Are CDS spreads predictable? An analysis of linear and non-linear forecasting models

Transcription

1 Are CDS spreads predicable? An analysis of linear and non-linear forecasing models Davide Avino and Ogonna Nneji* ICMA Cenre, Universiy of Reading, Henley School of Business, PO Box 242 RG6 6BA, UK Curren version: Sepember 2012 Absrac This paper invesigaes he forecasing performance for CDS spreads of boh linear and non-linear models by analysing he itraxx Europe index during he financial crisis period which began in mid The saisical and economic significance of he models forecass are evaluaed by employing various merics and rading sraegies, respecively. Alhough hese models provide good in-sample performances, we find ha he non-linear Markov swiching models underperform linear models ou-of-sample. In general, our resuls show some evidence of predicabiliy of itraxx index spreads. Linear models, in paricular, generae posiive Sharpe raios for some of he sraegies implemened, hus shedding some doubs on he efficiency of he European CDS index marke. JEL classificaion: G01; G17; G20; C22; C24 Keywords: Credi defaul swap spreads; itraxx; Forecasing; Markov swiching; Marke efficiency; Technical rading rules * addresses: d.avino@icmacenre.ac.uk (D. Avino), o.nneji@icmacenre.ac.uk (O. Nneji). 1. Inroducion 1

2 Credi defaul swaps (CDS) have araced considerable aenion in he finance world since heir inroducion in he nineies. These financial producs allow invesors o rade and hedge asses which bear credi risk wih a cerain ease. In he pas, rading credi risk was only possible via he use of bonds. However, shoring credi risk in he cash marke is made difficul by he fac ha is repo marke is no very liquid and he mauriy of he agreemen is shor. These shor-sale resricions in he cash marke do no apply o he CDS marke, and as such i is usually preferred by invesors who wan o rade credi risk a a known cos (he CDS spread) and for longer mauriies. Over he las decade, he CDS marke has experienced an impressive growh, reaching is peak a he end of 2007 wih a noional amoun ousanding of abou USD 62 rillion. Since hen, he marke hi by he Grea Recession winessed a downward rend and large decrease in amoun ousanding. The marke has, however, recovered from he subprime-induced financial marke urmoil of and as of Augus 2012, i boased an ousanding value of almos USD 25 rillion. 1 The rading volume of CDS indices of approximaely USD 8 rillion (as of Augus 2012) accouns for abou a hird of he oal rading volume of he credi derivaives marke. A CDS index conrac is an insurance conrac which proecs he invesor agains he defaul of a pool of names included in he index. Unlike a single-name conrac, he defaul of one member of he pool does no cause he erminaion of he conrac, which insead coninues unil he mauriy bu wih a reduced noional amoun. 2 Trading of CDS indices was made possible in June 2004, when he Dow Jones itraxx index family was creaed. Marki owns, compiles and publishes he itraxx index series, which include he mos liquid European and Asian single-name CDSs. itraxx Europe is an equally weighed index which comprises 125 single-name invesmen grade CDSs and is divided ino he sub-indices financials senior, financials subordinae and non-financials. Trading of CDS index is available for mauriies ranging from 3 o 10 years, being he 5-year mauriy he mos liquid. In his paper, we focus on he itraxx Europe CDS index and address, for he firs ime in he finance lieraure, he quesion of wheher CDS index spreads can be forecased. We focus our aenion on he non-financials and financials senior indices, which are he wo main sub-indices of he itraxx CDS index family. 3 Our choice o run a separae analysis on hese wo indices is explained by he fac ha indusrial and financial eniies are characerised by very dissimilar capial srucures. Predicing CDS spreads of an 1 See for more informaion on CDS rading daa. 2 The oal noional amoun of he CDS index conrac is reduced by he noional amoun of he defauled eniy. 3 The remaining wo sub-indices are financials subordinae and high volailiy. 2

3 index which includes heerogeneous eniies can negaively affec he forecasing abiliy of he index iself. Clearly, our sudy would be of ineres o boh academics and praciioners, who could ge a beer undersanding on he efficiency of he CDS marke and he possibiliy o implemen sound hedging models and profiable rading sraegies. Wheher CDS spreads are characerised by he exisence of predicable paerns is an ineresing research quesion whose invesigaion is useful in erms of asse pricing and credi porfolio managemen. In addiion, single-name credi spreads, and especially CDS index spreads, have become a crucial indicaor of he financial condiions of he whole economy and, similarly o he VIX index, of he level of volailiy presen in he financial markes. These consideraions make our sudy fascinaing as well as of common ineres for he sociey as a whole. While here is an exensive lieraure which analyses he forecasing performance of economeric models in he spo and fuure equiy, bond and foreign exchange markes, he research quesion of wheher CDS spreads can be forecased has no been direcly invesigaed by previous sudies. Hence, his sudy on he forecasabiliy of CDS spreads exends he lieraure on CDS spreads. To address our research quesion, poin ou-of-sample forecass are generaed from linear and non-linear economeric models. In paricular, we use wo linear models, namely a srucural model based on ordinary leas squares (OLS, hereafer) regression and an AR(1) model as well as he non-linear versions of hese models, based on he Markov regime-swiching approach. We es he saisical significance of he forecass obained, which are discussed a laer sages in he paper. We also examine he economic significance of hese forecass by implemening various rading sraegies, hus providing inference on he efficiency of he CDS marke. The res of he paper is as follows: Secion 2 reviews he lieraure. Secion 3 describes he daase. Secion 4 presens he forecasing models used in our analysis. Secion 5 analyses he in-sample performance of he models used, whereas Secion 6 discusses he saisical ou-of-sample performance of he forecasing models. Secion 7 describes he implemenaion of he rading sraegies used o evaluae he economic significance of he models forecass. Secion 8 concludes our paper. 2. Lieraure review The lieraure on credi spreads (and CDS spreads) has primarily focused on he developmen of srucural pricing models, which were inroduced in he seminal work of Meron (1974). Subsequen conribuions were from Black and Cox (1976), Longsaff and Schwarz (1995), Leland (1994) and Leland and Tof 3

