COUNTRY RISK RATINGS: STATISTICAL AND COMBINATORIAL NON- RECURSIVE MODELS

Transcription

1 R U T C O R R E S E A R C H R E P O R T COUNTRY RISK RATINGS: STATISTICAL AND COMBINATORIAL NON- RECURSIVE MODELS P.L. HAMMER a A. Koga b M.A. Lejeue c RRR , MARCH 2004 RUTCOR Rutgers Ceter for Operatios Research Rutgers Uiversity 640 Bartholomew Road Piscataway, New Jersey Telephoe: Telefax: rrr@rutcor.rutgers.edu a hammer@rutcor.rutgers.edu, Tel.: ; Fax: b koga@rutcor.rutgers.edu c mlejeue@adromeda.rutgers.edu a,b,c RUTCOR - Rutgers Uiversity Ceter for Operatios Research, Piscataway, NJ, USA a,b Rutgers Busiess School, Rutgers Uiversity, Newark-New Bruswick, NJ, USA

2 RUTCOR RESEARCH REPORT RRR , MARCH 2004 COUNTRY RISK RATINGS: STATISTICAL AND COMBINATORIAL NON-RECURSIVE MODELS P.L. Hammer A. Koga M.A. Lejeue Abstract. The cetral objective of this paper is to develop trasparet, cosistet, selfcotaied, ad stable coutry risk ratig systems, closely approximatig the coutry risk ratigs provided by a major ratig agecy (Stadard & Poor). We propose two models that achieve the stated objectives, the first oe utilizig the classical ecoometric techique of multiple liear regressio, ad the secod oe usig the combiatorial-logical techique of Logical Aalysis of Data. The proposed models use ecoomic-fiacial ad political variables, ad are orecursive (i.e., they do ot rely o the previous years ratigs). The accuracy of the proposed models predictios, measured by their correlatio coefficiets with Stadard ad Poor s ratigs, ad cofirmed by k-foldig cross-validatio, exceeds 95%. The stability of the costructed o-recursive models is show i three ways: by the correlatio of the predictios with those of other agecies (Moody s ad The Istitutioal Ivestor), by predictig 999 ratigs usig the o-recursive models derived from the 998 dataset applied to the 999 data, ad by successfully predictig the ratigs of several previously o-rated coutries. The cofidece i the results ad i the validity of both models is strogly reiforced by the fact that the traditioal liear regressio model ad the qualitatively differet combiatorial-logical model produce almost idetical results. Ackowledgemets: The authors express the appreciatio to Dr. Sori Alexe for his ivaluable help i the executio of computatioal experimets with LAD.

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4 Coutry Risk, Coutry Risk Ratigs ad Objectives of the Paper. Coutry risk, coutry risk ratigs ad their importace The globalizatio of the world ecoomies, ad i particular the iteratioalizatio of fiacial markets i the last decades, have dramatically expaded ad diversified ivestmet possibilities, leadig to umerous ew opportuities, accompaied by ew risks. Cosequetly, there has bee growig iterest i obtaiig reliable estimates of the risk of ivestig i differet coutries. These cocers have led to the developmet of the cocept of coutry risk, ad eve to the regular publicatio of coutry risk ratigs by various agecies. The importace of ratigs has bee magified by the recommedatios addressed i the Basel Capital Accord (200), that pipoits the role of agecies ratigs for the assessmet of credit risk. Differet defiitios have bee proposed for coutry risk, i.e. for the risk that a coutry defaults o its obligatios. The existig literature o the topic recogizes both fiacial/ecoomic ad political compoets of coutry risk. Accordig to the degree to which some of these compoets are emphasized, coutry risk is viewed either from the fiacial/ecoomic perspective oly, or from the combied fiacial/ecoomic ad political perspectives. There are two basic approaches to the iterpretatio of the reasos for defaultig. The debtservice capacity approach focuses o the deterioratio of solvecy of a coutry, which prevets it from fulfillig its commitmets. For istace, Bourke ad Shamugam (990) defie coutry risk as the risk that a coutry will be uable to service its exteral debt due to a iability to geerate sufficiet foreig exchage. Withi this framework, coutry risk is viewed as a fuctio of various fiacial ad ecoomic coutry parameters. The cost-beefit approach views a default o commitmets or a reschedulig of debt as a deliberate choice of the coutry, which may prefer this alterative over repaymet, i spite of its possible log-term egative effects (e.g. the coutry s exclusio from certai capital markets (Reihart,2002), reputatio damage). Sice the deliberate decisio to default results from a political process, political coutry parameters are icluded i this type of coutry risk modelig, alog with the fiacial ad ecoomic oes. This approach is strogly recommeded by Brewer ad Rivoli (990, 997) as well as Citro ad Neckelburg (987), who emphasize the impact of the political stability idicator o coutry risk ratigs. I respose to the icreased demad for the evaluatio of creditworthiess, several agecies such as Moody s, Stadard & Poor, Fitch, The Istitutioal Ivestor, Euromoey, Du & Bradstreet, etc. have developed expertise i estimatig coutry risk. These estimates are preseted i the form of ratigs, or scores, ad are geerally viewed as idicative of possible future default. Haque et al. (996) defie coutry credit risk ratigs compiled by commercial sources as a attempt to estimate coutry-specific risks, particularly the probability that a coutry will default o its debt-servicig obligatios. Sovereig ratigs ca be viewed as the probability that a borrowig coutry will fail to pay back. Coutry (or sovereig) risk ratigs impact coutries i a umber of ways. The primary sigificace of ratigs is due to their ifluece o the iterest rates at which coutries ca obtai credit o the iteratioal fiacial markets: the higher the ratigs (i.e., the lower the risk of

