Spring 2006 Universiy of Lund School of Economics and Managemen Deparmen of Economics Masers Thesis Alernaive Deerminans of Credi Defaul Swap Premia: Alman s Z and he empirical componens approach Auhor: Charles Thorburn Supervisor: Hossein Asgharian
Acknowledgemens As his is my las major piece of coursework a he Universiy of Lund I feel ha I should wrie somehing here 1. Firs of all I would like o recognize my parens who are always here for me, hanks for leing me walk my own way. I am also eernally graeful o all of my friends who have made my ime in Lund exremely enjoyable, you know who you are. I would also like o hank my supervisor, Hossein Asgharian, you seem o have an answer o everyhing. I would also like o give a special hanks o a person wihou whom I would no be an economis oday. Alhough you probably considered me somehing of a slacker, which I was, I horoughly enjoyed being your suden for hree years. Don go belly-up Ma! Now, for hose of you who are acually ineresed in credi derivaives, urn he page! I would raher be vaguely righ, han precisely wrong. -J.M. Keynes Show me he una!! -Ma McGee 1 Also in order o fill he required number of pages! 1
Absrac This paper conducs an empirical sudy of he deerminans of credi defaul swap (CDS) prices. By using a new se of CDS quoes and explanaory variables for hiry major corporaions, a se of linear panel daa regressions are performed. The sudy confirms earlier research where risk free ineres rae, volailiy and leverage are found o be highly significan. In addiion o his, a new variable, Alman s Z-score, is inroduced and found o have a significan effec on he CDS price. The Z-score is inroduced as a poenial subsiue for leverage and he wo variables are hence compared in erms of significance and explanaory power. I is found ha he Z-score is inferior o leverage in explaining he changes of he CDS price for one firm over ime. However, for iner-firm cross-secional analysis, he Z-score ouperforms leverage. Hence, he conclusion is ha Alman s Z-score and leverage have differen srenghs and ha he variable o use is bes chosen considering he ype of sudy a hand. 2
Glossary Alman s Z-score CDS Spread CDS Price CDS Premia CDS Quoe Credi Defaul Swap Credi Derivaive Credi Even Credi Risk Credi Spread Defaul Poin Defaul Risk Disance o Defaul Empirical Componens Approach Geomeric Brownian Moion A saisic using a combinaion of financial raion o predic he defaul probabiliy of a firm. Equivalen o CDS Price The price a which a CDS is quoed. Measured in basis poins of he noional amoun of he conrac. Equivalen o CDS Price Equivalen o CDS Price The simples and mos common credi derivaive which consiues an insurance agains a decrease in he value of bonds due o defaul of he issuer. The price is quoed in basis poins of he noional amoun proeced. A derivaive produc which has he purpose of ransferring credi risk beween differen paries. An even riggering he payou of a CDS conrac. Usually a bankrupcy. The risk of now geing repaid on ousanding loans due o defaul of he counerpary. See Z-spread A saisic of Moody s KMV, which defines he poin where a firm is likely o defaul. This is defined as a poin where he asse value of he firm equals he par value of shor erm deb plus half of he long erm deb. The risk ha a corporaion will become bankrup. One of he saisics in Moody s KMV, measuring how many sandard deviaions exis beween a firm s expeced value and is defaul poin. An approach for explaining CDS prices hrough regressions of explanaory marke variables on CDS prices. A ype of ime series process ofen used o illusrae he value of a firm. Each consecuive move is independen of he las. 3
Long Posiion Moody s KMV Noional Amoun Reduced Form Model for CDS Pricing Reference Eniy Repo Marke Shor Posiion Srucural Model Z-Score Z-Spread Having a long posiion means o somehing means ha you have a posiive exposure o i and will gain if i increases in value. A well known commercial srucural model for predicing defaul probabiliies. The face value of bonds ha are proeced using a CDS. A model for deermining he appropriae price of a CDS based on he informaion inheren in he prices of exising bonds issued by he reference eniy. The issuer of he underlying bond in a credi derivaives conrac. Usually a corporaion or a governmen. The marke for borrowing money while using bonds as securiy in order o ge a beer rae. Also used by marke paricipans who wish o borrow specific bonds. Opposie of long posiion. A ype of model for predicing he risk of defaul of a company and pricing is deb by viewing he deb as a risk free bond and a shor pu opion. Originally suggesed by Meron (1974). See Alman s Z-score The spread over he risk free rae acquired from owning a riskbearing bond. 4
ACKNOWLEDGEMENTS... 1 GLOSSARY... 3 1. INTRODUCTION... 7 1.1 CREDIT DERIVATIVES... 7 1.2 SUBJECT OF STUDY... 8 1.2.1 Problem specificaion and purpose... 9 1.2.2 Hypohesis... 10 1.3 LIMITATIONS... 11 1.4 OUTLINE... 12 2. THEORY AND BACKGROUND... 13 2.1 CREDIT DERIVATIVES AND THE MARKET STRUCTURE... 13 2.2 CREDIT DEFAULT SWAPS... 14 2.1.1 Credi Defaul Swaps and Bond spreads... 16 2.1.2 Basis beween CDS prices and bond spreads... 17 2.2 VALUATION MODELS... 19 2.2.1 The srucural models... 20 2.2.2 A pracical example: Moody s KMV... 22 2.2.3 Reduced Form models... 24 2.2.4 The empirical componens approach... 26 3. METHOD... 28 3.1 MOTIVATION... 28 3.2 CHOOSING THE VARIABLES... 29 3.2.1 Volailiy... 30 3.2.2 Almans Z-score... 31 3.2.3 Risk-free rae... 32 3.2.4 Leverage... 33 3.3 THE REGRESSION MODELS... 34 3.3.1 Pooled cross secion (level)... 34 3.3.2 The fixed effecs model... 35 3.3.3 Regression wih firs differences... 37 4. DATA... 38 4.1 REFERENCE ENTITIES... 38 4.2 CDS PREMIA... 39 4.3 RISK-FREE RATE... 40 4.4 VOLATILITY... 40 4.5 ALTMAN S Z-SCORE... 40 4.6 DATA MATCHING... 41 5. RESULTS... 42 5.1 KEY STATISTICS AND REGRESSION RESULTS... 42 5.1.1 Summary of regression resuls... 47 6. DISCUSSION... 49 6.1 RISK FREE RATE... 49 6.2 VOLATILITY... 50 5
6.3 ALTMAN S Z-SCORE... 50 6.4 LEVERAGE... 51 6.5 WEAKNESSES AND POSSIBLE FUTURE RESEARCH... 52 7. CONCLUSION... 53 APPENDIX... 54 A. SUMMARY STATISTICS... 54 B. REGRESSION OUTPUT AND DIAGRAMS... 55 B.1 Fixed effecs model... 55 B.2 Regressions from he one-sep differenced model... 61 B.3 Level regression... 62 C. LIST OF REFERENCE ENTITIES... 64 REFERENCES... 65 PUBLICATIONS... 65 WORLD WIDE WEB... 66 6
1. Inroducion This secion sars by inroducing he reader o he growing marke for credi derivaives and credi defaul swaps. Furhermore, he reader is given a background o he research surrounding he sudy conduced. This is followed by a saemen of purpose and a hypohesis. Finally, he limiaions and srucure of he paper are explained. 1.1 Credi Derivaives Credi derivaives are derivaive producs wih deb (credi) as underlying asse. By aking a posiion in credi derivaives, an invesor can choose he size of his exposure o credi risk. The issuer of he bond which is used as underlying is commonly referred o as he reference eniy. The simples way of viewing a credi derivaive is as insurance for lenders of money. Therefore, one par in a ransacion is long credi risk and one par is shor credi risk. The former is called proecion seller and he laer is called proecion buyer. The marke for credi derivaives is relaively new and sill unknown o mos people. In he secluded world of high finance however, credi derivaives is he new buzz-word and he volumes raded in hese producs are growing wih incredible speed. The producs were inroduced o he markeplace by a small group of invesmen banks 2 in he mid 1990 s and have oday grown o become one of he bigges inernaional markes wih a projeced volume of $40 rillion noional ousanding by he end of 2006 3. This makes i comparable in size o he enire cash bond marke. The bigges produc by volume is he credi defaul swap which has reained a marke share of close o 50 percen of volume in he credi derivaives marke. Figure 1 illusraes he growh of credi derivaives compared o corporae deb. 2 FT Magazine, March 25/26 2006, The Dream Machine, pp. 20-26 3 Global Finance, New York: Jan 2006 Vol. 20, Iss. 1; p.8 7
Figure 1: A comparison of marke size: Credi derivaives and Corporae Bonds. Source: IMF Global Financial Sabiliy Repor 2006 1.2 Subjec of sudy This paper will focus on he credi defaul swap which is by far he mos raded credi derivaive. The CDS is also he mos vanilla credi derivaive available, vanilla meaning sandardized and simple. Coninuing o look a credi derivaives as ways o reduce exposure o credi risk, he CDS is a sandard insurance policy. The buyer of proecion pays a premium o he hird pary proecion seller and receives a large payou in case of defaul of he counerpary. 8
The majoriy of CDS conracs are raded wih large public companies or governmens as reference eniy. Oher credi derivaives are usually variaions of he CDS principle. For example proecion agains an index of corporae deb or differen ways o limi he proecion offered by he conrac. Therefore, in valuing credi derivaives, he CDS is he leas complicaed produc and usually he saring poin. 1.2.1 Problem specificaion and purpose From exising models for valuaion of a CDS, a number of imporan variables can be exraced. More specifically, so called srucural models ofen quoe volailiy, risk free rae and firm leverage as he hree mos imporan facors in deermining he price of a CDS. Earlier sudies have been made where hese and oher facors are used as explanaory variables in regressions rying o explain levels and variaions in CDS premium 4. This paper will label his mehod he empirical componens approach (ECA). Due o he relaive infancy of he CDS marke, low liquidiy and volume has made i difficul o access large and synchronous price samples 5. Earlier research has herefore ofen been forced o inerpolae beween quoes or resric he sample size in heir sudies of he empirical componens. This sudy will apply he ECA and in a similar way o earlier papers aemp o explain variaions in CDS prices using observable marke variables. The daa used for CDS prices is aken from Daasream and is quoed on daily basis. I daes back hree years, giving a comparably large sample size. Four explanaory variables are employed; risk free rae, volailiy, leverage and Alman s Z-score. 4 For examples of such sudies, see Collin-Dufresne e al (2001), Campbell and Taksler (2003), Benker (2004), Cremers e al (2004) and Ericsson e al (2004). 5 In his paper, he words price and premium are used inerchangeably for CDSs. The price of a CDS is quoed as a number of basis poins. 9