4 (1996). This srand of lieraure on srucural credi risk models provides he heoreical framework o idenify he deerminans of changes in credi spreads as well as CDS spreads. Meron (1974) and subsequen sudies (as saed above) assume some sochasic process for he value of a firm s asses and ha defaul occurs whenever he firm s asses value falls below a defined hreshold value (or defaul barrier), which is a funcion of he ousanding deb of he firm. The value of he firm s deb is obained by compuing is expeced fuure cash flows discouned a he risk-free rae (under he risk-neural measure). Hence, he CDS spreads, a any poin in ime, are a funcion of he firm s asses value, he risk-free rae and some sae variables. Changes in hese sae variables should hen deermine changes in CDS spreads. Below is a brief summary of he heoreical drivers of credi (and CDS) spreads: 1. The level of he risk-free ineres rae. Longsaff and Schwarz (1995) have shown ha a higher spo rae would increase he risk-neural drif in he firm value process which, in urn, reduces he probabiliy of defaul and hence CDS spreads. 2. The slope of he yield curve. Srucural models include one spo rae only; however, he fuure spo rae is affeced by he slope of he yield curve. Hence, an increase in he laer increases he expeced fuure spo rae which, again, should reduce CDS spreads. 3. The equiy reurns as a proxy for he overall sae of he economy. Whenever he firm s asses value decreases, he probabiliy of defaul will increase as here is a higher likelihood of hiing he defaul hreshold. Because a firm s asses value is no direcly observable, is equiy value can be observed and used as a proxy for he asses value. 4. The asses volailiy. Higher asses volailiy implies a higher probabiliy of defaul (and higher CDS spreads) as here is a higher likelihood for he asse value process of hiing he defaul barrier. However, asses volailiy is unobservable. Again, we can exploi he posiive relaionship beween he volailiy of he asses value and equiy volailiy and hen use he laer as a proxy for he asses volailiy. Empirical sudies which analysed he pricing accuracy of srucural models were from Jones e al. (1984), Eom e al. (2004) and Huang and Huang (2003). These sudies focused on credi spreads obained from bonds and found ha, on average, credi risk models under-predic spreads. However, Ericsson e al. (2009) showed ha credi risk models seem o perform beer when applied o CDS spreads. Promped by he findings on credi risk pricing models, a new srand of lieraure developed and i is aimed a invesigaing he deerminans of boh levels and changes in credi spreads and CDS spreads. A seminal paper in his new area of research was from Collin-Dufresne e al. (2001). They idenified a series of credi variables (as suggesed by he heory of srucural pricing models) and liquidiy variables and 4

5 used hem as independen variables o explain changes in credi spreads. They found ha hese variables have limied explanaory power and ha a common sysemaic facor is responsible for mos of he variaion in credi spread changes. Successive similar sudies were hose from Elon e al. (2001), Delianedis and Geske (2001), Driessen (2005), Campbell and Taksler (2003) and Cremers e al. (2008). Recen sudies which have ried o explain CDS spread levels and changes are from Blanco e al. (2005), Longsaff e al. (2005), Benker (2004), Alexander and Kaeck (2008), Zhang e al. (2009), Ericsson e al. (2009) and Cao e al. (2010). Their findings are generally more encouraging (han previous sudies on credi spreads) as credi variables seem o explain a grea deal of he variaion in CDS spreads. All hese sudies are based on a regression analysis which is used o sudy he conemporaneous correlaions beween he independen variables and he dependen variable (eiher level or change in credi spread or CDS spread). Oher han Alexander and Kaeck (2008), who analysed he deerminans of itraxx Europe CDS index spreads, all he aforemenioned sudies focussed on spreads obained for individual firms. Mos recen papers have ried o analyse he lead-lag relaionship beween credi spreads (of individual firms) obained from differen markes and sock reurns. Blanco e al. (2005) and Zhu (2004) analyse he price discovery beween CDS spreads and credi spreads; Fore and Peña (2009) sudy he price discovery beween CDS, bond and equiy-implied spreads; Longsaff e al. (2003) and Norden and Weber (2009) sudy he lead-lag relaionships among CDS spreads, credi spreads and equiy reurns. These sudies use eiher a vecor auoregressive model or vecor error correcion model approach o invesigae which marke leads he ohers and heir findings, based on he in-sample esimaion of he models, show ha he equiy marke leads he CDS and bond markes. Anoher sudy which is similar o Alexander and Kaeck (2008) and is based on he analysis of he itraxx Europe CDS index is Bysröm (2006). The former sudy used a Markov swiching regression model o explain changes in itraxx CDS speads in differen regimes over he period from June-2004 o June Their main conclusion is ha opion-implied volailiies represen he main deerminan of changes in CDS spreads in a volaile regime, whereas in sable condiions equiy marke reurns have a predominan role. The laer sudy showed how, during he period from June-2004 o March-2006, CDS index spread changes presened a posiive and significan firs-order auocorrelaion, which was eviden from he applicaion of an auoregressive model of order 1 (AR(1), hereafer). A simple rading rule which ried o exploi his posiive auocorrelaion generaed posiive profis before ransacion coss, which urned negaive ne of rading coss. These wo sudies showed how a Markov swiching regression model and an AR(1) model give boh a good in-sample fi of he daa. However, he quesion of wheher hese models are useful for forecasing fuure CDS spread changes has no been invesigaed. 5