5 RRR PAGE default) the lower the iterest rate. Followig its sovereig ratig dowgrade, Japa s borrowig became more expesive as iterest rates have icreased, reflectig the higher chace of default, which deteriorates eve more the situatio of the heavily idebted Japaese govermet ad ecoomy. Secod, sovereig ratigs also ifluece credit ratigs of atioal baks ad compaies, ad affect their attractiveess to foreig ivestors. Ferri et al. (200) call sovereig ratigs the pivot of all other coutry s ratigs. Similarly, Erb et al. (995a) uderlie that raters have historically show a reluctace to give a compay a higher credit ratig tha that of the sovereig where the compay operates. For example, after Moody s dowgraded Japa i November 998 (from Aaa to Aa), all other Aaa Japa issuers have bee dowgraded (Jütter ad McCarthy, 2000). This led sovereig ratigs to be amed sovereig credit risk ceiligs. Third, istitutioal ivestors are sometimes cotractually restricted o the degree of risk they ca assume, implyig i particular that they caot ivest i debt rated below a prescribed level. Ferri et al. (200) refie this aalysis, poitig out the cotrast betwee the ratigs of baks operatig i high- ad low-icome coutries, ad show that ratigs of baks operatig i lowicome coutries are sigificatly affected by variatios i sovereig ratigs, while the ratigs of baks operatig i high-icome coutries do ot seem to deped sigificatly o coutry ratigs. Similarly, Kamisky ad Schmukler (2002) as well as Larrai et al. (997) ote that sovereig ratigs are crucial for developig ecoomies, which have a very high sesitivity to ratig aoucemets..2 Critiques of preset ratig systems The purpose of ratigs is that of compressig a variety of iformatio about a coutry ito a sigle parameter which ca be easily uderstood, ad therefore coveietly used i a decisio makig process ivolvig comparisos betwee differet coutries. Cosequetly, ratigs provide aggregatios of diverse idicators ito a sigle metric ad ca be viewed as a kid of commesuratio (Kuczik, 2000). The iterpretatio of ratigs is complicated by the heterogeeity of idicators (political stability, iflatio, etc.) which may have bee used i derivig them. Comprehesibility: The coutry risk ratigs published by differet agecies appear as outputs of black boxes, the real cotet ad meaig of which are uexplaied ad hard to uderstad, sice ratig agecies specify either the factors which are take ito cosideratio i determiig their ratigs, or the rules of compressio of multiple factors ito a sigle ratig. This raised the discotet of Japa s Prime Miister, Juichiro Koizumi, who was railed at beig rated i the same eighborhood as Africa coutries to which Japa is providig assistace. Officials of Japa s Miistry of Fiace added that big ratig agecies are makig ufair qualitative judgmets, while Moody s deied ad claimed that the motives for the dowgrade lie i the icreased debt load of Japa. I view of such cotroversy, ucoverig both the factors which are take ito accout by these black boxes, ad the mechaisms of derivig ratigs, are essetial for ascertaiig the cosistecy of a coutry ratig system. Ukow factors: It is geerally assumed that ratigs are obtaied by aggregatig ecoomic/fiacial ad/or political variables. Clearly, the mai objective of ay coutry risk ratig system is to represet the creditworthiess of coutries, i.e., their capacity to pay off loas.

6 PAGE 2 RRR It is ot clear however which oes of the may possible factors do actually ifluece the payback capacity of a coutry. This questio is subject to differet aalyses. Haque et al. (998) claim that it is sufficiet to restrict the scope of aalysis to ecoomic/fiacial factors oly, while others (Brewer ad Rivoli,990) claim that both ecoomic/fiacial ad political factors impact coutry risk ratigs. Ratig failures: Some recet failures have challeged the trustworthiess of coutry risk ratigs (Reihart, 2002, Levich et al., 2002). Criticisms directed towards ratigs istitutios have bee especially itese after the Tequila ad the Asia crises. Ideed, the tequila crisis i Mexico (994-95) had ot bee preceded by a ratig dowgrade, implyig that either the crisis was ot predicted, or that its sigificace was overlooked. Similar observatios apply to the Asia crisis (997-99): Ftich admitted that it ad its larger rivals Stadard s & Poor ad Moody s Ivestors Services of the US had largely failed to predict the recet turmoil i Asia. O the other had, ratig agecies have bee more isightful i aticipatig other crises, e.g. i Russia (998), Brazil (998) ad Argetia (200). Regioal bias: Diverse explaatios have bee provided for the failure of ratig agecies to sigal crisis emergecies i various coutries. There are claims that certai ratig agecies favor certai regios. For istace, Haque et al. (997) ote that Euromoey usually gives higher ratigs to Asia ad Europea coutries tha to Lati or Caribbea coutries, while the Istitutioal Ivestor is more geerous to Asia ad Europea coutries tha to Africa oes. Latecy: Aother criticism lies i the time take by the ratig agecies to react to ew facts (e.g., accordig to The Ecoomist, ratig agecies may have bee too slow to dowgrade Japa. Markets have already moved ahead of them ). Overreactios: The IMF criticizes ratig agecies claimig that they reacted i paic durig the Asia crisis. After they had missed to predict the Asia crisis, they reacted by harshly dowgradig coutries such as Thailad or South Korea, thus acceleratig the flight of capital. I this ad other situatios, ratig agecies gave the impressio of overreactig (Figure ) istead of beig a stabilizig force. Figure : Precrisis ad postcrisis ratig of coutries The Istitutioal Ivestor's ratigs Precrisis Postcrisis Thailad Korea Idoesia Euromoey's ratigs Precrisis Postcrisis Thailad Korea Idoesia It appears that the objectivity ad reliability of coutry risk ratigs is questioable, maily because of huma itervetio ad coflictig goals ad/or iterests.