The effecs of volailiy, leverage and risk free rae have already been esed and his sudy aims o confirm heir effec on a new daa se. The new variable which is inroduced is Alman s Z-score which is compared o leverage in erms of explanaory power. The Z-score is a measure combining differen key raios in order o give an indicaion of he probabiliy of defaul for a corporaion. Hence, his measure includes more facors concerning he financial healh of a corporaion compared o leverage and may be appropriae as a subsiue. This paper herefore ess wheher Alman s Z-score can achieve a higher explanaory power han leverage. There have been no previous aemps o apply Alman s Z-score in he ECA. A successful applicaion of he variable would herefore have he poenial for new conclusions regarding CDS prices and furher research. 1.2.2 Hypohesis The hypohesis of his paper is ha he inroducion of Alman s Z as an explanaory variable for CDS prices will increase he explanaory power of exising models. Furhermore, he effecs of leverage, risk free rae and volailiy are prediced o be significan and consisen wih earlier sudies in explaining CDS prices. In shor, his paper uses he empirical componens approach o explain CDS prices on a new daa se for hiry major corporaions. The radiional explanaory variables volailiy, leverage and risk free rae are esed o see if heir effec confirm earlier resuls. Furhermore, he variable Alman s Z-score is inroduced as an alernaive o leverage. The aim is o invesigae wheher he Z-score has properies which may complemen or even replace leverage as an explanaory variable. 10
1.3 Limiaions The mehod employed is linear regressions wih panel daa where he effecs of he differen variables are esed. The paper is limied o esing effecs for hiry major corporaions beween he beginning of 2003 and he end of 2005. The ime inerval was chosen o ensure availabiliy of CDS daa. Furhermore, because he paper uses cerain key raios from he balance shee as par of he Z-score, he frequency of observaions was limied by he number of repor daes. In order o maximize he number of observaions, corporaions were chosen so ha quarerly daa would be available. This limied he sample o U.S. and European firms wih an emphasis on he former. An alernaive approach employed in similar sudies is he inerpolaion of balance shee daa over he year o achieve daily frequency. The auhor of his paper chose no o apply such a mehod as he sample was already large enough o draw meaningful conclusions and he mehod risks creaing a bias due o false assumpions. Furhermore, he model proposed does no aim o produce accurae predicions of CDS prices. The purpose is insead o gain an undersanding of how changes in he chosen variables affec CDS prices. Alhough a level regression is performed, he focus is on he regressions measuring he dynamic relaionship beween he changes in explanaory variables and CDS prices. The reason for no focusing on he levels is ha he daa sample is no well suied for such an analysis as we have relaively few observaions per period sudied. 11
1.4 Ouline Secion 2 will provide a more deailed explanaion of he properies of credi defaul swaps. I will also give he reader a background of he research on his and relaed subjecs. Finally, i describes and briefly compares differen mehods of valuing CDS conracs. Secion 3 gives a moivaion for he sudy and he mehod employed. The secion hen proceeds o describe he mehod furher, including regression echniques and explanaions of he variables in he daa se. Secion 4 offers a more deailed descripion of he daa including formaing, sources and oher characerisics. Secion 5 presens and briefly commens he resuls of he regressions performed. Secion 6 proceeds wih a more horough discussion of he resuls and links hem o he hypohesis. Secion 7 concludes he paper and provides suggesions for furher research. 12
2. Theory and background This secion gives he reader addiional undersanding of he marke for credi derivaives. Furhermore, he design of a Credi Defaul Swap is given a reamen along wih a discussion of is specific properies. A background is also given o he earlier research and pricing models wihin he field of credi and credi derivaives. 2.1 Credi derivaives and he marke srucure When buying corporae deb in he markeplace, an invesor effecively becomes long he credi risk of he issuing corporaion. The credi derivaives conracs available enable he invesor o offse he credi risk of he corporae deb by buying proecion. I is imporan o see he difference beween aking a long posiion in credi risk by selling proecion and aking i by buying a corporae bond. In buying a corporae bond he invesor exposes himself o a variey of risks (noably ineres rae risk) whereas a seller of proecion exclusively deals in credi risk. The possibiliy of aking posiions in credi risk wihou geing exposure o oher risks 6 has araced many paricipans o he marke and is he reason for he rapid growh of credi derivaives. The larges group of invesors is banks. In 2004 hey accouned for more han half of he proecion buying and 38 percen of he selling. The big issuers in he bank secors include invesmen banks who wish o increase heir exposure o risk or have he possibiliy o hedge heir exposure in he bond markes. Oher major paricipans are hedge funds and securiy houses who use credi derivaives o opimize heir porfolios. This is done eiher by hedging heir posiions or by aking ourigh views on he credi-worhiness of deb. 6 This is no enirely rue. A posiion in credi derivaives always includes counerpary risk. This is especially rue for he buyer of proecion. The saemen refers o he possibiliy o avoid e g ineres rae risk. 13
The credi derivaives are also ineresing o invesors because hey allow hem o express more complex marke views. Examples are capial srucure views senior deb versus subordinae deb, raing views B-raed deb versus BB-raed deb and correlaion views he correlaion beween defauls of corporaions in a secor/counry. Addiionally, insurers and re-insurers rade large volumes of credi derivaives. They are large sellers of proecion and use heir experise in calculaing risk probabiliies o expand ino he financial markes 7. 2.2 Credi Defaul Swaps The credi defaul swap insrumen is by far he mos common insrumen in he markes for credi derivaives. Alhough here are many differen producs in hese markes, mos are jus simple variaions of he CDS. The CDS is in essence nohing more han an insurance policy on he value of a bond where he policy kicks in when he issuer defauls on is deb. The exac erms and definiions of defaul are specified in he agreemen and his kind of even is commonly referred o as a credi even. When a credi even occurs, he buyer of proecion is compensaed by he seller wih he difference beween he par value of he bond and he curren marke value. The early CDS conracs specified ha he bond should be delivered by he proecion buyer in reurn for he par value. Nowadays mos deals are seled in cash and he marke values of he bonds are deermined by hird paries. This enables marke paricipans such as hedge funds o express marke views on credi risk wihou ever owning he underlying credi. Figure 2 illusraes he cash flows involved in a CDS ransacion. Figure 3 depics he composiion of he credi derivaives marke as of Sepember 2004. 7 Saemens abou numbers and composiion of he credi derivaive markes are aken from he Briish Bankers Associaion Credi Derivaives Repor (Execuive Summary) 2003/2004 and he Merrill Lynch Credi Derivaive Handbook 2003. 14
Figure 2: Cash flows involved in a sandard CDS conrac. Figure 3: The composiion of he Credi Derivaives markes by marke share. 8 8 Credi Derivaives Repor 2003/2004 Execuive summary, Briish Bankers Associaion, Sepember 2004 15
2.1.1 Credi Defaul Swaps and Bond spreads In a classic paper, Meron (1974) saed ha a corporae bond can be viewed as a combinaion of a owning a risk-free bond and issuing a pu opion on he value of a firm s deb. Consequenly, he excess reurn of a corporae bond over he risk-free rae equals he price of he pu opion. A CDS conrac is very similar o such a pu opion and herefore has a price which mus be close o he bond spread of he reference eniy over he risk-free rae. The issuer of a CDS (lef hand side in Figure 2) herefore has a credi risk profile of owning a corporae bond whereas he invesor on he righ hand side who buys he CDS has a credi risk profile equal o ha of shoring a corporae bond. Perhaps more inuiively, we can say ha buying a corporae bond and a he same ime buying insurance in he form of a CDS should yield he same ne reurn as owning a risk free bond. This is illusraed in Figure 4. Figure 4: The heoreical relaionship beween CDS premium and credi spread 16