6 3. The daase We download daily quoes of itraxx Europe CDS indices for financials senior and non-financials from Bloomberg and focus on he 5-year mauriy, which is he mos liquid. We cover he daa period which goes from 20 Sepember 2005 o 15 Sepember 2010 for a oal of 1235 observaions for each of he 2 indices. Every six monhs a new series of itraxx indices is launched o updae he membership of he index such ha only he mos liquid CDSs are included. In order o base our analysis on he mos liquid names a every poin in ime, we consruc a ime series for each index which conains he mos recen series. We also download daa for he following economic variables, which have been idenified as he deerminans of CDS spreads by he heory of srucural credi risk models: he level of he risk-free ineres rae, he slope of he yield curve, he equiy reurn for he itraxx indices and he asse volailiy. We discuss each of hese variables individually. 1. As a proxy for he level of he risk-free ineres rae, we download Euro swap raes for he 5-year mauriy. According o Houweling and Vors (2005), swap raes are considered as a superior proxy for he risk-free rae han governmen bond yields. 2. The slope of he yield curve is defined as he difference beween he 10-year and 2-year Euro swap raes (see also Collin-Dufresne e al., 2001). 3. As a proxy of he equiy reurn for he itraxx indices we need o creae a porfolio of socks comprising he same members as he CDS indices. As he CDS indices are equally weighed, we keep an equal weighing scheme even for he sock porfolios. If, for any reason, a firm in he sample lacks informaion on he raded price, we omi i from he sock porfolio and increase he weigh of he oher companies in he index equally. 4. We proxy firms asse volailiies wih implied volailiies. Since mos of he companies in our sample lack liquid raded opions, we use he VSoxx index, which is an implied volailiy index of opions on he DJ Eurosoxx 50 index. 4 All forecasing models are esimaed over hree periods: 20 Sepember 2005 o 31 December 2006; 20 Sepember 2005 o 31 December 2007; 20 Sepember 2005 o 31 July This allows us o es he sabiliy of he models over a period characerised by differen marke regimes and simulaneously generae ou-of-sample forecass from he end of he hree differen periods o 15 Sepember This 4 Daa on VSoxx is rerievable from 6

7 way, we are able o es how and wheher he various phases of he Grea Recession may have affeced he forecasing performance of he models. Table 1 presens he summary saisics for he variables levels (Panel A) and changes (Panel B). According o he Augmened Dickey Fuller (ADF) es 5, all variables are non-saionary when measured in levels. However, aking he firs-order differences makes he series saionary. The variables levels show a posiive firs-order auocorrelaion, whereas i disappears for mos of hem when firs differences are aken. CDS spreads are he mos volaile variables and all variables show clear rais of non-normaliy as confirmed by he Bera-Jarque es and he values assumed by skewness and kurosis. 4. The forecasing models 4.1 Linear models: Srucural Model and AR(1) Previous sudies which analysed he deerminans of credi spreads used a se of independen variables as suggesed by he heory of srucural credi risk models inroduced by Meron (1974). While hese sudies focused on he conemporaneous relaionship beween he credi spreads and he explanaory variables, we are however ineresed in he forecasing abiliy of hese variables in predicing fuure credi spreads. Hence, we use lagged variables o forecas fuure CDS spreads. We esimae he following regression for each CDS index i (wih i=1 for financials senior and i=2 for non-financials): CDS CDS r ( r r ) EQUITY _ R V (0.1) i i i i 5 i 10 2 i i i i where is he daily change in he ih CDS index. is he change in he 5-year Euro swap rae, ( ) is he change in he slope of he yield curve (which is proxied by he difference beween he 10-year and he 2-year Euro swap raes), denoes he reurn on he ih sock porfolio and is he change in he VSoxx volailiy index. Some evidence of predicive power of he aforemenioned explanaory variables can be found in previous lieraure. For insance, Norden and Weber (2009) and Bernd and Osrovnaya (2008) have shown ha equiy reurns and opion-implied volailiies are more likely o lead CDS spreads in he price discovery process. The sudy by Bysröm (2006) found a posiive auocorrelaion in itraxx CDS index spreads, hus promping us o also invesigae he forecasing power of a simple AR(1) model, which is a reduced form 5 See Dickey and Fuller (1981). 7

8 of equaion (1.1). This will enable us o find wheher fuure CDS spreads can be forecased by using informaion on pas CDS spreads only and no he economic variables discussed earlier: CDS CDS (0.2) i i i 1 We would like o reierae ha previous sudies which have used hese models have done so in order o eiher explain changes in credi spreads and sudy he conemporaneous correlaion exising beween he dependen variable and he independen variables (his is he case for he srucural model) or analyse he in-sample performance of he forecasing model (as for he AR(1)). Hence, no aemp has been made o es he ou-of-sample performance of hese linear models. This is he main objecive of our analysis. 4.2 Non-linear models: Markov Swiching Srucural Model and Markov Swiching AR(1) The aforemenioned linear models in equaions (1.1) and (1.2) are exended o allow swiching in he explanaory variables. We follow he Markov regime-swiching approach inroduced by Hamilon (1989, 1994). In hese Markov swiching augmened models, he effecs of hese seleced explanaory variables on he changes in CDS spreads depend on he CDS marke condiion or regime. Therefore, he magniude of he effec of changes in he righ-hand-side variables depends on wheher he CDS marke is in a highvolailiy or low-volailiy regimes. Given hese, equaion (1.1) is now ransformed mahemaically as: CDS CDS r ( r r ) EQUITY _ R V (0.3) i i i i 5 i 10 2 i i i i S1 S1,1 1 S1,2 1 S1,3 1 1 S1,4 1 S1,5 1 S 2 where S, ~ N 0, S and S j(for j = 1 or 2) In his Markov regime-swiching augmened version of equaion (1.1), he erm S is he laen sae variable. This could equal 1 or 2 depending on wheher or no he CDS marke is in a high or low volailiy regime, hus, implying ha he impac of he explanaory economic variable on CDS spreads depend on he CDS marke condiion. Noe ha a firs-order Markov chain wih fixed ransiion probabiliy marix (P) governs he laen sae variable S : Pr S 1 S 1 1 Pr S 2 S 1 1 p11 p12 Pr S 1 S 1 2 Pr S 2 S 1 2 p21 p 22 (0.4) where p jk are he ransiion probabiliies from sae j o sae k. 8