7 RRR PAGE 3 Negative impact of ratig chages: It is reported that the hesitatio or reluctace of raters to dowgrade a coutry stems from the fact that a dowgrade aoucemet ca precipitate a coutry ito crisis. Durig the Asia crisis, the ratig agecies arouse the discotet of the Malaysia Prime Miister, Dr Mahathir bi Mohamad, who codemed them ad charged them with rederig the crisis eve more acute. The ratig agecies, whe we have a eed to borrow moey, they immediately dowgraded us so that it will cost us 5% to borrow moey. They stop us completely from borrowig moey (999). Alog the same lie, Reise ad Vo Maltza (999) claim that such a sharp dowgrade impeded commercial baks to issue letters of credit, forced ivestors to offload Asia assets to maitai portfolios i ivestmet-grade securities. They argue that ratig agecies laggig behid rather tha aticipatig the state of fiacial markets reiforce positive expectatios ad capital iflows whe they upgrade coutries ad itesify outflows of capital ad crisis whe they dowgrade. Coflicts of iterest: A eve more poited criticism is that raters, havig started chargig fees to rated coutries, ca be suspected of reluctace to dowgrade them, because of the possibility of jeopardizig their icome sources. This is claimed, for example, by Tom McGuire, a executive vice-presidet of Moody s, who states that the pressure from fee-payig issuers for higher ratigs must always be i a delicate balace with the agecies eed to retai credibility amog ivestors 2. The ecessity to please the payers of the ratigs, ivestors as well as issuers, lead to what Robert Grossma, the chief credit officer at the ratig agecy Fitch, calls a tedecy we do with ivestors ratig committees, outlooks, meetigs, the the press release, all to softe the blow of the ratig chage 3. Studyig the ratig trasitios, Altma ad Sauders (998) otice that a dowgrade i the ratig of a coutry is regularly followed by further dowward adjustmets. The explaatio give by Altma ad Sauders is that agecies gradually dowgrade the ratig of a coutry, sice they do ot wat to hurt the coutry, which is also their cliet. Kuczik (200) ote that the IMF (999) fears the dager that issuers ad itermediaries could be ecouraged to egage i ratig shoppig a process i which the issuer searches for the least expesive ad/or least demadig ratig. The problems described above will become more acute as the role of ratigs icreases. Ideed, the Basel Accord will itesify the pressure o coutries to obtai high ratigs, potetially leadig to a switch from ratig shoppig to ratig fraud. For istace, Pakista has bee forced to pay back $55 millio credits to the IMF because of budget falsificatio, the blame beig put o the former Prime Miister Nawaz Sharif, accused of havig falsified the budget deficit. Similarly, Ukraie has bee prove to have reported misleadig data o its reserves i foreig exchages, attemptig to obtai IMF credits. Kuczik (200) says that it is oly a questio of time whe firms will specialize i ratig advisig for sovereigs. This article appeared i the February 9, 999 issue Executive Itelligece Review. Iterview: Datuk Seri Dr. Mahathir bi Mohamad Malaysia Prime Miister: `We had to decide thigs for ourselves'. O Jauary 22, 999, Gail G. Billigto of EIR's Asia Desk ad Dio de Paoli of the Schiller Istitute were give the opportuity to iterview Datuk Seri Dr. Mahathir bi Mohamad, Prime Miister of Malaysia. 2 The Ecoomist, July 5, 995, 62 3 Euromoey, Jauary 2002, 38, Ivestors tur cool o the ratig game 3

8 PAGE 4 RRR Ca yield spreads replace coutry risk ratigs? To mitigate the problems described above, it is sometimes advocated to use yield spreads istead of sovereig ratigs as a proxy for default risk, sice large yield spreads correspod to high risk. Yield spreads refer to the differece betwee sovereig yields ad US treasury bill yields of the same maturity. Market yields are less stable, fluctuatig daily ad sometimes substatially. Figure 2: Precrisis ad postcrisis yield spreads o a aggregate basis Basis poits Jue 997 Jue 998 Emergig ocrisis coutries Crisis coutries It appears that the use of market spreads rather tha coutry ratigs is ot more efficiet. Ideed, for Asia coutries, spreads have substatially wideed after the crisis. As exhibited by Figure 2, spreads were roughly of the same order of magitude before the crisis. While spreads of o-crisis coutries have wideed by less tha 00% after the crisis, spreads of crisis coutries have more tha tripled. Cosequetly, we coclude that spreads provide about the same iformatio as sovereig ratigs do, ad are much more volatile. This coclusio ca be exteded to the Brazilia ad the Russia crises. This discussio implies that yield spreads are characterized by a lack of predictive power ad caot be used to obtai a reliable early warig of coutry isolvecy. This latter coclusio is cofirmed by Mathieso ad Schiasi (999)..4 Recursive versus o-recursive models The recet literature o coutry risk ratigs cotais several studies (Cator ad Packer, 996, Haque et al., 998, Mofort ad Mulder, 2000) which use multiple regressio. The set of idepedet variables used by Haque et al. (998) as well as Mofort ad Mulder (2000) icludes the lagged sovereig ratigs of Stadard & Poor, or Moody s, or The Istitutioal Ivestor. The correlatio levels betwee the ratigs of various agecies ad the predicted values or ratigs obtaied usig multiple regressio models refereced above are remarkably high. To illustrate the actual meaig ad importace of these results, we shall examie the approach take by Haque et al. (998). That paper uses as its eight idepedet variables seve macro-ecoomic variables 4, ad the lagged ratig, i.e. it icludes The Istitutioal Ivestor ratigs both at times t ad t-, the former as a depedet variable, ad the latter as a idepedet oe. It is importat to ote that coutry risk ratigs are very stable, as show by the trasitio probabilities of the ratigs published by Stadard & Poor (999) (see Table 9 i Appedix) ad Nickell et al. (2000). 4 T-bill rate, GDP growth rate, iflatio rate, exports growth rate, ratio curret accout to GDP, the ratio of exteral debt to GDP, the ratio of reserves to imports.