Furhermore, if we look a he combinaion of owning a risk free bond and selling CDS proecion, he cash flows should equal hose from owning he corporae bond of he reference eniy. However in pracice, here are a number of facors which make sligh divergences from his possible. The difference beween CDS spread and he Z-spread is called basis and may exis for a number of differen reasons. 2.1.2 Basis beween CDS prices and bond spreads CDS conracs, like oher swaps, are priced so ha here is no iniial paymen or inrinsic value of he conrac upon iniiaion. Also, he mos common conracs are designed o have he mauriy of five years from he day he deal is made. Therefore, CDS prices become he equivalen of Z-spreads for bonds wih a consan mauriy of five years ha always rade a par. Duffie (1999) concluded ha he heoreical relaionship of Figure 4 is only valid for floaing rae noes ha are currenly rading a par. Needless o say his creaes a source of basis beween he asses. Neverheless, his effec is comparably small and Duffie (1999) proceeds by showing ha his bias is no sufficienly large o explain he empirically observed basis in he marke. Oher srucural differences creaing basis are embedded opions in corporae bonds, differing coupon convenions beween a CDS and a bond as well as he fac ha coupons may be reaed differenly upon a credi even. A bond wih an opion making i callable by he issuer has a lower value because i limis he righs of he lender. Day coun convenions are also a facor o consider. A sandard CDS premium is paid A/360 whereas corporae bonds usually pay 30/360. Upon defaul, a CDS normally does no compensae he holder for he aggregaed ineres on he reference eniy whils his is normally par of he claim by he bondholder o he issuer. 17
Oher imporan sources of basis are he more marke-oriened facors. In he case of negaive basis, a higher Z-spread han he CDS-spread, an invesor could make heoreical arbirage by borrowing a he risk-free rae, invesing in he bond a he same ime as buying proecion. This is no an implausible scenario and we migh expec large insiuional invesors o ake advanage of such opporuniies, should hey arise. For a posiive basis, however, he process is no quie as simple. The bond is now expensive compared o he CDS and he heoreical arbirage would be made by shoring he bond, issuing he CDS and invesing a he risk-free rae. The problem wih his is ha i requires he rader o be able o shor he reference eniy more or less wihou cos. This is no realisic for a marke paricipan who does no own he bond as i enails borrowing i in he repo marke. For corporae bonds wih relaively small issues compared o governmens, his usually enails a difficul search process, shor repo mauriies (usually one day) and high coss. Even if an invesor is able o fund himself a close o he risk-free rae i is no uncommon o have o pay over 100 basis poins for a reverse repo in he bond. This creaes an inheren rigidiy in any posiive basis in he CDS marke. Naurally, marke paricipans owning he reference eniy could sell heir holdings and insead issue a CDS and inves a he risk-free rae. This rade would have he same effec as he arbirage in eliminaing he bias. This does no occur on any large scale and he reasons are likely o be a combinaion of facors, one of which may be he naure of bondholders. One par of he group are passive invesors and are herefore no aware of he opporuniy, anoher is indeed aware bu is resriced by urnover limiaions or resricions regarding he use of derivaives. A second facor may be ha he size of holdings may be limied o relaively small amouns. CDS conracs are usually raded in sizes of $10 million noional, which may make i hard for invesors o mach heir exposures. 18
Anoher facor worh menioning is ha he CDS is no a perfec hedge agains credi risk as here is always a counerpary risk involved. This also acs o reduce he price of he CDS. Furhermore, a liquidiy premium on eiher asse may creae a discrepancy in he pricing. Longsaff e al (2004) sudy he componens of corporae yield spreads and find ha he wo main componens are defaul risk and liquidiy premium, wih defaul risk being he dominaing componen. Hence a difference in he liquidiy premium beween he CDS and he bond is likely o creae a bias. The combinaion of facors saed above help o explain he reasons why CDS conracs and corporae bonds usually rade a a small basis. Noe, however, ha hese facors are comparably small and ha he CDS spread and he Z-spread are boh good proxies for credi risk ha are affeced by mosly he same facors. This is imporan o remember as he models for CDS-spreads presened in his paper are largely based on models of he Z-spread. 2.2 Valuaion models Because he marke for Credi Defaul Swaps has grown rapidly during he las years, a significan body of research has emerged on he subjec of valuaion. Essenially, he valuaion of a CDS is very similar o deermining he appropriae bond spread over he risk free rae. A mehod for his was formalized by Meron (1974) whose work is sill oday par of he foundaion used o value credi derivaives. The ype of model creaed by Meron (1974) has come o be known as a srucural model and has been developed and modified ever since 9. Meron viewed equiy as a call opion on he value of a firm which makes i possible o value he opion according o he principles laid ou by Black and Scholes (1973). 9 The well known Moody s KMV model which is used o asses defaul risks in companies oday is indeed enirely based on he model firs suggesed by Meron (1974). 19
As a consequence of his, he deb of a corporaion can be viewed as a risk-free bond plus a shor posiion in a pu opion on he value of he firm. The price of he pu opion hen becomes equivalen o he risk-premium on he corporae bonds and can also be deermined using a common opion pricing formula. This mehod is called he srucural approach for deermining credi spreads. Once again, for all purposes of his sudy, we can view he corporae bond spread over he risk-free rae o be inerchangeable wih he price of a CDS. Therefore, he srucural model approach is commonly applied o boh CDS conracs and corporae bond spreads. In addiion o he srucural models, anoher se of models for seing CDS prices has emerged during recen years. These models are called reduced form and ake a less academic approach o valuaion in ha hey do no aemp o explain he underlying facors of CDS prices. The reduced form model for CDS pricing was inroduced by Jarrow and Turnbull (1995). In addiion o reduced form and srucural models here are oher pricing models available. A noable example is JPMorgan s CrediMerics which bases he pricing on he probabiliy of a corporaion moving from one credi raing o anoher. Neverheless, his secion will limi iself o describing srucural and reduced form models. 2.2.1 The srucural models Beginning wih Meron (1974), he srucural models of credi spreads gained momenum during he sevenies and were adjused and improved in numerous papers in order o fi realiy beer. Building on he work of Black and Scholes (1973), Meron (1974) modelled he asses of a firm o follow a log-normal process where he firm would defaul if he value wen below a specific level, called he defaul boundary. As a consequence, he equiy of he firm could be viewed as a call opion on he asses of a firm. Coninuing his reasoning enabled Meron (1974) o also price he deb as an opion and hereby exrac is value. 20
Today, a large par of he academic research on credi spreads and credi derivaives sill build on he principles suggesed by Meron (1974) and here are several commercial models available ha are based on his work. In pracice, wha characerizes he srucural models of credi spreads compared o he reduced form models is he pracical use of real economic variables. The basic posulae proposed by Meron (1974) was o look a he firm value (V) as he value of a single equiy issue (E) and a single zero-coupon bond (F), mauring a =1, wih face value b. V + = E F Equaion 1 Therefore, if he value of he firm exceeds b a ime (1), i will pay off is loans and he remaining value will belong o he sockholders. If he value of he deb is larger han he value of he firm, he bondholders will liquidae he firm s asses and he equiy becomes worhless. E 1 1 = max( V b,0) Equaion 2 The expression in Equaion 2 is idenical o he payoff from a call opion wih srike b and he firm s value as underlying. This is exacly he model suggesed by Meron (1974). A direc consequence of his reasoning is ha he deb of he firm can be viewed as a risk-free bond plus a shor pu opion on he firm. 21
F 1 1 = b max( b V,0) Equaion 3 From Equaion 2, i can be seen ha he value of he deb a ime (1) equals b unless b exceeds he value of he firm. From his simple model, differen assumpions can be made in order o value he deb and equiy using he formula proposed by Black and Scholes (1973). b would equal srike price, V would equal price of underlying and (1)-(0) would be ime o mauriy. Volailiy and he risk free rae can be acquired from observable marke variables. The above represenaion presens he mos basic version of a srucural model. Noe ha i is of course an over-simplificaion o assume ha he deb of a firm is a zero coupon bond wih one specific mauriy. I is also difficul o measure he firm value and is volailiy. 2.2.2 A pracical example: Moody s KMV 10 Perhaps he mos well-known curren pracical applicaion of he srucural model is he Kealhofer, MvQuown and Vasicek (KMV) model creaed by KMV Corporaion which is now par of Moody s. The marke value of a firm is solved for using he curren marke price of a firm. E E = f ( V σ = g( V, σ, K. c, r) V, σ, K, c, r) V Equaion 4 In Equaion 4, noaions are he same as above and σ V denoes he volailiy of asse value, σ E denoes equiy volailiy, K denoes leverage raio, c denoes average coupon paid and r denoes he risk free rae. The equaions in Equaion 4 once again apply he view of equiy as a call opion in order o exrac firm value and volailiy of firm value. 10 Descripion of he KMV model is aken mainly from he discussion in Crouhy e al (1999) 22
