o y.
The con ibu ion o each ca ego y o he o al FICO sco e is shown in Figu e
2-6. As we can see, he signi ican ac o s in c edi assessmen a e paymen his o y
and amoun s owed.
Figu e 2–6 FICO Sco e ca ego ies
Sou ce: Fai Isaac Co po a ion (2017), au ho
The p ocess by which he lende decides whe he an applican is c edi wo hy
and should ecei e a loan is called unde w i ing. The equi emen s speci ied by
he lende o g an he loan a e called unde w i ing s anda ds. The app o al p ocess
can be judgmen al, ully au oma ed, o a combina ion o he abo emen ioned
ypes; howe e , i should conside all necessa y in o ma ion o suppo loan
g an ing decisions. In he case o secu ed loans, colla e al iden i ica ion should
also be conside ed (FDIC, 2017).
Fo example, he wo p ima y quan i a i e unde w i ing s anda ds o g an ing
esiden ial mo gage loans a e:
• Paymen - o-income a io (PTI) ha e e s o he a e o mon hly paymen s
o mon hly income. PTI is used o measu e an applican 's abili y o make
mon hly paymen s. The highe he a io, he lowe he isk.
• Loan- o- alue a io (LTV) is he a io o he loan amoun o he ma ke o
app aised p ope y's alue. The lowe he a e, he lowe he isk o a
lende (Fabozzi, 2013).
Paymen
his o y
35%
Amoun s owed
30%
C edi
his o y
15%
Accoun
di e si y
10%
New c edi
10%
The Essen ials o C edi Ra ing Assessmen 21
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
2.5.2 Co po a e C edi Risk
Co po a e c edi isk assessmen examines i m-le el c edi isk ha can be
a ec ed by a ious ac o s. Fi m c edi isk analysis ypically in ol es wo pa s
o he e alua ion: business and inancial isks.
Fi s ly, business o ope a ing isks a e associa ed wi h isks ha o igina e om
o he han he company's inancial aspec s. These isks include ou side and inside
e en s wi h a po en ial impac on he business c edi isk, o example, changes in
economic, egula o y, clima ic, indus y, demog aphic, geo-poli ical, p oduc
inno a ions, quali y o managemen , o o he ac o s. Fo example, Joseph (2013)
sugges s he ollowing h ee ca ego ies o isks om he ope a ing en i onmen :
• Ex e nal,
• indus y,
• in e nal.
Ex e nal isks can be seen as sys ema ic isks ha in ol e he impac o he
business cycle, economic condi ions (p i a e consump ion, go e nmen spending,
in es men , impo s and expo s), in la ion, he balance o paymen s, exchange
a es, poli ical ac o s, iscal policy, mone a y policy, demog aphic ac o s,
egula o y amewo k, echnology, en i onmen al issues, in e na ional
de elopmen s and o he ypes o sys ema ic isks. I should also be conside ed ha
hese ex e nal a iables a e usually in e ela ed.
Indus y analysis ocused on indus y li e s age, composi ion, na u e, o
s uc u e is ano he c ucial pa o c edi isk analysis. In his pa o he s udy, he
s age o he indus y li e cycle, go e nmen suppo , ac o s o p oduc ion, he
sensi i i y o indus y o he business cycle and indus y p o i abili y should be
examined, ollowed by compe i o g oup analysis. Indus y p o i abili y
assessmen is usually based on he analysis o o ces ha de e mine he po en ial
o an indus y, known as Po e 's model, which p o ides a basis o analysing he
le el o compe i ion Figu e 2-7.
Figu e 2–7 Po e ’s model
Sou ce: Joseph (2013, p. 67), au ho
Ba gaining powe o
supplie s Th ea o subs i u es
Th ea o new en an s Ba gaining powe o
buye s
Indus y i al y
22 Chap e 2
2024 Ma ina No o ná
Finally, in e nal o company c edi isk analysis is ocused on he capabili ies,
esou ces s a egies, compe encies, s eng hs and weaknesses o he bo owe s
(Joseph, 2013). In addi ion, a en ion is paid o business ac i i ies and iden i ying
in e nal isks, including pee compa ison and SWOT analysis. O he in e nal isks
include, o example, p oduc ion, human esou ce, p oduc , cus ome /supplie
concen a ion, legal, epu a ion o inancial isks.
The second ype o i m c edi isk is o igina ed solely om he inancial
aspec s o a business. Because e en a success ul business may go bank up due o
inapp op ia e inancial decisions, subs an ial a en ion is paid o analysing
inancial isks. Financial isks a e linked o a company's inancing policies,
s a egies, and decision-making ha can subs an ially a ec he c edi isk le el.
Financial isk analysis is p ima ily based on he analysis o inancial s a emen s,
he balance shee , income s a emen , and cash low s a emen ; howe e , o he
inancial s a emen in o ma ion, such as a s a emen o s ockholde s’ equi y, can
also be use ul. Fo c edi isk assessmen , a business's comp ehensi e economic
analysis is conduc ed o iden i y he inancial s eng hs and weaknesses and
wa ning signals o inancial isks. The s udy in ol es common size analysis,
indexed end analysis and inancial a io analysis. Typically, he ocus is paid o
all ca ego ies o inancial a ios (liquidi y, sol ency, ac i i y and p o i abili y
a ios), including s udying hei ela ionships and e en ually p edic ing inancial
de aul . The p ocedu e o he analysis o inancial s a emen s and hei
in e p e a ion ha e al eady been discussed in many publica ions, see o example,
F idson and Al a ez (2011), Be k and DeMa zo (2017), B ealey e al. (2014),
Megginson e al. (2008), Joseph (2013) o Dluhošo á e al. (2014). The analysis
o ela ions among inancial a ios is usually examined h ough he DuPon Model;
howe e , sco ing models a e ypically applied o de aul p edic ion. To
summa ise, business and inancial isks should be s udied oge he , and he inal
c edi isk assessmen should be based on he company's o e all si ua ion.
2.5.3 Co po a e C edi Sco ing Models
We can unde s and c edi sco es as s a is ically de i ed indica o s o isk ha
indica e he ela i e isk ha a bo owe will expe ience an ad e se c edi e en ,
o example, delinquency o de aul . When he c edi sco ing model is buil , he
s a is ical model's ou pu is usually ans e ed o gene a e a se numbe o sco e
poin s o he p obabili y o a c edi e en occu ence (Mays and Lynas, 2011).
Lende s de elop models o assess bo owe s' c edi isk, bo h a an indi idual and
co po a e le el. While an example o a well-known indi idual c edi sco ing
model used by inancial ins i u ions is he FICO model, speci ic models a e
de eloped o assess co po a e c edi isk. Co po a e c edi sco ing models include
bo h he models de eloped by banks based on hei bo owe s’ beha iou and
publically a ailable sco ing models. Di e en en i ies may use he la e models o
ge an o e all pic u e o a coun e pa y's c edi wo hiness, o example, business
pa ne s. In con as o indi idual bo owe c edi sco ing models, co po a e c edi
sco ing models use di e en inpu a iables, ypically inancial a ios and o he
co po a e inancial pe o mance indica o s.
The Essen ials o C edi Ra ing Assessmen 23
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Se e al me hods can be used o de i e sco ing models, as explained u he in
he ex . The p oposed models a e hen used o calcula e he sco e alues o en i ies
and can be used o classi y hem in o p e-de ined ca ego ies. One o he bes -
known models in his a ea was de eloped by E. I. Al man (1968), whose de aul
model is o en known as he Al man’s model o Z- Sco e model as a ool in he
inancial analysis o a company. This model can iden i y companies wi h possible
inancial p oblems, namely de aul isk, and i can be p oposed based on
mul i a ia e disc iminan analysis, whose p oduc is a so-called Z-sco e,
classi ying companies.
The o iginal e sion o he Z-Sco e model can be used o p edic he likelihood
o a i m going bank up , and he sco e can be calcula ed using he ollowing
o mula (Joseph, 2013),
1 2 3 4 5
1.2 1.4 3.3 0.6 0.999Z X X X X X= + + + +
,
(2.3)
whe e he a iables in he o mula e e o he ollowing a ios:
1
X
wo king
capi al/ o al asse s;
2
X
e ained ea nings since incep ion/ o al asse s;
3
X
p o i
be o e in e es and ax/ o al asse s;
4
X
ma ke alue o equi y/book alue o o al
deb ;
5
X
sales/ o al asse s.
The i s Al man’s p edic ion model is based on a weigh ing sys em o i e
inancial a ios. I was de eloped based on s a is ical da a om sizeable public
manu ac u ing companies wi h mo e han $1 million in asse s. I s p ima y pu pose
is o measu e a company’s inancial heal h and p edic he p obabili y o
bank up cy wi hin wo yea s. Al hough some empi ical s udies show ha he
model has a 72% – 80% eliabili y o p edic ing bank up cy, we should ealise ha
i can only be used o o ecas i a company being analysed can be compa ed o
he da abase. The esul ing sco es o he o iginal Z-Sco e model o public
manu ac u ing companies and hei implica ions can be seen in Table 2-3.
Table 2–3 O iginal Z-Sco e model
Z-Sco e
Fo ecas
Abo e 3.0
Bank up cy is no likely
1.8 o 3.0
Bank up cy canno be p edic ed –
GREY AREA
Below 1.8
Bank up cy is likely
Sou ce: Wilkinson (2013)
Al hough he model is ela i ely simple, i is s ill used and is mainly ele an
o manu ac u ing companies. Acco ding o Cao (2016), Al man decided on wo
po en ially e y powe ul a iables among all possible inancial a iables ha had
no been used ye . One o he a iables is he e ained ea nings because, as Al man
explains, “a i m ha has g own i s asse s mainly by ein es ing ea nings is
heal hie han a i m ha has g own he asse s by using o he people’s money.
Re ained ea nings is also a measu e o he company's age and le e age” The o he
24 Chap e 2
2024 Ma ina No o ná
a iable is he ma ke alue o he equi y ela i e o he book alue o he deb , an
indica ion o he company's abili y o aise money om capi al ma ke s. Today,
equi y's ma ke alue is a undamen al pa o s uc u al models p o ided, o
example, by Me on (1974) o he KMV model by Moody’s Analy ics (2017).
Since he i s e sion o Al man’s model, se e al modi ica ions ha e been
sugges ed, o some commen s ha e been published by Al man, Al man e al. (i.e.
1970, 1977, 2005, 2007, 2010) o o he au ho s. I is necessa y o ealise ha such
models' de elopmen is highly demanding due o da a in ensi y and modelling
speci ics. These echniques a e di icul o employ wi hou in o ma ion
echnologies and speci ic ma hema ical-s a is ical applica ions.
2.6 Issue-Speci ic C edi Risk
Issue-speci ic c edi isk ypically e e s o a bond issue 's c edi isk, speci ic bond
issues, o o he issues o deb secu i ies, which ep esen a con ac ual ag eemen
be ween a lende (in es o o bondholde ) and a bo owe (issue ). Howe e , c edi
isk can also be associa ed wi h inno a i e con ac s such as asse -backed
secu i ies o c edi de i a i es. In his chap e , hese h ee ca ego ies o secu i ies
will be discussed in mo e de ail, pa icula ly in he con ex o c edi isk.
2.6.1 C edi Analysis o Bonds
A bond can be de ined as a deb ins umen equi ing he issue o epay he
in es o he amoun bo owed plus in e es o e a speci ied pe iod (Fabozzi,
2013). Mos ly, he p incipal mus be epaid on he ma u i y da e. Thus, we can see
an analogy be ween inancial ins i u ions o o he en i ies lending money and he
issuance o secu i ies om a c edi isk pe spec i e. Simila ly, he c edi isk
assessmen will be conduc ed based on he bo owe ’s abili y o epay all
con ac ual paymen s when he amoun s a e due. The e o e, he analysis is ocused
on he s udy o issue business and inancial isks, including he analysis o
inancial s a emen s. On he o he hand, bond c edi isk analysis should conside
some ea u es speci ic o bonds, such as he s udy o inden u e and co enan s.
As Fabozzi (2013) sugges s, he issue 's na u e is a i al ea u e o a bond.
The e a e h ee ypes o issue s o bonds: go e nmen s, municipali ies, and
co po a ions. Some bonds a e issued wi h an amo isa ion ea u e, meaning ha
he p incipal epaymen can be epaid o e he bond's li e; hese secu i ies a e
called amo ising secu i ies. In addi ion o simple o ‘plain anilla’ bonds, he e
a e also bonds wi h embedded op ions, o example:
• Bonds wi h a call p o ision: The issue has he igh o e i e he deb be o e
he scheduled ma u i y da e.
• Bonds wi h a pu p o ision: The bondholde has he igh o sell he issue
back o he issue a pa alue on p e-speci ied da es.
• Con e ible bonds: The bondholde has he igh o exchange he bond o
a speci ied numbe o sha es o common s ock.
The Essen ials o C edi Ra ing Assessmen 25
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
• Exchangeable bonds: The bondholde can exchange he issue o a
speci ied numbe o common s ock sha es o a co po a ion di e en om
he bond issue .
In es ing in bonds is associa ed wi h some isks, such as in e es a e,
ein es men , call, c edi , in la ion, exchange, liquidi y, o ola ili y isks. While
a en ion in his chap e will be paid o bond c edi isk, he desc ip ion o o he
ypes o isks can be ound in a as li e a u e on his subjec , o example, Fabozzi
(2013), Bodie e al. (2011), Reilly and B own (2015), Pe i e al. (2015).
Co po a e bond c edi analysis consis s o h ee a eas (Fabozzi, 2013):
• Analysis o co enan s,
• analysis o colla e al, and
• assessing an issue ’s abili y o pay.
Analysis o co enan s is linked o he s udy o he inden u e p o isions ha
o m ules o essen ial a eas o ope a ion o co po a e managemen . These
p o isions, including bond co enan s, can be ound in a company’s p ospec us o
i s bond o e ing. The e a e gene ally wo co enan s: a i ma i e (p omises by he
co po a ion) and nega i e o es ic ed (limi a ions on he bo owe ). Res ic i e
co enan s may limi he absolu e amoun o ou s anding deb o a ixed cha ge
co e age a io es . Fo example, he main enance es equi es he bo owe ’s
ea nings a io o be a ailable o in e es o ixed cha ges a a minimum o a
ce ain pe iod. On he o he hand, he deb incu ence es is used o adjus in e es
o ixed cha ge co e age when he company akes on addi ional deb . In some
inden u es, we can also ind limi a ions on subsidia ies’ bo owing om all o he
companies excep he pa en .
Analysis o colla e al e e s o he ca e ul unde s anding o a co po a e deb
obliga ion secu i y when he deb can be secu ed o unsecu ed. Gene ally, i he
company is liquida ed, p oceeds om bank up cy a e p e e ably dis ibu ed o
c edi o s. Secu ed bonds a e colla e alized by an asse (i.e. p ope y, equipmen ).
In he e en o de aul , in es o s claim he issue ’s asse s o eco e hei loss o
some ex en . Howe e , mos co po a e bonds a e unsecu ed, and in es o s ha e no
claim on speci ic colla e al. We can see his ac in Table 2-4, which shows he
p opo ion o secu ed and unsecu ed bonds issued by Eu opean indus ial
companies as o he end o 2010
4
. While he balance o unsecu ed bonds is mo e
han 90% o o al bonds, secu ed bonds ep esen a mino i y in bo h g oups o
coun ies.
4
The e a e 23 coun ies included and di ided in o wo g oups EU-15 (Aus ia, Belgium,
Denma k, Finland, F ance, Ge many, G eece, I eland, I aly, Luxembou g, Ne he lands,
Po ugal, Spain, Sweden, Uni ed Kingdom) and EU-8 (Czech Republic, Es onia, Hunga y,
La ia, Li huania, Poland, Slo akia, Slo enia).
26 Chap e 2
2024 Ma ina No o ná
Table 2–4 P opo ion o secu ed and unsecu ed bonds
EU-15
EU-8
To al
p opo ion (%)
Secu ed/Senio Secu ed
80
2
7.9
Unsecu ed/Senio /Subo dina ed
Unsecu ed
875
85
92.1
To al
955
87
100
Sou ce: Reu e s da abase (accessed 1s Decembe 2010), au ho ’s calcula ions
The hi d a ea o he bond c edi analysis is ocused on assessing an issue ’s
abili y o make imely paymen s o in e es and p incipal. Al hough a subs an ial
pa is based on he analysis o inancial s a emen s, we should also analyse o he
ac o s ha may impac he abili y o gene a e cash low, hus se ice he deb .
This pa o he c edi analysis is analogical o he esea ch desc ibed in Chap e
2.1.2. I in ol es s udying business isk and inancial isk, including assessing
co po a e go e nance isk wi h an emphasis on he owne ship s uc u e o he
co po a ion, he p ac ices ollowed by managemen and policies o inancial
disclosu e.
Go e nmen bond c edi isk is associa ed wi h he coun y's o e all si ua ion
and ins i u ional s eng h, especially he banking sys em's s abili y and policy
c edibili y. T adi ionally, go e nmen bonds ha e been conside ed ela i ely isk-
ee secu i ies; howe e , we can ind signi ican di e ences among di e en
coun ies' isks. Go e nmen bond c edi isk, so-called so e eign c edi isk, is
usually assessed by a ing agencies in e ms o a ing. Howe e , inancial
ins i u ions, o he en i ies o in es o s may also use hei c edi sco ing models,
simila o co po a e loans. Acco ding o Moody’s a ing agency
5
, he e a e ou
ac o s o go e nmen c edi isk analysis:
• Economic s eng h: GDP (pe -capi a), economy size and deg ee o
di e si ica ion, medium- e m ends (p oduc i i y, in as uc u e).
• Ins i u ional s eng h: Policy p edic abili y (con inui y), ins i u ional
quali y, egula o y amewo k.
• Go e nmen inancial s eng h: Fiscal balance, deb indica o s ( a ios o
GDP and e enue), deb a o dabili y (in e es / e enue), deb s uc u e, and
ma ke access.
• Suscep ibili y o e en isk: The impac o economic, inancial and poli ical
e en s.
The wo c i ical ac o s in he c edi wo hiness analysis a e go e nmen
inancial s eng h, mone a y policy, and economic powe , indica ing he economic
end. Suscep ibili y o e en isk is he ac o ha shows he shock esis ance o a
coun y, o example, he impac o he inancial c isis, B exi o a US p esiden ial
elec ion on he economy and iscal ou look.
5
Moody’s In es o s Se ice, Moody’s 7 h Annual CEE C edi Risk Con e ence, Czech
Na ional P ague, 16 Ap il 2013.
The Essen ials o C edi Ra ing Assessmen 27
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
In addi ion o go e nmen bonds, he e a e deb secu i ies issued by local
go e nmen s, dis ic s, o ci ies called municipal bonds. The c edi isk o
municipal bonds is also assessed and published by a ing agencies o help in es o s
make in es men decisions.
The main ac o s o c edi isk analysis co e (SEC, 2017; Pe e son, 1998):
• Sou ces o unds o pay p incipal and in e es ,
• pu pose o he inancing, and
• he inancial condi ion o he issue .
In his case, inancial condi ion analysis is ocused on he magni ude and
s uc u e o local deb , including a p oposed bo owing. Economic analysis can be
used as an adequa e indica o o municipal deb bu den and municipal bo owe ’s
abili y o se ice he deb . Fo example, he mos impo an inancial a ios include
deb se ice ela ed o ecu ing e enues, ope a ing su plus o o al income and
o al deb o he ax base.
Finally, c edi isk is associa ed wi h sho - e m secu i ies, such as
comme cial pape s and o he sho - e m deb s wi h ma u i ies o up o one yea .
The c edi analysis is sligh ly di e en om long- e m bonds as i usually does no
conside he likely eco e y o he deb ins umen s. The p incipal ac o s o he
c edi analysis include assessing he undamen al long- e m c edi quali y.
Howe e , he sho - e m c edi isk is d i en p edominan ly by he issue ’s
liquidi y posi ion, which indica es he abili y o epay he deb om in e nal o
ex e nal sou ces.
2.6.2 C edi Risk o Asse -Backed Secu i ies
Asse -backed secu i ies a e conside ed an inno a i e and al e na i e way
co po a ions o lende s can aise unds. Th ough secu i iza ion, a co po a ion
pools loans o ecei ables and uses he pool o asse s as colla e al o secu i y
issuance (Fabozzi, 2013). Since he cash lows a e sold in he o m o secu i ies
backed by he cash lows o he e y asse s sold, he secu i ies a e called asse -
backed secu i ies. Compa ed o adi ional ways o deb inancing, such as
bo owing in he o m o a loan o issuing bonds, secu i iza ion is associa ed wi h
speci ic ea u es and ep esen s a di e en way o inancing. Issue s o asse -
backed secu i ies ypically aise unds o inance he o igina ion o loans, and om
an accoun ing poin o iew, his issuance is conside ed an asse sale. The e a e
a ious backing asse s, such as esiden ial o comme cial mo gages, consume
loans, comme cial leases, o any inancial ins umen s wi h p edic able and s able
ecei able cash lows (i.e. c edi ca d ecei ables, au o loans, s uden loans). As
lende s issue asse -backed secu i ies by s uc u ing u u e ecei able cash lows o
unde lying asse s, hey a e also called s uc u ed inance secu i ies.
The e a e he ollowing speci ic ea u es o he secu i iza ion p ocess (Hu, 2011):
• The asse -backed secu i ies a e issued h ough a special pu pose en i y,
• o accoun ing aspec s, he issuing o asse -backed secu i ies is an asse sale
(no a deb inancing),
28 Chap e 2
2024 Ma ina No o ná
• se icing o he unde lying asse s o he in es o is equi ed,
• he c edi o he asse -backed secu i y depends on he c edi o he
unde lying asse ,
• c edi enhancemen is usually needed.
Asse -backed secu i ies a e issued in he o m o ce i ica es en i ling he
in es o s o ecei e a p e-de e mined sha e in a speci ic pool o asse s' cash lows.
F om his pe spec i e, hey a e simila o bonds because in es o s accep egula
paymen s, usually based on a coupon a e. Howe e , in asse -backed secu i ies,
he paymen s depend on he cash lows gene a ed by unde lying asse s. Thus,
p incipally, we can dis inguish be ween wo ypes o asse -backed secu i ies:
• Pass- h ough secu i ies ha a e issued as single-class mo gage-backed
secu i ies (i.e. agency MBS) and
• secu i ies s uc u ed in se e al bond classes called anches (i.e. non-
agency MBS, ABS).
A mo gage pass- h ough secu i y is issued as one bond class, which means
ha in es o s a e en i led o ecei e a p o- a a sha e o he cash lows o he
speci ic mo gage loan pool. When pass- h ough secu i y is i s issued, he
p incipal is known; howe e , o e ime, due o egula ly scheduled p incipal
paymen s and p epaymen s, he amoun o he pool’s ou s anding loan balance
declines. Paymen s o pass- h ough secu i y a e made each mon h, and he
mon hly cash low is less han he mon hly cash low o he loan pool by an amoun
equal o se icing and o he ees. Agency mo gage pass- h ough secu i ies, so-
called mo gage-backed secu i ies (agency MBS), a e issued by US go e nmen
agencies known as F eddie Mac o Fannie Mae, and Ginnie Mae, which is no he
issue ; howe e , i p o ides gua an ees. Since hese pass- h ough secu i ies ca y
hei wa an y and ul il unde w i ing s anda ds, hey can be conside ed asse -
backed secu i ies wi h he lowes le el o c edi isk.
Secu i ies s uc u ed in bond classes a e c ea ed o edis ibu e c edi isk using
a senio -subo dina e s uc u e. While bond classes wi h he lowes c edi isk and
he highes a ing a e e e ed o as he senio bond classes, he subo dina ed
classes ha e a lowe a ing o a e no a ed. Losses a e dis ibu ed based on he
bond class's posi ion in he s uc u e when losses s a om he bo om and mo e
o he senio le el. The ules o he cash low dis ibu ion (in e es and p incipal)
and losses a e explained in he p ospec us. They a e usually e e ed o as cash
low wa e all (Fabozzi, 2013; Hu, 2011; Choud y, 2010).
The Essen ials o C edi Ra ing Assessmen 35
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
• coun ies,
• c edi de aul swaps,
• insu ance companies,
• municipali ies,
• s uc u ed inance coun e pa y ins umen s,
• s uc u ed inance coun e pa ies,
• s uc u ed inance in e es -only secu i ies.
Bo h agencies also use na ional scale a ings o he opinions o issue s'
ela i e c edi wo hiness and inancial obliga ions wi hin a pa icula coun y.