9 RRR PAGE 5 The 98% correlatio level 5 betwee The Istitutioal Ivestor ratigs published respectively i September 997 ad September 998 cofirms the stability property of sovereig ratigs. I light of this fact, the excellet correlatio levels achieved by utilizig lagged ratigs amog the idepedet variables ca be attributed to a certai possibly large extet to this stability, ad may ot ecessarily give idicatios about the predictive power of the ecoomic ad political variables used as predictors. Although Cator ad Packer (996) do ot iclude the lagged ratigs i their set of predictors, they create a dummy variable, which is determied by the past ratigs issued by Stadard ad Poor (Claesses ad Embrechts, 2002). This dummy variable is defied to be equal to if a coutry has ever bee rated D or SD by Stadard & Poor sice 970, ad equal to 0 otherwise. Eve though their regressio R-square is above 90%, their results are criticized by Claesses ad Embrechts (2002) ad Jütter ad McCarthy (2000). Claesses ad Embrechts metio that the dates of the explaatory variables are ot cosistet, e.g. the values of some variables are measured i 994 or 995, while that of others are averages for the period or O the other had, Jütter ad McCarthy evaluated the regressio model of Cator ad Packer for some other years, cocludig that for 998, it loses its predictive power. A recet paper of Hu et al. (2002) develops a model usig ordered probit to estimate coutry ratigs. Their model has a 83% correlatio level ad relies o ecoomic variables ad ratig history of coutries. A commo feature of the ecoometric models above is the direct or idirect iclusio of iformatio derived from past Stadard & Poor ratigs (lagged ratigs, ratig history) amog their idepedet variables. A major drawback of such ratig models is the impossibility of applyig them to ot-yet-rated coutries..5 Objectives ad mai results Our discussio i the precedig subsectios idicates a eed for makig coutry risk ratigs more (i) trasparet ad (ii) cosistet. A third criterio we would like to impose o a ideal coutry risk ratig system is that of (iii) self-cotaimet, i.e. its o-reliace o ay other past or preset coutry risk ratigs. Clearly, this requiremet precludes the use of lagged ratigs as idepedet variables. It is importat to ote that this approach is i marked cotrast with that of the curret literature (discussed i the previous subsectio), which does rely i oe form or aother o lagged ratigs. Fially, a fourth requiremet imposed o the model is its (iv) stability, i.e. extesibility both to subsequet years ad to previously o-rated coutries. The wide acceptace of several of the major ratig systems idicates that, while they may ot be perfect, they provide the curretly best kow evaluatio of coutry risk. It is therefore reasoable to base the desig of ay ew ratig system o oe of the existig oes. The cetral objective of this paper is to develop a trasparet, cosistet, self-cotaied, ad stable system, closely approximatig the coutry risk ratigs provided by a major ratig agecy. We have selected the Stadard & Poor coutry risk ratig system as a bechmark for the desired system. It is to be expected that, o the oe had, i most cases the ratigs of the ew system should closely resemble those of Stadard ad Poor, ad o the other had, i the (hopefully few) cases where the two ratigs differ, the objective reasos, which determie the ratigs of the proposed model, should be justified by subsequet developmets coutries are cosidered. 5