9 A maximum likelihood procedure is used o esimae he Markov swiching model and assuming ha he error erm has a normal disribuion, he densiy of he dependen variable condiioned on he regime is given as: 1 f CDS S j, X, ; exp CDS 2 X 1 j i, j j (0.5) where, CDS, CDS,..., X, X,... represens all he pas informaion o ime 1, is he vecor of parameers S, S, S, S, S, S, p, p,0,1,2,3, o be esimaed and X represens he vecor of explanaory variables. Therefore, he condiional densiy a ime is obained from he combined densiy of CDS and S : ;, 1 ;, 2 ; f y f y S f y S (0.6) which is equivalen o: 2 j1 f ( y S j, 1 ; ) P( S j 1; ) (0.7) Markov swiching models allows us o make inferences as o wha regime he CDS marke is in by generaing filered probabiliies which are calculaed recursively. The filered probabiliies are compued using informaion up o ime and as such are dependen on real-ime daa: Pr S k ; k 2 i1 f p jk i, 1 k 1 y ; (0.8) Noe ha he Markov swiching version of equaion (1.2) is compued using he exac same approach and defined as: CDS CDS (0.9) i i i S1 S1,1 1 S The only difference is ha equaion (1.5) for he densiy of he dependen variable now becomes: 1 f CDS S j, CDS, ; exp CDS 2 jcds 1 i, j j (0.10) 9

10 A forecas from hese Markov swiching models can be made as follows: ˆ ˆ pˆ 1 pˆ ˆ e CDS 1 ( 1 2 ) 1 pˆ ˆ ˆ 11 p22 2 (0.11) where 1 ˆ and ˆ 2 are he esimaed mean changes in CDS spreads for sae 1 and sae 2, respecively. In paricular, hey are given by aking he expecaion of he CDS change in equaions (1.3) and (1.9) for he Markov swiching srucural model and Markov swiching AR(1) model, respecively. Moreover, ˆ 1 and ˆ 2 are he filered probabiliies where S equals 1 and 2, respecively. Muliplying hese filered probabiliies by he ransiion probabiliy marix will give us an esimae of he probabiliy ha saes 1 and 2 will hold a ime + 1. In urn, muliplying hese probabiliies by he esimaed mean change in each sae will generae an expeced change in he CDS spread. 5. In-sample performance of he models Tables 2, 3 and 4 show he in-sample performances of he linear models, he Markov swiching srucural model and he Markov swiching AR(1), respecively. For each CDS index, we repor coefficien esimaes (and heir significance), -saisics (in parenheses) and ransiion probabiliies of he Markov swiching models. The majoriy of he explanaory variables are highly significan for each model, in boh regimes and for boh indices. The probabiliies of remaining in each regime are very high, hus implying persisence. Ineresingly, in he case of he non-financials itraxx index, we find ha he auoregressive erm is no significan in he high volailiy sae and akes a negaive sign. However, our sample period is clearly affeced by differen regimes of volailiy in he CDS marke. The oupus from he Markov swiching models sugges ha CDS spreads are posiively auocorrelaed in low volailiy periods. However, when volailiy is high, he auocorrelaion disappears. In he period we analysed, which includes one of he wors crisis in he financial markes, he laer finding is probably due o he fac ha credi invesors sold off heir CDS posiions eiher o reap profis (if any) or o avoid furher losses. 6. Ou-of-sample saisical performance of he models The analysis of he saisical performance of he forecasing models is based on he comparison beween he poin forecass generaed by each model and he acual values of he daily changes in CDS spreads. As 10

11 saed in Secion 2, we esimaed he models over hree differen sample periods. This allows us o analyse hree ses of daily poin forecass over hree ou-of-sample periods. In paricular, he hree ou-of-sample periods are (1) from January 1, 2007 o Sepember 15, 2010; (2) from January 1, 2008 o Sepember 15, 2010; (3) from Augus 1, 2008 o Sepember 15, In order o generae he daily forecass, each model is esimaed recursively. We employ hree main indicaors o evaluae he saisical performance of each model s forecass, namely he roo mean squared error (RMSE), he mean absolue error (MAE) and he mean correc predicion (MCP) of he direcion of CDS spread changes. These forecass are hen compared wih hose obained from he AR(1) model, which consiues our benchmark model. We choose he AR(1) as a benchmark model because i has been used by Bysröm (2006), who found ha i well describes he saisical feaures of itraxx CDS spreads. Subsequenly, we perform he modified Diebold and Mariano (1995) es (MDM, hereafer) for he RMSE and MAE indicaors and a raio es for he MCP indicaor. These wo saisical ess are used o es he null hypohesis ha he model under consideraion and he AR(1) have equal forecasing abiliy. 6.1 Descripion of he saisical ess We now describe he main characerisics of hese wo ess. As we are performing pairwise comparisons of models forecass, we have o define wo series of forecased changes in he itraxx index price. The firs one corresponds o he series of forecas changes generaed by our benchmark model (he AR(1) model) defined as ( ). The second one is he series of forecas changes generaed by model i, where i corresponds o he model under consideraion, which can be any of he remaining models we esimaed, namely he random walk, he srucural model, he Markov swiching srucural model, he Markov swiching AR(1). This second series is defined as ( ). The nex sep is o define, for each of he wo series of forecas changes, a loss funcion, namely ( ) and ( ) for he benchmark model and he ih model under consideraion, respecively. ( ) represens he forecas errors beween he benchmark model and he acual series of CDS spread changes. Similarly, ( ) represens he forecas errors beween he ih model under consideraion and he acual series of CDS spread changes. Finally, a loss differenial in period, defined as ( ) ( ), consiues he basis for our hypohesis esing. In paricular, we es he null hypohesis ( ) for he MDM es, defined as ( ), agains he alernaive hypohesis ( ) ha ( ). As we are performing one-sep ahead forecass, we use he es saisic suggesed by Harvey e al. (1997): 11