They a e no designed o be compa ed among s a es; con e sely, hey add ess
ela i e c edi isk wi hin a gi en coun y. Thus, hey a e opinions o an obligo ’s
c edi wo hiness o o e all capaci y o mee speci ic inancial obliga ions ela i e
o o he issue s and issues in a gi en coun y o egion. The no a ion o na ional
scale a ing is based on he cha ac e s ha indica e he s a e in which he issue is
loca ed, o example, ‘Aaa.b ’ (Moody’s), o ‘b AAA’ (S&P) a ings demons a e
he s onges c edi wo hiness ela i e o o he domes ic issue s in B azil.
Na ional scale sys ems a e main ained only o some coun ies. We can use he
case o he Czech Republic o demons a e na ional scale a ings and hei use
(Table 2-6). The e a e municipal a ings in he able, bo h long- e m and na ional
scale a ings. Al hough mos long- e m a ings a e A2, he e is a ela i e di e ence
among issue s acco ding o na ional scale a ings wi hin he coun y.
Table 2–6 Long- e m and na ional scale municipal a ings in he Czech Republic
Issue
Long- e m a ing
Na ional scale a ing
Ceska Lipa, Ci y o
A2
Aa2.cz
Kla o y, Ci y o
A2
Aa2.cz
Libe ec, Ci y o
Baa1
A3.cz
Libe ec, Region o
A2
Aa3.cz
P os ejo , Ci y o
A1
Aa1.cz
Sou h-Mo a ian Region
A2
Aa3.cz
T ebic, Ci y o
A2
Aa2.cz
Uhe ske H adis e, Ci y o
A2
Aa3.cz
Us i, Region o
A2
Aa3.cz
Zda nad Saza ou, Ci y o
A2
Aa2.cz
Sou ce: Moodys’ Co po a ion (2017), au ho
Wi hou conside ing some cu en issues in he c edi a ing indus y and he
p oblem o misleading some a ings, hey gene ally p o ide a handy ool o all
pa icipan s in he inancial ma ke . The e a e many a ing use s in he inancial
ma ke ; howe e , he mos impo an a ing bene icia ies a e in es o s and issue s.
Fo in es o s, a ings p o ide an easily unde s andable and eliable guide abou
he likelihood o issue de aul on a pa icula ixed-income ins umen . Thus,
a ing o e s he basis o in es men decisions. In addi ion, since a ing inc eases
knowledge and anspa ency, i can educe unce ain y and p o ide a benchma k
o compa isons.
36 Chap e 2
2024 Ma ina No o ná
2.7.2 Bene i s and Cos s o Ra ing
The main oles o a ing o in es o s a e as ollows (Nye, 2014):
• Ra ings can help long- e m in es o s (e.g. pension unds, insu ance
companies) o e alua e a ious long- e m in es men op ions.
• Ra ings p o ide he basis o in es o s o make a mo e in o med in es men
decision and o ma ch he ela i e c edi isk o deb wi h hei isk
ole ance.
• The a ing sys em allows he issue ’s c edi undamen als o be compa ed
agains he indus y pee g oup.
• Ra ings educe in es o s’ cos s o ga he ing, analysing and moni o ing
bo owe s' inancial posi ions.
Ra ings also ha e bene i s o o he ma ke pa icipan s, such as deb issue s.
Issue s such as co po a ions, inancial ins i u ions, go e nmen s, ci ies and
municipali ies use c edi a ings o p o ide independen iews o hei
c edi wo hiness and he c edi quali y o hei deb issues. Thus, a ings play a
use ul ole in enabling issue s o aise money in he capi al ma ke s and acili a e
he p ocess o issuing and pu chasing bonds by p o iding a measu e o ela i e
c edi isk. In addi ion, deb issue s ha acqui e a ings may bene i om:
• A b oade base o in es o s, lende s, cus ome s o business pa ne s,
• al e na i e inancing op ions,
• a s anda d measu e o c edi wo hiness ela i e o o he issue s in an
indus y o a coun y,
• lowe inancing cos s and mo e dependable access o liquidi y,
• a mo e accu a e es ima e o bo owing cos s,
• a use ul discipline on senio managemen (Nye, 2014).
The e a e addi ional bene i s o a ings o an issue ha is a co po a e
en e p ise. These include lowe inancing cos s, be e nego ia ion powe wi h
banks, he basis o o e ing deb issues in he ma ke , highe isibili y and
c edibili y o a pee benchma k. Fo comme cial banks, a ing gi es con idence o
deposi o s, egula o s and may help a ac equi y in es o s. I he issue is a
so e eign go e nmen , a a ing helps a ac in e na ional capi al, suppo he
de elopmen o local capi al ma ke s, mee in e na ional s anda ds o anspa ency
and coope a ion o achie e mo e excellen unding s abili y (Nye, 2014).
E en hough a ings play a c ucial ole in he inancial ma ke , we should also
conside some a ing scales' weaknesses. The disad an ages o a ing a e ela ed
o he issues discussed in Chap e 2.9, p ima ily he nega i e in luence o he high
concen a ion o he CRA ma ke on inancial s abili y, con lic s o in e es , and
anspa ency. The lack o accoun abili y in he a ing indus y may lead o he
limi ed eliabili y o a ing scales and consequen ly o inc eased ine iciency in he
inancial ma ke s. As men ioned in he p e ious chap e , a ing scales a e easy o
ead and use; howe e , he e migh also be a po en ial p oblem when unquali ied
use s use and in e p e hese scales. I is essen ial o ealize ha a ings a e opinions
abou c edi isk and do no p o ide an absolu e measu e o de aul p obabili y.
The Essen ials o C edi Ra ing Assessmen 37
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
The o e all c edi a ing indus y is based on he scheme ha issue s pay he
c edi a ing agency. F om he poin o iew o new issue s, agency ees should be
conside ed, and he issue should conduc a cos -bene i analysis o acqui ing a
a ing. Typically, agency ees a e nego iable, and issue s can discuss ee op ions
wi h he agencies. Acco ding o Nye (2014), compe i ion among CRAs keeps
p ices ela i ely modes , depending on he a ed en i y. Fo example, acco ding o
he S&P
7
, he minimum ee o indus ial co po a ions and inancial se ice
companies is $150,000.
2.8 Desc ip ion o C edi Ra ing P ocess
The c edi a ing p ocess ypically in ol es se e al s eps, equi ing close
coope a ion be ween he a ing agency and he issue . Fi s , new issue s mus
choose and con ac a a ing agency ha i s hei needs. Second, he a ing p ocess
begins wi h an ini ial mee ing o in oduce he issue 's app oach, me hodology, and
p oduc s. Finally, he s eps o he a ing p ocess (Figu e 2-9) include he ollowing
ac i i ies:
• The issue signs an applica ion,
• a ing agency analys s a e assigned o he cus ome o e iew he ele an
in o ma ion,
• analys s mee wi h he managemen eam o e iew and discuss
in o ma ion,
• analys s e alua e in o ma ion and p opose he a ing o a a ing commi ee,
• he commi ee e iews he lead analys ’s a ing ecommenda ion and hen
o es on he c edi a ing,
• he issue is gene ally p o ided wi h a p e-publica ion a ionale o i s
c edi a ing o ac -checking and accu acy pu poses,
• a p ess elease announcing he public a ing is ypically published,
• he a ing is kep cu en by iden i ying issues ha may esul in ei he an
upg ade o a downg ade (S&P Global Ra ings, 2017).
7
Global Ra ings U.S. Ra ings Fee Disclosu e [online]. A ailable a :
h p://www.s anda dandpoo s.com/, [Accessed 19 Sep embe , 2017]
38 Chap e 2
2024 Ma ina No o ná
Figu e 2–9 S eps o a ing p ocess
Sou ce: S&P Global Ra ings (2017), au ho
Du ing he a ing p ocess, he issue , an indus ial company, p o ides ele an
inancial and non- inancial in o ma ion. Then, he discussion a he managemen
mee ing gene ally ocuses on he ollowing subjec s
8
:
• Backg ound and his o y o he en i y,
• indus y and sec o ends,
• he na ional poli ical and egula o y en i onmen ,
• managemen policies, expe ience, ack eco d, a i ude owa d isk- aking,
• managemen s uc u e,
• p ima y ope a ing and compe i i e posi ion, co po a e s a egy and
compe i i e philosophy,
• deb s uc u e, including s uc u al subo dina ion and p io i y o claim,
• inancial si ua ion and liquidi y sou ces (cash low, ope a ing ma gin, a
balance shee analysis o deb p o ile and ma u i y).
As we can see, assessing companies' c edi wo hiness is a complex ask based
on bo h quan i a i e and quali a i e analysis. CRAs emphasize he quali a i e
side, a guing ha no a ios can cap u e he ull complexi y o a company’s
inancial posi ion, cash a ailable o mee i s u u e obliga ions, and managemen 's
willingness o pay p incipal o bondholde s. Abo e all, CRAs e alua e long- e m
undamen als ela ed o he company’s c edi s eng hs and weaknesses ela ed o
i s abili y o gene a e cash, plausible s ess scena ios, and elemen s o u u e cash
low (Nye, 2014). Ra ing agencies use di e en assignmen me hodologies
acco ding o he coun e pa y’s na u e (i.e. co po a ions, coun ies, public en i ies)
and he na u e o p oduc s (i.e. bonds, s uc u ed inance). Since he empi ical
analysis in he applica ion pa ocuses on co po a e bo owe s, he p ima y
a en ion is concen a ed on isk ac o s o co po a e a ings o indi idual deb
issues speci ically.
8
Moody’s In es o s Se ice (2017)
The Essen ials o C edi Ra ing Assessmen 39
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Analys s o CRAs ypically s a wi h e alua ing he issue 's c edi wo hiness
be o e assessing he c edi quali y o a speci ic deb issue. The main ac o s o
a ing assessmen desc ibed in he p e ious ex conside inancial and non-
inancial ac o s, including key pe o mance indica o s, economic, egula o y and
geopoli ical in luences, managemen and co po a e go e nance a ibu es, and
compe i i e posi ion. In a a ing o an indi idual deb issue, analys s p ima ily
ocus on (S&P Financial Se ices, 2014):
• The e ms and condi ions o he deb secu i y, including i s legal s uc u e,
• he ela i e senio i y o he issue conce ning he issue ’s o he deb issues
and p io i y o epaymen in he e en o de aul ,
• he exis ence o ex e nal suppo o c edi enhancemen s (i.e. le e s o
c edi , gua an ees, insu ance o colla e al).
The c i ical ac o s o assessing he co po a e a ing can be summa ized using
he a ing analy ical py amid (Figu e 2-10).
Figu e 2–10 Ra ing analysis py amid
Sou ce: Moodys’ Co po a ion (2017), au ho
Ra ing agencies can use bo h op-down and bo om-up app oaches o assess
he a ing, wi h he main pa s o he assessmen ocusing on he coun y, indus y,
company, and inden u e analysis.
C edi a ings can be upg aded, downg aded, o unchanged, and he pe cen age
o unchanged a ings can be used o measu e a ing s abili y. Acco ding o he
a ing changes, we can calcula e he ansi ion equency om one a ing class o
ano he . Thus, we can assess he mig a ion isk. The en i e possible s a es a a ing
can ake o e a gi en ime ho izon is usually called a ing ansi ion o mig a ion
ma ix. T ansi ion ma ices a e based on ime se ies o a ing changes, and hey
can be es ima ed using a ious app oaches. Fo example, Gunn ald (2014) use he
Ma ko chain me hod and he du a ion me hod, Hu e al. (2002) use he
combina ion o a Bayesian app oach and o de ed p obi es ima e o so e eign
a ings, and Koopman e al. (2008) use an in ensi y-based du a ion model.
INDENTURE ANALYSIS
Issue s uc u e
COMPANY SPECIFIC ANALYSIS
Financial isk
Business isk and managemen
INDUSTRY ANALYSIS
Ma ke posi ion
Indus y ends
COUNTRY ANALYSIS
Legal and egula o y amewo k
So e eign mac oeconomic analysis
40 Chap e 2
2024 Ma ina No o ná
F ydman and Schue mann (2008) applied Ma ko mix u e models o a mix u e o
wo Ma ko chains. Thei esul s show ha a i m’s a ing depends on i s cu en
c edi a ings and i s pas a ing his o y.
T ansi ion ma ices a e published by CRAs and can be used o analyse
ansi ion a es and a ing beha iou . Fo example, acco ding o S&P (2015),
in es men -g ade a ed issue s exhibi g ea e a ing s abili y (measu ed by he
equency o a ing ansi ion) han specula i e-g ade issue s. I is con i med by
he one-yea ansi ion a es (Table 2-7): The lowe he a ing, he lowe he a ing
s abili y. Fo ins ance, while 93.26% o AA issue s a e s ill a ed as AA one yea
la e , 79.97% o BB issue s s ay wi hin he BB a ing ca ego y in one yea . The
a ing ca ego y AAA is ela i ely s able; howe e , i should be conside ed ha
because he numbe o issue s wi h AAA a ings is ypically de icien , he
downg ade o e en one issue may ha e a la ge e ec on his ca ego y’s a ing
s abili y.
Table 2–7 One-yea co po a e global ansi ion a es (2015, in %)
F om/ o
AAA
AA
A
BBB
BB
B
CCC/C
D
NR
AAA
100.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
AA
0.29
93.26
4.40
0.00
0.00
0.00
0.00
0.00
2.05
A
0.00
1.43
89.87
5.48
0.00
0.00
0.00
0.00
3.23
BBB
0.00
0.06
3.12
85.52
4.90
0.00
0.00
0.00
6.40
BB
0.00
0.00
0.00
3.63
79.97
6.87
0.24
0.16
9.13
B
0.00
0.00
0.00
0.15
3.58
76.04
4.57
2.39
13.27
C/CCC
0.00
0.00
0.00
0.00
0.00
5.85
49.71
25.73
18.71
Sou ce: S&P (2015), au ho
The le el o a ing s abili y depends no only on he a ing ca ego y bu also on
he ime ho izon. O e he long e m, a ing s abili y is also consis en wi h highe
a ings; howe e , he a e age long- e m ansi ion a es a e usually highe han
one yea . Fo example, om 1981 o 2015, AAA- a ed issue s we e s ill a ed
AAA one yea la e 87.1% o he ime, while CCC/C a ings emained CCC/C
44.2% o he ime (Table 2-8).
The ca ego y deno ed as D means paymen de aul on one o mo e o an
obligo ’s inancial obliga ions (acco ding o a ing agency’ de ini ion o de aul ),
o issue ’s iling o bank up cy, and NR s ands o no a ed.
The analysis o c edi mig a ion is he basis om he C edi Me ics app oach
de eloped by JP Mo gan, he U.S. bank in 1997, subsequen ly e ised as
RiskMe ics, Inc. and acqui ed by MSCI in 2010. In p ac ice, banks widely use
his app oach o es ima e he ull one-yea o wa d dis ibu ion o any bond o loan
po olio alues, whe e he changes in alues a e only ela ed o c edi mig a ion.
The c i ical assump ion is ha a ed bonds' pas mig a ion his o y accu a ely
desc ibes he p obabili y o mig a ion in he nex pe iod (C ouhy e al., 2014).
The Essen ials o C edi Ra ing Assessmen 41
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Table 2–8 Long- e m co po a e global ansi ion a es (1981 – 2015, in %)
F om/ o
AAA
AA
A
BBB
BB
B
CCC/C
D
NR
AAA
87.08
9.00
0.53
0.05
0.08
0.03
0.05
0.00
3.18
AA
0.53
86.69
8.06
0.53
0.06
0.02
0.02
0.02
4.02
A
0.03
1.81
87.65
5.39
0.33
0.02
0.02
0.06
4.58
BBB
0.01
0.11
3.55
85.43
3.82
0.12
0.12
0.19
6.24
BB
0.00
0.03
0.13
5.08
76.78
0.64
0.64
0.73
9.63
B
0.00
0.03
0.09
0.21
5.25
4.39
4.39
3.77
11.99
C/CCC
0.00
0.00
0.14
0.20
0.61
44.19
44.19
26.36
15.66
Sou ce: Sou ce: S&P (2015), au ho
2.9 Cu en Issues in Ra ing Indus y
CRAs p oduce a ings in bo h local and in e na ional ma ke s. The c edi a ing
indus y is egula ed by Regula ion (EC) No 462/2013
9
and Di ec i e
2013/14/EU
10
in he Eu opean Union. This egula ion (he ea e e e ed o as EC
Regula ion) aims o egula e he ac i i y o c edi a ing agencies o p o ec
in es o s and Eu opean inancial ma ke s agains he isk o malp ac ice. The i s
incen i es o s eng hen he egula o y and supe iso y amewo k o CRAs in he
EU and he i s se o ules came in o e ec a he end o 2009, connec ed wi h
he global inancial c isis 2008 – 2009. To be egis e ed in he Eu opean Union
(EU), c edi a ing agencies mus (EC, 2017):
• A oid con lic s o in e es : Fo example, c edi a ing analys s mus no a e
an en i y in which hey ha e a holding;
• ensu e he quali y o hei a ings and a ing me hods;
• p o ide a high deg ee o anspa ency, o example, by publishing an
annual anspa ency epo .
In addi ion o he egula o y amewo k, he Eu opean Secu i ies and Ma ke s
Au ho i y (ESMA) was c ea ed in 2011 o supe ise CRAs egis e ed in he EU.
Since July 2011, ESMA has been esponsible o egis e ing c edi a ing agencies
and has exclusi e supe iso y powe s conce ning such agencies. Unde he CRA
egula ion, i is possible o a a ing agency es ablished ou side he EU o ha e i s
a ing ecognised and used o egula o y pu poses in he EU. I can happen in wo
ways: ce i ica ion h ough he equi alence egime and endo semen . The
equi alence ce i ica ion applies o he CRAs es ablished and supe ised ou side
he EU ha ha e no a ilia ion in he EU. These CRAs ha mee he equi emen s
o he egula ion may apply o he ESMA o ce i ica ion. The endo semen
egimes apply o CRAs a ilia ed wi h o wo king closely wi h EU- egis e ed
agencies, and hey mus also comply wi h speci ic legal equi emen s. The lis o
egis e ed o ce i ied CRAs in he EU is a ailable in Appendix 1. Fo example,
we can see ha as o 24 Ma ch 2022, he e a e 33 CRAs egula ed in he EU.
9
Regula ion (EC) No 462/2013 o he Eu opean Pa liamen and he Council o 21 May
2013 on c edi a ing agencies
10
Di ec i e 2013/14/EU o he Eu opean Pa liamen and he Council o 21 May 2013
42 Chap e 2
2024 Ma ina No o ná
Rega ding he c i ical p o isions o he las EC Regula ion e o ms, a ecen
s udy on he s a e o he c edi a ing ma ke was published in 2016 (EC, 2016).
Acco ding o his documen , he ea e e e ed o as Repo , he cu en c edi
a ing ma ke has an oligopolis ic s uc u e, and i is domina ed by he h ee global
CRAs: Moody’s, S&P and Fi ch. The EC Regula ion on c edi a ing agencies is
awa e ha CRAs play a c ucial ole in he global secu i ies and banking ma ke s.
A signi ican numbe o inancial ins i u ions use hei c edi a ings o es ima e
hei capi al equi emen s o sol ency pu poses o e alua e isks. I is sugges ed
ha hese en i ies make hei c edi isk assessmen and hus less eliance on c edi
a ings.
Conce ning c edi a ing agencies, he main issues ha conce n he Eu opean
Commission include (EC, 2016):
• Con lic s o in e es due o he issue -pays model,
• con lic s o in e es due o he emune a ion model o c edi a ing agencies,
• disclosu e o s uc u ed inance ins umen s,
• anspa ency,
• p ocedu al equi emen s and he iming o publica ion speci ically o a
speci ic pe iod.
Thus, speci ic measu es ha e been adop ed in he Eu opean Union o imp o e
he si ua ion. Fo example, he C edi Ra ing Agency (CRA3) Regula ion's las
e o ms ocused on enhancing compe i ion in he c edi a ing ma ke , u he
add essing con lic s o in e es , enhancing disclosu e on s uc u ed inance
ins umen s, and he o a ion mechanism o CRAs (EC, 2017).
2.9.1 Ma ke Concen a ion
As said in he Repo , ma ke sha es based on o al e enues and he He indahl-
He indahl Index (HHI)
11
sugges ha he ma ke o CRAs is highly concen a ed,
bo h o e all and a he indi idual p oduc ca ego y le el, wi h a small inc ease o
concen a ion be ween 2012 and 2014. The summa y o ma ke sha es o c edi
a ing ac i i y and ancilla y se ices p o ided in he Eu opean Union can be seen
in Table 2-9. The h ee la ges CRAs co e mos o he ma ke , eaching a ound
96% du ing he e e ence pe iod, while he emaining sha e, abou 4%, is illed by
he o he , much less c i ical CRAs.
11
Acco ding o he epo , HHI p o ides an indica ion o concen a ion wi hin ma ke s,
wi h an HHI o e 1,000 gene ally conside ed o be concen a ed.
The Essen ials o C edi Ra ing Assessmen 43
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Table 2–9 Ma ke sha es o c edi a ing ac i i y and ancilla y se ices
CRA
2012
2013
2014
Moody’s
36.69%
36.38%
36.99%
S&P
32.88%
36.00%
38.43%
Fi ch
17.67%
16.47%
18.40%
Eule He mes Ra ing GmbH
0.24%
0.26%
0.25%
Fe i Eu oRa ing Se ices AG
0.84%
0.78%
0.76%
BCRA-C edi Ra ing Agency AD
0.02%
0.03%
0.00%
C edi e o m Ra ing AG
0.51%
0.54%
0.51%
Scope Ra ings AG
0.10%
0.20%
0.17%
GBB-Ra ing Gesellscha ü Boni ä sbeu eilung
GmbH
0.34%
0.34%
0.33%
ASSEKURATA (Asseku anz Ra ing-Agen u
GmbH)
0.30%
0.31%
0.27%
ARC Ra ings, S.A. (p e iously Companhia
Po uguesa de Ra ing, S.A)
0.04%
0.03%
0.02%
AM Bes Eu ope-Ra ing Se ices L d. (AMBERS)
0.75%
0.73%
0.47%
DBRS Ra ings Limi ed
0.82%
1.23%
1.39%
CRIF S.p.A.
0.35%
0.77%
0.07%
Capi al In elligence (Cyp us) L d
0.00%
0.00%
0.03%
Eu opean Ra ing Agency, a.s.
0.00%
0.00%
0.00%
Axeso SA
1.85%
1.41%
0.73%
The Economis In elligence Uni L d
6.48%
4.41%
1.05%
Dagong Eu ope C edi Ra ing S l (Dagong
Eu ope)
0.01%
0.01%
0.01%
Sp ead Resea ch
0.09%
0.09%
0.13%
Eu oRa ing Sp. z o.o.
0.01%
0.01%
0.00%
HHI-index
2,787
2,916
3,189
Sou ce: EC (2016)
2.9.2 Con lic s o In e es
CRAs, simila ly o o he inancial in e media ies, play a c ucial ole in he
inancial sys em because hei expe ise in in e p e ing signals and collec ing
in o ma ion om hei cus ome s gi es hem a cos ad an age in p oducing
in o ma ion. Thus, CRAs posi i ely a ec he p oblem o asymme ic in o ma ion
in he inancial ma ke because bo owe s ha e some in o ma ion hey do no
disclose o lende s. Hence, one pa y in he con ac o en does no ha e enough
in o ma ion o make accu a e decisions. Howe e , he e is a po en ial p oblem o
con lic s o in e es : One pa y in a inancial ag eemen may ha e incen i es o ac
in hei in e es a he han in he in e es o he o he pa y. Since CRAs p o ide
e y specialized, usually mul iple inancial se ices, con lic s o in e es may a ise
in he a ing indus y; see, o example, Mishkin and Eakins (2009) o Cecche i
and Schoenhol z (2015).
Con lic s o in e es can subs an ially educe he quali y o in o ma ion and
e en inc ease asymme ic in o ma ion p oblems. Fo his eason, he nex issue o
he Repo is he p oblem o con lic s o in e es a ising om he ac ha while
44 Chap e 2
2024 Ma ina No o ná
in es o s and egula o s demand a well- esea ched c edi quali y assessmen ,
issue s need a a ou able a ing. Since he issue s o secu i ies pay a a ing i m o
ha e hei secu i ies a ed, in es o s and egula o s may ques ion hei a ing
quali y (Mishkin and Eakins, 2009). O he con lic s o in e es migh be be ween
CRAs and sha eholde s and CRAs on a i m le el and i s employees (e.g. a ing
analys s). They a e linked o ancilla y consul ing se ices p o ided by CRAs in
e ms o audi ing and consul ancy se ices. CRAs may deli e a ou able a ings
o a ac mo e clien s and hus inc ease asymme ic in o ma ion in inancial
ma ke s (EC, 2016). Ano he p oblem o con lic s o in e es migh be connec ed
o s uc u ed deb ins umen s (E ing and Hau, 2015).