The KMV model defines he poin of defaul as he poin where asse value equals he par value of shor erm deb plus half of he long erm deb. This approximaion is based on empirical sudies of hundreds of defauls. In addiion, he expeced value of he firm s asse value in one year is calculaed by leing i follow a sandard geomeric Brownian moion plus a drif. The hird sep of he analysis is o sandardize he difference beween he expeced value of he firm s asses and he defaul poin (DPT) using he volailiy of he asse value. This creaes a measure labelled Disance o Defaul (DD). The expression is illusraed in Figure 5. DD = E( V 1 ) DPT Equaion 5 σ V Figure 5 is an edied figure from Crouhy e al (1999) which illusraes he relaionship beween he differen variables. Figure 5: The relaionship beween he variables in he KMV-model. Source: Crouhy e al (1999), Noe: he figure has been edied from is original form. 23
The las sep of he KMV model is o derive he Expeced Defaul Frequency (EDF). This is based on empirical observaions of a large number of firms, where he DD has been calculaed and he oucome observed. Based on hese observaions, a probabiliy of defaul is arrived a. For applicaion o credi spreads, he EDF can easily be combined wih assumpions of recovery rae in case of defaul o calculae presen values of expeced cash flows from a bond and herefore also he appropriae bond spread 11. In order oo see how hese srucural models are applicable o CDS conracs one needs only consider he similariy of he wo insrumens. The corporae bond pays coupons according o credi risk and loses is value if he firm defauls. The seller of a CDS ges premia-paymens and loses money a defaul. Also, he credi spread approximaely equals he CDS spread. Therefore, he variables in a srucural model will have he same impac on bonds and CDSs. 2.2.3 Reduced Form models The second school of modelling credi-risk is more recen bu has neverheless received much aenion. The reduced form approach has goen is name because i assumes ha he firm s defaul ime is inaccessible or unpredicable and hereby reaed as exogenous 12. Insead of measuring marke fundamenals, he approach for achieving credi spreads is based on he acuarial approach used by insurance companies in calculaing such hings as moraliy raes. 11 I is probably fair o say ha he main difficuly in pricing CDS conracs and corporae bonds lies in esimaing heir probabiliies of defaul. 12 Arora e al (2005) An alernaive o his view is presened by Jarrow and Proer (2004) who argue ha he disincion is in erms of informaion. The srucural models implicily assume complee informaion abou a firm whereas he reduced form models limi he informaion o ha available in he markeplace. Irrespecively, reduced form models can be viewed as using relaive pricing o a higher degree han fundamenals. 24
The basic concep is finding a funcional form for defaul inensiy of a firm which is defined as he firs derivaive of he probabiliy of defaul wih respec o ime. This funcional form is specified so ha he defaul inensiy is a funcion of corporae bond spreads. By insering he marke spreads, he implici probabiliy of defaul can hen be exraced. Hull and Whie (2000) sugges a reduced form model for he pricing of a sandard CDS wih no counerpary risk. The model uses assumpions abou he expeced recovery rae and he size of he claims by bondholders o acquire implici probabiliies of defauls in corporae bond spreads. By adjusing he CDS premia o make he expeced payoff equal o zero, a fair value of he spread is decided. The expeced recovery rae is acquired from hisorical values and he claim size is assumed o equal face value plus accrued ineres in accordance wih Jarrow and Turnbull (1995). In essence, his model is dependen on he exising prices available in he corporae bonds. Oher noable conribuions in he area are Duffie and Singleon (1999), Duffie, Pedersen and Singleon (2003) and Driessen (2004). The Reduced form models are by heir naure very useful for valuing credi claims, as hey are able o give more accurae predicions of prices 13. On he oher hand, hey conain no informaion regarding he fundamenal deerminans of defaul probabiliies. 13 For a discussion of his, see Houweling and Vors (2005) 25
2.2.4 The empirical componens approach Neiher he reduced form nor he srucural models are perfec in explaining he CDS spreads and here seems o be no consensus on he superioriy of any one model. The reason for he failure o creae definie model of credi spreads is ha i would require an arbirage opporuniy ha has no been found and may no exis. The srucural models proposed in differen papers seem o sugges he imporance of he same hree empirical facors for deermining he Z-spread. These are financial leverage, volailiy and risk-free erm srucure 14. These facors and ohers have herefore been he subjec of a new approach o analyzing Z-spreads and CDS premium. Insead of building a classic srucural model, Collin-Dufresne, Goldsein and Marin (2001) 15 exraced he componens deermining he price in srucural models and used hem for inpu in a regression. This aemp resuled in low explanaory power and significance bu neverheless consiued he firs aemp a a new approach for explaining credi spreads. Campbell and Taksler (2003), Benker (2004), Cremers e al (2004) and Ericsson e al (2004) coninued on he same road. Their mehods were similar in ha hey used differen financial variables o explain he CDS premium in regressions. I will refer o his mehod as he empirical componens approach (ECA). Campbell and Taksler (2003) uses panel daa of bond prices in he nineies o explain he Z-spreads using hisorical equiy volailiy and credi raing. They find ha he wo facors used explain approximaely one hird of he spread levels each. 14 Ericsson e al (2004) p. 3 15 Henceforh referred o as CGM (2001) 26
Benker (2004) and Cremers e al (2004) exend he work of Campbell and Taksler (2003) by concluding ha opion implied equiy volailiy has a higher explanaory power han hisorical volailiy in explaining CDS premia. Ericsson e al (2004) focuses on a se of CDS spreads insead of Z-spreads and finds ha equiy volailiy, firm leverage and risk-free rae explain 60 percen of he CDS level in he sample. This paper presens an empirical componens model where CDS spreads are explained by regressions of a number of variables similar o hose of earlier sudies. The mehod will be similar o ha of Ericsson e al (2004) bu we will use newer CDS quoes and inroduce a new variable o ry o reach a higher explanaory power. The academic and pracical usefulness of his approach comes from is abiliy o direcly es and even quanify he effec of he differen explanaory variables. Thus, he aim of his paper is no o build a model ha accuraely predics CDS prices, bu raher o increase he undersanding of which empirical facors have an effec on said prices. By doing his i is he hope of he auhor o increase general undersanding of he consiuens and deerminans of CDS spreads as well as providing empirical resuls ha may help in he creaion and modificaion of fuure srucural models. 27
3. Mehod This secion sars by giving a moivaion for he model employed in his paper. Nex, he model is specified and explained o he reader wih added specificaions for each variable. 3.1 Moivaion The empirical componens mehod of explaining CDS spreads which will be used in his paper is as explained above a coninuaion of earlier research. The approach is differen from he reduced form and srucural models because i is merely an invesigaion of he effec of a few variables on CDS prices and no a complee model. The mos obvious drawback would be ha he resuling model is no likely o display any accurae predicive power for he enire CDS spread. The reason for his is ha a regression is no likely o reach an explanaory power (e g R-squared) which is high enough o explain all changes in he spread. Neverheless, he model is no wihou meris. The regression allows comparaively simple sudy of he effec of individual facors on he level of he CDS spread. We can also compare he relaive effec of differen variables. This in urn gives he researcher a possibiliy o gain a deeper undersanding of he imporance of differen facors as well as es he significance of new ones. Ericsson e al (2004) summarizes hree differen variables ha seem o be recurring as significan in mos sudies. These facors are leverage, volailiy and riskfree rae of reurn. By regressing hese on he CDS levels, Ericsson e al (2004) manages o explain approximaely 60 percen of he level of he CDS spread. This paper aemps o explain he CDS premium using similar fundamenal variables, bu using differen proxies o measure hem. The aim is o confirm he resuls of previous research on a new daa se and o invesigae he explanaory power of he explanaory variable Alman s Z-score. The Z-score is in paricular compared o leverage in erms of explanaory power. 28
I is imporan o noe, as poined ou by Ericsson e al (2004) ha alhough he fundamenal effecs of hese variables are he same on CDS prices and bond spreads, here are a few advanages wih choosing he CDS daa in making a sudy of his ype. Firs of all, here is no need o calculae he Z-spread 16. This may sound rivial, bu calculaing he Z-spreads requires a clear specificaion of he riskfree yield curve, which may be hard o proxy even if we are able o rack is consan changes. The difficuly of finding he correc measure for risk-free rae is furher addressed by Hull and Whie (2004). A second advanage of using CDS spreads is ha hey reflec he credi risk and nohing else. Oher componens of he bond spreads may obscure he impac of changes in credi risk. 3.2 Choosing he variables In order o perform regressions and measure he effecs of he chosen variables, i was imporan o carefully specify he daa o be used. The volailiy is calculaed using daily equiy reurns during he 90 days prior o each daa poin. This mehod is similar o ha of Ericsson e al (2004). Oher papers have insead chosen implied equiy opion volailiy as he proxy for volailiy. The reason for his is ha i may incorporae informaion abou fuure expecaions and may herefore conain more informaion 17. I is also logical if we choose o, like Meron (1974) 18, hink of a CDS as a pu opion on he value of a firm o use he opion implied volailiy. The reason why his paper uses hisorical equiy volailiy is ha opion daa was no available for he companies sudied. Furhermore, he focus of his paper is no o maximize explanaory power of he volailiy bu o confirm is effec on CDS prices. The second facor, leverage, is imporan because he defaul probabiliy increases as he leverage raio approaches uniy. The calculaion of leverage is specified in secion 4. 16 The Z-spread, as illusraed in figure (4) is he spread of corporae bond yield over he risk free rae of reurn. 17 For examples of his mehod, see Benker (2004) and Cremers e al (2004) 18 Meron referred o he Z-spread in his famous paper. However, he principle is he same. 29