10 PAGE 6 RRR I lie with the existig literature, we use i the first part of this paper the techique of multiple liear regressio to achieve our objectives. We shall call the proposed system a orecursive multiple regressio model of the S&P coutry ratig system. I the secod part of the paper, we reaalyze the same problem, usig this time a combiatorial-logical techique, i order to derive a set of logical ratig scores of coutries, ad show that they tur out to be surprisigly similar to both the S&P ratigs ad the o-recursive regressio scores. The fact that the traditioal liear regressio model ad the qualitatively differet combiatorial-logical model produce almost idetical results strogly reiforces the cofidece i the results ad i the validity of both models. I additio to the mai result, we also demostrate that the ew ratig systems ca be successfully applied to the ratig of yet o-rated coutries, are temporally stable, are cosistet with the ratigs of other agecies (Moody ad The Istitutioal Ivestor)..6 Paper structure The paper is structured as follows. Sectio describes the data cosidered ad selected for use i this paper. We provide a thorough literature review (see refereces i Tables 3 ad 4) ad describe the selectio of explaatory variables. I Sectio 2, we use the 998 Stadard & Poor coutry risk ratigs to develop a o-recursive multiple regressio model for the ratigs cosidered as the depedet variable, regressed o a set of ecoomic ad political variables (cosidered as the predictor variables). To evaluate the accuracy of liear regressio predictios, we use the k-foldig cross-validatio techique. We show that the model correlates well ot oly with the ratigs of Stadard & Poor (95%), but also with those of Moody s (94.6%) ad The Istitutioal Ivestor (93.6%). We also evaluate the stability of the costructed o-recursive regressio model i two ways. First, we show the temporal stability of the o-recursive multiple regressio model derived from the 998 dataset by applyig it to the 999 data. Secod, we show that the proposed model ca successfully predict the ratigs of several previously o-rated coutries. I Sectio 3, we aalyze the same problem by usig a combiatorial-logical techique, the logical aalysis of data (LAD) (Hammer, 986, Crama et al., 988, Boros et al., 2000), for developig a model that evaluates the creditworthiess of coutries. Based exclusively o the S&P orderig of coutries by their riskiess, i.e., without makig ay assumptios about the magitude of differeces betwee cosecutive ratigs, we costruct a discrimiat fuctio, which provides a approximate measure of relative riskiess of a arbitrary coutry i compared with aother coutry j. The discrimiat is expressed as a highly oliear polyomial i biary variables, which idicate whether the values of relevat ecoomic ad political attributes of oe coutry do or do ot exceed the values of the correspodig attributes of aother coutry by certai thresholds. The discrimiat does ot ivolve ay iformatio about past ratigs. Further, it is show how to calculate a umerical measure of coutry risk (the logical ratig score ) i such a way that the differeces betwee the logical ratig scores of all pairs of coutries provide the best L 2 -approximatio of the correspodig discrimiat values. Subsectio 4. itroduces the cocept of a pseudo-observatio P ij, associated to a pair of coutries i, j, which provides a comparative descriptio of i ad j i the form of a multidimesioal vector, whose compoets are the differeces of the values of those ecoomic ad

11 RRR PAGE 7 political attributes of coutries i ad j which were idetified i the first part of the study. A additioal compoet of a pseudo-observatio is a idicator which takes the value (-, 0) if the coutry i i the pseudo-observatio has a higher (lower, idetical) ratig tha the coutry j. The fudametal idea of this study is that a ratig system ca be essetially recostructed from the kowledge of the relative orderigs of all pairs of rated coutries. I other words, all that matters i a ratig is the qualitative order relatio betwee coutries, but ot a quatitative measure of the magitude of differeces betwee ratigs. The study focuses o derivig a model of the order relatio betwee coutries usig the LAD methodology which is briefly described i Subsectio 4.2. No-statistical ad highly oliear, this methodology is ot restricted by the satisfactio of the assumptios uderlyig ecoometric techiques. Based o the patters of the LAD model, a discrimiat, (P ij ), called relative preferece, is computed for each pseudo-observatio, P ij, The value of (P ij ) idicates whether coutry i should be rated higher or lower tha coutry j. Relyig o the assumptio that the (P ij ) values provide good approximatios of the differeces of the ratigs, the relative prefereces are used to derive a approximatio of the ratigs called logical ratig scores of coutries; these are calculated usig multiple liear regressio, as described i Subsectio 4.3. More precisely, deotig by I the set of coutries, the ratig of a coutry k is the regressio coefficiet, β, i the regressio model ( Pij ) = βi βj, for all i, j I, i j. Subsectio 4.4 is devoted to a thorough aalysis of the results provided by the logical ratig score model. It is show that the correlatio betwee the logical ratig scores ad the S&P ratigs exceeds 95%. Moreover, the correlatio betwee the logical ratig scores ad the scores provided by the o-recursive liear regressio model of Sectio 3 exceeds 98%. The robustess of the model was cofirmed by jackkife cross-validatio. Furthermore, the discrimiat derived o the basis of the 998 S&P ratigs was applied to the 999 data, ad the correlatio betwee the resultig logical ratig scores ad the 999 S&P ratigs is show to exceed 94%. Sice the discrimiat does ot ivolve ay iformatio about past ratigs, it ca be used to derive the logical ratig scores of previously o-rated coutries; this is doe i Sectio 4.4 where it is also show that the logical ratig scores are i agreemet with subsequet S&P ratigs. Sectio 5 presets geeral coclusios of this study. 2 Data k 2. Sources I this paper, we focus o the Stadard & Poor coutry risk ratigs. The risk of default is geerally defied by Stadard & Poor as the probability that a sovereig obligor fails to meet a pricipal or iterest paymet o the due date ad i full. Stadard & Poor s ratigs are based o the iformatio provided by the debtors themselves ad by other sources cosidered reliable. Stadard & Poor provides sovereig ratigs for local ad foreig currecy debt. I this paper, we used the foreig currecy sovereig ratigs. Coutries are more vulerable to foreig currecy obligatios. A obligor's capacity to repay foreig currecy obligatios may be lower tha its capacity to repay obligatios i its local currecy, owig to the sovereig govermet's 7