12 MDM i i d (0.12) i var d where and ( ) [ ] [ ( ) ]. represens he sample variance of he series, denoes he is ih auocovariance and h is he forecas horizon which is se equal o 1 in our case. As he value of ( ) degrees of freedom. ( ) has o be esimaed, he es saisic in (1.12) follows a -disribuion wih As highlighed earlier, we also use a raio es o analyse he saisical performance of he models in erms of he MCP indicaor. Again, he null hypohesis o be esed is ha he forecas errors from he benchmark model and he model under consideraion are idenical. The alernaive hypohesis is ha he given pair of models produces differen forecas errors. In order o perform he es, we calculae he following F-saisic: F n 1 n AR e 1 i 2 e 2 (0.13) If he null hypohesis is rue, (1.13) follows a sandard F-disribuion wih ( ) degrees of freedom. For clariy, i is worh menioning ha he MCP canno be calculaed for he random walk model. In his case, in order o be sill able o compue he F-saisic, we follow Konsaninidi e al. (2008) and assign a value of 50% for he MCP, based on he assumpion ha he possibiliy of having eiher a posiive or negaive forecas of CDS spread changes is equal o 50%. 6.2 Saisical predicabiliy: resuls Table 5 and Table 6 repor he ou-of-sample performance of he forecasing models for he nonfinancials and financials senior CDS indices, respecively. Boh ables repor he values obained for he RMSE, MAE and MCP, which are based on forecass produced by he random walk model (Panel A), he srucural model (Panel B), he AR(1) model (Panel C), he Markov swiching srucural model (Panel D) and he Markov swiching AR(1) model (Panel E). *, ** and *** represen rejecion of he null hypohesis in favour of he alernaive a he 10%, 5% and 1% significance levels, respecively. 12

13 For boh CDS indices, he ess clearly show ha, based on he RMSE and MAE merics, he random walk and he Markov swiching srucural model generae forecass which are saisically differen (a he 1% significance level) from he forecass generaed by our benchmark model, namely he AR(1) model. Ineresingly, he srucural model and he Markov swiching AR(1) produce forecass which are saisically equal o he AR(1) model. Thus, we can conclude ha hese wo specificaions are superior o boh he random walk and he Markov swiching srucural model. Based on hese merics and saisical ess, we find ha here is supporing evidence of a saisically predicable paern in he evoluion of he changes in spreads for boh he non-financials and financials senior CDS indices. 7. The economic performance of he models In he previous secion, he resuls showed ha here is some evidence of saisical predicabiliy in he itraxx CDS index spreads. For his reason, i is worh invesigaing his in more deph. In order o do ha, we examine he economic significance of he models performance by creaing rading sraegies based on poin forecass. 7.1 The rading rules In order o build rading sraegies based on itraxx index CDS spreads, we follow Bysröm (2006) and rea he CDS index spread as a corporae bond spread. We add he index spread o he risk-free ineres rae and use heir sum o price a hypoheical 5-year zero coupon corporae bond wih noional amoun N (arbirarily chosen). 6 We use he following rading rule: If ( ) ( ), hen a rader would go shor (long) a 5-year zero coupon bond; represens a rading rigger defined by he rader. The use of a rading rigger is inroduced in order o 6 We are aware ha itraxx indices are no raded his way in he real world. However, ours represens a simple and accurae way o quanify he magniude of profis ha can be made from rading he index. In he real world, a rader willing o buy (sell) he index would have o pay (receive) a quarerly fixed coupon in addiion o upfron paymens made a iniiaion and close of he rade (o reflec he change in price of he index). Furhermore, he would have o accoun for any accrued ineres beween he launch of he index and he rade dae. In order o compue upfron paymens, he price of he index a he rade dae has o be deermined. This is given by he par minus he presen value of he spread differences. Bloomberg provides a funcion, namely <CDSW>, which compues he index price for any level of spread and recovery rae assumpions. 13

14 reduce he impac of ransacion coss on he overall profiabiliy of he sraegies. In fac, he use of no (or low) riggers resuled in exremely negaive reurns in he similar sudy conduced by Bysröm (2006). This rading rule is based on he fac ha if he forecased change in he CDS spread is considerably higher (lower) han he curren spread, hen he CDS index spread is expeced o increase (decrease). The laer, in urn, would induce a conemporaneous decrease (increase) in he price of he zero coupon bond. Based on his predicion, a rader would sell (buy) he bond. Following Bysröm (2006), we assume ha all rades are made eiher a he bid or ask prices, in order o include ransacion coss when implemening he rading rule. Specifically, we buy a he ask price and sell a he bid price. We experimen he implemenaion of hree differen rading sraegies, which are based on he same rading rule. In paricular, he firs sraegy uses a rading rigger which equals 1 basis poin and a holding period of one day. The second sraegy explores a rading rigger of 2 basis poins and a holding period of one day. The hird sraegy does no use a rading rigger ( ) bu is characerised by a holding period of one week (5 days). The laer sraegy draws on he finding of Blanco e al. (2005) abou he average half-life of deviaions beween CDS spreads and credi spreads. They argue ha spreads rever o equilibrium in approximaely 6 days, on average. Even hough heir sudy is on individual credi obligors, hey compue he average half-life of deviaions across he pool of companies in heir daase. Our focus is on he itraxx CDS index, which is a pool of companies wih differen credi risk characerisics. Hence, he comparison beween our daa sample and heirs is appropriae. By implemening his sraegy, we hen capure poenial delays in he expeced change in CDS spreads. 7.2 Resuls on he profiabiliy of he rading sraegies In Table 7 we repor he annualised Sharpe raios generaed by he rading rules (described in he previous secion) for each sraegy over he hree ou-of-sample periods, namely January 2006 o Sepember 2010, January 2008 o Sepember 2010 and Augus 2008 o Sepember The number of rades and he reurns (expressed in percenages) of he sraegies are also repored. In paricular, resuls are shown for boh he non-financials and financials senior CDS indices for rading sraegies based on forecass produced by he srucural model (Panel A), he AR(1) model (Panel B), he Markov swiching srucural model (Panel C) and he Markov swiching AR(1) model (Panel D). In he case of he financials senior CDS index, we noice ha he Sharpe raios are negaive mos of he imes, excep for hree cases. However, for he non-financials itraxx index, we observe posiive Sharpe raios more frequenly. In paricular, he linear AR(1) model generaes posiive values over every ou-ofsample period for sraegies which require a rading rigger (of 1 or 2 basis poins) and a daily holding 14