Theory also suggess ha business climae may be an imporan facor for credi spreads. Therefore, insead of limiing he sudy o one raio, Almans Z-score 19 is used as a proxy for boh leverage and business climae. The Z-score model was developed by Edward Alman in he lae 1960 s as a measure of defaul risk in a firm. By combining five differen key financial raios, Alman graded firms in erms of risk of defaul. The model has since been developed and he version used in his paper is presened below. Leverage and he Z-score were regressed separaely as subsiues o explain changes in he CDS price. Because he sudy employs fixed effecs models, he mos imporan conribuion of an explanaory variable is he effec i has on he regressand when i changes. Therefore, one migh find ha i is no pracically imporan wheher one chooses e.g. he Treasury yield or he Swap rae as a proxy for he risk-free rae as hey are likely o be moving ogeher mos of he ime. Neverheless, his paper uses he Swap rae minus en basis poins as suggesed by Hull and Whie (2004). 3.2.1 Volailiy The hisorical equiy volailiy was acquired using he daabases of Daasream. The daa used consised of daily closing prices for each of he firms. The volailiy was calculaed as he variance of he daily sock reurn for each period. Daily _ reurn = r Volailiy = σ r = P P = P 1 T T = 1 1 1 ( r r) 2 Equaion 6 Because he daa is quarerly, T in Equaion 6 will be around 70 (business) days. 19 Caouee e al (1998) 30
3.2.2 Almans Z-score In he field of insolvency predicion, few models if any have combined simpliciy, innovaion and efficiency in such an elegan way as Alman s Z-score. The model was originally suggesed by Edward I. Alman in 1968 wih he publishing of his famous paper Financial Raios, Discriminae Analysis and he Predicion of Corporae Bankrupcy in he Journal of Finance. The Z-score of a firm is calculaed using a mulivariae model aking ino accoun various financial raios. The resuling value hen pus he firm in a caegory o which Alman assigns a cerain probabiliy of defaul. The model is based on hisorical daa for an original sample of 66 firms, of which 33 had filed chaper eleven bankrupcy. The analysis of Alman was focused on finding common characerisics of he firms ha survived ha differed significanly from he characerisics of hose ha wen ino bankrupcy. The resuling model conains five differen raios which are presened in Equaion 7. Equaion 7 presens he raios as hey are combined in Alman s model 20. 1,2 X where X X X X X 1 2 3 4 5 1 + 1,4 X + 3,3X Toal _ curren _ asses Curren _ liabiliies = Toal _ asses Reained _ earnings = Toal _ asses Operaing _ resul = Toal _ asses Toal _ marke _ cap = Toal _ liabiliies Re venue = Toal _ asses 2 3 + 0,6X 4 + 1,0 X 5 Equaion 7 20 The model has been revised since is original form, he numbers used below are aken from Reuers 3000 Xra and may be no be as exac as he original model proposed by Alman. 31
Z-score Inerpreaion >3,0 Defaul no likely 1,8-3,0 Gray area <1,8 Likely o defaul Table 1: Classificaions in Alman s Z-score model The classificaions presened in Table 1 are referring o bankrupcy wihin he nex wo years. The probabiliies for each value are no of ineres in his paper as we are measuring he differences in Alman s Z. The fixed-effecs model will herefore invesigae he effec of a changed Z-score of a firm on he CDS-premia. We expec a posiive significan effec as a higher Z-score implies a higher likelihood of defaul which should increase he price of bond insurance. 3.2.3 Risk-free rae The poenial arbirage demonsraed in diagram 3 saes ha he risk-free rae plus he CDS premia mus equal he corporae bond yield. One of he problems ha makes his an approximae raher han exac arbirage is he specificaion of he riskfree rae. Hull and Whie (2004) conclude ha alhough here is no consensus on which rae o use, he Swap rae minus en basis poins appears o be he marke riskfree rae. This conclusion is reached by regressions using he assumpions based on he approximae arbirage discussed earlier. Oher sudies use he U.S. reasury yield or unadjused Swap rae. 32
Hull and Whie (2004) however, argue ha he reasury yield is oo low due o special ax reamen and ha he Swap rae is oo high because i conains a riskpremium. This paper will follow he recommendaion of Hull and Whie (2004) and use he Swap rae minus en basis poins. Neverheless, he choice of a differen rae would probably no aler he resuls significanly as his paper sudies he changes in he risk-free rae. Because he spread beween he reasury and he Swap rae is usually sable, he changes are he same. 3.2.4 Leverage The leverage is he second variable, along wih Alman s Z which is no available daily. The leverage is calculaed in accordance wih earlier empirical componens research as he value of oal liabiliies divided by he sum of oal liabiliies and marke capializaion. Toal _ Liabiliies Leverage = Equaion 8 ( Toal _ Liabiliies + Marke _ Cap) 33
3.3 The regression models 3.3.1 Pooled cross secion (level) One approach would be o explain he CDS premium, S i,, using he levels of equiy volailiy, vol i,, leverage, lev i, Alman s Z-score, i Z, and he swap rae minus en basis poins, rf. However, because i is panel daa, pooling he observaions and running a cross-secional regression would produce he risk of heerogeneiy bias. Such a regression would also assume a consan inercep over ime and beween differen reference eniies, which may no be plausible 21. S S i, = 0 + β vvoli, + β zz i, + β rrf + ai + u i, β Equaion 9 i, = β 0 + β vvoli, + β qlevi, + + β rrf + ai + u i, Equaion 9 22 illusraes he risk of heerogeneiy bias by separaing he composie error, ε i,, ino wo componens, +. The a i represens he componen of he a u i i, composie error which is no ime-changing, whereas he u i, represens he componen ha changes wih ime. An example of a non-changing unobservable could be he marke view ha managemen in a cerain corporaion is very poor which migh affec he CDS spread. This view may persis during he sample period. The exisence of such consan effecs which are no capured in he model creaes he implici assumpion ha hey are no correlaed o any of he explanaory variables. Such correlaion would creae a heerogeneiy bias which is really nohing more han an omied variable bias. Neverheless, he pooled cross secion regression in Equaion 9 was esimaed alhough he focus of his paper is on oher esimaion mehods. 21 This could be avoided using dummy variables, bu his approach is no suiable as we have relaively few daa poins for each ime period. 22 The regression equaions are presened in pairs o illusrae he comparison beween leverage and Alman s Z. 34
3.3.2 The fixed effecs model The heerogeneiy bias can easily be avoided by adoping a fixed effecs 23 model. The fixed effecs ransformaion, or wihin ransformaion, allows he unobserved, imeconsan effecs o be correlaed o he included explanaory variables by sudying he variaion insead of he levels of he daa. The ransformaion of he daa is achieved by subracing he average values of he parameers in he expression from he original expression. In Equaion 10, he line above he leers indicae he sample average. S = β β β β Equaion 10 i, 0 + v vol i, + zz i, + r rf + a i + u i, S = β β β β i, 0 + q lev i, + v vol i, + r rf + a i + u i, By subracing Equaion 10 from Equaion 9, we obain Equaion 11, Si, Si, = β vvoli, β v voli, + β zz i, β zz i, + β rrf β r rf + u u Equaion 11 i, i, Si, Si, = β qlevi, β q lev i, + β vvoli, β v voli, + β rrf β r rf + u u i, i, where he ime-consan error and he inercep disappear from he equaion. This can be rewrien as in Equaion 12. = β β β β Equaion 12 S i, + v voli, + z Z i, + r rf + ui, = β β β S i, q lev i, + v voli, + r rf + ui, 23 Specificaion of erms: This paper will refer o he wihin ransformaion as a fixed effecs model and he firs difference model as a firs difference model alhough some people would refer o boh mehods as variaions of he fixed effecs approach. 35
The new variables in Equaion 12 are said o be ime-demeaned and include only he deviaions of he observaions from heir sample mean. Hence, he fixed effecs esimaion in Equaion 12 is no affeced by any ime-consan unobservables. Insead, i is very similar o a firs-differenced equaion in ha i measures how much he CDS spread changes when one of he explanaory variables changes. The drawbacks wih he fixed effecs model are ha we lose he inercep and also he effec of any individually non-changing explanaory variables. The only case where his migh be a problem would be for he Z-score which differs more beween firms han wihin firms over ime. Because hese firm-specific differences are no included in he model, he explanaory power of he Z-score may be underesimaed in a fixedeffecs model. This is reaed furher in he discussion of he resuls. Noe ha he variables are calculaed as deviaions from he mean of he individual firms. The raw daa is recorded from 30 firms during 12 quarers. This gives 360 individual daa poins. Because he levels of he CDS price differs a grea deal beween differen firms according o iniial credi risks, i may be more ineresing o view he percenage changes in he CDS spreads. We herefore add anoher regression: Equaion 13, which measures he percenage deviaions from he mean. This is done by performing he seps in Equaion 10 o Equaion 12 again, his ime using he logarihm of he CDS spread as dependen variable. ln( = β β β + Equaion 13 S i, ) v voli, + z Z i, + r rf ui, ln( = β β β + S i, ) q lev i, + v voli, + r rf ui, 36