12 PAGE 8 RRR relatively lower capacity to repay exteral versus domestic debt. As oted by Cator ad Packer (996), foreig currecy ratigs remai the decisive factor i the iteratioal bod market. Ideed, foreig currecy obligatios are more likely to be acquired by iteratioal ivestors tha domestic obligatios. Foreig currecy ratigs reflect ecoomic factors, as well as the coutry itervetio risk, i.e. the risk of a coutry imposig, for example, exchage cotrols or a debt moratorium, while local currecy ratigs exclude coutry itervetio risk. Table 5 i the Appedix lists the differet coutry risk levels or labels used by Stadard & Poor, ad also provides descriptios associated with these labels. Coutries which are assiged a label iferior to BB+ are cosidered as o-ivestmet grade (speculative) coutries. Coutries rated CCC+ or lower are regarded as presetig serious default risks. BB idicates the least degree of speculatio ad CC the highest. Ratigs labeled from AA to CCC ca be modified by the additio of a plus or mius sig to show relative stadig withi the major ratig categories. We cosider such subcategories as separate ratigs i our aalysis. We have coverted the Stadard & Poor ratig scale (ragig from AAA to SD) ito a umerical scale (ragig from 2 to 0) (see Appedix, Table 6) ad shall liberally refer to both of them as S&P ratigs. This type of coversio is commoly used i the literature, see e.g., Bouchet et al. (2003), Estrella (2000), Ferri et al.(200), Kräussl (2000), Mofort ad Mulder (2000), Mulder ad Perelli (200), Hu et al. (2002), Sy [2003]. Moreover, Bloomberg, a major provider of fiacial data services, developed a stadard cardial scale for comparig Moody s, S&P ad Fitch-BCA ratigs (Kamisky ad Schmukler, 2002); i this scales, a higher umerical value deotes a higher probability of default. I Table 6 of the Appedix, we display Stadard & Poor s foreig currecy sovereig ratigs of 69 coutries published at the ed of December 998. Stadard & Poor rates a limited umber of coutries, with a special focus (at least i the past) o the idustrial oes. However, i the last decade, the umber of Asia, Lati America ad Easter Europea ecoomies rated by Stadard & Poor has sigificatly icreased. We refer the reader to Hu et al. (2002) for the evolutio of the umber of coutries rated by Stadard & Poor. As metioed above, coutry risk ratigs ecompass ecoomic, fiacial ad political aspects. The statistical data of the ecoomic ad fiacial variables cosidered i this paper come from the Iteratioal Moetary Fud (World Ecoomic Outlook database), from the World Bak (World Developmet Idicators database) while those about the ratio of debt to gross domestic product come from Moody s publicatios. Values of political variables are provided by Kaufma et al. i two papers (999a,b) that are joit products of the Macroecoomics ad Growth, Developmet Research Group ad Goverace, Regulatio ad Fiace Istitutes which are affiliated with the World Bak. Before describig the relevace of the selected variables, we discuss i Sectio 2.2 the selectio method used. 2.2 Variable selectio criteria As uderlied by Bilso et al. (200), the selectio of variables leds itself to criticism due to the subjectivity ad arbitrariess ivolved i this process. I this paper, the selectio of relevat variables is based o three criteria. The first criterio is the sigificace of variables for estimatig a coutry s creditworthiess. We have performed a extesive literature review which played a importat role i defiig the set of cadidate variables for iclusio i our model. Tables 3 ad 4 list variables that have bee cosidered i the existig literature o coutry risk.

13 RRR PAGE 9 The secod criterio is the availability of complete ad reliable statistics. We wat to avoid difficulties related to missig data that could reduce the statistical sigificace ad the scope of our aalysis. For istace, accordig to recet iformatio received from The World Bak 6, their research cocetrates o developig ecoomies ad they have data o the debt of 37 coutries to whom they loa fuds ad who report their exteral debt to The World Bak. Sice high icome coutries do ot receive World Bak fuds, they do ot report their debt umbers to The World Bak. Such situatios have sigificatly complicated the process of compilig complete debt statistics. Hu et al. (2002) also report the problem of data availability. The third criterio is the uiformity of data across coutries. We have cosidered, for example, icorporatig the uemploymet rate statistics disclosed by the World Bak. However, the World Bak uderlies that uemploymet is aalyzed ad compiled accordig to defiitios which differ from coutry to coutry. It is worth otig that i additio to the variables listed i Tables 3 ad 4 (see Appedix), Haque et al. (996), Cator ad Packer (996), Larrai et al. (997), Mofort ad Mulder (2000) ad Hu et al. (2002) use a dummy variable that represets the historical solvecy of a coutry. Haque et al. (996) use the lagged ratig at time (t-) as a idepedet variable i their regressio model. Mofort ad Mulder (2000) claim that membership i the OECD is likely to be a sigificat idicator for coutry risk ratigs. The same authors emphasize also the importace of the locatio of coutries, by addig to their set of idepedet variables two dummy variables to characterize the coutry s locatio i Asia or i Lati America. Hu et al. (2002) also use regioal dummy variables. 2.3 Selected variables Based o the criteria of relevace, availability ad uiformity described above, we have decided to icorporate the followig variables 7 i our model: Gross domestic product per capita 8 (GDPc): the GDP is the sum of gross value added by all residet producers i the ecoomy plus ay product taxes ad mius ay subsidies ot icluded i the value of the products. It is calculated without makig deductios for depreciatio of fabricated assets or for depletio ad degradatio of atural resources. The GDP is a idicatio of the capacity of the govermet to solve a balace-of-paymets crisis without havig to default o exteral debt. The larger the GDP, the wider the potetial tax base ad thus the higher the ability of the govermet to fulfill its exteral obligatios. The GDPc is a measure of the relative wealth of a coutry ad its level of developmet. The gross domestic product (GDP) is coverted to iteratioal dollars usig purchasig power parity rates. The iteratioal dollar has the same purchasig power over GDP as the U.S. dollar has i the Uited States. Iflatio rate (IR): the iflatio rate is the chage i the atioal price level betwee two periods. The iflatio rate used i our study is based o the cosumer price idex ad is the aual percetage chage i the cost to the average cosumer of acquirig a fixed basket of goods ad services. High iflatio rates idicate structural problems i the coutry s fiaces ad may lead to sovereig ecoomic crises, as govermets hike iterest rates sharply i order to stregthe their coutries currecies. Should a coutry be uable or uwillig to pay the curret budgetary 6 Aat Lewi, Private Commuicatio, Developmet Data Group, The World Bak, Jue 06, Acroyms i paretheses followig the ame of variables are used i tables ad appedices for referrig to variables. 8 Calculated o the basis of purchasig power parity i iteratioal dollars. 9