The Repo (EC, 2016) highligh s ha con lic s o in e es a e ela ed o
compe i ion in he indus y. The e a e wo phenomena linked o his p oblem and
discussed in he li e a u e (EC, 2016, p. 72):
• Ra ing shopping: In his si ua ion, issue s solici a ings om mul iple
agencies and hen choose he mos a ou able one. This phenomenon can
lead o a ing in la ion.
• Ra ing ca e ing: A si ua ion s ic ly ela ed o a ing shopping. CRAs may
be incen i ised o loosen hei s anda ds o compe e wi h mo e a ou able
a ings om o he CRAs, usually in booming ma ke s, when CRAs ha e
ewe conce ns abou hei epu a ion and ma ke sha es (Sangio gi and
Spa , 2013).
2.9.3 T anspa ency
I he ope a ing ac i i ies and ac ions o CRAs a e easy o o he pa icipan s o
see and unde s and, hen he CRAs a e conside ed anspa en . As Nye (2014)
sugges s, he a ing agencies ha e become a po en o ce in demanding
anspa ency in he accoun s o issue s hey a e since he Asian inancial c isis o
1997 – 1998. Thus, CRAs emphasised mo e p ecise da a, mo e open accoun ing,
and con o ming o in e na ional s anda ds o inc ease hei epu a ion. Howe e ,
du ing he inancial c isis o 2008 – 2009, a ing agencies ailed o publish accu a e
and adequa e a ings in many cases, especially in assessing s uc u ed p oduc s.
Due o he Basle ules, he e was a s ong demand o high a ings by inancial
ins i u ions ha a e no pe mi ed o hold asse s wi h lowe a ing g ades. Fo
example, as C o y (2009) says, in 2005, mo e han 40% o Moody’s e enue came
om a a ing o secu i ized deb . Due o inancial boom, inexpe ience o
igno ance, CRAs issued absu dly high a ings o illiquid, non- anspa en
s uc u ed inancial p oduc s. While he explosion o hese inno a i e secu i ies
c ea ed la ge p o i s a inancial ins i u ions, i also des oyed he anspa ency
necessa y o any aspec o ma ke e iciency.
Al hough CRAs aim o imp o e hei c edibili y and anspa ency, he e is s ill
a lack o accoun abili y in he c edi a ing indus y. Some a gumen s p o ided
(e.g. Pagano and Volpin, 2010) ha issue s should disclose all he in o ma ion
ele an o assessing he p oduc s' isk ins ead o equi ing CRAs o disclose he
in o ma ion hey used. On he o he hand, he e a e also a gumen s ega ding
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 51
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Fishe (1959). Reg ession analysis became one o he mos used me hods o
es ima e a ings in his pe iod. An al e na i e app oach o p edic ing bond a ings
is he mul iple disc iminan analysis in oduced, o example, by Pinches and
Mingo (1973), Ang and Pa el (1975), Al man and Ka z (1976) and Belkaoui
(1980). O he esea ch compa ed pa icula s a is ical me hods; e.g. Kaplan and
U wi z (1979) compa e o de ed p obi analysis wi h o dina y leas squa e
eg ession, and Wingle and Wa s (1980) compa e o de ed p obi analysis wi h
mul iple disc iminan analysis. O he s udies eplica e he p ocess o bond a ing
model es ima ion and modi y he app oaches by conside ing new a iables, such
as he s udy o Chan and Jegadeesh (2004), o examine he impac o inancial
a iables on c edi a ing o a gi en coun y o egion, e.g. G ay e al. (2006).
Recen s udies come om he heo e ical amewo k men ioned abo e and ex end
s a is ical me hods o new non-conse a i e app oaches such as neu al ne wo ks
(Du a and Shekha , 1988; Su kan and Single on, 1990). Fo example,
Waagepe e sen (2010) assesses he ela ionship be ween quan i a i e models and
expe a ing e alua ion. Mo e ecen ly, Al man e al. (2010) ocused on he
impo ance o non- inancial in o ma ion wi hin isk managemen .
Resea ch in a ing p edic ion has shi ed mainly o applying machine lea ning
me hods in ecen yea s. Hsu e al. (2018) p opose a model based on he a i icial
bee colony app oach and suppo ec o machine echnique. The au ho s ind ha
hei bio-inspi ed compu ing mechanism imp o es p edic ion accu acy compa ed
o o he s a is ical me hods. Golbayani e al. (2020) compa e neu al ne wo ks,
suppo ec o machines and decision ees. The au ho s ind ha he decision ee-
based model achie es he bes pe o mance. In hei esea ch, hey apply
con en ional accu acy measu es and in oduce he no ch dis ance app oach, which
is sui able o compa ing he pe o mance o a ious machine lea ning me hods.
As i u ns ou , all he abo e echniques a e app op ia e o a ing p edic ion. The
indi idual models di e mainly in he me hodology, used a iables, and abili y o
p edic he a ing. The e o e, esea ch in his a ea is ocused p ima ily on
imp o ing he p edic i e accu acy o models. Fo example, Wang and Ku (2021)
de eloped he pa allel a i icial neu al ne wo ks model ha c ea es se e al
independen a i icial neu al ne wo ks. As he au ho s sugges , hei app oach
achie ed compe i i e esul s compa ed o con en ional a i icial in elligence
echniques.
Cu en esea ch shows ha con en ional app oaches and newe me hods
based on a i icial in elligence a e widely used o model c edi a ings. The huge
ad an age o hese models is hei p ac ical applicabili y and he possibili y o
using hem o po en ial a ing e isions. In addi ion, esea ch s udies show ha
models' p edic i e powe is su icien and compa able o o he commonly used
me hods in aluing his o ical da a based on a e ages o g ow h a es. Fo example,
Jones e al. (2015) examine he p edic i e pe o mance o bina y classi ie s using
a la ge sample o in e na ional c edi a ings. They apply con en ional echniques
(logi and p obi eg ession, linea disc iminan analysis) and ully nonlinea
classi ie s (neu al ne wo ks, suppo ec o machines, gene al boos ing, AdaBoos
and andom o es s). The au ho s conclude ha al hough he newe classi ie s
52 Chap e 3
2024 Ma ina No o ná
ou pe o m o he s, simple ones can be iable al e na i es o mo e sophis ica ed
app oaches, pa icula ly i in e p e abili y is an impo an objec i e o p edic i e
models.
The li e a u e e iew shows ha a ious s udies a e ocused on modelling
a ings using undamen al-based app oaches. Howe e , om he applica ion poin
o iew, hese s udies do no pay su icien a en ion o Czech en i ies o companies
om CEE coun ies. A he same ime, knowledge o he a ing and i s in luencing
ac o s has u iliza ion in many a eas. I is p ima ily an assessmen o he
in es men quali y o un a ed bonds. Ano he applica ion is, o example,
co po a e inance and he issue o de e mining he cos o capi al. In any case, he
absence and una ailabili y o a ing models a e he main mo i a ion o his s udy.
The main bene i is applying CEE coun ies' da a, including he applica ion o
models co esponding o Czech condi ions and needs. The pa ial goal is o p esen
he models’ es ima ion p ocess, in e p e a ion, and mu ual compa ison.
An al e na i e way p o ided in his wo k o model a ings is based on ime- o-
e en o su i al analysis. Fo example, Glennon and Nig o (2005) use a disc e e-
ime haza d amewo k o measu e he de aul isk o small business loans. Roa e
al. (2009) p opose a su i al analysis me hodology o analyze alling a ing
du a ion. They es mac oeconomic a iables o p edic his e en in selec ed
coun ies and ind di e ences be ween de eloped and eme ging economies. In
u he esea ch, Zhang and Thomas (2012) compa e linea eg ession and su i al
analysis o modelling eco e y a es. The au ho s ind ha linea eg ession is
be e o eco e y a e modelling; howe e , hey sugges some adjus men s and
addi ional alida ion. O e all, su i al analysis me hods a e ypically used o
a ing o c edi ansi ions and ime se ies a ing pa e ns (e.g. Pa nes, 2007;
Figlewski e al., 2012; Louis e al., 2013; Leow and C ook, 2014). Thus, we can
model he a ing beha iou o e ime and measu e, o example, he p obabili y o
a ce ain change in he a ing depending on ime and o he ele an a iables.
The e o e, su i al analysis allows us be e o unde s and he da a and i s
dynamics o e ime. In addi ion, i is a me hod used by a ing agencies o es ima e
de aul a es, which a e egula ly published and used by analys s and esea che s
in he inancial ma ke .
As pa o c edi isk measu emen , a en ion is also hea ily paid o bank up cy
p edic ion. The bank up cy o companies is ypically analysed based on c edi
sco e models, which a e s a is ically de i ed models o p edic ing c edi isk.
Among all he s udies on sco ing models, he s udy by Al man (1968) and he
model known as Al man´s o Z-sco e model a e wo h men ioning. Since he i s
publica ion o his model, ex ensi e esea ch has been conduc ed in bank up cy
p edic ion and he applica ion o disc iminan analysis, logis ic eg ession,
classi ica ion ees, and neu al ne wo ks. In addi ion, he su i al analysis
app oach can be seen as an al e na i e way o examine co po a e bank up cy.
Howe e , his a ea has no ye a ac ed adequa e a en ion compa ed o he
adi ional me hods men ioned abo e.
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 53
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Ne e heless, some s udies apply su i al analysis o p edic co po a e ailu e
in di e en coun ies. Fo example, he ea lie esea ch includes Lane e al. (1986),
who employed he Cox model o p edic bank ailu e using a sample o 130 banks.
As he au ho s sugges , he o e all accu acy o hei model is simila o he
disc iminan analysis esul s. Among o he s udies, Lai inen and Kankaanpää
(1999) discuss he six mos popula al e na i e me hods o inancial ailu e
p edic ion, including su i al analysis. Howe e , hei esea ch p oposes no only
one way, e en hough he accu acy o ailu e p edic ion a ies depending on he
echnique applied. O he empi ical esul s include he s udy by Aga wal and
Aud e sch (2001), who ocus on he e ec o companies’ size on hei su i al.
Thei esea ch inds ha smalle companies a e less likely o su i e han la ge
companies. Howe e , hey sugges ha gene al p onouncemen s a e haza dous
because he size changes o e he indus y cycle and wi h he echnological
demands o ha indus y.
Simila ly, Glennon and Nig o (2005) examined he e ec o ime on he
p obabili y o de aul on medium–ma u i y loans unde a loan gua an ee p og am
o small i ms. The au ho s ind ha he de aul beha iou o hese loans is ime-
sensi i e. As loan seasons, he p obabili y o de aul ini ially inc eases, and i
declines a e he second yea . They also sugges ha he likelihood o de aul is
condi ional on he bo owe , lende , loan cha ac e is ics and changes in economic
condi ions. Finally, De Leona dis and Rocci (2008) used a disc e e- ime su i al
analysis app oach o assess he de aul isk o small and medium-sized I alian
companies om 1995-1998. The au ho s sugges ha he p edic ion accu acy o
he du a ion model is be e han ha p o ided by a single-pe iod logis ic model.
In addi ion o examining he e ec o inancial and economic ac o s on
co po a e ailu e, some s udies assess he impac o o he ac o s. Fo example,
Moka ami and Mo e a es (2013) examine he e ec o he in e nal mechanisms o
co po a e go e nance on he bank up cy o i ms enlis ed in he Teh an S ock
Exchange. Using he Cox model o su i al analysis, he au ho s claim a
signi ican ela ionship be ween CEO eplacemen and bank up cy. O he esea ch
includes, o example, Pe ei a (2014), who applied he Cox p opo ion haza d
model in p edic ing business ailu e o companies in he ex ile indus y, and Kelly
e al. (2015), who ocused on co po a e liquida ions in I eland. Louzada e al.
(2014) modelled he ime o de aul on a pe sonal loan po olio. They s a e ha
su i al models a e being p oposed in inancial isk managemen as al e na i e
ools due o he con inuous moni o ing o isk o e ime. Thei empi ical s udy is
illus a ed by c edi da a om a B azilian comme cial bank. Thei esul s show
ha a en ion should be paid o con inuously checking he alidi y o equi emen s
o using he a ailable models. Besides he p oblems o loan de aul and
bank up cy, K is an i and Isynuwa dhana (2018) examined he e ec o ce ain
p edic o s on he p obabili y o inancial dis ess o companies enlis ed on he
Indonesia S ock Exchange. Applying he Cox haza d model o su i al analysis,
hey ound e idence ha he e is an in e se ela ionship be ween he con ol o
co up ion and he p obabili y o inancial dis ess, excep o he p edic o s such
as le e age, ope a ional isk, and size.
54 Chap e 3
2024 Ma ina No o ná
O e all, he e is a as li e a u e on p edic ing co po a e bank up cy using
a ious echniques. Howe e , he e is s ill li le a en ion o modelling co po a e
bank up cy using ime- o-e en me hods. This ac is one o he mo i a ions o ou
esea ch, which is o compa e commonly used app oaches wi h less equen ly
applied su i al analysis me hods. The main con ibu ion o his monog aph is he
expansion o exis ing esea ch in his a ea and he applica ion o selec ed models
o speci ic da a om CEE coun ies, espec i ely, om he Czech Republic. The
main goal is o ind a link be ween a ing and su i al models, iden i y he main
p edic i e a iables and p opose a p ocedu e o con e bank up cy a es in o
a ing e alua ions. As a esul , he associa ion be ween he p obabili y o su i al
and he a ing, o he p edic ed de elopmen o he a ing o e ime, can be be e
unde s ood. Fu he mo e, as he a ing is widesp ead and used globally, we belie e
he in e p e a ion o c edi isk using he a ing is mo e sui able o use s,
especially o indi idual in es o s.
All pa icipan s in c edi con ac s can use he main indings o his wo k. In
addi ion, i is use ul o analy ical depa men s ha c ea e ma hema ical-s a is ical
models o moni o ing and measu ing c edi isk in banks and o he inancial
ins i u ions. Ne e heless, we see he main use on he pa o e ail in es o s,
whe he indi iduals o companies, who can use he pa ial esul s o he wo k in
se e al di ec ions, mainly o a be e unde s anding o he ac o s ha
signi ican ly in luence he su i al p obabili y and, hus, he o e all a ing
e alua ion. Fu he mo e, he esul s o his wo k can be u he used o apply
selec ed models o hei own da a and hei subsequen use o measu e c edi isk.
Finally, his wo k can also be used in academic esea ch as an example o
connec ing wo di e en app oaches o c ea ing mic o c edi isk models and
possibly expanding u he .
3.2 Disc iminan Analysis
Disc iminan analysis is a s anda d s a is ical me hod used o sepa a e g oups and,
hus, a sui able me hod o c edi sco ing o bond a ing modelling. The analysis
can be used o wo p ima y objec i es: i s , he desc ip ion o g oup sepa a ion;
second, p edic ing o alloca ing obse a ions o g oups. Hube y and Olejnik
(2006) dis inguish be ween desc ip i e disc iminan analysis (DDA) and
p edic i e disc iminan analysis (PDA). The pu pose o DDA is usually he s udy
o compa ison among a ce ain numbe o g oups, o each o which we ha e
se e al ou come a iable sco es. Howe e , suppose a single se o esponse
a iables is used as p edic o s, and he e is a single g ouping a iable. In ha case,
he p ima y pu pose is o analyse how well g oup membe ship o analysis uni s
may be p edic ed using PDA. Co espondingly, Renche (2002) di e en ia es
be ween disc iminan and classi ica ion unc ions. Disc iminan unc ions sepa a e
g oups, while classi ica ion unc ions assign indi idual uni s o one o mo e
g oups. In g oup sepa a ion, linea unc ions o a iables desc ibe he di e ences
be ween wo o mo e g oups. The main objec i e is o iden i y he ela i e
con ibu ion o p a iables o spli . The la e p oblem is ocused on he p edic ion
o alloca ion o obse a ions o g oups, which is a common goal o disc iminan
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 55
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
analysis. A p edic ion ule hen consis s o a se o linea combina ions o
p edic o s, whe e he numbe o combina ions e lec s he numbe o g oups.
Disc iminan unc ions a e linea combina ions o a iables ha bes sepa a e
g oups, o example, he k g oups o mul i a ia e obse a ions. The desc ip ion o
disc iminan analysis and me hods can be ound, o ins ance, in Renche (2002),
Manly (2005), Hube y and Olejnik (2006), Tabachnik and Fidell (2007), Ha ell
(2010) o Hai e al. (2014). As Renche (2002) sugges s, linea unc ions o
a iables (disc iminan unc ions) desc ibe he di e ence be ween wo o mo e
g oups o g oup sepa a ion. The goal is o iden i y he ela i e con ibu ion o he
p a iables o sepa a ion and de i e disc iminan unc ions as linea combina ions
o a iables ha bes sepa a e g oups.
Fi s ly, we assume he disc iminan unc ion o wo g oups ( he ollowing
de ini ions and equa ions a e aken om Renche , 2002):
• The wo popula ions o be compa ed ha e he same co a iance ma ix bu
dis inc mean ec o s
1
and
2
,
• we assume samples
1
11 12 1
, , , n
y y y
and
2
21 22 2
, , , n
y y y
om he wo
popula ions,
• each ec o
ij
y
consis s o measu emen on p a iables.
The disc iminan unc ion is he linea combina ion o hese p a iables ha
maximizes he dis ance be ween he wo ( ans o med) g oup ec o s. Thus, a
linea combina ion
'z=ay
ans o ms each obse a ion ec o o a scala :
1 1 1 1 1 2 1 2 1 1,
' ... , 1,2,...,
i i i i p ip
z a y a y a y i n= = + + + =ay
,
1 2 1 2 1 2 2 2 2 2,
' ... , 1,2,...,
i i i i p ip
z a y a y a y i n= = + + + =ay
.
Then he
12
nn+
obse a ions in wo samples,
12
11 21
12 11
12
,
nn
yy
yy
yy
a e ans o med in o scala s,
12
11 21
12 11
12
.
nn
zz
zz
zz
56 Chap e 3
2024 Ma ina No o ná
We ind he means
1
1 1 1 1
1
n
i
i
z z n
=
==
ay
and
22
z
=ay
, whe e
1
1 1 1
1
n
i
in
=
=
yy
and
2
2 2 2
1
n
i
in
=
=
yy
. Then, we ind he ec o a ha maximises
he s anda d di e ence
12
( )/ z
z z s−
. Finally, we use he squa ed dis ance
22
12
( ) / z
z z s−
so ha he esul is posi i e:
( )
2
212
12
2pl
()
z
zz
s
−
−
=
a y y
a S a
,
(3.1)
whe e Spl is he pooled co a iance ma ix and n1 + n2 – 2 > p. The maximum o
(3.1) occu s when
-1
pl 1 1
( ),=−a S y y
(3.2)
o when a is any mul iple o
-1
pl 1 1
()=−a S y y
. The maximizing ec o is no
unique; howe e , i s di ec ion, o he ela i e alues o a ios o
12
, , , p
a a a
a e
unique, and
z
=ay
p ojec s poin s y on o he line on which
22
12
( ) / z
z z s−
is
maximized.
The linea disc iminan analysis (LDA) can be used o mo e han wo g oups.
Thus, we can ex end he p e ious case o he s udy o se e al g oups. The
objec i e is o ind linea combina ions o a iables ha bes sepa a e he k g oups
o mul i a ia e obse a ions. We assume ha o k g oups wi h ni obse a ions in
he i h g oup, we ans o m each obse a ion ec o
ij
y
o ob ain
ij ij
z
=ay
, whe e
i = 1, 2,..., k and j = 1, 2,..., ni. Then, we ind he means
ij i
z
=ay
, whe e
1
i
n
ij i
jn
=
=
i
yy
. Simila ly, o he wo-g oup analysis, we seek he ec o a ha
maximally sepa a es
12
, , , k
z z z
. In his case, he o mula (3.2) will be ex ended
o k-g oups. Assuming ha
( ) ( )
1 2 1 2
− = −a y y y y a
, hen
( ) ( ) ( )( )
2
2
12
1 2 1 2 1 2
2pl pl
z
zz
s
−
− − −
==
a y y a y y y y a
a S a a S a
(3.3)
In he case o k-g oups, he sepa a ion c i e ion among
12
, , , k
z z z
can be
exp essed in e ms o ma ices, whe e he H ma ix deno es
( )( )
1 2 1 2
−−y y y y
and he ma ix E eplaces Spl,
=
a Ha
a Ea
,
(3.4)
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 57
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Ma ix H has a be ween sum o squa es on he diagonal o each o he p
a iables, and ma ix E has a wi hin sum o squa es o each a iable on he
diagonal.
Al e na i ely, he sepa a ion c i e ion can be exp essed as
SSZ( )
SSE( )
z
z
=
,
(3.5)
whe e SSH (z) and SSE (z) a e he be ween and wi hin sums o squa es o z. The
o mula (3.4) can be ew i en as:
( )
,
0.
=
−=
a Ha a Ea
a Ha Ea
(3.6)
Nex , we examine alues o
and a ha a e solu ions o (3.6):
1
0,
( ) 0,
−
−=
−=
Ha Ea
E H I a
(3.7)
whe e I e e s o he in e sion ma ix. The solu ions a e he eigen alues
12
, , , s
and co esponding eigen ec o s
12
, , , s
a a a
o
1−
EH
. F om he s
eigen ec o s, we ob ain s disc iminan unc ions
1 1 2 2
, , , ss
z z z
= = =a y a y a y
which show he dimensions o di ec ions o di e ences among
12
, , , .
k
y y y
The
a io o i s eigen alue can calcula e he ela i e impo ance o each disc iminan
unc ion as a p opo ion o he o al:
1
i
s
j
j
=
(3.8)
The coe icien s in disc iminan unc ions can be used o assess he
con ibu ion o he y’s o he sepa a ion o g oups. As Renche (2002, p. 283)
sugges s, his compa ison is in o ma i e i he y’s a e measu ed on he same scale
and wi h compa able di e ences. Fo his eason, we use s anda dized
disc iminan unc ions (see, o example, Renche (2000) o a mo e de ailed
desc ip ion).
3.2.1 Tes s o Signi icance
To es hypo heses, we assume mul i a ia e no mali y. The disc iminan c i e ion
(3.8) is maximized by
1
, he la ges eigen alue. The emaining eigen alues
2,,
s
a e associa ed wi h o he disc iminan dimensions.
The signi icance es is usually based on he Wilks’ lambda (Wilks’
), and
he eigen alues a e used in he es o signi ican di e ences among mean ec o s.
I he hypo hesis H0 is ejec ed, we conclude ha a leas one
's
is signi ican ly
58 Chap e 3
2024 Ma ina No o ná
di e en om ze o. The e o e, he e is a leas one dimension o sepa a ion o
mean ec o s. Each
i
is g adually es ed un il a es ails o ejec H0. The es
s a is ic a he m h, s ep (m = 2, 3, …, s) is:
1
1
s
mim i
=
= +
,
(3.9)
which is dis ibu ed as
1, , 1p m k m N k m− + − − − +
. The s a is ic
( ) ( ) ( )
11
1 ln 1 ln 1
22
s
m m i
im
V N p k N p k
=
= − − − + = − − + +
(3.10)
has an app oxima e
2
- dis ibu ion wi h (p-m+1)(k-m) deg ees o eedom. I
mo e
's
a e s a is ically signi ican , we may no conside he associa ed
disc iminan unc ion i
/
ij
j
is small, e en i i is signi ican (Renche ,
2002).
3.2.2 In e p e a ion o Disc iminan Func ions
The main pu pose o in e p e a ion is o assess he con ibu ion o each a iable.
Howe e , he signs o he coe icien s a e conside ed. Acco ding o Renche
(2002), he e a e h ee gene al app oaches o assessing he con ibu ion o each
a iable o sepa a ing he g oups:
• S anda dized disc iminan unc ion coe icien s,
• pa ial F- es o each a iable,
• co ela ion be ween each a iable and he disc iminan unc ion.
S anda dized coe icien s a e use ul when he a iables a e measu ed on
di e ing scales. In ha case, coe icien s a e adjus ed so ha hey apply o
s anda dized a iables. Fo example, o he obse a ions in he i s o wo g oups,
11
1 1 11 1 2 12
1 1 2
12
,
ip p
ii
ip
p
yy
y y y y
z a a a
s s s
−
−−
= + + +
(3.11)
whe e i =1, 2,…, n1. The s anda dized a iables
11
/
i
y y s−
a e scale- ee, and
he s anda dized coe icien s
a s a
=
, whe e = 1, 2,…, p. This s anda diza ion
is applied o each o he s disc iminan unc ions. The con ibu ion o he a iables
o sepa a ing he g oups is based on he absolu e alues o he coe icien s. The
s abili y o coe icien s may a y om sample o sample; o example, i N/p is
oo small, one sample's impo an a iables may eme ge as less impo an in
ano he sample.