As noed in earlier research, he explanaory power of differenced regressions is generally lower han ha of level regressions 24. They may herefore provide more rigorous es of he heory. An alernaive approach would be o run ime series regressions for each of he 30 firms individually and calculae he average coefficiens from he regressions. The problem wih his approach is ha i would resul in very few observaions for each regression and herefore creae unreliable esimaes. 3.3.3 Regression wih firs differences In addiion o he fixed effecs model, a one-sep differenced regression was creaed. The expression for his model is illusraed in Equaion 14.This mehod also eliminaes he heerogeneiy bias bu runs he risk of moving average correlaion in he residuals. Anoher drawback is ha i eliminaes 30 daa poins in our sample, reducing he es o 330 observaions. This mehod should indicae he same effecs as he fixed effecs model, and he reason for including i along wih he fixed effecs model is parly ha i may have a more pracical inerpreaion of achieved coefficiens. However he main reason is o faciliae he possibiliy of direc comparison o earlier sudies using differenced regressions. S i, = β v voli, + β z Z i, + β r rf + u Equaion 14 S i, = lev + vol β q i, β v i, + β rf r + u 24 For an example of his, see Ericsson e al (2004) 37
4. Daa The daa secion concerns he raw daa used in he sudy. The source, forma and range are specified and discussed for each daa se. 4.1 Reference Eniies Because we are sudying CDS premia, i is meaningful o say somehing abou he how he reference eniies were chosen. The iniial selecion was made o achieve a global mix of secors and naionaliies of some of he larges companies in he world. The main reason for choosing large companies was o make sure ha daa would be available. Naurally, his also leads o a bias owards companies wih higher credi raings. One migh suspec ha companies wih worse raings reac differenly o changes in he explanaory variables. However, he sign of he coefficiens should be he same regardless of credi raing. The effecs should also be saisically significan for all firms. The reason for choosing differen secors and counries was o be able o draw general conclusions abou CDS spreads. Unforunaely, differing accouning sandards and availabiliy of daa reduced he sample o mosly U.S. and a few European companies. We were also forced o exclude a few firms such as banks and insurance companies as hey are no compaible wih he Alman s Z explanaory variable. Despie hese adjusmens in he selecion process, he goal is for he resuling regression o be quie general and applicable o he CDS prices of mos firms. This is a realisic noion as long as he above resricions are kep in mind. 38
4.2 CDS premia The CDS prices were found as daily daa from he Daasream daabase. The hisory daes back o he beginning of 2003, giving us abou hree years of quoes and making he CDS spreads he limiing facor o he sudy in erms of ime span. The daa is aken as he mid price a closing each day and is quoed in basis poins. All of he CDS conracs are for five-year proecion on senior deb as i is he mos raded conrac ype. For example, a quoe of 100 basis poins means ha he price of insurance is one percen of he noional amoun, usually paid quarerly. The sandard day-coun measure for CDS agreemens is A/360. Figure 6 illusraes he CDS prices quoed in he sudy. There are a few exreme values which may have reduced he explanaory power of he sudy somewha. However, no adjusmen was made o he daa. 500 Observaions of CDS premia 450 400 350 300 250 200 150 100 50 0 0 50 100 150 200 250 300 350 400 Figure 6: Represenaion of he CDS prices used in he sudy. The daa consiss of 360 observaions spread ou on 30 corporaions beween 2003-01-01 and 2005-12-31. 39
4.3 Risk-free rae As saed above, he rae used o represen he risk-free rae is he five year ineres rae swap spread minus en basis poins. The rae was obained from Daasream and represens he mid price a close 25. The daa could be obained daily, bu he regression only requires quarerly raes. The sudy separaed European and U.S. firms in erms of risk free rae and seleced he appropriae swap rae depending on he geographic posiion of he firm. 4.4 Volailiy The measure of volailiy was calculaed from daily equiy closing prices obained via Daasream. The volailiy is calculaed as he sandard deviaion of sock-reurns during he las quarer. This is in accordance wih Equaion 6 above. The calculaions are made so ha he daes included are in accordance wih he ime since he las quarerly repor for each firm. 4.5 Alman s Z-score The daa needed o calculae Alman s Z-score is available four imes per year from Reuers and Daasream. Because quarerly measuremen gives comparably few daa poins, firms wih less han quarerly repors were excluded from he sample and replaced by ohers. This approach creaes 30 imes four daa poins per year for hree years, giving a oal of 360 daa poins. The daa for oal curren asses, curren liabiliies, oal asses, operaing resul, oal liabiliies and revenue were obained from Reuers. All of hese are repored quarerly and recorded in he local currency. Reained earnings was acquired from Daasream and is defined by Alman as he oal nominal sum of reained earnings in he hisory of he firm. Toal marke cap was also acquired via Daasream and represens he share price imes he number of shares ousanding. The Z-score is hen calculaed according o Equaion 7 in secion 3. 25 The mid price refers o he average of he bid and ask price. 40
4.6 Daa maching The daa in he sample is mached according o he daes of he quarerly repors. If a repor is released on he 31 s of December, he CDS spread and risk-free rae are aken as he closing quoes of ha day or he closes following day where a quoe is available. The volailiy is calculaed from he daily sock reurns since he las repor and up o he curren. The Z-score and leverage are calculaed from he numbers presened in he repor on ha same day. 41
5. Resuls This secion will sar by presening he summary saisics of he CDS daa and he explanaory variables. This is followed by key resuls of he performed regressions along wih shor explanaions. 5.1 Key saisics and regression resuls The full regression oupu is placed in he appendix. However, he Regression Summary below provides an overview of he resuls. Tables 2 and 3 in he appendix presen summary saisics of he differen variables employed in he regressions. We can see from Table 2 ha he difference beween he highes and lowes observaion of CDS is around 525 basis poins. This is a very large difference compared o he 5,3 basis poins beween he maximum and minimum individual deviaion from he mean in Table 3. Similar observaions can be made for all firm-specific variables. This illusraes he loss of variaion inheren in he fixed effecs mehod. The firs regression performed 26 was he fixed effecs model specified in Equaion 12 27, he resuls are presened in Tables 4 and 5. As we can see from Table 4, all of he coefficiens display he expeced sign along wih a high level of significance. This confirms he basic hypohesis ha Alman s Z-score is inversely correlaed o he CDS price of a firm. I also confirms earlier research on he effec of volailiy and he risk free rae. The hree facors combined explain abou a hird of he variaion in he CDS price. 26 All regressions are performed using OLS and he Eviews 4 sofware. 27 For quick reference o all he regression resuls, see he Regression Summary below. 42
Fixed Effecs Model Table # in Dependen Variable appendix 4 CDS, disance from mean Explanaory Coefficien T-sa R-squared of Variable regression Volailiy 33,97503 9,109415 31,66% Risk Free Rae -6,757889-2,417556 Alman s Z -14.70174-4.357318 5 Volailiy 27.66095 7.965071 43,35% Risk Free Rae 0.599408 0.228119 Leverage 4.029940 9.824837 6 CDS, percenage disance from mean Volailiy 43.23010 10.32875 41,72% Risk Free Rae -12.62711-4.025319 Alman s Z -23.58420-6.228774 7 Volailiy 35.78464 9.181644 51,68% Risk Free Rae -3.141622-1.065352 Leverage 5.050240 10.97084 8 Risk Free Rae -27.42389-8.293810 16,08% 9 Volailiy 52.51571 13.36308 33,22% 10 Alman s Z -25.77219-5.441598 7,62% 11 Leverage 6.849639 14.48723 36,89% One-sep Differenced Model 12 CDS-CDS(-1) Volailiy 24.96421 7.356008 11,39% Risk Free Rae -0.193608-0.073010 Alman s Z -3.572131-1.148429 13 Alman s Z -6.712035-2.023224 3,39% 14 Volailiy 20.41442 6.197900 20,27% Risk Free Rae -0.212938-0.084668 Leverage 2.876288 6.155277 Level Regressions 15 CDS Alman s Z -6.204084-4.839888 6,14% Consan 66.56379 16.52352 16 Leverage 0.557863 4.348380 5,02% Consan 30.04495 5.278860 17 Volailiy 43.74737 10.84688 34,46% Risk Free Rae -4.297312-1.150179 Alman s Z -7.625669-6.983836 Consan 20.31865 1.179650 Regression summary: Each regression is provided in full in he appendix. 43