14 PAGE 0 RRR expeses, it must resort to iflatioary moey fiacig. High iflatio rate results i a substatial cosumers purchasig power reductio ad icreases political discotet. Trade balace (TB): trade balace is the balace of trade i goods expressed as a percetage of GDP (purchasig power parity-ppp). This is the differece i value betwee a coutry's total imports ad exports (icludig iformatio of oil ad o oil exports, cosumer goods, capital goods) measured i curret U.S. dollars divided by the value of GDP coverted ito iteratioal dollars usig purchasig power parity rates. Exports growth rate (EGR): aual growth rate of exports of goods ad services based o costat local currecy. Exports of goods ad services represet the value of all goods ad other market services provided to the rest of the world. They iclude the value of merchadise, freight, isurace, trasport, travel, royalties, licese fees, ad other services, such as commuicatio, costructio, fiacial, iformatio, busiess, persoal, ad govermet services. They exclude labor ad property icome as well as trasfer paymets. Coutries havig a high export growth rate are expected to be more creditworthy. Ideed, exports are the primary source of foreig currecy iflows ad therefore have a sigificat ifluece o the capacity of the coutry to fiace imports ad service debt obligatios. Iteratioal reserves (RES): this variable refers to gross iteratioal reserves, expressed i terms of the umber of moths for which the existig reserves ca cover the cost of imports of goods ad services. It gives a idicatio of the short-term capacity of a ecoomy to meet its imports obligatios. The higher the value of RES, the lower the risk of default ad the higher the creditworthiess. Fiscal balace (FB): fiscal balace is approximated by the ratio of cetral govermet fiacial balace (surplus or deficit) to GDP. The cetral govermet s balace represets the yearly fiscal balace. Fiscal balaces ad debt stocks of govermets are crucial idicators whe aalyzig sovereig risk. The ability of govermets to extract reveues from taxpayers ad users of services is a key factor that helps to determie whether govermets will be able to make full ad timely paymets of iterest ad pricipal o outstadig debt. Debt to GDP (DGDP): here debt refers to the geeral govermet debt. The geeral govermet debt as defied by the IMF (200) icludes the cosolidated budgets of the cetral, state/regioal, ad local govermets, alog with the social security system ad other extrabudgetary fuds egaged i ocommercial activities. Excluded are ledig ad refiacig ad the assets/liabilities of commercial state-owed or guarateed eterprises, except for ay et fiacial trasfers made as subsidies to these eterprises. This balace, i.e., the differece betwee total reveues ad total expeditures, determies the et borrowig requiremet of geeral govermet, which ca be met oly by ruig dow fiacial assets or borrowig et ew resources from the public ad, thereby, addig to debt. We have cosidered icorporatig the uemploymet rate ad the ratio of the curret accout balace to GDP. While the latter tured out to be redudat with trade as a percetage of GDP, the former has bee excluded from cosideratio due to the lack of cosistecy i its defiitio. As oted by the World Bak, the treatmet reserved to temporarily laid off workers, to those lookig for their first job, ad the criteria referred to for beig cosidered as uemployed, differ sigificatly betwee coutries. For political variables, it is very difficult to fid reliable ad complete data. I our model, we have cosidered the six variables provided by Kaufma et al. (999a). These six variables are: political stability ad violece, voice ad accoutability, govermet effectiveess, regulatory burde, corruptio, rule of law. These variables are viewed as capturig the fudametals of the