The second app oach o assessing he con ibu ion o each a iable is based on
a pa ial F- alue. We can calcula e a pa ial F- es o any a iable y and ank he
a iables. Fo example, in he case o wo g oups, he pa ial F- alue is:
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 59
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
( )
22
1
21
1,
pp
p
TT
Fp T
−
−
−
= − + +
(3.12)
whe e
2
p
T
is he wo-sample Ho elling
2
T
wi h all p a iables,
21p
T−
is he
2
T
-
s a is ic wi h all a iables excep y , and
12
2nn
= + −
. The F-s a is ic is
dis ibu ed as
1, 1p
F
−+
.
Con e sely o s anda dized coe icien s, he pa ial F- alues a e no associa ed
wi h a single dimension o g oup sepa a ion. Fo example, y2 will ha e a di e en
con ibu ion in each o he s disc iminan unc ions; howe e , he pa ial F o y2
c ea es an o e all index o he con ibu ion o y2 o g oup sepa a ion, conside ing
all dimensions.
Finally, he co ela ion be ween a iables and disc iminan unc ions can be
used o assess each a iable's con ibu ion. These co ela ions a e usually e e ed
o as loadings o s uc u e coe icien s. Renche (2002) poin s ou ha hese
co ela ions show each a iable's con ibu ion in a uni a ia e con ex a he han
in a mul i a ia e one.
In addi ion o LDA, which is one o he well-known me hods, we use quad a ic
and logis ic me hods o disc iminan analysis in he applica ion pa .
• Quad a ic disc iminan analysis (QDA) is a a ian o LDA ha allows o
he non-linea sepa a ion o da a.
• Logis ic disc iminan analysis (LogDA) is when he pos e io p obabili ies
a e es ima ed by mul i-nominal logis ic eg ession (MLR).
3.2.3 Selec ion o Va iables
The e a e usually a la ge numbe o dependen a iables a ailable in disc iminan
analysis applica ions. Fo his eason, i is use ul o selec only some o he
a iables ha will be inally conside ed o sepa a ing g oups. Fo he selec ion o
a iables, we can use he ollowing me hods o disc iminan analysis (Renche ,
2002):
• Fo wa d selec ion is when we begin wi h a single a iable ( he one ha
maximally sepa a es g oups). Then, he a iable en e ed a each s ep is he
one ha maximises he pa ial F-s a is ic based on Wilks’s lambda.
• Backwa d selec ion, when we begin wi h all he a iables, and hen a each
s ep, he a iable ha con ibu es leas is dele ed acco ding o he pa ial F-
s a is ic.
• S epwise selec ion is when we combine he o wa d and backwa d
app oaches. Va iables a e added one a a ime, and a each s ep, hey a e e-
examined. The p ocedu e ends when he la ges pa ial F among a iables
a ailable o en y ails o exceed a p e-se h eshold alue.
60 Chap e 3
2024 Ma ina No o ná
3.2.4 Classi ica ion Analysis
The a en ion in he p e ious ex was paid p ima ily o a desc ip i e aspec o
disc iminan analysis. On he o he hand, he disc iminan analysis can also sol e
alloca ion and g oup membe ship p edic ion. In classi ica ion, a sampling uni
wi h unknown g oup membe ship is assigned based on he ec o o p measu ed
alues, y. As Renche (2002) sugges s, he one app oach is o compa e y wi h he
mean ec o s
12
, , , .
k
y y y
o he k samples. Then, he uni is assigned o he g oup
whose
i
y
is closes o y.
We can use a classi ica ion p ocedu e sugges ed by Fishe (1936, ci ed in
Renche , 2002) in wo popula ions. Using Fishe ’s app oach, we assume ha he
wo popula ions ha e he same co a iance ma ix,
12
=
, no mali y is no
equi ed. Supposing ha we ge wo samples om wo popula ions, we can
compu e
12
,yy
and Spl. The classi ica ion is based on he disc iminan unc ion,
( )
1
1 1 pl
z−
= = −a y y y S y
,
(3.13)
whe e y is he ec o o measu emen s on a new sampling uni ha we classi y
in o one o he wo g oups.
To de e mine he g oup membe ship, we compa e z wi h he ans o med mean
1
z
o
2
z
. Fo each obse a ion
1i
y
om he i s sample, we e alua e (3.13),
ob ain
1
11 12 1
, , , n
z z z
and ge
( )
11
1 1 1 1 1 2 pl 1
1/
n
i
i
z z n −
=
= = = −
a y y y S y
, simila ly
22
z
=ay
. Assuming wo g oups a e e e ed o as G1 and G2, y is assigned o G1
i
z
=ay
is close o
1
z
han o
2
z
acco ding o he Fishe ’s linea classi ica ion
p ocedu e, o o G2 i
z
is close o
2
z
.
In he wo-g oup case, he linea classi ica ion unc ion is exp essed as he
disc iminan unc ion o g oup sepa a ing. Howe e , he classi ica ion unc ions
a e di e en in he se e al-g oup case. Supposing classi ica ion o se e al g oups,
k, we ind he sample mean ec o s
12
, , , k
y y y
. We can use a dis ance unc ion
o assign a g oup membe ship o a ec o y o ind he mean ec o ha y is closes
o and se y o he co esponding g oup.
I we assume equal popula ion co a iance ma ices,
12 k
= = =
, hen we
ob ain linea classi ica ion unc ions. A linea unc ion
( )
i
Ly
can be exp essed
as:
( )
0 1 1 2 2 0,
i i i i i ip p i
L c c y c y c y c
= + = + + + +y c y
(3.14)
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 67
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
( )
( )
( )
( )
2
0
P ,
j
k
g
jg
k
e
Yj
e
=
= = =
x
x
xx
(3.34)
whe e he ec o
00=β
and
( )
00.g=x
The a iables a e coded as ollows:
• I Y = 0, hen Y0 = 1, Y1 = 0, Y2 = 0,
• i Y = 1, hen Y0 = 0, Y1 = 1, Y2 = 0,
• i Y = 2, hen Y0 = 0, Y1 = 0, Y2 = 1,
and he sum o hese a iables is
2
01.
j
jY
==
Then he condi ional likelihood
unc ion o a sample o n independen obse a ions is:
( ) ( ) ( ) ( )
0 1 2
0 1 2
1
,
i i i
ny y y
i i i
i
l
=
=
β x x x
(3.35)
and he log-likelihood unc ion can be exp essed as:
( ) ( ) ( )
( ) ( )
( )
12
1 1 2 2
1
ln 1 .
ii
ngg
i i i i
i
L y g y g e e
=
= + − + +
xx
β x x
(3.36)
The likelihood equa ions can be ound by aking he i s pa ial de i a i es o
( )
Lβ
wi h espec o each o he 2(p + 1) unknown pa ame e s (see o example
Hosme e al. (2013) o mo e de ails).
Analogically o he bina y model, he mul i a iable model is in e p e ed by
odds a ios. Fo example, i we assume ha he ou come a iable
0Y=
is he
e e ence ou come, hen he odds a io o he ou come
Yj=
e sus ou come
0Y=
o co a ia e alues o x = a e sus x = b is:
( )
( ) ( )
( ) ( )
P P 0
,.
P P 0
j
Y j x a Y x a
OR a b Y j x b Y x b
= = = =
== = = =
(3.37)
The impo ance o he a iable in he model is based on he likelihood a io
es . To es he signi icance o coe icien s, we compa e he log-likelihood om
he i ed model con aining he coe icien s
( )
1
L
o he log-likelihood o he
model con aining only cons an e ms
( )
0
L
, one o each logi unc ion. The es
s a is ic can be exp essed as:
01
2.G L L= − −
(3.38)
68 Chap e 3
2024 Ma ina No o ná
The signi icance o he coe icien s o a a iable has deg ees o eedom equal
o he numbe o ou come ca ego ies minus one imes he deg ees o eedom o
he a iable in each logi .
Conce ning applying mul inomial logis ic eg ession o he bond a ing
p edic ion, ou c edi a ing analysis o i e ca ego ies will equi e ou logi
unc ions and de e mina ion o he baseline a ing ca ego y, which is hen
compa ed wi h o he logi s. A gene al exp ession o he condi ional p obabili y
in he i e-ca ego y model is:
( )
( )
( )
( )
5
1
P ,
j
k
g
jg
k
e
Yj
e
=
= = =
x
x
xx
(3.39)
and we o m ou logi s compa ing Y = 1, Y = 2, Y = 3 and Y = 4 o i . The ou
logi unc ions a e hen deno ed as:
( )
( )
( )
1 10 11 1 12 2 1 1
P 1
ln ,
P 5 pp
Y
g x x x x
Y
=
= = + + + + =
=
xxβ
x
(3.40)
( )
( )
( )
2 20 21 1 22 2 2 2
P 2
ln ,
P 5 pp
Y
g x x x x
Y
=
= = + + + + =
=
xxβ
x
(3.41)
( )
( )
( )
3 30 31 1 32 2 3 3
P 3
ln ,
P 5 pp
Y
g x x x x
Y
=
= = + + + + =
=
xxβ
x
(3.42)
( )
( )
( )
4 40 41 1 42 2 4 4
P 4
ln .
P 5 pp
Y
g x x x x
Y
=
= = + + + + =
=
xxβ
x
(3.43)
In addi ion o mul inomial logis ic eg ession analysis, we can also use an
o dinal logis ic eg ession app oach.
3.3.3 O dinal Logis ic Reg ession
Gene ally, mul inomial logis ic eg ession can be used i he ou come a iables
a e no nominal bu o dinal scale. Howe e , i is sugges ed o use he o dinal
logis ic eg ession, which espec s he ca ego ical ou come's na u al anking in
some cases. Mena d (2010) desc ibes o dinal a iables as ei he c ude
measu emen o a a iable ha could be measu ed on an in e al o a io scale o
measu emen o an abs ac cha ac e is ic o which he e is no na u al me ic o
uni o measu emen . Hosme e al. (2013) a gue ha mul inomial logis ic
eg ession could be used e en in hese cases. S ill, i mus be ealised ha no
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 69
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
conside ing he na u al o de ing o ou come a iables may lead o he p oblem ha
es ima ed models migh no add ess he analysis's ques ions. Thus, he o dinal
logis ic eg ession seems o be an app op ia e me hod o assessing bond a ing
ha conside s he ank o de ing o a ing ca ego ies. As Mena d (2010) says,
di e en models make di e en assump ions abou whe he he dependen a iable
is in insically o dinal o e lec s an unde lying con inuous in e al o a io
a iable. Va ious models can be p oposed o analyse o dinal dependen a iables,
such as he cumula i e logi model, he con inua ion a io logi model, he adjacen
ca ego ies logi model o he s e eo ype model. The cumula i e logi model is he
mos widely used logis ic eg ession model, and i is desc ibed in mo e de ail in
his chap e .
Acco ding o Hosme e al. (2013), he o dinal logis ic model can be desc ibed
using he ollowing de ini ions. We assume ha he o dinal ou come a iable, Y,
can ake on K + 1 alues coded 0,1,…, K. The p obabili y ha he ou come is equal
o k condi ional on a ec o x o p co a ia es is deno ed
( )
( )
P k
Yk
==xx
. I
he model is assumed o be mul inomial, hen
( ) ( )
kk
=xx
, whe e he model is
gi en in equa ions (3.31 – 3.33) o K = 2.
The mul inomial model is called he baseline logi model in he case o o dinal
logis ic eg ession. When we assume an o dinal model, we mus decide wha
ou comes o compa e and he mos easonable model o he logi . The e a e h ee
ollowing main al e na i es:
• Compa e each esponse o he nex la ge esponse (adjacen -ca ego y
logis ic model),
• compa e each esponse o all lowe esponses (con inua ion- a io logis ic
model),
• compa e he p obabili y o an equal o smalle esponse o he likelihood
o a la ge esponse (p opo ional odds model).
As he p opo ional odds model will be used o model bond a ing in he
applica ion pa , we desc ibe his app oach's p inciples in he ollowing ex . Using
he p opo ional odds model, we compa e he p obabili y o an equal o smalle
esponse,
Yk
, o he likelihood o a la ge esponse,
Yk
,
( )
( )
( )
( ) ( ) ( )
( ) ( ) ( )
01
12
P
ln ln ,
P
k
kk
k k K
Yk
cYk
++
+ + +
= = = −
+ + +
xx x x
xxβ
x x x
x
(3.44)
o k = 0, 1, …, K – 1. Supposing
1K=
, he model is simpli ied o he usual
logis ic eg ession model in ha i yields odds a ios o
0Y=
e sus
1Y=
.
The me hod used o i he o dinal model is based on adap ing he mul inomial
likelihood and log (3.36) o K = 2. The basic p ocedu e in ol es he ollowing
s eps (Hosme e al., 2013, p. 292):
70 Chap e 3
2024 Ma ina No o ná
a) The exp essions de ining he model-speci ic logi s a e used o c ea e an
equa ion de ining
( )
k
x
as a unc ion o he unknown pa ame e s.
b) The alues o a K + 1-dimensional mul inomial ou come,
( )
01
, , , k
z z z
=z
a e c ea ed om he o dinal ou come as
1
k
z=
i
yk=
and
0
k
z=
o he wise, whe e only one alue o z equals 1.
The gene al o m o he likelihood o a sample o n independen obse a ions
( )
, , 1,2, , ,
ii
y i n=x
is:
( ) ( ) ( ) ( )
01
01
1
,
i i Ki
nz z z
i i K i
i
l
=
=
β x x x
(3.45)
whe e
β
deno es bo h he p slope coe icien s and he K model-speci ic in e cep
coe icien s. Then, he log-likelihood unc ion can be exp essed as:
( ) ( ) ( ) ( )
0 1 1
1
ln ln ln .
n
i o i i i Ki K i
i
L z z z
=
= + + +
β x x x
(3.46)
When applying he me hod, i should be checked whe he he da a suppo he
assump ion o p opo ional odds. Tes s o assessing he goodness o i a e based
on he compa ison o he model o an augmen ed model in which he coe icien s
o he model co a ia es a e allowed o be di e en :
( )
( )
( )
P
ln ,
P
Yk k
ckk
Yk
= = −
β
x
xx
x
(3.47)
whe e
1kk
+
o
1, , .kK=
No ušis (2012, p. 70) explains a minus sign be o e he coe icien s o he
p edic o a iables, which is done so ha la ge coe icien s indica e an associa ion
wi h la ge sco es. Fo a con inuous a iable, posi i e coe icien s sugges ha he
likelihood o a la ge sco e inc eases as he a iable's alues inc ease. Each logi
has i s
k
e m bu he same coe icien , which means ha he independen
a iable's e ec is he same o di e en logi unc ions. The
k
e ms a e called
h eshold alues, and hey a e used in he calcula ions o p edic ed alues.
In he applica ion sec ion, he assigned a ing ca ego y is conside ed as he
ou come a iable in he model. Fo ins ance, in ou analysis (Chap e 4), he
a ings a e classi ied in o i e o dinal ca ego ies, anging om he lowes (BB) o
he highes (A) in e ms o bond in es men quali y. The e o e, we accoun o i e
dis inc a ing g ades, wi h he e en o in e es being he obse a ion o a speci ic
a ing g ade o lowe . In his con ex , he o dinal model will e alua e a se ies o
dicho omies be ween successi e a ing ca ego ies:
• g ade (1) e sus g ades (2, 3, 4 o 5),
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 71
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
• g ades (1 o 2) e sus g ades (3, 4 o 5),
• g ades (1 o 2 o 3) e sus g ades (4 o 5),
• g ades (1 o 2 o 3 o 4) e sus g ade (5).
Thus, in e ms o bond a ing g oups, we will es ima e he ollowing odds based
on he p opo ional odds model:
( )
( )
( )
( )
( )
( )
( )
( )
1
2
3
4
P a ing 1 ,
P a ing g ea e han 1
P a ing 1 o 2 ,
P a ing g ea e han 2
P a ing 1 o 2 o 3 ,
P a ing g ea e han 3
P a ing 1 o 2 o 3 o 4 .
P a ing g ea e han 4
=
=
=
=
(3.48)
The highes ca ego y, 5, does no ha e associa ed odds because he p obabili y
o being in ha ca ego y o any lowe ca ego y is 1. Unlike he mul inomial
app oach, o dinal logis ic eg ession equi es es ima ing only one se o eg ession
coe icien s.
3.3.4 ROC Analysis
The es ima ed models ep esen a classi ica ion ule used o assign objec s in o
classes. Thus, we need o know how e ec i ely his classi ica ion ule wo ks,
p e e ably using he alida ion sample. I means ha he a ailable da a a e spli
in o wo da ase s: an expe imen al sample ( aining) used o cons uc ing he ule
and he alida ion sample used o assessing he pe o mance. The e a e o he
ways o spli he da a, o example, he lea e-one-ou me hod, when only one da a
poin is pu in he alida ion sample and o he s in he expe imen al sample, o he
boo s ap me hods.
To unde s and how he pe o mance is measu ed, we need o speci y some
e ms equi ed o u he analysis. Acco ding o K zanowski and Hand (2009), a
classi ica ion ule yields a sco e s(X) o each objec . I will esul in dis ibu ion
( P)ps
o objec s in he posi i e g oup, P, and dis ibu ion
( N)ps
o objec s in
he nega i e g oup, N. Then, he classi ica ions a e gi en by compa ing he sco es
wi h a h eshold, T. The au ho s claim ha i we can ind a h eshold
T =
such
ha all membe s o class P ha e sco es ha a e all g ea e han
, and all membe s
o class N ha e sco es all less o equal o
, we a ain he pe ec classi ica ion.
Howe e , he wo se s o sco es ypically o e lap o some ex en , and pe ec
classi ica ion is impossible. In his case, pe o mance is measu ed by he ex en o
which sco es o objec s in class P end o ake la ge alues, and sco es o objec s
in class N end o ake small alues. The me hods used o hese measu emen s a e
72 Chap e 3
2024 Ma ina No o ná
based on he wo-by- wo classi ica ion able esul ing om c oss-classi ying he
ue class o each objec by i s p edic ed class. K zanowski and Hand (2009) s a e
ha he p opo ions o he alida ion se ha all in his able's cells a e empi ical
ealisa ions o join p obabili ies
( , ), ( , ), ( , ), ( , )p s P p s N p s P p s N
.
Then, di e en ways o summa ising hese ou join p obabili ies yield a ious
measu es o classi ica ion pe o mance. Gene ally, we can use he
misclassi ica ion o e o a e measu e, which is he p obabili y o a class N objec
ha ing a sco e g ea e han
o a class P objec ha ing a sco e less han
. The
misclassi ica ion a e is a widely used c i e ion; howe e , i weigh s wo kinds o
classi ica ion (class N misclassi ied as P, and ice e sa) equally impo an .
We use he ollowing wo condi ional p obabili ies and one ma ginal
p obabili y in he e alua ion o classi ica ion abili y (K zanowski and Hand,
2009):
• The alse posi i e a e
() p
– he p obabili y ha an objec om class N
yields a sco e g ea e han
: ( N) p s
,
• he ue posi i e a e
() p
– he p obabili y ha an objec om class P
yields a sco e g ea e han
: ( P) p s
,
• he ma ginal p obabili y ha an objec belongs o class
P: (P)p
.
Nex , we use wo complemen a y condi ional a es and one complemen a y
ma ginal p obabili y (K zanowski and Hand, 2009):
• The ue nega i e a e (
n
),
( N)p s
- he p opo ion o class N objec s
which a e co ec ly classi ied as class N, equal o
1 p−
,
• he alse nega i e a e (
n
),
( P)p s
- he p opo ion o class N objec s
which a e co ec ly classi ied as class N, equal o
1 p−
,
• he ma ginal p obabili y ha an objec belongs o class
: (N) 1 (P).N p p=−
The ue posi i e a e is ypically called he Sensi i i y (
Se
), and he ue
nega i e a e is he Speci ici y (
Sp
). The a es desc ibed abo e a e all condi ional
p obabili ies o ha ing a pa icula p edic ed class gi en he ue class. As
K zanowski and Hand (2009) poin ou , he e a e ob ious ela ionships be ween
he a ious condi ional, ma ginal, and join p obabili ies. Fo example, he
misclassi ica ion a e
e
o a classi ica ion ule can be exp essed as a weigh ed sum
o he ue posi i e and alse posi i e a e:
(1 ) (P) (N).e p p p p= − +
(3.49)
Since a classi ica ion ule's ue posi i e and nega i e a es a e
complemen a y, hey a e ypically used oge he as join pe o mance measu es.
Gene ally, he ue posi i e a e inc eases as
dec eases, while he ue nega i e
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 73
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
a e dec eases wi h a lowe
. Thus, we can ind he misclassi ica ion a e as he
alue o
which leads o he o e all minimum o he weigh ed sum
e
in he
o mula (3.49). K zanowski and Hand (2009) sugges ano he way o de e mine
he h eshold by choosing he maximum
p p−
, o
1 p n+−
(Sensi i i y +
Speci i y – 1). The maximum alue is called he Youden index (YI).
Gene ally, he pe o mance measu es a e based on compa ing he dis ibu ions
o he sco es o he posi i e and nega i e popula ions. A good classi ica ion ule
ends o p oduce high sco es o he posi i e popula ion and low sco es o he
nega i e popula ion. The la ge he ex en o which hese dis ibu ions di e , he
be e he classi ie . The g aphical depic ion o bo h wo dis ibu ions is p esen ed
by he ROC (Recei e Ope a ing Cha ac e is ic) cu e. The me hod based on he
ROC cu e is a commonly used way o assessing he pe o mance o
classi ica ion ules. Fi s , he g aph shows he ue posi i e a e (
p
) on he e ical
axis and he alse posi i e a e (
p
) on he ho izon al axis, as he classi ica ion
h eshold
a ies. Then, he misclassi ica ion a e is he minimum dis ance
be ween he cu e and he uppe le co ne o he squa e con aining he ROC plo .
I we de elop a classi ica ion ule o mo e han wo classes, we ace a mo e
complex p oblem. Fo example, he a ing models assign objec s o se e al a ing
ca ego ies. In his case, we combine mul iple ROC cu es and use di e en
app oaches o assess pe o mance. K zanowski and Hand (2009) sugges ea ing
he si ua ion using wo-class analyses.
The e a e wo main app oaches o how he ROC analyses can be achie ed:
• Assuming
k
classes, we p oduce
k
di e en ROC cu es by conside ing
each class in u n as popula ion P and he union o all o he classes as
popula ion N,
• we ha e all
( 1)kk−
dis inc pai wise-class ROC cu es.
Bo h app oaches a e sui able o summa y s a is ics, such as he AUC (A ea
Unde he Cu e). In he case o pe ec sepa a ion o P and N, AUC is he a ea
unde he uppe bo de s o he ROC ( he a ea o a squa e o side one, so he uppe
bound is 1). In andom alloca ion, AUC is he a ea unde he chance diagonal ( he
a ea o a iangle whose base and heigh a e equal o 1, so he lowe band is 0.5).
Based on K zanowski and Hand (2009), he AUC can be gene ally exp essed as
1
0( ) .AUC y x dx=
(3.50)
The AUC can be de ined as he a e age posi i e a e, aken uni o mly o e all
possible alse-posi i e a es in he ange (0,1). A equen ly used in e p e a ion o
AUC is ha i is a p obabili y ha he classi ie will alloca e a highe sco e o a
andomly chosen indi idual om popula ion P han i will o a andomly and
independen ly chosen indi idual om popula ion N.
74 Chap e 3
2024 Ma ina No o ná
3.4 Su i al Analysis
The la e applica ion s udy ocuses on applying he mos popula su i al analysis
echniques. I is sugges ed o use he eg ession models app op ia e o su i o
da a o analyse ime o e en . As Hosme e al. (2008, p. 3) claim, he mos
impo an di e ences be ween he ou come a iables modelled ia linea and
logis ic eg ession analyses and he ime a iable a e ha we may only pa ially
obse e he su i al ime. I he e en 's occu ence is unimpo an , he e en can
be analysed as a bina y ou come using he logis ic eg ession model. As Ha ell
(2010) poin s ou , su i al analysis is used o analyse he da a in which he ime
un il he e en is o in e es . The inpu a iable is he ime un il he e en o
du a ion ime. The su i al analysis allows he esponse o be incomple ely
de e mined o some subjec s; pe haps we canno ollow all obse a ions in he
da ase . Fo example, some companies a e s ill ali e a e he obse a ion ime o
los o ollow-up. As we ace incomple e in o ma ion, we need o analyse he da a
using specialised su i al echniques. The analysis in ol es a censo ing
mechanism when we de ine he censo ed and uncenso ed obse a ions. Fo
example, Hosme e al. (2008, p. 18) explain a censo ed obse a ion as one whose
alue is incomple e due o andom ac o s o each subjec . I we analyse da a
using he su i al p ocedu e, he da es o s a and inish a e no deal wi h because
hey a e di e en . Ra he , we conside he leng h o ime be o e he ini ial e en ,
= 0, and he e minal e en o da e o he las in o ma ion abou he objec , = 1.