Table 5 replaces Alman s Z wih leverage and performs he same regression. This produces some ineresing effecs. We firs noice ha he leverage is highly significan wih he expeced sign. The imporance of volailiy is largely unchanged, bu he risk free rae has los all significance. The reason for his loss of significance may be serial correlaion in he sample. Analysis shows ha he loss of significance only occurs when leverage is included in he regressions. When calculaing he correlaion beween he leverage and he risk free rae in he sample we ge a correlaion of -0,39. Also, a regression rying o explain leverage wih he risk free rae or vice versa yields highly significan coefficiens. Noe ha his is sill performed wihin he fixed effecs framework. The resul ha higher ineres raes would lead o lower leverage in firms has no been discussed in earlier papers performing empirical componens analysis. This paper noes ha here may well be an economic negaive relaionship beween leverage and he risk free rae as he presen value of deb would decrease wih higher ineres raes. However, no furher acion is aken o invesigae he maer and i is lef for fuure research. Coninuing he analysis of Table 5, we see ha he R-squared is abou en percen higher when including leverage. Hence, leverage appears o be more suied for explaining variaions in he CDS spread. This is seen more clearly in Tables 10 and 11 where he individual variables are regressed separaely agains he percenage deviaion of CDS from is mean. 44
Tables 6 and 7 proceed by exchanging he deviaion of CDS from is mean by he percenage deviaion. This is done because he levels of differ grealy beween firms, and a deviaion of e.g. five basis poins maer relaively more for firms wih lower spreads. As expeced, he coefficien values increase in absolue size compared o Table 4. Once again we see he expeced signs and even higher levels of significance, noably for he risk free rae. Also, he ransformaion succeeded in increasing he explanaory power of he regression o 41 percen. The resuls of Table 7 are also as expeced. Higher significance compared o Table 7 and Table 8 indicaes he beer fi wih percenage changes in CDS. The ables also confirm ha leverage has a higher explanaory power compared o he Z-score. Tables 8 o 11 illusrae he oupu from regressing he individual explanaory variables on percenage deviaions of CDS. The resuls from he same regressions on he CDS mean are no included bu yield similar oupu, only wih lower explanaory power. Table 8 illusraes more clearly he negaive individual effec of he risk free rae on CDS prices 28. We can also see ha i has an individually high explanaory power and significance. The reason for he low significance in combinaion wih oher variables may be as suggesed earlier, he presence of serial correlaion, perhaps due o exogenous variables. From Table 9 we can see ha he individual regression confirms he effec of volailiy and indicaes a high explanaory power. In comparing Tables 10 and 11, he effecs and significances of boh leverage and Alman s Z-score are confirmed. However, he explanaory power of leverage is abou 37 percen whereas Alman only reaches seven percen. This once again speaks in favour of leverage as a beer indicaor of CDS changes. 28 This negaive bias is documened by Longsaff and Schwarz (1995), Duffee (1998) and Ericsson (2004) 45
The nex sep is he difference regressions illusraed in ables (34) and (36). These regressions confirm he high significance of volailiy and leverage bu once again show an insignifican coefficien for he risk free rae. Also, one noes ha Alman s Z-score is insignifican in Table 12. The explanaory power of he included variables is lower in general and he highes R-squared reached is 20 percen which is o be compared o above 50 percen in he fixed effecs model. The reason for he lower significance is ha he difference mehod of analyzing daa places higher demands on he comovemen of variables. The insignificance of Alman s Z is probably o a furher decrease in variaion in he difference sample. Table 13 illusraes ha he Z- score is sill significan when regressed on is own. Tables 15, 16 and 17 are ineresing o sudy as hey show he resul of regressing he variables leverage and Alman s Z on he levels of CDS prices. This means ha he abiliy o explain iner-firm differences is included in he regression. Boh variables are sill significan, bu we can see ha all of a sudden he Z-score has almos wice he explanaory power of he leverage variable. This indicaes ha he Z-score may be a bi oo blun o accuraely explain he smaller changes in a firm over ime, bu has abeer abiliy o see he big picure and compare differen firms. Table 17 shows he earlier variables in a simple pooled cross-secion on he CDS prices. The explanaory power is quie low 29 and once again, he coefficien for he risk free rae is insignifican. 29 Ericsson e al (2004) reached an R-squared of around 60 percen for level regressions. 46
5.1.1 Summary of regression resuls The fixed effec regressions performed displayed explanaory levels of beween 40 and 50 percen. The signs and significance for leverage, volailiy and Alman s Z- score were as expeced and confirmed earlier research. The explanaory power of Alman s Z, however, was lower han ha of leverage. This may be due o he fac ha he variaion in he Z-score is mainly beween differen firms and no so much over ime wihin a firm. The risk free rae of reurn was significan and had he prediced negaive effec on CDS spreads in he regression wih he Z-score and volailiy. When including he leverage, however, he risk free rae became insignifican. This may be an indicaion of serial correlaion in he variables. This is an unexpeced resul as here has been no indicaion of similar resuls in earlier research on empirical componens. One reason for his may be he fac ha we in pracice only have much fewer observaions of he risk free rae compared o he oher variables. The risk free rae is measured on each repor dae for he differen firms. And since mos firms repor heir quarerly figures on he same sandard daes, he observaions will be he same. This could in urn lead o unwaned effecs such as oo lile variaion in he variable, resuling in insignifican coefficiens. This paper leaves a more horough invesigaion ino his maer o fuure research and concludes ha i canno fully confirm he earlier resuls on risk free rae. 47
The differenced regressions produced similar resuls o he fixed effecs model bu wih lower overall significances. This was expeced and is due o he srucural differences in he models. Wha is noable, however, is ha Alman los is saisical significance. This is anoher indicaion ha Alman is more appropriae for iner-firm level explanaion. The level regression also suffers from low levels of significance. The main finding, however is ha i swiches he order of imporance of leverage and Alman s Z. In he level regressions, where iner-firm differences are included, he Z- score has a significanly higher explanaory power compared o he leverage variable. 48
6. Discussion This secion will discuss he regression daa presened in he las secion and link he resuls o exising heory. In order o give he reader a beer overview, he discussion is separaed ino one secion per variable. Apar from discussing he resuls, weaknesses of he sudy are brough up along wih suggesions of improvemens and furher research. 6.1 Risk free rae This variable was expeced o follow he resuls of Longsaff and Schwarz (1995), CGM (2001), Benker (2004) and Ericsson e al (2004) in having a significan negaive effec on he CDS price. The reasons for his effec have been discussed, bu he main argumen seems o be ha a higher risk-free rae decreases he risk of defaul when one models he geomeric Brownian drif of a firm. Also, because we view he CDS price as he price of a pu opion on he firm, i is naural ha a higher risk-free rae should lead o a decrease in he CDS price. Neverheless, he resuls were no sricly in accordance wih heory. In he regressions where he variable was significan, i indeed had a negaive coefficien. On he oher hand, several of he ess performed rendered he risk free rae insignifican o he price of a CDS. More specifically, he significance was los in he fixed effecs regression when Alman s Z-score was subsiued for leverage. This is an ineresing resul as i suggess he possibiliy of serial correlaion beween he leverage and risk free rae. Also, a simple regression of leverage on risk free ineres rae yields a highly significan negaive coefficien in he sample used. Such correlaion is inuiively plausible if one considers he value of a firm s liabiliies o be negaively correlaed o he discoun rae. 49
Also, one migh consider he fac ha companies will increase heir leverage during imes when credi is cheap. Anoher explanaion would be ha he relaively few observaions of risk free rae in he sample 30 have led o a random covariaion wih he leverage of he included firms. In any case, he significance of he risk free rae is weak and his sudy canno uncondiionally suppor he resuls of earlier research. However, he significan resuls achieved appear o confirm earlier resuls. The apparen correlaion beween he risk free rae and leverage is lef for fuure research. 6.2 Volailiy Earlier empirical componens research and he srucural models all agree ha he coefficien for volailiy should be posiive 31. The reason for his is inuiive as increased volailiy increases he risk of defaul and also he price of a pu opion. The regressions of hisorical equiy volailiy all confirm his resul and hereby also earlier sudies. 6.3 Alman s Z-score The Z-score is a combinaion of differen financial raios which has he purpose of predicing wheher or no a company is risking defaul. The higher he value of Alman s Z-score, he beer he healh of he company. Therefore, Alman s Z was prediced o have a negaive coefficien. The hypohesis also saed ha he Z-score would have a higher explanaory power han he leverage of a firm because i akes ino accoun oher raios as well. The Z-score urned ou o be a highly significan esimaor wih he prediced sign. However, in erms of explanaory power, i was ouperformed by leverage in all of he regressions measuring differences wihin a firm over ime 32. This may be eiher because leverage is beer a predicing defaul 30 The sample conains welve daa poins per firm, each on a quarerly repor dae. Because many firms repor on he same dae and he ohers on nearby daes, similar risk free raes are repeaed in he sample. 31 See CGM (2001), Campbell and Taksler (2003), Cremers e al (2004), Benker (2004) and Ericsson e al (2004) 32 Noe ha he fixed effecs model and he difference model measures differences wihin firms over ime whereas he level regression also includes differences beween firms. 50