15 period. In he laer case, holding posiions for one week would resul in highly negaive reurns and Sharpe raios. On he oher hand, a 1-week holding period would be beneficial for he srucural model as posiive reurns and Sharpe raios would be gained in 2 (ou of 3) ou-of-sample periods. The use of a high rading rigger (2 basis poins) also generaes posiive Sharpe raios for he Markov swiching AR(1) model in all ou-of-sample periods. The Markov swiching srucural model generaes negaive Sharpe raios in every case. Ineresingly, he main conclusion we can draw from hese resuls is ha a AR(1) model seems o be bes suied for higher frequency raders (wih a rading horizon of 1 day), whereas a srucural model seems more appropriae for raders wih a longer holding period (1 week). An argumen for his finding may relae o he fac ha he itraxx marke akes longer han a day o adjus o new informaion embedded in he srucural deerminans of CDS spreads. The fac ha posiive Sharpe raios are found in some insances is no surprising and in line wih our analysis in Secion 5, where we analysed he saisical performance of he models and found ha he random walk model generaes worse forecass han he AR(1), he srucural model and he Markov swiching AR(1) model. The rading sraegies which are based on he laer models are indeed he only ones for which we observe some evidence of profiabiliy. 8. Conclusion Previous sudies on he CDS marke have predominanly focused on deermining he economic facors ha influence CDS spreads. To our knowledge, none of hese sudies have examined wheher fuure CDS spreads are predicable using hese economic deerminans. This sudy aims o bridge ha gap in he lieraure. Our paper is novel as i is he firs paper o invesigae wheher i is possible o forecas CDS spreads using advanced economeric models. I is also he firs sudy o evaluae rading sraegies for CDS spreads using forecass from robus economeric models. We consider he mos liquid CDS marke in Europe, namely he itraxx CDS index and focus on he nonfinancials and financials senior itraxx Europe indices. We employ boh linear and non-linear forecasing models. In he former caegory we include he srucural model and he AR(1) model, whereas in he laer we consider he Markov swiching srucural model and he Markov swiching AR(1) model. Poin forecass based on each model are generaed and heir saisical and economic performance is assessed. Specifically, he saisical performance of he models is evaluaed via he use of saisical merics (RMSE, MAE and MCP), while heir economic performance is esed by implemening rading sraegies 15

16 based on itraxx Europe CDS spreads. We find ha he saisical analysis of he models is coheren wih heir rading resuls. In fac, he models which perform beer from a saisical viewpoin - he srucural model, he AR(1) model and he Markov swiching AR(1) model - are also he models ha generae posiive reurns and Sharpe raios in some insances. The rading sraegies based on hese models are beer suied o be implemened for he non-financials index, whereas hey do no seem o generae posiive profis for he financials senior index (excep in hree occasions). Overall, we find ha linear models ouperform Markov swiching models. The laer provide a good fi for itraxx index daa, bu should no be used for forecasing purposes. Furhermore, among he linear models, auoregressive models should be preferred by raders wih a shorer rading horizon (such as 1 day), whils a srucural model should be used by lower frequency raders (willing o hold heir posiions for a leas 5 days). Anoher ineresing finding relaes o he exisence of firs-order auocorrelaion in itraxx Europe spreads. In low-volailiy regimes, we find posiive auocorrelaion in CDS spreads, in line wih previous sudies which analysed he itraxx index. However, in high-volailiy saes, he auocorrelaion coefficien becomes insignifican. The laer finding may be explained by he jiery reacion of credi invesors who had been selling off heir CDS posiions while he financial crisis was sluggishly unfolding. In conclusion, our findings show some evidence of predicabiliy for he mos liquid CDS index in Europe. As a resul, he itraxx index canno be regarded as informaionally efficien in is weak form alogeher, and hence rading he index should be incenivised based on speculaive reasons. In oher words, rading he index could be profiable for an invesor who is eager o exploi marke inefficiencies. References Alexander, C., Kaeck, A., Regime dependen deerminans of credi defaul swap spreads. Journal of Banking and Finance 32, Benker, C., Explaining credi defaul swap premia. Journal of Fuures Markes 24, Bernd, A., Osrovnaya, A., Do equiy markes favour credi marke news over opions marke news? Working Paper, Carnegie Mellon Universiy. Black, F., Cox, J., Valuing corporae securiies: some effecs of bond indenure provisions. Journal of Finance 31, Blanco, F., Brennan, S., Marsh, I.W., An empirical analysis of he dynamic relaionship beween invesmen grade bonds and credi defaul swaps. Journal of Finance 60, Bysröm, H., CrediGrades and he itraxx CDS index marke. Financial Analyss Journal 62,