Usually, when an obse a ion begins a he de ined ime = 0 and e mina es be o e
he ou come o in e es , i is assumed o be a censo ed obse a ion. I no esponses
a e censo ed, s anda d eg ession models o con inuous esponses could analyse
he ailu e imes (Ha ell, 2010).
Based on he dis ibu ion o ailu e imes, we use pa ame ic, semipa ame ic,
and nonpa ame ic me hods. Su i al analysis is he app oach ha allows wo king
wi h incomple e da a and modelling he ime o an e en , such as a co po a e
ailu e o de aul . Two ime poin s mus be clea ly de ined o ime o e en
modelling: he beginning poin and an endpoin when he e en o in e es occu s.
In his con ex , su i al ime e e s o he dis ance on he ime scale be ween hese
wo poin s (Hosme e al., 2008).
3.4.1 Censo ing
When applying he su i al analysis, we deal wi h censo ing he da a ha
comes om he ac ha we can ace he p oblem o incomple e obse a ion o
ime. Two mechanisms can lead o incomple e obse a ion in ime: censo ing and
unca ion. These wo e ms can be de ined as ollows:
• A censo ed obse a ion: he alue o an obse a ion is incomple e due o
andom ac o s o each subjec .
• A unca ed obse a ion: he alue o an obse a ion is incomple e due o a
selec ion p ocess inhe en in he s udy design.
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 75
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Acco ding o Hosme e al. (2008), he e a e se e al ypes o incomple e
obse a ions:
• Righ censo ing,
• le censo ing,
• in e al censo ing,
• le unca ion,
• igh unca ion.
Fo su i al analysis, we ha e o speci y a poin when obse a ion ends on all
subjec s. Thus, subjec s may en e he s udy a di e en imes; howe e , hey will
ha e a iable leng hs o maximum ollow-up ime.
Fo example, in Figu e 3-1, we can see a hypo he ical s udy o ou subjec s,
he end o he s udy is Sep embe 2016. The bond issue 1 en e ed he s udy in
Janua y 2015 and de aul ed in Feb ua y 2016. The bond issue 2 joined he s udy
in Feb ua y 2015 and was los o ollow up in Decembe 2015. The bond issue 3
en e ed he s udy in May 2015, and he e was no de aul un il Sep embe 2016, he
end o he s udy. Finally, bond issue 4 joined he s udy in Augus 2015 and
de aul ed in Ap il 2016.
Figu e 3–1 Line plo in calenda ime ( ollow-up s udy)
Sou ce: Hosme e al. (2008, p. 7), au ho
Fo he p ac ical easons o su i al analysis, we can assume ha all subjec s
en e ed he s udy a he same calenda ime and we e ollowed un il hei espec i e
endpoin . Thus, we mus con e he collec ing da a om calenda ime o analysis
ime (Figu e 3-2).
Calenda ime
Subjec
01/15 02/15 05/15 12/15 02/16 09/16
1
2
3
4
08/15 04/16
76 Chap e 3
2024 Ma ina No o ná
Figu e 3–2 Line plo in he ime scale ( ollow-up s udy)
Sou ce: Hosme e al. (2008, p. 7), au ho
The p e ious example is he case o he mos common ype o censo ing, igh
censo ing. The incomple e obse a ions occu in he igh ail o he ime axis,
usually when he obse a ion begins a he de ined ime and e mina es be o e he
ou come o in e es is obse ed. In some cases, le censo ing can be used i he
e en o in e es has al eady occu ed when obse a ion begins. I he ime is no
obse able con inuously, we can use in e al censo ing. I is a special ype o
ailu e da a ha include he igh -censo ed ailu e ime da a bu ha e a much mo e
complex s uc u e; o mo e de ails, you can see, o example, Sun and Li (2014).
Since he le and igh unca ion a e less common o ms o incomple e da a, hey
will no be conside ed in his ex , and o p ac ical easons, he ocus will be
especially on igh censo ing.
3.4.2 Su i al and Haza d Func ions
In he case o igh censo ing, wo andom a iables need o be de ined
(Houwelingen and S ijnen, 2014):
• The su i al ime (Tsu ),
• he censo ing ime (Tcens),
whe e he e mina ion o he s udy usually de e mines he censo ing ime. The
necessa y condi ion o s a is ical analysis is ha su i al ime and censo ing ime
a e independen . This condi ion can be weakened o he independence o su i al
ime and censo ing ime condi ional on he explana o y a iables in he p esence
o explana o y a iables.
Then, we can de ine cumula i e dis ibu ion unc ions o bo h andom
a iables:
( ) P ( ),
su su
F T =
(3.51)
Time in mon hs
Subjec
1
2
3
4
810 13 16
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 83
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
The eg ession coe icien s can be es ima ed by he maximum likelihood
me hod (see Gou ie oux and Jasiak, 2007, p. 99; Hosme e al., 2008). A e i ing
he model, he signi icance o he model and he o ma ion o a con idence in e al
o key es ima ed pa ame e s should ollow. The la e men ioned au ho s sugges
h ee ela ed es s o assess he signi icance o he coe icien :
• The pa ial likelihood a io es ,
• he Wald es ,
• he sco e es .
The pa ial likelihood es is based on he ollowing s a is ic:
ˆ
2 ( ) (0) ,
pp
G L L
=−
(3.74)
whe e
p
L
e e s o he log pa ial likelihood o he model con aining he
co a ia e and
0
L
is he log pa ial likelihood o he model no con aining he
co a ia e. The log pa ial likelihood e alua ed a
0
=
is:
1
(0) ln( ),
m
pi
i
Ln
=
=−
(3.75)
whe e
i
n
deno es he numbe o subjec s in he isk se a obse ed su i al
ime
i
. Unde he null hypo hesis ha he coe icien is equal o ze o, his s a is ic
will ollow a
2
-dis ibu ion wi h 1 deg ee o eedom and hus can be used o
ob ain p- alues o es he signi icance o a coe icien (Hosme e al., 2008).
The Wald s a is ic es is based on he a io o he es ima ed coe icien o i s
es ima ed s anda d e o , assuming ha he s a is ic ollows a s anda d no mal
dis ibu ion. Unlike he linea eg ession, he Wald and log pa ial likelihood a io
es a e no nume ically ela ed. The Wald s a is ic is gi en by
ˆ.
ˆ
()
zSE
=
(3.76)
The hi d app oach, he sco e es , is based on he a io o he de i a i e o he
log pa ial likelihood o he squa e oo o he obse ed in o ma ion all e alua ed
a
0
=
(see Hosme , e al., 2008).
Cle es e al. (2010) use he e m ela i e haza d o
x
e
, and he log ela i e
haza d, o isk sco e, o
x
. To e i y he model's speci ica ion
x
and adequa e
pa ame e isa ion, we can use es s called es s o he p opo ional-haza d
assump ions (P-H assump ions). In he applica ion, he es s will be based on he
analysis o esiduals. As o he ac ha he p opo ional haza ds model o censo ed
su i al da a is i using he pa ial likelihood, he calcula ion o esiduals di e s
om he usual eg ession models. Fo his eason, a ious app oaches ha e been
84 Chap e 3
2024 Ma ina No o ná
de eloped o Cox p opo ional model. The esiduals used in he empi ical s udy
will be based on Schoen eld esiduals. Fo mo e de ails, see, o example, Hosme
e al. (2008), Cle es e al. (2010), Ha el (2010). Since he su i al models
es ima e he ime o e en , he explained a ia ion should also be assessed a e
i ing he model. The measu es o explained a ia ion o use wi h censo ed
su i al da a di e om he adi ional concep o a ia ion using he index o
de e mina ion. In ou case, we apply he measu e p oposed by Roys on (2006)
wi h he cha ac e o explained a ia ion in p opo ional haza ds models, which
can be used as an adjus ed index o de e mina ion in PH models.
3.4.5 Pa ame ic Models
While nonpa ame ic analysis is a use ul ool o desc ibing ou su i o da a,
semipa ame ic models a e used especially o he es ima ion o haza d a ios and
hei u he explana ions. In many cases, semipa ame ic analysis based on he
Cox model can su icien ly analyse ou da a. Howe e , i we aim o p edic he
ime o ailu e, some pa ame ic assump ion is necessa y. Pa ame ic models
gene ally p o ide smoo h es ima es o he haza d and su i al unc ions and
enable us o model also a nonp opo ional e ec on he haza d scale (Roys on and
Lambe , 2011). Compa ed o semipa ame ic models, pa ame ic models a e used
when he dis ibu ion o su i al ime has a known pa ame ic o m. In his case,
he ully pa ame ic model enables us o be e analyze su i al da a. Cle es e al.
(2010) desc ibe six s anda d pa ame ic su i al models: exponen ial, Weibull,
Gompe z, logno mal, and gene alized gamma.
Acco ding o Hosme e al. (2008), using hese models may ha e he ollowing
ad an ages:
• Full maximum likelihood may be used o es ima e he pa ame e s,
• he es ima ed coe icien s o hei ans o ma ions can p o ide clinically
meaning ul es ima es o e ec ,
• i ed alues om he model can p o ide es ima es o su i al ime,
• esiduals can be compu ed as di e ences be ween obse ed and p edic ed
alues o he ime.
In pa ame ic models, we assume ha he dis ibu ion o ime o e en (T) can
be desc ibed as a unc ion o a single co a ia e:
01 .
x
Te
+
=
(3.77)
Since he ime mus always be posi i e, he equa ion (3.77) can be exp essed
as he p oduc o a posi i e sys ema ic componen ,
01
exp( )x
+
, and an e o
componen ,
, ha also akes only posi i e alues.
a) Exponen ial Reg ession Model
The exponen ial su i al model is he simples pa ame ic model wi h a cons an
haza d unc ion. We deno e he exponen ial dis ibu ion wi h su i al unc ion
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 85
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
( ) exp( )S =−
as
(1).E
The model can be exp essed by aking he na u al log o
each side o he equa ion (3.77):
*
01
ln( ) ,Tx
= + +
(3.78)
whe e
*ln( ).
=
I he e o componen
ollows he exponen ial dis ibu ion,
hen he e o componen
*
ollows he ex eme minimum alue dis ibu ion
deno ed as
(0,1)G
. The model in (3.76) is called he exponen ial eg ession model.
I his model is gene alized by allowing he shape pa ame e o be di e en om
1 by using
(0, )G
dis ibu ion:
*
01
ln( ) ,Tx
= + +
(3.79)
we ge he Weibull eg ession model (3.79).
Su i al ime models ha a e linea ized by aking logs a e called accele a ed
ailu e ime models. The co a ia e e ec in hese models is mul iplica i e on he
ime scale, as we can see in (3.77). In o he wo ds, he impac o he co a ia e is
said o accele a e su i al ime.
To desc ibe he me hod o he exponen ial eg ession model, i s ly, we assume
he single co a ia e model (3.77), whe e he e o dis ibu ion is log-exponen ial.
Then, he su i al unc ion o he model can be exp essed as:
01
( , , ) exp( 1 ).
x
S x e
+
=−β
(3.80)
I we se he igh -hand side o his equa ion equal o 0.5 and sol e he esul ing
equa ion, we ge an equa ion o he co a ia e speci ic median su i al ime o
01
50 ( , ) ln(0.5).
x
x e
+
= − β
(3.81)
Assuming he dicho omous co a ia e in (3.79) coded 0 o 1, hen he a io o he
median su i al ime o he g oup wi h
1x=
o he g oup wi h
0x=
is:
01
1
0
50
50
( 1, ) ln(0.5)
TR( 1, 0) ,
( 0, ) ln(0.5)
x e
x x e
x e
+
=−
= = = = =
=−
β
β
(3.82)
whe e TR deno es ime a io. The ela ionship be ween he wo median imes can
be w i en as:
1
50 50
( 1, ) ( 0, ). x e x
= = =ββ
(3.83)
Fo example, i
1
exp( ) 2
=
, hen he median su i al ime in he g oup wi h
1x=
is wice he median su i al ime in he g oup wi h
0x=
. The quan i y
1
exp( )
is usually called he accele a ion ac o , al hough i can accele a e o
decele a e su i al ime.
86 Chap e 3
2024 Ma ina No o ná
The mul iplica i e co a ia e e ec can be p esen ed using he ollowing o m
o su i al unc ion,
1
( , 1, ) ( , 0, ).S x S e x
−
= = =ββ
(3.84)
The equa ion shows ha he alue o he su i al unc ion a ime o he
g oup wi h
1x=
can be ob ained by e alua ing he su i al unc ion o he g oup
wi h
1x=
a ime
1
exp( ).
−
In addi ion o he su i al unc ion, he model in (3.80) can be exp essed in e ms
o he haza d unc ion as ollows,
01
( , , ) ,
x
h x e
+
=β
(3.85)
ha is cons an o e ime because i depends only on model coe icien s and
co a ia e alues. Thus, on he one hand, he haza d unc ion is ela i ely simple.
Howe e , i may be oo simple o p o ide a ealis ic desc ip ion o he su i al
da a. The haza d a io o a dicho omous co a ia e is
1
HR( 1, 0) .x x e
−
= = =
(3.86)
The model can be es ima ed using he maximum likelihood me hod. The i ed
alues a e p edic ions o alues om a censo ed exponen ial dis ibu ion. The
es ima o o a iances and co a iances o he es ima o o he coe icien s a e
ob ained using he second pa ial de i a i e o he log-likelihood unc ion. The
in luence o indi idual subjec s on he alues o he es ima ed pa ame e s is based
on he sco e esiduals (see Hosme e al., 2008).
In pa ame ic models, he assump ion o p opo ional haza ds is eplaced by
he p ocedu e ha de e mines whe he he da a suppo he pa icula pa ame ic
o m o he haza d unc ion. Hosme e al. (2008) sugges using he model-based
es ima e o he cumula i e haza d unc ion o o m he Cox-Snell esiduals. The
es ima ed cumula i e haza d unc ion alues can be conside ed obse a ions om
a censo ed sample om an exponen ial dis ibu ion wi h a pa ame e equal o one.
Then, he model diagnosis is based on he plo ha compa es he model-based
cumula i e haza d o he haza d ob ained om a nonpa ame ic es ima o (Kaplan-
Meie , Nelson-Aalen). As he au ho s say, he nonpa ame ic es ima o uses he
model-based es ima es o he cumula i e haza d a each obse ed ime as he ime
a iable and he censo ing indica o om he su i al ime a iable as he
censo ing a iable. Thus, his plo should ollow a line h ough he o igin wi h a
slope equal o one i he pa ame ic model is co ec . The es ima o o Cox-Snell
esiduals can be ob ained by exponen ia ing he addi i e esiduals on he log ime
scale (see Hosme e al., 2008, p. 257 o mo e de ails). Simila o Cox p opo ional
haza ds model, he signi icance o a iables can be assessed using he sco e es ,
likelihood a io o Wald es .
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 87
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
b) Weibull Reg ession Model
We conside he Weibull dis ibu ion a na u al gene aliza ion o he exponen ial
(Roys en and Lambe , 2011). The Weibull eg ession model can be exp essed
using he na u al log as in equa ion (3.80). Compa ed o he exponen ial model,
he Weibull model allows he shape pa ame e
o be di e en om 1 by using
(0, )G
dis ibu ion.
The haza d unc ion o he single co a ia e model is
01
1
()
( , , , ) ,
x
h x e
−
+
=β
(3.87)
and we assume ha
1.
=
The p opo ional haza ds o m o he unc ion can be exp essed as
0 1 0 1
()
11
( , , , ) , o
xx
h x e e e
− + − −
−−
==β
(3.88)
011
10
( , , , ) ( ) ,
xx
h x e e h e
−−
−
==β
(3.89)
whe e
0 0 1 1
exp( ) exp( ),
= − = = −
and he baseline haza d unc ion is
1
0( ) ,h
−
=
(3.90)
and
1
=
is usually called he shape pa ame e . Al hough he pa ame e
is a
a iance-like pa ame e on he log-scale, we can e e o
as he shape pa ame e
in his ex , as sugges ed by Hosme e al. (2008, p. 261). The pa ame e
is called
he scale pa ame e . Fo example, he exp ession in (3.80) leads o a haza d a io
in e p e a ion o he pa ame e
1.
The Weibull dis ibu ion can p o ide a ie y o
shapes o he haza d unc ion de e mined by he es ima ed pa ame e
. When
1
=
, he haza d is cons an , and he Weibull model educes o he exponen ial
model. When
1
, he haza d in mono one dec easing, and when
1
, i is
mono one inc easing. Thus, he Weibull model is sui able o modelling da a ha
exhibi mono one haza d a es (Cle es e al., 2010).
The accele a ed ailu e- ime o m o he haza d unc ion can be exp essed as
01 11
()
11
( , , , ) ( ) .
xxx
h x e e e
−+ −−
−−
==β
(3.91)
The ela ionship be ween he wo se s o es ima ed coe icien s using he
p opo ional haza ds o m and he accele a ed ailu e- ime o m o he haza d
unc ion is
.θ = -β σ
The su i al unc ion ha co esponds o he accele a ed ailu e- ime o m o he
haza d unc ion in (3.92) is
88 Chap e 3
2024 Ma ina No o ná
01
( , , , ) exp exp ( 1 )( ) .
x
S x
= − − +β
(3.92)
Then, he median su i al ime can be ob ained by se ing he su i al unc ion
equal o 0.5 and sol ing o ime,
01
50 ( , , ) ln(0.5) .
x
S x e
+
=−β
(3.93)
I he co a ia e is dicho omous and coded 0/1, hen he ime a io a he median
su i al ime is (Hosme e al., 2008, p. 262):
01
1
0
50
50
ln(0.5)
( 1, , )
TR( 1, 0) ( 0, , ) ln(0.5)
e
x
x x e
x e
+
−
=
= = = = =
=−
β
β
.
(3.94)
The in e p e a ion o he
β
o m o he coe icien s is he same as in he
exponen ial eg ession model. The assessmen o model i is based on he sco e
esiduals, simila ly o he exponen ial eg ession model. See, o example, Hosme
e al. (2008) o a de ailed desc ip ion.
c) Flexible Pa ame ic Models
Roys on and Lambe (2011) sugges ha simple pa ame ic models may no be
lexible enough o ep esen he haza d unc ion adequa ely and hus i ou da a
well. Fo example, he haza d unc ion o a Weibull model always goes in he same
di ec ion wi h ime. The e o e, he au ho s p opose new pa ame ic models ha
include lexible PH models, lexible p opo ional odds (PO), and p obi -scale
models. Thus, we ge al e na i e models which ex end he ange o su i al
dis ibu ions ha can be es ima ed. Fu he mo e, hese models allow nonlinea i y
unc ions and hus inc ease hei p ac ical use and applica ions.
Roys on and Lambe (2011) p opose Roys on-Pa ma (RP) models, which
ha e conside ably g ea e lexibili y conce ning he shapes o he su i al
dis ibu ions hey can model. In his case, he baseline dis ibu ion unc ion is a
es ic ed cubic spline unc ion o log ime ins ead o simply as a linea unc ion
o log ime. The complexi y o models wi h spline unc ions is de e mined by he
numbe and he posi ions o he connec ion poin s in log ime (kno s) o he
spline’s cubic polynomial segmen s. The pa ame e s o models a e es ima ed
based on maximum likelihood; o mo e de ails and desc ip ion o models, see, o
example, Roys on and Lambe (2011). The au ho s conside RP models as an
ex ension o he Weibull, loglogis ic, and logno mal models. While we assume
ha he e ec o co a ia es is p opo ional on he app op ia e scale (haza d, odds
o ailu e, o p obi o ailu e p obabili y) in hese models, he assump ion o
linea i y is elaxed in RP models. The gene alisa ion o he Weibull model using
spline unc ions is desc ibed by he au ho s as ollows. Fi s ly, we exp ess he
Weibull cumula i e haza d unc ion in loga i hmic o m:
1 0 1
ln ( ) ln ln lnH
= + = +
,
(3.95)
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 89
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
whe e
ln ( )H
is a sum o wo componen s: a cons an (
0
) and a linea unc ion
o log ime (
1ln
). In he case when he la e componen does no co ec ly
cap u e he shape o he (log) cumula i e haza d unc ion, we migh need a mo e
lexible model:
ln ( ) ( ; )H
=
,
(3.96)
whe e
( ; )
ep esen s some gene al amily o a nonlinea unc ion o ime
,
ha ing some pa ame e ec o
. Roys on and Lambe (2011) sugges ac ional
polynomials and splines as sui able unc ions. Fo example, hey desc ibe a
es ic ed cubic spline unc ion as
(ln ; )s
wi h s s anding o splines and ln o
show ha we use he scale o log ime:
0 1 2 1 3 2
ln ( ) (ln ; ) ln (ln ) (ln ) ...,H s z z
= = + + + +
(3.97)
whe e
12
ln , (ln ), (ln ) z z
and so on a e he basis unc ions o he es ic ed cubic
spline. Thus, i he e a e no kno s, hen
0 1 0 1
(ln ; , ) lns
=+
, which is he
Weibull model. The pa ame e s
a e es ima ed by maximum likelihood, as
p oposed by Lambe and Roys on (2009). In p ac ical applica ion and es ima ion
o models, he chosen numbe o in e io kno s speci ies he deg ees o eedom
(one plus he numbe o kno s). So hen, he PH(d) model is a PH model whose
spline unc ion has d deg ees o eedom (d – 1 in e io kno s and when d > 1, wo
bounda y kno s).
The i o es ima ed pa ame ic models can be compa ed based on he Akaike
in o ma ion c i e ion (AIC), de ined as he de iance plus
2k
, whe e
k
is he
dimension o he model ( he numbe o i ed pa ame e s).
Al e na i ely, we can use he Bayes in o ma ion c i e ion (BIC), which is he
de iance penalized by adding
logkn
, whe e n is he sample size. Because
pa ame ic models a e es ima ed by he maximum likelihood me hod, bo h c i e ia,
AIC and BIC, can be used o compa e i ed models. Howe e , since he Cox
model is es ima ed by he maximum pa ial likelihood me hod, his model canno
be compa ed wi h pa ame ic models based on AIC and BIC c i e ia (Roys on and
Lambe , 2011).
3.4.6 Mul iple Failu e-Time Da a
Cle es (2000) desc ibes mul iple ailu e- ime da a as da a when wo o mo e
e en s ( ailu es) occu o he same subjec o om iden ical e en s occu ing o
ela ed subjec s. The ypical ea u e is ha ailu e imes a e co ela ed wi hin a
clus e (subjec o g oup), iola ing he independence o ailu e imes assump ion
equi ed in adi ional su i al analysis. As he au ho poin s ou , ailu e e en s
should be classi ied acco ding o whe he hey ha e a na u al o de and ecu ences
o he same ype o e en s. The e en s a e supposed o be o de ed when he second
90 Chap e 3
2024 Ma ina No o ná
e en canno occu be o e he i s e en . On he con a y, uno de ed e en s can
happen in any sequence.
The e a e mo e app oaches o examining mul iple ailu e- ime da a. Fi s ly, we
can examine he ime o he i s e en , igno ing addi ional ailu es. Howe e , i
means we do no use all a ailable da a. The second me hod is based on he
a ailable da a analysis while accoun ing o he lack o independence o he ailu e
imes. Cle es (2000) sugges s co esponding p ocedu es o es ima ing hese
models using he Cox p opo ional haza d model. Unde he p opo ional haza d
assump ion, he haza d unc ion (3.72) o he i h clus e o he k h ailu e ype is
as ollows:
,
0
( , ) ( ) ,
i
Z
k ki
h Z h e
=
(3.98)
whe e
ki
Z
is a p- ec o o possibly ime-dependen co a ia es o i h clus e o he
k h ailu e ype. While we p esume in equa ion (3.98) ha he baseline haza d
unc ion is equal o e e y ailu e ype, he baseline haza d unc ion is allowed o
di e by ailu e ype in he ollowing o mula:
,
0
( , ) ( ) .
i
Z
k ki k
h Z h e
=
(3.99)
As Cle es (2000) sugges s, he maximum likelihood es ima es o he models
(3.98) and (3.99) a e ob ained om Cox's pa ial likelihood unc ion
()L
,
assuming independence o ailu e imes.
Conce ning he analysis o mul iple ailu e- ime da a, Cle es (2000)
emphasizes he need o de e mine whe he i is o de ed o uno de ed da a and
selec a sui able me hod o es ima ing models acco dingly. In he case o
uno de ed imes, which is he case o a ing analysis, i is i s necessa y o
de e mine whe he he e en s a e o he same o di e en ypes. Simila ly,
deciding whe he he baseline haza d is he same o di e en o all e en ailu es
is necessa y. In any case, i is essen ial o implemen he me hods o co ec ly
s uc u ing he da a, including iden i ying indi idual ailu e e en s.