risk or because he differences in firms over ime were oo small o be refleced significanly in he Z-score. The laer explanaion seems more plausible in ligh of he fac ha he Z-score dominaed he leverage variable in erms of explanaory power in he level regressions. 6.4 Leverage Earlier research on empirical componens 33 has noed leverage as one of he hree mos significan variables exraced from he srucural models o be used in he empirical componens approach. The leverage of a firm basically denoes he raio of deb o asses of a firm and should have a posiive correlaion wih he CDS price. As wih volailiy, he resuls are significan in all cases and we can confirm our predicions in all regressions. The only hing worh commening is once more he subsiuabiliy wih Alman s Z. When he wo variables appear in he same regression, one becomes insignifican and here is obviously a correlaion beween hem. This sudy indicaes ha leverage is more imporan in explaining inra-firm changes over ime, whereas he Z-score is beer a explaining level differences beween firms. 33 See references for he risk free rae. 51
6.5 Weaknesses and possible fuure research The general level of explanaory power in he regressions was low compared o earlier sudies. This is likely o be he resul of using fewer daa poins and no inerpolaing he daa. However, an ineresing ask for fuure research would be o conduc principal componens analysis of he residual series in order o possibly idenify addiional explanaory variables 34. Anoher subjec of fuure sudy migh be he correlaion of ineres raes and leverage o see wheher he problem experienced in his sudy was a coincidence or somehing o be regarded during model-building. Given ha his sudy has indeed moved away from sricly srucural-model-based variables by including he Z-score, here is no reason o sop here. Fuure sudies could aemp o find oher significan variables which may no be subsiues, bu complemens o exising ones 35. 34 This was aemped by Ericsson e al (2004) wihou idenifying any addiional variables for heir series. 35 CGM (2001) found a high level of negaive significance when using he S&P 500 index as an explanaory variable. The explanaion suggesed was ha he sock index is a proxy of general economic condiions which would have a negaive correlaion o CDS spreads. 52
7. Conclusion This secion will provide a summary of he resuls achieved in his paper and conclude he sudy. This paper se ou wih wo aims. The firs was o confirm earlier research on he effec of cerain empirical componens on a new daa se. The second was o es he hypohesis ha Alman s Z-score is superior o leverage in explaining CDS prices. The paper also provided a background of he credi derivaives markes and of he research leading up o he empirical componens approach. The resuls were a parial achievemen of he goals se ou. Earlier resuls using he empirical componens approach were confirmed albei wih a quesion mark regarding he risk free rae. The hypohesis regarding he Z-score was also pu ino quesion. Alhough he variable had a saisically and economically significan effec on he price changes of he CDS in our main regressions, he leverage sill had a higher explanaory power. This was in essence a rejecion of he hypohesis of his paper. However, in he level regressions conduced a he end, he hierarchy changed wih he Z-score showing almos wice he level of explanaory power o ha of leverage. This is likely o be due o he fac ha he pooled cross secional regression includes he iner-firm differences. The Z-score may be weaker in picking up small changes wihin a firm over ime, bu sronger a comparing differen firms. One of he subjecs suggesed for furher research may herefore be o coninue he analysis wih Alman s Z as an explanaory variable and also o include new previously unesed variables o increase he explanaory power of he es. Anoher maer worh anoher menion is he seemingly negaive relaionship beween he risk free rae and leverage. If he relaionship is srong enough o affec he inference in similar ECA sudies, i may well be worh fuure research. 53
Appendix A. Summary saisics CDS ALTMAN RISKFREE VOL LEV Mean 56.38199 2.423303 3.735493 0.016013 38.68462 Median 37.62130 1.781306 3.716500 0.013942 36.64613 Maximum 532.5000 11.75962 4.915000 0.045033 91.43010 Minimum 7.500000-1.802600 2.277500 0.005593 5.637170 Sd. Dev. 63.82412 2.111046 0.654278 0.007103 20.81080 Sum 20297.52 872.3889 1344.777 5.764531 13926.46 Sum Sq. 1462393. 1599.889 153.6806 0.018113 155479.1 Dev. Observaions 360 360 360 360 360 Table 2: Summary saisics of he variables used in he regressions. ALTMAN CDS LEVERAGE PERCCDS VOL RISKFREE Mean -1.57E-16-1.03E-15-1.18E-15-2.21E-15 5.18E-17 2.96E-16 Median -0.012229-2.568066-0.096675-8.597440-0.094313 0.028771 Maximum 2.998871 364.9715 20.94600 304.0706 1.985641 1.014625 Minimum -2.356810-82.36961-11.41347-67.71452-1.476910-1.495458 Sd. Dev. 0.476292 36.59455 3.943330 44.46883 0.488039 0.648777 Sum -6.05E-14-4.26E-13-3.20E-13-4.83E-13 1.87E-14 1.31E-13 Sum Sq. 81.44065 480758.8 5582.397 709914.3 85.50749 151.1073 Dev. Observaions 360 360 360 360 360 360 Table 3: Summary saisics of deviaion from mean 54
B. Regression oupu and diagrams B.1 Fixed effecs model Dependen Variable: CDS Mehod: Leas Squares Dae: 06/12/06 Time: 17:58 Sample: 1 360 Included observaions: 360 Variable Coefficien Sd. Error -Saisic Prob. VOL 33.97503 3.729661 9.109415 0.0000 RISKFREE -6.757889 2.795340-2.417556 0.0161 ALTMAN -14.70174 3.374034-4.357318 0.0000 R-squared 0.316639 Mean dependen var -1.03E- 15 Adjused R-squared 0.312811 S.D. dependen var 36.59455 S.E. of regression 30.33573 Akaike info crierion 9.670828 Sum squared resid 328531.7 Schwarz crierion 9.703212 Log likelihood -1737.749 Durbin-Wason sa 1.309386 Table 4: Regression oupu Dependen Variable: CDS Mehod: Leas Squares Dae: 06/12/06 Time: 17:59 Sample: 1 360 Included observaions: 360 Variable Coefficien Sd. Error -Saisic Prob. RISKFREE 0.599408 2.627617 0.228119 0.8197 VOL 27.66095 3.472782 7.965071 0.0000 LEVERAGE 4.029940 0.410179 9.824837 0.0000 R-squared 0.433476 Mean dependen var -1.03E- 15 Adjused R-squared 0.430302 S.D. dependen var 36.59455 S.E. of regression 27.62096 Akaike info crierion 9.483325 Sum squared resid 272361.4 Schwarz crierion 9.515709 Log likelihood -1703.999 Durbin-Wason sa 1.243299 Table 5: Regression oupu 55
Dependen Variable: PERCCDS Mehod: Leas Squares Dae: 06/12/06 Time: 18:01 Sample: 1 360 Included observaions: 360 Variable Coefficien Sd. Error -Saisic Prob. VOL 43.23010 4.185414 10.32875 0.0000 RISKFREE -12.62711 3.136922-4.025319 0.0001 ALTMAN -23.58420 3.786331-6.228774 0.0000 R-squared 0.417213 Mean dependen var -2.21E- 15 Adjused R-squared 0.413949 S.D. dependen var 44.4688 3 S.E. of regression 34.04267 Akaike info crierion 9.90140 5 Sum squared resid 413728.5 Schwarz crierion 9.93378 9 Log likelihood -1779.253 Durbin-Wason sa 1.65371 0 Table 6: Regression oupu Dependen Variable: PERCCDS Mehod: Leas Squares Dae: 06/12/06 Time: 18:03 Sample: 1 360 Included observaions: 360 Variable Coefficien Sd. Error -Saisic Prob. VOL 35.78464 3.897411 9.181644 0.0000 RISKFREE -3.141622 2.948906-1.065352 0.2874 LEVERAGE 5.050240 0.460333 10.97084 0.0000 R-squared 0.516789 Mean dependen var -2.21E- 15 Adjused R-squared 0.514081 S.D. dependen var 44.4688 3 S.E. of regression 30.99827 Akaike info crierion 9.71403 8 Sum squared resid 343038.7 Schwarz crierion 9.74642 3 Log likelihood -1745.527 Durbin-Wason sa 1.66633 5 Table 7: Regression oupu 56
Dependen Variable: PERCCDS Mehod: Leas Squares Dae: 06/12/06 Time: 18:04 Sample: 1 360 Included observaions: 360 Variable Coefficien Sd. Error -Saisic Prob. RISKFREE -27.42389 3.306549-8.293810 0.0000 R-squared 0.160798 Mean dependen var -2.21E- 15 Adjused R-squared 0.160798 S.D. dependen var 44.4688 3 S.E. of regression 40.73700 Akaike info crierion 10.2549 2 Sum squared resid 595761.6 Schwarz crierion 10.2657 2 Log likelihood -1844.886 Durbin-Wason sa 1.44818 9 Table 8: Regression oupu Dependen Variable: PERCCDS Mehod: Leas Squares Dae: 06/12/06 Time: 18:05 Sample: 1 360 Included observaions: 360 Variable Coefficien Sd. Error -Saisic Prob. VOL 52.51571 3.929910 13.36308 0.0000 R-squared 0.332182 Mean dependen var -2.21E- 15 Adjused R-squared 0.332182 S.D. dependen var 44.4688 3 S.E. of regression 36.33998 Akaike info crierion 10.0264 9 Sum squared resid 474093.3 Schwarz crierion 10.0372 8 Log likelihood -1803.768 Durbin-Wason sa 1.52713 4 Table 9: Regression oupu 57
Dependen Variable: PERCCDS Mehod: Leas Squares Dae: 06/01/06 Time: 17:39 Sample: 1 360 Included observaions: 360 Variable Coefficien Sd. Error -Saisic Prob. ALTMAN -25.77219 4.736143-5.441598 0.0000 R-squared 0.076197 Mean dependen var -2.21E- 15 Adjused R-squared 0.076197 S.D. dependen var 44.4688 3 S.E. of regression 42.74107 Akaike info crierion 10.3509 7 Sum squared resid 655821.0 Schwarz crierion 10.3617 7 Log likelihood -1862.175 Durbin-Wason sa 1.44545 5 Table 10: Regression oupu Dependen Variable: PERCCDS Mehod: Leas Squares Dae: 06/01/06 Time: 17:39 Sample: 1 360 Included observaions: 360 Variable Coefficien Sd. Error -Saisic Prob. LEVERAGE 6.849639 0.472805 14.48723 0.0000 R-squared 0.368935 Mean dependen var -2.21E- 15 Adjused R-squared 0.368935 S.D. dependen var 44.4688 3 S.E. of regression 35.32586 Akaike info crierion 9.96988 1 Sum squared resid 448001.9 Schwarz crierion 9.98067 6 Log likelihood -1793.579 Durbin-Wason sa 1.47176 8 Table 11: Regression oupu 58
Figure 7: Acual, fied and residual graph from Table 6. 59
Figure 8: Acual, fied and residual graph from Table 7. 60