17 Campbell, J., Y., Taksler, G., B., Equiy volailiy and corporae bond yields. Journal of Finance 58, Cao, C., Yu, F., Zhong, Z., The informaion conen of opion-implied volailiy for credi defaul swap valuaion. Journal of Financial Markes 13, Collin-Dufresne, P., Goldsein, R.S., Marin, S.J., The Deerminans of Credi Spread Changes. Journal of Finance 56, Cremers, M., Driessen, J., Maenhou, P., Weinbaum, D., Individual sock-opion prices and credi spreads. Journal of Banking and Finance 32, Delianedis, G., Geske, R., The componens of corporae credi spreads: defaul, recovery, ax, jumps, liquidiy, and marke facors. Working Paper 22-01, Anderson School, UCLA. Dickey, D.A., Fuller, W.A., Likelihood raio saisics for auoregressive ime series wih a uni roo. Economerica 49, Diebold, F.X., Mariano, R., Comparing predicive accuracy. Journal of Business and Economic Saisics 13, Driessen, J., Is defaul even risk priced in corporae bonds? Review of Financial Sudies 18, Elon, E.J., Gruber, M.J., Agrawal, D., Mann, C., Explaining he rae spread on corporae bonds. Journal of Finance 56, Eom, Y., Helwege, J., Huang, J., Srucural models of corporae bond pricing: an empirical analysis. Review of Financial Sudies 17, Ericsson, J., Jacobs, K., Oviedo, R., The deerminans of credi defaul swap premia. Journal of Financial and Quaniaive Analysis 44, Fore, S., Peña, J.I., Credi spreads: An empirical analysis on he informaional conen of socks, bonds, and CDS. Journal of Banking and Finance 33, Hamilon, J., Time series analysis. Princeon, NJ: Princess Universiy Press. Hamilon, J.D., Kim, D.H., A re-examinaion of he predicabiliy of economic aciviy using he yield spread. NBER Working Paper Series, No Harvey, D.I., Leybourne, S.J., Newbold, P., Tesing he equaliy of predicion mean squared errors. Inernaional Journal of Forecasing 13, Houweling, P., Vors, T., Pricing defaul swaps: empirical evidence. Journal of Inernaional Money and Finance 24, Huang, J.Z., Huang, M., How much of corporae-reasury yield spread is due o credi risk?: a new calibraion approach. Working Paper. 17

18 Jones, E.P., Mason, S.P., Rosenfeld, E., Coningen claims analysis of corporae capial srucures: an empirical invesigaion. Journal of Finance 39, Konsaninidi, E., Skiadopolous, G., Tzagkaraki, E., Can he evoluion of implied volailiy be forecased? Evidence from European and US implied volailiy indices. Journal of Banking and Finance 33, Leland, H., Risky deb, bond covenans and opimal capial srucure. Journal of Finance 49, Leland, H., Tof, K.B., Opimal capial srucure, endogenous bankrupcy, and he erm srucure of credi spreads. Journal of Finance 51, Longsaff, F.A., Mihal, S., Neis, E., The credi-defaul swap marke: is credi proecion priced correcly? Working Paper, UCLA. Longsaff, F.A., Mihal, S., Neis, E., Corporae yield spreads: defaul risk or liquidiy? New evidence from he credi defaul swap marke. Journal of Finance 60, Longsaff, F.A., Schwarz E.S., A simple approach o valuing risky and floaing rae deb. Journal of Finance 50, Meron, R., On he pricing of corporae deb: he risk srucure of ineres raes. Journal of Finance 29, Norden, L., Weber, M., The co-movemen of credi defaul swap, bond and sock markes: an empirical analysis. European Financial Managemen 15, Zhang, B.Y., Zhou, H., Zhu, H., Explaining credi defaul swap spreads wih he equiy volailiy and jump risks of individual firms. Review of Financial Sudies 22, Zhu, H., An empirical comparison of credi spreads beween he bond marke and he credi defaul swap marke. Journal of Financial Services Research 29,

19 Table 1 Summary saisics This able repors he summary saisics for he variables used in our analysis over he whole sample period. The CDS spreads for financials senior ( ) and non-financials ( ) represen our dependen variables. The independen variables are he equally weighed porfolio of socks comprising he same members of he CDS indices ( and, respecively for he financials senior and non-financials sub-indices), he level of he risk-free ineres rae ( ), he slope of he yield curve ( ), he VSoxx implied volailiy index ( ). Mean Sd dev Skewness Kurosis Bera-Jarque ADF Panel A: Summary saisics for variables levels *** 0.995*** *** 0.995*** *** 0.997*** *** 0.995*** *** 0.997*** *** 0.999*** *** 0.982*** Panel B: Summary saisics for variables changes *** 0.127*** *** *** *** *** 0.052* *** *** *** *** *** *** 0.094*** *** *** *** *, **, *** denoe rejecion of he null hypohesis a he 10%, 5%, 1%, respecively. 19

20 Table 2 - Parameer esimaes for Srucural Model and AR(1) Esimaed parameers, over he whole sample, for he OLS regressions of changes in European itraxx CDS indices on lagged heoreical deerminans of CDS spreads (as defined in equaion 1.1) and on lagged CDS spreads (as defined in equaion 1.2) are shown in Panel A and B, respecively. Sandard - saisics are given wihin brackes. Δ Δ Δ( ) Panel A: Srucural Model Non-financials ** (0.472) (-2.247) Financials senior *** (0.532) (3.966) Panel B: AR(1) Non-financials (0.340) (-1.423) Financials senior ** (-2.041) (-1.165) (-0.428) *** (-3.433) ** (-2.265) (0.012) (0.266) *** (-4.717) *** (0.550) (4.361) *, **, *** indicae rejecion of he null hypohesis a he 10%, 5% and 1%, respecively. 20