3.5 Chap e Summa y
The pu pose o his chap e was o cla i y he main mo i es o conduc ing an
applica ion s udy in his wo k. The e o e, he basic cha ac e is ics and meaning o
mic o app oaches o measu ing c edi isk we e p o ided a he beginning o his
sec ion. Subsequen ly, a en ion was paid o he esea ch e iew, based on which
i was de e mined which p ocedu es a e sui able o modelling indi idual c edi
isk and which esul s he selec ed au ho s eached. Hence, he mo i a ion and he
main goal we e speci ied, and he main con ibu ion o he cu en esea ch was
ou lined.
The nex pa o he chap e was de o ed o desc ibing he econome ic models
used in he applica ion pa o his wo k, namely disc iminan , eg ession and
su i al analysis. Since plen y o p o essional publica ions deal wi h hese
App oaches o C edi Ra ing and Co po a e Bank up cy Modelling 91
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
app oaches in g ea de ail and p o essionally, he selec ed me hods we e only
b ie ly desc ibed in his sec ion. The main a en ion was paid o unde s anding he
main p inciples and he possible use o models.
Finally, he me hods desc ibed in his chap e a e applied in he ollowing ou
sec ions. The i s s udy aims a modelling he in luence o selec ed ac o s on
a ings and hei downg ades. Nex , we ind ou whe he he e is a ela ionship
be ween a ing and co po a e bank up cy a es. Then, we analyse he e ec o
selec ed co po a e cha ac e is ics on he su i al p obabili y. Finally, we
o mula e pa ame ic su i al models based on he p e ious esul s and es ima e
bank up cy a es and a ings.
The E ec o Selec ed Fac o s on Ra ing and i s Dynamics 99
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Table 4–6 S anda dized canonical disc iminan unc ion coe icien s (model 1)
Va iable
Func ion
1
2
3
4
oa
0.8919
1.2621
0.8018
0.2660
oe
-0.3216
-0.4274
-0.0586
0.0642
eq a
0.7286
-0.5229
0.3506
0.2142
ln a
-0.3680
1.6715
1.7264
0.7928
lnin co
0.4202
-0.0856
-0.6401
-0.2755
lnc
0.3627
-1.6822
-2.1066
-0.8115
lnliq
0.2756
-0.0771
0.5208
-0.7117
lncu
0.0955
-0.0001
-0.7138
1.0340
lnl d a
-0.0644
-0.0112
0.0435
0.1917
ebi da
0.0371
0.1531
-0.5950
0.3354
b) Classi ica ion abili y
The coe icien s o classi ica ion unc ions (Fishe ’s linea disc iminan unc ions)
o he es ima ed models a e shown in Table 4-7. The classi ica ion unc ions a e
used o classi y indi idual cases: Fi s , he alues o i e unc ions a e compu ed
and compa ed. Then, he g oup co esponding o he unc ion wi h he highes
alue is selec ed as he a ge a ing ca ego y.
Table 4–7 Classi ica ion unc ion coe icien s (model 1)
Va iable
1
2
3
4
5
oa
1.2600
1.4491
1.6511
2.0131
2.7745
oe
0.1019
0.0861
0.0694
0.0346
-0.0262
eq a
9.2790
22.2835
37.4865
51.4774
62.9647
ln a
34.2175
33.1949
31.7998
30.5193
32.5883
lnin co
0.3915
1.0540
1.9416
3.3279
4.1108
lnc
-26.6527
-25.8531
-24.6153
-23.3636
-25.4225
lnliq
-4.5765
-2.4185
-1.2134
0.0995
1.8487
lncu
-0.3275
-1.6194
-0.9198
0.0149
0.0925
lnl d a
0.4275
0.3187
0.2539
0.1220
0.0150
ebi da
-0.3804
-0.4616
-0.4653
-0.4115
-0.3934
cons an
-77.2415
-73.9966
-77.9575
-93.3122
-126.6945
Fo example, using he mean, minimum and maximum alues o inpu
a iables ep esen ing h ee hypo he ical companies, he classi ica ion unc ions
assign hem o di e en a ing g oups (Table 4-8). The a e age company is gi en
o he middle g oup 3 – BBB. This esul is no su p ising because, as men ioned
abo e, mos companies ha e he middle a ing assessmen . Since he g oups a e
no equally sized, he classi ica ion unc ions a e weigh ed mo e hea ily o classi y
g oup h ee in ou case. The hypo he ical company wi h he minimum (maximum)
alues is classi ied as g oup 1 – B (5 – AA). This esul is also no su p ising, as
100 Chap e 4
2024 Ma ina No o ná
he highe alue o mos a iables is gene ally associa ed wi h a be e company's
inancial si ua ion.
Table 4–8 Example o classi ica ion
1
2
3
4
5
Mean
65.48
74.35
78.48
74.84
60.93
Minimum
33.05
28.52
13.21
-10.44
-31.02
Maximum
121.33
122.26
143.74
175.39
191.59
The main cha ac e is ics o he classi ica ion abili y o models a e summa ised
in Table 4-9 . The c i e ia o compa ison and anking he models a e classi ica ion
ables (con usion ma ices) and e o a es:
• The esubs i u ion classi ica ion able, ob ained by classi ying he
obse a ions used o build he disc iminan model, is Class. (ES).
• The classi ica ion able, based on he hold-ou sample's es ima ion abili y,
is called Class. (hold).
• The e o a e, which ep esen s he o e all e o a e and he e o a e o
each g oup and co esponds o he classi ica ion able, is based on he
coun -based es ima e.
Table 4–9 Pe cen age co ec ly classi ied (PCC) – 5ca models
Me hod
Model
Expe imen al
sample (ES)
Numbe o
obs. (ES)
Class. (ES)
Class. (hold)
LDA
1
non- andom
3518
0.8511
0.8775
LDA
2
andom
3274
0.8525
0.8600
Al hough he classi ica ion abili y o models is simila (Table 4-9), i di e s
ac oss he a ing g oups (Table 4-10). Fo example, while only 8.35% o subjec s
om a ing 3 a e misclassi ied, i is 47.01% om a ing 1. The leas accu a e is,
he e o e, he classi ica ion in o a ing 1, i.e. ca ego y B. F om he lende 's poin
o iew, he model ends o educe he classi ica ion abili y o he companies wi h
he wo s a ings. The esul s o he second model a e p opo ionally simila .
Table 4–10 E o a e (5 ca )
Model
Misclas.
Ra ing
To al
1
2
3
4
5
1
E o a e
0.4701
0.1978
0.0835
0.1816
0.2123
0.1489
P io s
0.3326
0.2041
0.4801
0.2317
0.0509
2
E o a e
0.4205
0.2750
0.0677
0.1745
0.2473
0.1476
P io s
0.0269
0.1677
0.5100
0.2398
0.0559
Acco ding o he o e all e o a e c i e ion, bo h i e-ca ego y disc iminan
models achie e a simila classi ica ion abili y. Fo example, he o al e o a e o
model 1 shows ha he p opo ion o misclassi ied obse a ions is 14.89%.
The E ec o Selec ed Fac o s on Ra ing and i s Dynamics 101
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
O e all, he non- andom LDA model has a be e classi ica ion abili y on he
hold-ou sample. Howe e , he gene al esul s o bo h models do no allow a clea
choice o a mo e sui able model. Fu he mo e, he classi ica ion accu acy o hese
models is s ongly in luenced by he ac ha he bounda y ca ego ies a e no
e enly ep esen ed in he sample. The e o e, we elimina e his sho coming by
de i ing models o only h ee in e nal a ing ca ego ies: 2, 3, and 4 (Table 4-11).
Table 4–11 Pe cen age co ec ly classi ied (PCC) – 3ca models
Me hod
Model
Expe imen al
sample (ES)
Numbe o
obs. (ES)
Class. (ES)
Class. (hold)
LDA
3
non- andom
3222
0.8858
0.8986
LDA
4
andom
3274
0.8878
0.8882
Unsu p isingly, bo h he classi ica ion abili y and he e o a e p o ide be e
esul s. The de ailed e o a es a e summa ized in Table 4-12.
Table 4–12 E o a e (3 ca )
Model
Misclas.
Ra ing
To al
2
3
4
3
E o a e
0.1671
0.0787
0.1411
0.1142
P io s
0.2228
0.5242
0.2529
4
E o a e
0.2332
0.0641
0.1300
0.1122
P io s
0.1828
0.5560
0.2613
In his case, he classi ica ion abili y o he 3-ca ego y models is simila .
Howe e , model 3 (non- andom) achie es a lowe misclassi ica ion a he lowes
a ing and highe classi ica ion accu acy on he hold-ou sample. Fo his eason,
his model can be conside ed mo e sui able o a ing p edic ion.
4.1.4 Mul inomial Logis ic Models
Since we use wo logis ic eg ession analysis me hods, we es ima e eigh models
(Appendix 3). The models a e summa ized in Table 4-13.
Table 4–13 O e iew o logis ic models
Model
Me hod
No. o
p edic o s
No. o
ca ego ies
Sample
Model 5
MLR
10
5
Non- andom
Model 6
MLR
10
5
Random
Model 7
OLR
10
5
Non- andom
Model 8
OLR
10
5
Random
Model 9
MLR
10
3
Non- andom
Model 10
MLR
10
3
Random
Model 11
OLR
10
3
Non- andom
Model 12
OLR
10
3
Random
102 Chap e 4
2024 Ma ina No o ná
a) Main Resul s and In e p e a ion
The o e all esul s based on he logis ic eg ession sugges ha he es ima ed
models do no di e signi ican ly. The e o e, simila ly o disc iminan analysis,
only one model will be desc ibed in mo e de ail in he ollowing ex . The
in e p e a ion o o he models is analogous.
The ollowing ex ocuses on model 5 (MLR, non- andom, i e ca ego ies).
Howe e , we will pay a en ion o bo h app oaches because we use wo me hods.
In addi ion, some ables om Appendix 3 a e ew i en in he nex sec ions o
be e cla i ica ion. Fi s , ou logi unc ions a e es ima ed because i is a i e-
ca ego y model. We a bi a ily use he middle a ing ca ego y 3 (BBB) as a
e e ence alue. Thus, we o m ou logi s,
1 2 4 5
( ), ( ), ( ), ( ),g x g x g x g x
compa ing
each g oup o he e e ence ca ego y. Equa ions (3.40) – (3.43) a e used o es ima e
he unknown pa ame e s based on he maximum likelihood me hod o i he
model. The pa ame e es ima es a e summa ized in Table 4-14, and he de ails a e
p o ided in Appendix 3. The assessmen o pa ame e es ima es and hei
signi icance is based on he Wald es used o es he null hypo hesis ha each o
he indi idual coe icien s is ze o o each logi .
Table 4–14 MLR pa ame e es ima es (model 5)
Va iable
Ra ing
1
2
4
5
oa
-0.8719*
-0.3489*
0.4810*
0.8939*
oe
0.0288*
0.0253*
-0.1126*
-0.2060*
eq a
-50.6921*
-25.1934*
7.2455*
1.7041
ln a
2.3379*
1.9669*
-1.1749*
-1.0128
lnin co
-1.8130*
-1.3457*
2.2807*
4.3186*
lnc
-.19509*
-1.8375*
1.1257*
1.3755
lnliq
-4.5343*
-2.4685*
1.4070*
2.7621*
lncu
-3.6769*
-2.6221*
0.9934*
0.4867
lnl d a
0.3388*
0.1937*
-0.1992*
-0.3323*
ebi da
-0.0629*
-0.0588*
-0.9185*
-3.4539*
cons an
12.2038*
9.1524*
-12.0212*
-26.3962*
*signi ican a .05 le el
The pa ame e es ima es compa e pai s o ou come a iables (no e ha Ra ing
3 is a e e ence ca ego y). Thus, o example, he i s pa o he able labelled
Ra ing 1 compa es his ca ego y agains Ra ing 3, Ra ing 2 compa es his ca ego y
agains Ra ing 3 and so on. The e o e, he in e p e a ion is simila o he bina y
logis ic eg ession. The coe icien s in Table 4-14 a e exp essed in e ms o he
log odds. Fo example, he coe icien -0.8719 (Ra ing 1, oa) implies ha a one-
uni change in oa esul s in a -0.8719 uni change in he log o odds.
Howe e , we ypically p e e using he odds a ios o in e p e a ion, compu ed
by exponen ia ing he coe icien s (S a aCo p, 2021; UCLA, 2021a; UCLA,
2021b). The odds a ios o model 5 a e summa ized in Table 4-15.
The E ec o Selec ed Fac o s on Ra ing and i s Dynamics 103
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Table 4–15 MLR odds a ios (model 5)
Va iable
Ra ing
1
2
4
5
oa
0.4182
0.7055
1.6177
2.4446
oe
1.0292
1.0256
0.8935
0.8138
eq a
0.0000
0.0000
1401.7826
5.4964
ln a
10.3595
7.1485
0.3088
0.3632
lnin co
0.1632
0.2604
9.7835
75.0834
lnc
0.8228
0.1592
3.0824
3.9571
lnliq
0.0107
0.0847
4.0837
15.8331
lncu
0.0253
0.0727
2.7004
1.6269
lnl d a
1.4033
1.2137
0.8194
0.7173
ebi da
0.9390
0.9429
0.3991
0.0316
The mul inomial logis ic model is a simple ex ension o he bina y model.
Howe e , he in e p e a ion is mo e di icul because o ele an bina y
compa isons. Fo example, wi h i e ou comes ( a ing g oups), we ha e en bina y
compa isons o one model: R1 e sus R2, R1 e sus R3, R1 e sus R4, R1 e sus
R5, R2 e sus R3, R2 e sus R4, R2 e sus R5, R3 e sus R4, R3 e sus R5, and
R4 e susR5.
To demons a e he in e p e a ion o odds a ios, we compa e Ra ing 1 (B) agains
he e e ence ca ego y, Ra ing 3 (BBB):
• The odds a io o oa is 0.4182, meaning ha as oa inc eases, he company
is likely o ge a a ing 3, assuming ha all o he a iables in he model a e
held cons an . Simila ly, o eq a, lnin co , lnc , lnliq , lncu and ebi da
( hei odds a ios a e less han one).
• On he o he hand, he odds a io o oe is 1.0292. Thus, as oe inc eases,
he company is likely o ge a ing 1 ela i ely o a ing 3, simila ly, o ln a
and lnl d a ( hei odds a ios a e mo e han one).
Based on he es ima ed coe icien s, he ou logi unc ions can be w i en as:
1
2
0.87 0.03 50.69 2.34 1.81
0.2 4.53 3.68 0.34 0.06 12.2,
0.35 0.03 25.19 1.97 1.35
1.84 2.47 2.62 0.19
g oa oe eq a ln a lnin co
lnc lnliq lncu lnl d a ebi da
g oa oe eq a ln a lnin co
lnc lnliq lncu
= − + − + − −
− − − + − +
= − + − + − −
− − − + 0.06 9.15,lnl d a ebi da −+
4
5
0.48 0.11 7.25 1.17 2.28
1.26 1.41 0.99 0.2 0.92 12.02,
0.89 0.21 1.7 1.01 4.32
1.38 2.76 0.49 0.33
g oa oe eq a ln a lnin co
lnc lnliq lncu lnl d a ebi da
g oa oe eq a ln a lnin co
lnc lnliq lncu lnl
= − + − + +
+ + + − − −
= − + − + +
+ + + − 3.45 26.4.d a ebi da −−
104 Chap e 4
2024 Ma ina No o ná
The condi ional p obabili y o each a ing ca ego y can be exp essed as:
( )
( )
( )
( )
( )
1
5
1 2 4
2
5
1 2 4
5
1 2 4
4
5
1 2 4
5
1 2 4
()
1()
( ) ( ) ( )
()
2()
( ) ( ) ( )
3()
( ) ( ) ( )
()
4()
( ) ( ) ( )
()
5( ) ( ) (
1,
1
2,
11
3,
1
4,
1
51
g
g
g g g
g
g
g g g
g
g g g
g
g
g g g
g
g g g
e
Ye e e e
e
Ye e e e
Ye e e e
e
Ye e e e
e
Ye e e
==
+ + + +
==
+ + + +
==
+ + + +
==
+ + + +
==
+ + +
x
x
xxx
x
x
xxx
x
xxx
x
x
xxx
x
xx
x
x
x
x
x5()
).
g
e+x
x
b) Model i ing
The o e iew and main cha ac e is ics o es ima ed models a e summa ized in
Table 4-16, including:
• De iance (D=-2LLM): The alue o a likelihood- a io chi-squa ed o he
es o he null hypo hesis ha all he coe icien s associa ed wi h
independen a iables a e simul aneously equal o ze o (including deg ees
o eedom as he numbe o cons ained pa ame e s),
• pseudo R2 measu ed as McFadden’s,
• AIC and BIC.
Likelihood a io es s o he o e all models es he null hypo hesis ha all
coe icien s in he model a e ze o. Fi s ly, we calcula e he alue -2 log-likelihood
o models wi h only an in e cep e m and all a iables. Then, we ge he
di e ence be ween hese alues, Chi-squa e. I he obse ed signi icance is small,
we can ejec he null hypo hesis ha all coe icien s a e ze o and conclude ha
he inal model is signi ican ly be e han he in e cep -only. Acco ding o he
alues in Table 4-16, we conclude ha all models a e be e han he in e cep -only
models.
Table 4–16 Model- i ing
Model
De iance
LR
Chi2(d )
Pseudo
R2
AIC
BIC
Model 5
2176.797
6830.33 (40)
0.7583
2264.794
2536.082
Model 6
2004.445
6135.13 (40)
0.7537
2092.445
2360.571
Model 7
2683.156
6323.97 (10)
0.7021
2711.156
2797.475
Model 8
2450.653
5688.92 (10)
0.6989
2478.653
2563.965
Model 9
1509.218
5068.91 (20)
0.7706
1553.218
1686.928
Model 10
1347.236
4586.88 (20)
0.7730
1391.236
1523.406
Model 11
1812.961
4765.17 (10)
0.7244
1836.961
1909.894
Model 12
1602.200
4331.91 (10)
0.7300
1626.200
1698.292
The E ec o Selec ed Fac o s on Ra ing and i s Dynamics 105
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Nex , we conside he in o ma ion c i e ia AIC and BIC ( o he desc ip ion o
he measu e, see, o example, Long and F eese, 2014). Based on he c i e ion BIC,
we p e e model 6 among 5-ca models and model 10 among 3-ca models ( hey
ha e he smalles alue o BIC). These esul s a e also sugges ed by he c i e ion
AIC.
c) Classi ica ion abili y
Simila o he disc iminan analysis, we use he model o de e mine he a ing o a
hypo he ical i m wi h a e age, minimum and maximum alues o inpu a iables.
Howe e , unlike he disc iminan analysis, we calcula e he p obabili y o
belonging o a g oup and classi y i in o he g oup wi h he highes p obabili y
(Table 4-17).
Table 4–17 Example o classi ica ion
1
2
3
4
5
Mean
4.89E-05
9.98E-
04
9.94E-01
4.89E-
03
7.37E-10
Min
1.00E+00
1.81E-
10
2.02E-24
2.63E-
24
1.98E-23
Max
5.56E-45
2.42E-
26
1.00E+00
4.94E-
114
0.00E+00
The a e age company is assigned o he middle a ing 3 – BBB. The
hypo he ical company wi h he minimum (maximum) alues is a ed 1 – B (3 –
BBB). Compa ed wi h he disc iminan model (Table 4-8), he logis ic model
p edic s a di e en a ing g oup using he minimum alues o p edic o s.
Nex , we examine he classi ica ion accu acy o es ima ion and hold-ou
samples (Table 4-18). All models achie e a ela i ely high o e all classi ica ion
accu acy, and hei di e ences a e small. Fo example, he highes classi ica ion
accu acy on a hold-ou sample is achie ed by Model 9. O e all, i is clea ha
MLR models ha e a highe classi ica ion accu acy han OLR models. Also, 3-ca
models pe o m be e han 5-ca models.
Table 4–18 Pe cen age co ec ly classi ied (PCC)
Model
Class. (ES)
Class. (hold)
Model 5
0.8801
0.8850
Model 6
0.8861
0.8851
Model 7
0.8649
0.8468
Model 8
0.8494
0.8600
Model 9
0.9096
0.9060
Model 10
0.9105
0.8977
Model 11
0.8818
0.8882
Model 12
0.8986
0.8811
4.1.5 Compa ison o Es ima ed Ra ing Models
Ou applica ion de eloped classi ica ion ules o i e and h ee a ing classes,
which is mo e complex han he bina y ask. The e o e, we will combine mul iple
ROC cu es o assess he pe o mance o es ima ed models. As men ioned in
106 Chap e 4
2024 Ma ina No o ná
Chap e 3.2.4, he e a e wo main app oaches o mul iple ROC analysis: Each class
e sus he union o o he classes, o dis inc pai wise-class ROC cu es. Bo h
me hods a e sui able o summa y s a is ics, such as he AUC (A ea Unde he
Cu e).
We use he i s app oach in ou applica ion o compa e he abili y o p edic a
ca ego y e sus a union o o he ca ego ies. This way is su icien o ou pu poses
and e ec i e o o e all compa ison. Thus, o each 5-ca model, we p oduce ROC
cu es and calcula e he AUC as ollows:
• Ca 1 e sus he union o o he ca ego ies (ca 2 + ca 3 + ca 4 + ca 5),
• ca 2 e sus he union o o he ca ego ies (ca 1 + ca 3 + ca 4 + ca 5),
• ca 3 e sus he union o o he ca ego ies (ca 1 + ca 2 + ca 4 + ca 5),
• ca 4 e sus he union o o he ca ego ies (ca 1 + ca 2 + ca 3 + ca 5),
• ca 5 e sus he union o o he ca ego ies (ca 1 + ca 2 + ca 3 + ca 4).
The p ocedu e is analogical o 3-ca models when conside ing only h ee
a ing ca ego ies. The ROC analysis is based on a pa ame ic model, using he
maximum likelihood es ima ion. We analyse he whole expe imen al and hold-ou
sample o de e mine whe he he classi ica ion abili y a ies wi h he used sample
selec ion. P e e ably, we ocus on he classi ica ion abili y o he hold-ou sample
ha is no used o es ima e models.
Table 4–19 AUC (5-ca models)
Model/AUC
Ca 1
Ca 2
Ca 3
Ca 4
Ca 5
LDA (Model 1)
Es . sample
Hold-ou
0.9658
0.9647
++
0.9876
0.9887
++
0.9689
0.9793
0.9199
0.9803
0.9840
0.9696
0.9836
0.9797
0.9931
LDA (Model 2)
Es . sample
Hold-ou
0.9444
0.9556
0.9200
0.9815
0.9814
0.9816
0.9689
0.9676
0.9730
0.9804
0.9813
0.9779
0.9836
0.9721
0.9998
MLR (Model 5)
Es . sample
Hold-ou
0.9950
0.9947
++
0.9942
0.9956
++
0.9807
0.9892
0.9253
0.9902
0.9940
0.9741
0.9955
0.9957
0.9967
MLR (Model 6)
Es . sample
Hold-ou
0.9946
0.9926
0.9987
0.9927
0.9917
0.9953
0.9807
0.9794
0.9849
0.9902
0.9912
0.9866
0.9955
0.9924
0.9998
OLR (Model 7)
Es . sample
Hold-ou
0.9890
0.9884
++
0.9867
0.9884
++
0.9654
0.9749
0.9130
0.9798
0.9823
0.9701
0.9800
0.9746
0.9829
OLR (Model 8)
Es . sample
Hold-ou
0.9879
0.9854
0.9944
0.9832
0.9817
0.9878
0.9654
0.9635
0.9713
0.9798
0.9808
0.9772
0.9800
0.9712
0.9975
++ no su icien da a o pe o m ROC analysis; andom models (whi e), non andom models (g ey)
Fi s ly, we compa e he 5-ca models. Based on he AUC alues o 5-ca
models (Table 4-19), he classi ica ion abili y is su icien , and he e a e only
mino di e ences among he models. Ne e heless, we conclude ha he bes
classi ica ion abili y is pe o med by model 6 (MLR, andom). We can also see
The E ec o Selec ed Fac o s on Ra ing and i s Dynamics 107
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
ha he bes model is es ima ed by mul i a ia e eg ession analysis no ma e wha
sample we use ( andom, non andom).
Table 4–20 AUC (3-ca models)
Model/AUC
Ca 2
Ca 3
Ca 4
LDA (Model 3)
Es . sample
Hold-ou
0.9913
0.9934
++
0.9604
0.9732
0.8992
0.9927
0.9951
0.9803
LDA (Model 4)
Es . sample
Hold-ou
0.9870
0.9858
0.9911
0.9600
0.9589
0.9633
0.9923
0.9935
0.9877
MLR (Model 9)
Es . sample
Hold-ou
0.9900
0.9918
++
0.9711
0.9822
0.9121
0.9960
0.9979
0.9837
MLR (Model 10)
Es . sample
Hold-ou
0.9936
0.9929
0.9957
0.9753
0.9738
0.9798
0.9966
0.9974
0.9937
OLR (Model 11)
Es . sample
Hold-ou
0.9912
0.9931
++
0.9584
0.9718
0.8945
0.9930
0.9954
0.9803
OLR (Model 12)
Es . sample
Hold-ou
0.9875
0.9862
0.9911
0.9586
0.9571
0.9635
0.9923
0.9942
0.9894
++ no su icien da a o pe o m ROC analysis; andom models (whi e), non andom models (g ey)
Nex , we compa e 3-ca models (Table 4-20 ). O e all, he classi ica ion abili y
is sligh ly highe compa ed o he 5-ca models. Howe e , all models pe o m
su icien classi ica ion abili y, and he e a e mino di e ences among he AUC.
The esul s suppo he main indings om he 5-ca models because he bes
classi ica ion abili y is pe o med by model 10 (MLR, andom).
The ROC cu es a e p esen ed only o 5-ca models (Appendix 4). They
e lec he da a on AUC shown in Table 4-19. The classi ica ion o models is
simila and ela i ely high because we es he abili y o p edic one ca ego y
agains he union o o he ca ego ies. O e all, we p e e model 6, which p o ides
he bes esul s.
4.1.6 Summa y o Resul s
We es ima ed wel e a ing models in his s udy. We assumed en inancial
a iables and i e o h ee ou pu ca ego ies. In addi ion, we used wo samples o
de e mine whe he sample selec ion a ec s he models and hei p edic ion abili y.
All es ima ed models sugges ha all used inancial a iables a e good
p edic o s o a ing. The main indings o his s udy p o ide e idence ha
accoun ing-based a iables signi ican ly impac co po a e a ing in ou sample.
Howe e , he di ec e ec on pa icula a ings is no easily in e p e able and mus
be explained in he con ex o es ima ed models.
108 Chap e 4
2024 Ma ina No o ná
The impac o selec ed a iables on a ing in disc iminan models is measu ed
by es ima ing he coe icien s' con ibu ions. Howe e , since he con ibu ion o
he a iables o he o he a iables in he model di e s in each disc iminan
unc ion (s anda dised coe icien s), i is no concei able o d aw clea
conclusions. Thus, igno ing o he a iables in he models, he associa ion o
indi idual a iables wi h each disc iminan unc ion is compa ed h ough he
co ela ion coe icien s (s uc u e ma ix). Acco ding o he s uc u e ma ix, he
highes a e age associa ion wi h disc iminan unc ions apply o oa, eq a,
lnin co , lnliq and lncu .
The impac o he a iables on a ing in he logis ic eg ession models is
de e mined h ough hei s a is ical signi icance, pa icula ly in logi unc ions. Fo
example, a iables eq a, ln a, lncu and ebi da a e no s a is ically signi ican in
some logis ic unc ions; hus, hey a e no conside ed key a ing ac o s.
Fu he mo e, based on he logis ic models, he highe he alue o oa, lnin co ,
lnliq and lnc , he g ea e he p obabili y o a be e a ing assessmen . Con a y,
g ea e alues o oe and lnl d a inc ease he likelihood o a lowe a ing.
To summa ise all pa ial esul s o he ole o inancial a iables, we conclude
ha oa, oe, lnin co , and lnliq achie e he highes co ela ions wi h disc iminan
unc ions and a e s a is ically signi ican in all logi unc ions. Thus, hey a e
conside ed as he p ima y ac o s o a ing p edic ion, ollowed by lnc and lnl d a.
We p o ide e idence ha he ollowing inancial a iables a e he main ac o s o
a ing assessmen :
• Re u n on o al asse s,
• e u n on equi y,
• in e es co e ,
• liquidi y a io,
• cash low,
• long- e m deb o o al asse s.
The classi ica ion accu acy o all es ima ed models was de e mined based on
he o e all pe cen age co ec ly classi ied (PCC). The PCC, o hi a io, anges
om 88% o 90.6% o a hold-ou sample o ou models. To assess he o e all
classi ica ion abili y, we mus se an accep able le el and compa e he hi a io o
he s anda d. Fi s ly, we de e mine he pe cen age ha could be de e mined
co ec ly by chance. Since we compa e he hi a io o unequal g oup sizes, we
conside jus he la ges g oup. Fo example, he la ges andom sample g oup in
ou s udy is ep esen ed by a ing BBB (2353 obse a ions in he expe imen al
sample and 719 obse a ions in he hold-ou sample). Thus, we can a bi a ily
assign all he subjec s o he la ges g oup. The e o e, i we classi y each
obse a ion in o his la ges g oup in he case o andom models, we would achie e
a classi ica ion accu acy o 46.8% (expe imen al sample) and 44.4% (hold-ou
sample). Assuming non andom models, we ge 43.4% (expe imen al sample) and
61.63% (hold-ou sample). This app oach is e e ed o as he maximum chance
c i e ion, and unless a model achie es accu acy mo e han he compu ed alues,
The E ec o Selec ed Fac o s on Ra ing and i s Dynamics 115
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
cons uc ed o models wi h null alues o a iables (h0) and o a hypo he ical
company wi h i) mean and ii) medium alues (h1). Compa ing Figu es 4-3, 4-4
and 4-5, o speci ically he cumula i e haza d wi h smoo hed haza d cu es, we
can see ha plo ing anges a e na owe . As Cle es e al. (2010) explain, his is
because ke nel smoo hing equi es a e aging alues o e a mo ing window o
da a.
Figu e 4–4 Smoo hed haza d unc ions
4.2.4 Model Ve i ica ion
Ve i ying whe he he haza d unc ions a e mul iplica i ely ela ed is ad isable
when using he Cox model. The e o e, we assess he p opo ional haza ds
assump ion by plo ing he es ima ed haza ds on a log scale. The lines in all g aphs
(Figu e 4-5) seem pa allel. Thus, we conclude ha he p opo ionali y assump ion
in bo h models is no iola ed.
Figu e 4–5 Smoo hed haza d unc ions (log scale)
116 Chap e 4
2024 Ma ina No o ná
Table 4–24 Tes o PH assump ions
Indep. a iable
Single ho
(Chi2)
Mul iple ho
(Chi2)
ag
0.0217
(0.17)
-0.0060
(0.02)
oag
0.0387
(0.59)
0.0270
(0.39)
oeg
0.0048
(0.01)
0.0260
(0.40)
c g
0.0060
(0.03)
0.0131
(0.20)
in co g
-0.0716*
(6.55)
-0.0734*
(10.27)
liq g
0.0598
(2.05)
0.0403
(1.24)
Global
8.86
12.42
*signi ican a 0.05, s anda d e o adjus ed o 737 clus e s
The es o he p opo ional-haza ds speci ica ion is based on he Schoen eld
esiduals a e i ing he model. I is used o es he independence be ween
esiduals and ime. The es esul s in Table 4-24 sugges ha he haza d
assump ion is no p opo ional o he a iable in co g. Fu he mo e, we ind no
e idence ha ou speci ica ion iola es he p opo ional-haza d assump ion
ega ding o he a iables. The e o e, ou speci ica ion does no iola e he
p opo ional-haza ds assump ion in bo h models based on he global es .
The models a e e alua ed by he o e all model i using Cox-Snell esiduals.
Figu e 4-6 shows he Nelson-Aalen cumula i e haza d es ima o plo s o Cox-
Snell esiduals o bo h models. We can see some a iabili y a ound he 45°line,
pa icula ly in he igh -hand ail. Cle es e al. (2010) a gue ha some a iabili y
is expec ed due o he educed e ec i e sample caused by p io ailu es and
censo ing. Howe e , we can see ha bo h g aphs i he da a adequa ely based on
he cha s.
(a) Single (b) Mul iple
Figu e 4–6 Cumula i e haza d o Cox-Snell esiduals
The E ec o Selec ed Fac o s on Ra ing and i s Dynamics 117
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Howe e , we canno choose a be e model based on he g aphical illus a ion.
Fo his eason, we e alua e he p edic i e powe by compu ing he Ha ell’s C
conco dance s a is ics, which measu es he ag eemen o p edic ions wi h
obse ed ailu e o de . The s a is ics can be de ined as he p opo ion o all usable
subjec pai s in which he p edic ions and ou comes a e conco dan (Cle es e al.,
2010). The alues o C ange be ween 0 and 1. Addi ionally, we can use Some s’D,
which epo s he ank co ela ion alue, anging om -1 o 1. Bo h measu es a e
ela ed as
2( 0.5).DC=−
As Cle es e al. (2010) s a e, a alue o 0.5 Ha ell’s C
and 0 o Some ’s D indica e no p edic i e abili y o he model.
The alues o Ha ell’s C and Some ’s D and hei calcula ion p ocedu e a e
shown in Table 4-25. Ha ell’s C alues a e 0.8586 (single) and 0.8705 (mul iple).
Thus, we can co ec ly iden i y he o de o he su i al imes o pai s o subjec s
85.86%, o 87.05% o he ime. Al hough he esul s a e simila , he alues a e
sligh ly highe o he mul iple model. These esul s a e suppo ed by he alue o
Some ’s D, which is 0.7172 (single) and 0.7411 (mul iple).
The esul s p o ide e idence ha bo h models ha e su icien p edic i e
accu acy. We p e e he mul iple model o e he single one based on he alues.
Table 4–25 Ha ell’s C and Some ’s D
Single model
Mul iple model
Numbe o subjec s (N)
3554
3554
Numbe o compa ison pai s (P)
924134
984815
Numbe o o de ings as expec ed (E)
793479
857329
Numbe o ied p edic ions (T)
0
0
Ha ell’s C = (E + T/2) / P
0.8586
0.8705
Some ’s D
0.7172
0.7411
To conclude, he mul iple ailu e- ime da a analysis leads o a mo e sui able
model based on he s a is ical signi icance o he es ima ed coe icien s and
goodness o i . On he o he hand, i should be no ed ha bo h su i al models
a e e y simila based on es ima ed coe icien s and used c i e ia.
4.2.5 Summa y o Resul s
This s udy aimed o de elop a ing models using su i al analysis me hods.
Speci ically, we applied he Cox p opo ional haza ds model o analyze he
su i al ime un il he e en . In ou case, we ocused on using su i al analysis o
model he ime o a a ing downg ade. As a pa o he analysis, we examined he
e ec o inancial a iables on he p obabili y o nega i e annual a ing change.
We p o ide e idence ha annual changes in some a iables a e ela ed o he
a ing downg ade, speci ically using co a ia es ag, oag, oeg, c g, in co g and
liq g. On he con a y, a iables eq ag, ebi da g, l d ag and cu g a e no
s a is ically signi ican . Thus, we can conclude ha annual changes in he
ollowing inancial a iables a e good p edic o s o po en ial a ing de e io a ion
measu ed as a ing downg ade in ou sample:
118 Chap e 4
2024 Ma ina No o ná
• To al asse s,
• e u n on o al asse s,
• e u n on equi y,
• cash low,
• in e es co e ,
• liquidi y a io.
Two di e en app oaches we e used o es ima e he models, depending on
whe he we conside ed only one o mo e e en s ( a ing downg ades) o one
company. Fi s , he single model was de i ed, assuming ha he e en can occu
only once o each subjec . On he o he hand, he mul iple models accep ha he
e en can occu epea edly. Due o hese di e en assump ions, he inpu da a and
s uc u e also had o be adjus ed.
The esul ing models a e p esen ed based on he es ima ed coe icien s o he
a iables used in he analysis. Bo h models a e s a is ically signi ican , as a e he
es ima ed coe icien s o he indi idual a iables in he mul iple model.
We used baseline haza d and he haza d o he so-called a e age (medium)
company o in e p e he models based on mean (medium) alues o a iables. The
i o bo h models was assessed using Cox esiduals. Based on he main indings
o his s udy, we conclude ha he mul iple model app oach is mo e sui able o
e en s ha migh occu epea edly. The simple model should be p e e ably used
when he su i al ime un il he i s e en is a ma e o in e es . In o he cases,
we should use mul iple ailu e- ime da a analyses, making da a use be e .
O e all, he indings o his s udy show ha su i al analysis is, in addi ion o
ypical inancial p oblems, sui able o o he ypes o asks, such as he analysis o
su i al o bank up cy o de aul . Howe e , i is necessa y o conside he speci ic
da a s uc u e when applying i , especially whe he he e en can epea edly occu
o one subjec o whe he mo e e en s can occu o a gi en subjec . In hese
cases, i is app op ia e o use mul iple ailu e- ime analysis, which be e
co esponds o he p oblem.
4.3 Chap e Summa y
The ou h chap e 's main goal was o analyse co po a e da a o selec ed CEE
coun ies and unde s and he in luence o selec ed inancial a iables on he
MORE a ing. The e o e, we i s ocused on es ima ing a ing models using
disc iminan analysis and wo logis ic eg ession me hods. In o al, we ob ained
wel e a ing models, which we e compa ed wi h each o he . Nex , we iden i ied
inancial a iables ha can be conside ed p edic i e ac o s o he a ing
e alua ion. E en hough he indi idual models di e ed sligh ly in e ms o hei
o mula ion and classi ica ion abili y, he o e all conclusions con i m he main
ole o used inancial a iables in a ing assessmen .
In he nex sec ion, we used he same da a se and examined he ela ionship
be ween inancial a iables and a ing downg ades. In his case, we applied he
The E ec o Selec ed Fac o s on Ra ing and i s Dynamics 119
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
me hod o su i al analysis using he Cox model. Su i al analysis allows us o
es ima e he su i al p obabili y o subjec s o a p ede ined e en . Since a ing
de e io a ion is qui e a undamen al p oblem, especially o lende s, i is ce ainly
impo an o ecognize an impending a ing change ea ly. Fo his eason, he
a ing downg ade was chosen as he e en in he su i al analysis. Using he Cox
model, we subsequen ly ound six inancial a iables ha ha e a undamen al
connec ion wi h he annual de e io a ion o he a ing assessmen .
The main in luen ial inancial a iables based on bo h s udies a e summa ized
in Table 4-26. The esul s con i m ha common inancial indica o s in luence he
a ing assessmen and i s annual de e io a ion, ega dless o he me hod used o
he ou pu a iable. These a e i e commonly used inancial indica o s in inancial
analysis and e alua ion o he inancial pe o mance o companies. E en i hese
indica o s seem basic and simple, hey s ill play a majo ole in assessing he
bo owe 's c edi quali y and, hus, he a ing. O cou se, i is necessa y o ake
hem in he con ex o hei change and i s possible impac on he a ing, o a he
on i s de e io a ion.
Table 4–26 Main ac o s o a ing and i s downg ade
Ra ing
assessmen
Ra ing
downg ade
To al asse s
x
✓
Re u n on o al asse s
✓
✓
Re u n on equi y
✓
✓
Liquidi y a io
✓
✓
Cash low
✓
✓
In e es co e
✓
✓
Long- e m deb o o al asse s
✓
x
In gene al, i has been shown in his chap e ha he i s app oach, based on
disc iminan analysis and logis ic eg ession, and he second me hod, using
su i al analysis, lead o simila esul s. In addi ion, wi h he help o su i al
analysis, we could es ima e he haza d and su i al unc ions, which can be used
o p edic he p obabili y o su i al o he ime un il he a ing de e io a es.
Fu he mo e, i means we can look deepe in o he de elopmen o he moni o ed
a iable o e ime and i s dynamics. Fo his eason, su i al analysis will be used
in he ollowing sec ion, whe e he su i al ime o i ms un il bank up cy will be
modelled. Mo eo e , as his is a speci ic e en ela ed o he bo owe 's c edi
quali y, a sub-goal o he ollowing chap e will be o unde s and and link he
ela ionship be ween co po a e su i al p obabili y and c edi a ing.
Chap e 5
Rela ionship Be ween Ra ing and
Co po a e Bank up cy Ra es
This chap e p o ides an al e na i e iew on measu ing and p edic ing i m-based
c edi isk. While we es ima ed a ing models in he p e ious sec ion, he ocus is
on bank up cy models in he ollowing applica ion. Bank up cy, as a e minal s a e
o he company, and a ing a e ela ed because he wo s a ing assessmen is
ypically issued o insol en companies in inancial ouble, o en close o
bank up cy. Thus, we also examine and model co po a e bank up cy in his
esea ch o ex end he p e ious indings o he main p edic o s o a ing
assessmen .
The knowledge and unde s anding o a ing and bank up cy ac o s a e
essen ial o c edi isk managemen . The e idence o co po a e su i al and non-
de aul a es helps in es o s and lende s assess he c edi quali y o bo owe s and
p edic po en ial p oblems o de aul , insol ency o e en co po a e bank up cy.
Fo example, he analysis o ime o de aul , which CRAs conduc , is based on he
cumula i e dis ibu ion o de aul e s by he ime o de aul and su i al a es.
Acco ding o he his o ical de aul a es published by CRAs, he e is a clea
associa ion be ween a ing and de aul a es. Thus, assuming his ela ionship, we
can es ima e he su i al a es o a ce ain sample o companies and compa e hem
wi h his o ical non-de aul a es published by CRAs.
The main goal o his chap e is o de e mine whe he he e is a measu able
ela ionship be ween es ima ed bank up cy a es and de aul a es published by
a ing agencies using empi ical da a om Czech companies. In a posi i e case,
his ela ionship can be desc ibed in a ce ain way. Then, a p ocedu e can be
sugges ed in which he de ec ed bank up cy a es could be used o a a ing
assessmen co esponding o he a ing agencies' assessmen . This p ocedu e has
meaning and main applica ion, especially in cases whe e we ha e da a on
co po a e bank up cies. We can p ocess hem s a is ically, and ou goal is o
ansla e hem in a ce ain way in o he “language” o a ing agencies.
122 Chap e 5
2024 Ma ina No o ná
As men ioned in Chap e 3.1, he e is a as li e a u e on p edic ing co po a e
bank up cy using a ious echniques. Howe e , li le a en ion is paid o es ima ing
co po a e bank up cy using su i al analysis me hods compa ed o disc iminan ,
logis ic, neu al ne wo k me hods o classi ica ion ees. The e o e, he pa ial aim
o his s udy is o analyse su i o da a o Czech companies and assess he impac
o a ious ac o s on co po a e su i al.
Du ing he obse ed ime in e al, ou analysis conside s bank up cy he
ailu e e en . Thus, he ime be ween he s a o he business and bank up cy is
used o es ima e su i al and haza d unc ions. E en ually, he es ima ed su i al
a es can be compa ed wi h CRAs’ his o ical de aul a es and co esponding
a ing assessmen s. Hence, we conside h ee c edi isk measu es in he ollowing
s udy: bank up cy a es, de aul a es, and a ing.
The s uc u e is as ollows. Fi s ly, he associa ion be ween a ing and
co po a e de aul s obse ed and published by a ing agencies is s udied. Nex , he
Kaplan-Meie me hod is used o assess he e ec o selec ed cha ac e is ics o
Czech companies on he su i al p obabili y. Then, he ela ionship be ween
es ima ed cumula i e bank up cy a es and published de aul a es is explo ed.
Finally, based on he main indings, a p ocedu e is p oposed o con e ing he
bank up cy a es in o a ing assessmen s.
5.1 Associa ion Be ween Ra ing and Co po a e De aul s
This chap e p o ides an o e iew o he ela ionship be ween a ing and de aul
a es based on his o ical da a om a ing agencies. Nex , we desc ibe he app oach
a ing agencies use o calcula e cumula i e de aul a es.
5.1.1 CRA Annual De aul Ra es
The pu pose o his sec ion is o explo e he ela ionship be ween c edi a ing
g ades and co po a e de aul a es. Acco ding o he his o ical occu ence o
de aul s wi hin a ing g ades obse ed and published by CRAs, he e is an e iden
co ela ion be ween he ini ial a ing o a i m and i s ime o de aul . Typically,
he his o ical numbe o de aul s wi hin an in es men g ade is subs an ially lowe
when compa ed o a specula i e g ade (Table 5-1).
The highes numbe o de aul s, o he highes de aul a es, occu ed du ing
he inancial c isis o 2008 – 2009, e en wi hin he in es men g ade. Du ing he
las 30 yea s, om 1990 o 2020, he in es men g ade achie ed he highes de aul
a e, 0.42%, du ing he wo inancial c ises in 2002 and 2008 (S&P, 2021).
Rela ionship Be ween Ra ing and Co po a e Bank up cy Ra es 123
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Table 5–1 Co po a e de aul summa y, 2005 – 2020
Yea
To al
de aul s
In .-
g ade
de aul s
Spec.-
g ade
de aul s
De aul
a e (%)
In .-g ade
de aul
a e (%)
Spec.-g ade
de aul a e
(%)
2005
40
1
31
0.60
0.03
1.51
2006
30
0
26
0.48
0.00
1.19
2007
24
0
21
0.37
0.00
0.91
2008
127
14
89
1.80
0.42
3.71
2009
268
11
224
4.18
0.33
9.95
2010
83
0
64
1.21
0.00
3.02
2011
53
1
44
0.80
0.03
1.85
2012
83
0
66
1.14
0.00
2.59
2013
81
0
64
1.06
0.00
2.31
2014
60
0
45
0.69
0.00
1.44
2015
113
0
94
1.36
0.00
2.78
2016
163
1
143
2.09
0.03
4.24
2017
95
0
83
1.21
0.00
2.47
2018
82
0
72
1.03
0.00
2.10
2019
118
2
92
1.30
0.06
2.54
2020
226
0
198
2.74
0.00
5.50
Sou ce: S&P (2021)
CRAs also calcula e and publish annual de aul a es o a ing g ades, showing
he his o ical end o co po a e de aul s wi hin a ing ca ego ies (Table 5-2). Mos
a ed de aul e s come om he lowes ca ego ies, B and CCC/C, while he de aul
a es o he AAA ca ego y a e ze o.
Table 5–2 Global annual de aul a es by a ing ca ego y (%), 2005 – 2020
Yea
AAA
AA
A
BBB
BB
B
CCC/C
2005
0.00
0.00
0.00
0.07
0.31
1.74
9.09
2006
0.00
0.00
0.00
0.00
0.30
0.82
13.33
2007
0.00
0.00
0.00
0.00
0.20
0.25
15.24
2008
0.00
0.38
0.39
0.49
0.81
4.08
27.27
2009
0.00
0.00
0.22
0.55
0.75
10.91
49.46
2010
0.00
0.00
0.00
0.00
0.58
0.85
22.73
2011
0.00
0.00
0.00
0.07
0.00
1.66
16.42
2012
0.00
0.00
0.00
0.00
0.30
1.56
27.33
2013
0.00
0.00
0.00
0.00
0.10
1.63
24.34
2014
0.00
0.00
0.00
0.00
0.00
0.77
17.03
2015
0.00
0.00
0.00
0.00
0.16
2.39
25.73
2016
0.00
0.00
0.00
0.06
0.47
3.76
33.17
2017
0.00
0.00
0.00
0.00
0.08
1.00
26.56
2018
0.00
0.00
0.00
0.00
0.00
0.99
27.18
2019
0.00
0.00
0.00
0.11
0.00
1.49
29.76
2020
0.00
0.00
0.00
0.00
0.93
3.52
47.48
Sou ce: S&P (2021)
124 Chap e 5
2024 Ma ina No o ná
The his o ical end o he de aul a es is ela i ely s able and shows a clea
associa ion be ween a ing g ade and he gene al de aul a e o c edi isk. The e
is a nega i e co ela ion be ween he ini ial a ing o a i m and i s ime o de aul .
Fo example, he a e age ime o a de aul o en i ies ini ially a ed A g ade ( he
ime be ween i s a ing and da e o de aul ) is 14.1 yea s. In compa ison, he
a e age ime o de aul among en i ies o iginally B was 5.1 yea s based on 1981 –
2020 in he s udy by S&P Global Ra ings (S&P, 2021). Nex , he a e age ime o
AAA a ing is 18 yea s, BBB is 9.2 yea s, and CCC/C is only 2.2 yea s.
In addi ion o calcula ing ime o de aul , he cumula i e dis ibu ion o
de aul e s by he ime o de aul and su i al, o non-de aul a es, can also be used
o ge mo e in o ma ion on he a ing dynamics and de aul s. Fo example, he
su i al a e o he pe cen age o B co po a e issue s s ill ali e o one, h ee o
i e yea s was 97.6%, 93.4% and 89.6% o 2011 – 2015 (Table 5-3).