21 Table 3 Parameer esimaes for Markov Swiching Srucural Model Esimaed parameers, over he whole sample, for he Markov swiching regressions of changes in European itraxx CDS indices on lagged heoreical deerminans of CDS spreads (as defined in equaion 1.3). Sandard -saisics are given wihin parenheses. Non-financials Regime (1.426) Regime (0.341) Financials senior Regime (-1.506) Regime (0.316) Δ Δ Δ( ) 0.078*** (3.734) (-1.517) *** (-5.816) *** (-3.412) *** (-5.579) ** (-2.313) (1.562) (-0.348) 0.269*** (5.182) ** (-2.313) (-1.285) (-0.118) 0.081*** *** *** ** (2.923) ( ) (-5.155) (-2.542) *, **, *** indicae rejecion of he null hypohesis a he 10%, 5% and 1%, respecively *** (10.749) 0.654*** (4.781) 0.050*** (2.872) 0.256*** (3.081) Table 4 Parameer esimaes for Markov Swiching AR(1) Esimaed parameers, over he whole sample, for he Markov swiching regressions of changes in European itraxx CDS indices on lagged CDS spreads (as defined in equaion 1.9). Sandard -saisics are given wihin brackes. Non-financials Regime (0.204) Regime (-0.423) Financials senior Regime (0.432) Regime (-0.231) Δ *** (5.117) (1.000) 0.258*** (2.830) 0.162*** (4.211) *, **, *** indicae rejecion of he null hypohesis a he 10%, 5% and 1%, respecively

22 Table 5 Ou-of-sample performance of he forecasing models for he non-financials CDS index This able presens he ou-of-sample performance of each model for he non-financials CDS index. We repor he roo mean squared error (RMSE), he mean absolue error (MAE) and he mean correc predicion (MCP) of he sign of he CDS spread change. We generaed forecass by implemening he random walk model (Panel A), he srucural model (Panel B), he AR(1) model (Panel C), he Markov swiching srucural model (Panel D) and he Markov swiching AR(1) model (Panel E). In order o es he null hypohesis ha he AR(1) model and he model under consideraion generae equal forecass, we perform he Modified Diebold-Mariano es (for RMSE and MAE) and he raio es (for MCP). We esimaed he models recursively for hree differen sample periods: January 2007 o Sepember 15, 2010; January 2008 o Sepember 15, 2010 and Augus 2008 o Sepember 15, Jan 2007 Sep 2010 Jan 2008 Sep 2010 Aug 2008 Sep 2010 Non-financials: Panel A: Random Walk RMSE 8.24*** 9.49*** 9.18*** MAE 4.17*** 5.14*** 4.88*** Panel B: Srucural Model RMSE 5.74* 6.59* 6.49* MAE 2.95* 3.60* 3.43* MCP (%) Panel C: AR(1) RMSE MAE MCP (%) Panel D: Markov Swiching Srucural Model RMSE 5.85*** 6.63*** 6.52*** MAE 3.06*** 3.68*** 3.50*** MCP (%) Panel E: Markov Swiching AR(1) RMSE MAE MCP (%) *, **, *** denoe rejecion of he null hypohesis a he 10%, 5%, 1%, respecively. 22

23 Table 6 Ou-of-sample performance of he forecasing models for he financials senior CDS index This able presens he ou-of-sample performance of each model for he financials senior CDS index. We repor he roo mean squared error (RMSE), he mean absolue error (MAE) and he mean correc predicion (MCP) of he sign of he CDS spread change. We generaed forecass by implemening he random walk model (Panel A), he srucural model (Panel B), he AR(1) model (Panel C), he Markov swiching srucural model (Panel D) and he Markov swiching AR(1) model (Panel E). In order o es he null hypohesis ha he AR(1) model and he model under consideraion generae equal forecass, we perform he Modified Diebold-Mariano es (for RMSE and MAE) and he raio es (for MCP). We esimaed he models recursively for hree differen sample periods: January 2007 o Sepember 15, 2010; January 2008 o Sepember 15, 2010 and Augus 2008 o Sepember 15, Jan 2007 Sep 2010 Jan 2008 Sep 2010 Aug 2008 Sep 2010 Financials senior: Panel A: Random Walk RMSE 7.50*** 8.52*** 8.33*** MAE 4.72*** 5.82*** 5.66*** Panel B: Srucural Model RMSE MAE MCP (%) Panel C: AR(1) RMSE MAE MCP (%) Panel D: Markov Swiching Srucural Model RMSE 6.22*** 6.67*** 6.63 MAE 3.75*** 4.51*** 4.38 MCP (%) Panel E: Markov Swiching AR(1) RMSE MAE MCP (%) *, **, *** denoe rejecion of he null hypohesis a he 10%, 5%, 1%, respecively. Table 7 Profiabiliy of rading sraegies based on he models forecass 23

24 We implemen rading sraegies on he non-financials and financials senior CDS indices, which are based on poin forecass obained from he srucural model (Panel A), he AR(1) model (Panel B), he Markov swiching srucural model (Panel C) and he Markov swiching AR(1) model (Panel D). For each sraegy, we repor he number of rades, he reurns over he ou-of-sample period and he annualised Sharpe raio. Threshold Jan 2007 Sep 2010 Jan 2008 Sep 2010 Aug 2008 Sep 2010 Trades Reurn Reurn Reurn Sharpe Trades Sharpe Trades (%) (%) (%) Sharpe Non-financials: Panel A: Srucural Model +/- 1bp /- 2bp Hold 1week Panel B: AR(1) +/- 1bp /- 2bp Hold 1week Panel C: Markov Swiching Srucural Model +/- 1bp /- 2bp Hold 1week Panel D: Markov Swiching AR(1) +/- 1bp /- 2bp Hold 1week Financials senior: Panel A: Srucural Model +/- 1bp /- 2bp Hold 1week Panel B: AR(1) +/- 1bp /- 2bp Hold 1week Panel C: Markov Swiching Srucural Model +/- 1bp /- 2bp Hold 1week Panel D: Markov Swiching AR(1) +/- 1bp /- 2bp Hold 1week