Table 5–3 Co po a e de aul s and su i al a es (2011 – 2015)
Ra ing
One-yea pool (2015)
Th ee-yea pool
(2013 – 2015)
Fi e-yea pool
(2011 – 2015)
Numbe
o
de aul s
Non-
de aul
a e
Numbe
o
de aul s
Non-
de aul
a e
Numbe
o
de aul s
Non-
de aul
a e
AAA
0
100.0%
0
100.0%
0
100.0%
AA
0
100.0%
0
100.0%
0
100.0%
A
0
100.0%
0
100.0%
1
99.8%
BBB
0
100.0%
0
100.0%
0
100.0%
BB
2
99.8%
7
99.1%
22
97.1%
B
42
97.6%
93
93.4%
122
89.6%
CCC/C
38
73.8%
56
57.9%
47
59.8%
Sou ce: Sou ce: S&P (2015)
Fo compa ison, Table 5-4 summa ises de aul a es o 2016 – 2020, pa ly
al eady e lec ing he consequences o he COVID-19 pandemic.
Table 5–4 Co po a e de aul s and su i al a es (2016 – 2020)
Ra ing
One-yea pool (2020)
Th ee-yea pool
(2018 – 2020)
Fi e-yea pool
(2016 – 2020)
Numbe
o
de aul s
Non-
de aul
a e
Numbe
o
de aul s
Non-
de aul
a e
Numbe
o
de aul s
Non-
de aul
a e
AAA
0
100.0%
0
100.0%
0
100.0%
AA
0
100.0%
0
100.0%
0
100.0%
A
0
100.0%
2
99.9%
0
100.0%
BBB
0
100.0%
2
99.9%
13
99.3%
BB
12
99.1%
17
98.7%
28
97.8%
B
73
96.5%
175
90.9%
283
85.0%
CCC/C
113
52.5%
103
47.2%
103
48.2%
Sou ce: S&P (2021)
Rela ionship Be ween Ra ing and Co po a e Bank up cy Ra es 131
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
indus ial companies is he lowes among all g oups, ollowed by u ili y, se ices
and ag icul u e (see Figu e 5-2). The es s o equali y o o e all su i al unc ions
ac oss g oups based on he log- ank es (Chi2(3)=421.24), Wilcoxon
(Chi2(3)=384.24) and Pe o-Pe o es (Chi2(3)=416.54) ejec he hypo hesis ha
he su i al unc ions a e he same.
Figu e 5–2 Su i al and cumula i e unc ions by sec o s
b) The E ec o Legal Fo m
The mean es ima ed imes a e summa ised in Table 5-12. Join -s ock and limi ed-
liabili y companies ha e he lowes es ima ed su i al ime, ollowed by
coope a i es and o he legal o ms.
Table 5–12 Es ima ed mean su i al ime by legal s a us
G oup
Legal s a us
Mean
S anda d
e o
Con idence in e al
(95%)
1
Join -s ock
company
8517.66
40.5545
8438.17
8597.15
2
Coope a i es
8726.66
86.3793
8557.36
8895.96
3
Limi ed-liab.
8552.97
18.1951
8517.29
8588.62
4
O he
8996.49
65.7681
5567.59
9125.39
To al
8568.40
16.2197
8536.61
8600.19
The su i al and cumula i e unc ions o each legal o m a e depic ed in Figu e
5-3. The es s o equali y o o e all su i al unc ions ac oss g oups based on he
log- ank es (Chi2(3)=14.31), Wilcoxon (Chi2(3)=14.54) and Pe o-Pe o es
(Chi2(3)=15.96) ejec he hypo hesis ha he su i al unc ions a e he same.
132 Chap e 5
2024 Ma ina No o ná
Figu e 5–3 Su i al and cumula i e haza d unc ions by legal o m
c) The E ec o Business Size
While he lowes es ima ed mean su i al ime is associa ed wi h small companies,
he mean su i al imes o o he ca ego ies a e simila (Table 5-13). Mic o
companies ha e he highes es ima ed mean su i al ime, ollowed by medium
and la ge companies. The isual esul s sugges ha small companies ha e he
lowes p obabili y o su i al (Figu e 5-4).
Table 5–13 Es ima ed mean su i al ime by size
G oup
Business
ca ego y
Mean
S anda d
e o
Con idence in e al
(95%)
1
Mic o
8595.66
21.6411
8553.25
8638.08
2
Small
8488.22
29.7732
8429.86
8546.57
3
Medium
8568.99
44.0947
8482.56
8655.41
4
La ge
8556.97
109.99
8341.39
8772.54
To al
8644.55
16.4998
8612.21
8676.89
Figu e 5–4 Su i al and cumula i e haza d unc ions by size
Rela ionship Be ween Ra ing and Co po a e Bank up cy Ra es 133
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
The es s o equali y o o e all su i al unc ions ac oss g oups based on he
log- ank es (Chi2(3)=16.58), Wilcoxon (Chi2(3)=12.54) and Pe o-Pe o es
(Chi2(3)=15.86) ejec he hypo hesis ha he su i al unc ions a e he same.
5.3 The Rela ionship Be ween Bank up cy Ra es and Ra ing
Assessmen
Based on he esul s o ou p io analysis, he es ima ed bank up cy a es a e
compa ed wi h CRAs’ his o ical de aul a es o assess he a e age c edi quali y
o he obse ed i ms. Since bank up cy can be conside ed a legal p ocedu e o
liquida ing a business ha canno ully pay i s deb s, a s ong co ela ion be ween
bank up cy and de aul a es is assumed. Thus, we can compa e de aul a es wi h
bank up cy a es wi hou much impac on he o e all indings and hei
in e p e a ion.
The aim o his sec ion is o examine whe he he e is an associa ion be ween
he es ima ed co po a e bank up cy a es and a ing cumula i e de aul a es. Fi s ,
he es ima ed su i al unc ions a e used o de e mine cumula i e bank up cy a es
a he end o a pa icula yea . Nex , hey a e compa ed wi h CRAs’ his o ical
cumula i e de aul a es and, e en ually, co esponding a ing assessmen s.
Finally, h ough pee compa ison, we p opose a way ha bank up cy a es can be
ansla ed in o he a ing. Hence, he main pu pose o his s udy is o link he
bank up cy a es and a ing assessmen .
5.3.1 Associa ion Be ween Bank up cy Ra es and Ra ing
To assess he a e age a ing quali y o companies in ou da a sample, we examine
he associa ion be ween co po a e bank up cy a es and S&P a ing g ades. Fi s ly,
cumula i e bank up cy a es (CBR) o he sample a e calcula ed using he ull da a
se acco ding o he ime ho izon. Then, he bank up cy a es a e compa ed wi h
long- e m a e age global cumula i e de aul a es o S&P a ing (CDR, 1981-
2020); see Table 5-14.
The associa ion be ween co po a e bank up cy a es and S&P cumula i e
de aul a es is g aphically p esen ed in Figu e 5-5. I can be seen om his igu e
ha he e a e subs an ial di e ences be ween de aul a es o a ing g oups. Fo
example, cumula i e de aul a e CCC/C, B, and BB cu es lie abo e all o he
cu es, e lec ing he g ea es c edi isk. I is also e iden ha he bank up cy a es
lie be ween BBB and BB's a ing ca ego ies, app oaching BB wi h a longe ime
ho izon. Hence, acco ding o he a ing de ini ion, ou companies' in es men
quali y changes wi h ime.
134 Chap e 5
2024 Ma ina No o ná
Table 5–14 Cumula i e bank up cy a es and a e age cumula i e de aul a es
Time
ho iz.
CBR
CDR
AAA
CDR
AA
CDR
A
CDR
BBB
CDR
BB
CDR
B
CDR
CCC/C
1
0.0072
0.0000
0.0002
0.0005
0.0016
0.0063
0.0334
0.2830
2
0.0129
0.0003
0.0006
0.0013
0.0043
0.0193
0.0780
0.3833
3
0.0184
0.0013
0.0011
0.0022
0.0075
0.0346
0.1175
0.4342
4
0.0234
0.0024
0.0021
0.0033
0.0114
0.0499
0.1489
0.4636
5
0.0281
0.0034
0.0030
0.0046
0.0154
0.0643
0.1735
0.4858
6
0.0350
0.0045
0.0041
0.0060
0.0194
0.0775
0.1936
0.4961
7
0.0428
0.0051
0.0049
0.0076
0.0227
0.0889
0.2099
0.5075
8
0.0494
0.0059
0.0056
0.0900
0.0261
0.0990
0.2231
0.5149
9
0.0556
0.0064
0.0063
0.0105
0.0293
0.1082
0.2350
0.5216
10
0.0629
0.0070
0.0070
0.0120
0.0324
0.1164
0.2462
0.5276
11
0.0685
0.0072
0.0076
0.0134
0.0355
0.1233
0.2558
0.5321
12
0.0753
0.0075
0.0082
0.0146
0.0380
0.1299
0.2631
0.5368
13
0.0856
0.0078
0.0088
0.0159
0.0403
0.1359
0.2699
0.5423
14
0.0985
0.0084
0.0093
0.0171
0.0428
0.1409
0.2763
0.5469
15
0.1095
0.0090
0.0099
0.0184
0.0454
0.1465
0.2824
0.5476
Sou ce: S&P (2021), au ho
Figu e 5–5 Cumula i e bank up cy and de aul a es
Howe e , i is impo an o compa e cumula i e bank up cy a es wi h de aul
a es. Unlike a de aul e en ha e e s o he deb o ’s incapaci y o e usal o mee
hei deb obliga ions when due, bank up cy is he legal s a us o an en i y ha
canno epay deb s o c edi o s. Based on hei de ini ions, we assume de aul a es
o be gene ally highe han bank up cy a es. Ne e heless, his compa ison can
gi e us an in e es ing look a he associa ion be ween bank up cy and a ing de aul
a es and he o e all c edi isk o co po a es in he da a sample.
In addi ion o he a e age alues, we summa ize he bank up cy a es by sec o ,
legal o m and size (Appendix 5). The a es co espond o he main indings in
Chap e 5.2.2, speci ically Figu e 5-2, Figu e 5-3 and Figu e 5-4, showing su i al
and haza d unc ions.
Rela ionship Be ween Ra ing and Co po a e Bank up cy Ra es 135
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
Nex , we examine c edi de aul a es (CDRs) and hei ela ionship wi h
es ima ed co po a e bank up cy a es. Table 5-15 summa izes he a e age c edi
de aul a es o he ime ho izon o en yea s based on he s a is ics by S&P
(2021). We can see he global CDRs and he a es om Eu ope and eme ging
coun ies. In addi ion o he a e age a es by a ing g oups, no e he o e all a es
o in es men and specula i e g ades.
Table 5–15 A e age CDRs ( = 10 yea s)
Global CDR
Eu ope CDR
Eme ging CDR
AAA
0.0036
0.0000
0.0000
AA
0.0035
0.0017
0.0000
A
0.0057
0.0025
0.0003
BBB
0.0170
0.0070
0.0146
BB
0.0664
0.0363
0.0452
B
0.1659
0.1281
0.1191
CCC/C
0.4618
0.4599
0.2800
In es men
0.0097
0.0036
0.0109
Specula i e
0.1418
0.1065
0.0888
Sou ce: S&P (2021)
Based on Table 5-14, we calcula e he a e age cumula i e bank up cy a e o
a ime ho izon o 1–10 yea s (
0.0336CBR =
). Then, we ind he di e ences
be ween he a e age CDRs (Table 5-15 ) and he calcula ed a e age CBR. Finally,
we can see he di e ences be ween CDRs and CBR, e e ed o as a e age sp eads
(AS), in Table 5-16.
Table 5–16 A e age sp eads CDR-CBR ( = 10 yea s)
Global AS
Eu ope AS
Eme ging AS
AAA
-0.0299
-0.0336
-0.0336
AA
-0.0301
-0.0319
-0.0336
A
-0.0279
-0.0310
-0.0333
BBB
-0.0166
-0.0265
-0.0189
BB
0.0329
0.0027
0.0117
B
0.1323
0.0945
0.0855
CCC/C
0.4282
0.4263
0.2464
In es men
-0.0239
-0.0300
-0.0227
Specula i e
0.1083
0.0729
0.0552
The ela ionship be ween he calcula ed a e age sp eads and a ings is
g aphically p esen ed in Figu e 5-6. The highe he sp ead, he lowe he a e age
a ing assessmen , coded om 1 (AAA) o 7 (CCC/C). Hence, based on he
esul s, bank up cy a es seem o be good indica o s o a ing quali y.
136 Chap e 5
2024 Ma ina No o ná
Figu e 5–6 Ra ing and a e age sp eads
In he nex sec ion, a me hod is p oposed o how he calcula ed a e age
sp eads can be used o assign he p obable co po a e a ing. As shown abo e, he
CBRs a e based on he N-A es ima es o cumula i e haza d a es in his s udy.
The e o e, o a ing es ima ion, we need a e age sp eads by a ing g ades.
Fu he mo e, since we model he da a o Czech companies, he sp eads a e based
on Eu opean CDRs (Table 5-17).
Table 5–17 Sp eads by a ing and ime ho izon
Time
ho iz.
AAA
AA
A
BBB
BB
B
CCC/
C
In .
Spec.
1
-0.0072
-0.0072
-0.0069
-0.0066
-0.0036
0.0150
0.2792
-0.0069
0.0216
2
-0.0129
-0.0127
-0.0122
-0.0112
-0.0016
0.0442
0.3743
-0.0120
0.0430
3
-0.0184
-0.0179
-0.0174
-0.0154
0.0005
0.0705
0.4091
-0.0169
0.0594
4
-0.0234
-0.0224
-0.0219
-0.0191
0.0034
0.0910
0.4429
-0.0212
0.0730
5
-0.0281
-0.0265
-0.0258
-0.0227
0.0078
0.1075
0.4614
-0.0251
0.0842
6
-0.0350
-0.0329
-0.0321
-0.0272
0.0080
0.1170
0.4635
-0.0309
0.0889
7
-0.0428
-0.0404
-0.0390
-0.0332
0.0070
0.1222
0.4611
-0.0378
0.0906
8
-0.0494
-0.0467
-0.0453
-0.0383
0.0048
0.1242
0.4612
-0.0438
0.0904
9
-0.0556
-0.0526
-0.0513
-0.0429
0.0022
0.1265
0.4550
-0.0494
0.0897
10
-0.0629
-0.0599
-0.0585
-0.0487
-0.0011
0.1270
0.4557
-0.0562
0.0881
Sou ce: S&P (2021); au ho
5.3.2 T ansmission o Bank up cy Ra es o Ra ing Assessmen
In he p e ious sec ion, we obse ed he ela ionship be ween he es ima ed
bank up cy a es and he a ing using he sp eads be ween he a e age bank up cy
a es and de aul a es o di e en ime ho izons. In his pa , we p opose a
p ocedu e o con e ing he bank up cy a es o a ings using he calcula ed
a e age sp eads.
The p ocedu e s eps a e as ollows:
Rela ionship Be ween Ra ing and Co po a e Bank up cy Ra es 137
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
1. Es ima e a cumula i e bank up cy a e (ECBR), o example, o he
pa icula combina ion o a iables (based on he able in Appendix 5).
2. Calcula e he es ima ed sp ead be ween CDR and ECBR o each a ing
ca ego y (based on Table 5-14) using he equa ion (5.1),
ES CDR ECBR=−
.
(5.1)
3. Compa e ES wi h he a e age sp ead AS summa ized in Table 5-16 . Then,
choose he a ing ca ego y wi h he lowes absolu e alue o de iance based
on equa ion (5.2).
D ES AS=−
.
(5.2)
Al hough his p ocedu e is based on he Eu opean c edi de aul a es published
by he S&P agency, by analogy, i can be used o di e en geog aphical loca ions,
a ing agencies and ime ho izons. An applica ion example o his p ocedu e is
shown below in he ex .
Assuming ha bank up cy a es depend only on he sec o , legal o m and
co po a e size, we can es ima e a a ing based on he ollowing p ocedu e. Fo
example, he abo e echnique will be used o de e mine he p obable a ing o he
ollowing combina ions o co po a e cha ac e is ics:
a) Indus ials, limi ed-liabili y, mic o (i = 1),
b) se ices, join -s ock, la ge (i = 2),
c) ag icul u e, coope a i e, medium (i = 3).
We assume ime ho izons
15 =
and
210 =
yea s o assess he e ec o ime
on he de elopmen o a ing quali y.
Fi s ly, we ind he es ima ed cumula i e bank up cy a es (ECBRs) as simple
a e ages o 5-yea and 10-yea CBRs. Since ou cumula i e haza d a e es ima es
a e based on a nonpa ame ic analysis, we use he same weigh o each ca ego ical
a iable. Then, o i h combina ion o a iables (i = 1, 2, 3) and ime ho izon
( = 5, 10), he es ima ed cumula i e bank up cy a e is ound as:
,
1( _ _ _ ).
3
i
ECBR CBR sec o CBR legal CBR size= + +
(5.3)
Fo example, using he equa ion (5.3), we ge he ollowing ECBRs:
( )
( )
( )
1, 5
2, 5
3, 5
10.045+0.0304 0.0223 0.0326,
3
10.0216+0.0161 0.0097 0.0158,
3
10.0145+0.0306 0.159 0.0203.
3
ECBR
ECBR
ECBR
=
=
=
= + =
= + =
= + =
138 Chap e 5
2024 Ma ina No o ná
( )
( )
( )
1, 10
2, 10
3, 10
10.105 0.0647 0.0503 0.0733,
3
10.0448 0.0618 0.05 0.0522,
3
10.0275 0.0402 0.0526 0.0401.
3
ECBR
ECBR
ECBR
=
=
=
= + + =
= + + =
= + + =
The esul s sugges di e ences be ween he es ima ed cumula i e bank up cy
a es o wo ime pe iods. Fo example, assuming he ime ho izon o 5 yea s, he
g ea es cumula i e haza d a e is associa ed wi h a combina ion o i = 1
(indus ials, limi ed-liabili y, mic o), ollowed by i = 3 (ag icul u e, coope a i e,
medium) and i = 2 (se ices, join -s ock, la ge). In he 10-yea ime ho izon, he
g ea es cumula i e haza d a e is again associa ed wi h he scena io i = 1. I is
ollowed by i = 2, sugges ing ha he cumula i e haza d a es a y wi h ime o
ou combina ions o a iables.
Nex , we calcula e ES and D using he equa ions (5.1) and (5.2) and ind he
co esponding a ing ca ego ies wi h he minimum absolu e alues o D. The
esul s a e summa ized in Table 5-18. Thus, assuming he ime ho izon o 5 yea s
(since he company's ounding), we assign he middle a ing BBB o he companies
wi h he combina ion o a iables i = 2 and i = 3. In he longe ime ho izon, he
assigned a ing is he same o i = 3; howe e , i is es ima ed o be BB o i = 2.
The i s co po a e cha ac e is ics (i = 1) indica e a BB a ing ca ego y ega dless
o he ime ho izon. Ne e heless, he c edi a ing seems o ha e wo sened o a
long ime based on he sugges ed specula i e a ing g ade.
Table 5–18 Ra ing es ima ion (K-M model)
AAA
AA
A
BBB
BB
B
CCC/C
AS
-0.0336
-0.0319
-0.0310
-0.0265
0.0027
0.0945
0.4263
ES1, =5
-0.0326
-0.0310
-0.0303
-0.0272
0.0033
0.1030
0.4569
ES1, =10
-0.0733
-0.0703
-0.0689
-0.0591
-0.0115
0.1166
0.4453
ES2, =5
-0.0158
-0.0142
-0.0135
-0.0104
0.0201
0.1198
0.4737
ES2, =10
-0.0522
-0.0492
-0.0478
-0.0380
0.0096
0.1377
0.4664
ES3, =5
-0.0203
-0.0187
-0.0180
-0.0149
0.0156
0.1153
0.4692
ES3, =10
-0.0401
-0.0371
-0.0357
-0.0259
0.0217
0.1498
0.4785
D1, =5
0.0010
0.0010
0.0008
0.00064
0.00059
0.0085
0.0306
D1, =10
0.0398
0.0384
0.0379
0.0326
0.0143
0.0221
0.0189
D2, =5
0.0178
0.0177
0.0175
0.0161
0.0174
0.0253
0.0474
D2, =10
0.0186
0.0173
0.0168
0.0115
0.0069
0.0432
0.0401
D3, =5
0.0132
0.0132
0.0130
0.0116
0.0128
0.0208
0.0428
D3, =10
0.0065
0.0052
0.0047
0.0006
0.0190
0.0553
0.0522
The o e all esul s sugges ha he i s combina ion o a iables (indus ials,
limi ed-liabili y, mic o) is he iskies . The second case (se ices, join -s ock,
la ge) is associa ed wi h he a e age isk, po en ially wo sening wi h a longe ime
Rela ionship Be ween Ra ing and Co po a e Bank up cy Ra es 139
Mic o-Modelling App oaches o C edi Ra ing and Co po a e Su i al
ho izon. Finally, based on he es ima ed a ing, we ound he combina ion wi h he
lowes and mos s able le el o c edi isk (ag icul u e, coope a i e, medium). The
main indings show ha based on es ima ed bank up cy a es, we can es ima e he
u u e a ing de elopmen acco ding o he ime ho izon.
5.4 Chap e Summa y
This chap e ocused on unde s anding he ela ionship be ween bank up cy a es,
de aul a es published by CRAs, and c edi a ings. As was shown in he
in oduc o y pa o his chap e , me hods based on su i o ship analysis a e used
by a ing agencies o de e mine he de aul a es o a ed subjec s, bo h acco ding
o a ing ca ego ies and o he conside ed ime ho izon.
This sec ion used he su i al me hod o assess he in luence o selec ed
co po a e cha ac e is ics on he su i al p obabili y o Czech companies. Fo his
pu pose, he basic p ocedu e used was he Kaplan-Meie me hod. I is a non-
pa ame ic analysis wi h which we can disco e he basic ela ionships and
unde s and he da a su i o ship. We ocused on assessing he in luence o
indus y, legal o m and size on su i al ime. The esul s indica e ha all used
ac o s a e ela ed o he p obabili y o co po a e su i al. Two hypo heses we e
con i med, sugges ing ha small, indus ial i ms a e iskie compa ed o he o he
conside ed sec o s and sizes. On he o he hand, ou indings sugges ha join -
s ock companies a e iskie compa ed o o he legal o ms, unlike he assump ion.
The o e all esul s a e summa ized in Table 5-19. Fo example, a small, indus ial
join -s ock company can be conside ed he iskies compa ed o o he cases.
Table 5–19 Summa y o esul s
Co po a e
cha ac e is ics
Ca ego y
Mean su i al
ime
Indus y
Se ices
Indus ials
Ag icul u e
U ili y
•••
•
••••
••
Legal o m
Join -s ock
Coope a i es
Limi ed-liabili y
O he
•
•••
••
••••
Size
Mic o
Small
Medium
La ge
••••
•
•••
••
• (lowes ) •••• (g ea es )
Using he p ocedu es desc ibed abo e in Chap e 5.3, we de i ed su i al and
cumula i e haza d unc ions, which we e subsequen ly used o es ima e he a ing.
They we e de e mined using he p oposed app oach based on he a e age sp ead
be ween cumula i e bank up cy and de aul a es. Based on he a e age sp ead, i
140 Chap e 5
2024 Ma ina No o ná
was con i med ha he highe he sp ead, he lowe he a ing. Thus, he p oposed
p ocedu e was buil on his inding. The ele an a ing ca ego y was de e mined
using he absolu e de ia ion be ween he es ima ed and a e age sp ead. This
p ocedu e was subsequen ly used o de e mine he a ing o h ee hypo he ical
companies wi h di e en combina ions o he conside ed cha ac e is ics. E en
hough his is a g ea ly simpli ied app oach o de e mining he a ing based on only
h ee ca ego ical a iables, his me hod clea ly shows ha he isk associa ed wi h
he p obabili y o su i al can be be e unde s ood wi h he help o he a iables
used.
The calcula ion abo e conside ed only h ee ca ego ies o co po a e
cha ac e is ics, igno ing he po en ial e ec o o he ac o s. Al hough we canno
accu a ely de e mine he a ing based on he sec o , legal o m and co po a e size,
con e ing he cumula i e bank up cy a e in o a a ing will be u he examined
in he ollowing chap e s. The p ocedu e will be addi ionally used in he nex
sec ion based on su i al and cumula i e haza d unc ions es ima ed by o he
su i al analysis me hods. The Cox model will be used i s , and hen he Weibull
model. The indi idual s eps a e analogous o he las pa . Fi s , he su i al and
cumula i e haza d unc ions will be es ima ed. Then, he cumula i e bank up cy
a es o he selec ed ime ho izons will be de e mined, and he p oposed p ocedu e
will be used o de e mine he a ing.