15 RRR PAGE goverace cocept defied as the traditios ad istitutios by which authority i a coutry is exercised (Kaufma et al.,999a). As emphasized by Kaufma et al. (999, a ad b), political stability ad voice ad accoutability both refer to the process by which govermets are elected, moitored ad replaced. Govermet effectiveess ad regulatory burde reflect the capacity of the govermet to adopt soud policies. Corruptio ad rule of law are proxies for the respect of citizes ad istitutios for the rules which gover their iteractios. I order to avoid or at least limit redudacies i our model, we select oly oe variable for each dimesio of goverace. We have selected: Political stability (PS), Govermet effectiveess (GE), ad Corruptio (COR). The higher the values of these variables, the less likely the coutry is to default 9. The variables are defied o a (-3.5, 3.5) iterval ad are based o estimatios provided by polls of experts ad cross-coutry surveys. The variables we have described so far have bee cosidered previously i the literature ad are available i the form used i our study (as ratios or as growth rates). We have also decided to costruct a ew variable (ER) ad to add a variable (fiacial depth ad efficiecy) which, to the best of our kowledge, has ot bee used before i coutry ratig studies. Here are the descriptios of these two variables: Exchage rate (ER): is defied as the ratio of the curret value of the exchage rate to the movig average of the real effective exchage rate 0 over five years (994 to 998). While the exchage rate has bee used i previous coutry ratig studies, we cosider the ratio itroduced here to be more sigificat, sice it idicates the dyamics of chages i the exchage rate, by specifyig whether the tred is up (ER>) or dow (ER<). Fiacial depth ad efficiecy (FDE): is represeted by the ratio of the domestic credit provided by the bakig sector to the GDP. Households accumulate claims o fiacial istitutios that, actig as itermediaries, pass fuds to fial users. Correlated to the developmet of the ecoomy, the idirect ledig by savers to ivestors becomes more efficiet ad gradually icreases assets relative to the GDP. Viewed from this perspective, the ratio of domestic credit to the GDP reflects the fiacial depth ad efficiecy of the coutry s fiacial system. More specifically, this variable is used to measure the growth of the bakig system sice it reflects the extet to which savigs are fiacial. To our kowledge, the fiacial depth ad efficiecy variable has ot bee cosidered previously i the evaluatio of coutry risk ratigs. 2.4 Dataset cotet I summary, o the basis of the cosideratios described above, we have costructed a dataset ivolvig ie ecoomic/fiacial variables: gross domestic product per capita, iflatio rate, trade balace, iteratioal reserves, fiscal balace, exports growth rate, debt to GDP, fiacial depth ad 9 The higher the value of the corruptio variable, the less corrupted the cosidered coutry is perceived to be. This variable ca therefore be called corruptio quality. 0 Real effective exchage rate is the omial effective exchage rate (a measure of the value of a currecy agaist a weighted average of several foreig currecies) divided by a price deflator or idex of costs.

16 PAGE 2 RRR efficiecy, ad exchage rate (we have used the values take by these variables at the ed of 998); ad three political variables: political stability, govermet effectiveess ad corruptio level. We have compiled the values of these twelve variables for the sixty-ie coutries cosidered: 24 idustrialized coutries, Easter Europea coutries, 8 Asia coutries, 0 Middle Easter coutries, 5 Lati America coutries ad South Africa. We use the Stadard & Poor coutry risk ratigs for these coutries at the ed of December of A Statistical Model 3. No-recursive multiple regressio model 3.. The model, results, ad cosistecy with S&P I order to derive a o-recursive model of Stadard & Poor s ratigs, we shall fit the regressio equatio: M Y = α + βi * Xi + ε, (.) i= where the depedet variable Y is the coutry risk ratig give by Stadard & Poor at the ed of December 998 (or more precisely a umerical represetatio of Stadard & Poor s ratigs), the idepedet variables X i are the ecoomic ad political variables described i Sectio 2., ad ε is the error term. I view of the desired o-recursiveess of the model, the idepedet variables do ot iclude directly or idirectly ratigs of previous years. Results give i this sectio have bee obtaied usig the SPSS statistical package. The proposed model exhibits a excellet fit, with the coefficiet of multiple determiatio R- square beig 9.2%, ad the adjusted R-square 89.3%. The multiple correlatio level betwee the observed values (i.e. the Stadard & Poor ratigs) ad the predicted oes (i.e. the ratigs give by the o-recursive regressio model) is equal to 95.5%. The later are give i Appedix (Table 7, Colum 2). Table below details how the regressio equatio accouts for the variability i the respose variable, the last colum givig the statistical level (-p) at which the model is sigificat. Table : Aalysis of variace (ANOVA) Sum of Squares Degrees of Mea Square F-statistic p-value freedom Regressio Residual Total

17 RRR PAGE 3 Table 2 presets the regular ad the stadardized regressio coefficiets (i.e., those correspodig to the model fitted to stadardized data). The last colum i Table 2 idicates whether the correspodig idepedet variable is statistically sigificat (at the cofidece level of -p). Table 2: Regressio results Variables Ustadardized coefficiets Stadard error Stadardized coefficiets (Beta) t-statistic p-value Itercept FDE.693E RES IR -2.83E TB -.92E EGR -,28E GDPC 3.08E ER -.968E FB DGDP PS , GEF COR At the 5% sigificace level, it appears that five idepedet variables are statistically sigificat. These are: fiacial ad depth efficiecy (FDE), gross domestic product per capita (GDPc), ratio debt to gross domestic product (DGDP), political stability (PS) ad govermet efficiecy (GE). The regressio results described above idicate that the o-recursive regressio model has a excellet fit with the data. However, the excellece of the fit does ot automatically guaratee the predictive power of the model, if the model violates some of the critical assumptios of multiple regressio theory, as is the case with proposed model. Ideed, there is a strog correlatio betwee some of the variables cosidered, e.g. betwee the political variables, especially govermet efficiecy ad corruptio, possibly leadig to difficulties related to multicolliearity, ad the ill-coditioed ature of the resultig matrix; the predictors are ot ormally distributed; if too may predictor variables are used relatively to the umber of observatios, fittig multiple regressio ca lead to overfittig, ad the estimates of the regressio lie ca be ustable ad the results may ot be reproducible; the umber of variables used is geerally recommeded to be o more tha 5 to 0% of the umber of observatios, which is clearly ot the case of this study that ivolves 69 observatios ad 2 variables. I view of these issues, it is surprisig that the cross-validatio results preseted i the ext sectio provide a strog cofirmatio of the predictive power of the o-recursive regressio model preseted above. 3

18 PAGE 4 RRR Cross-validatio To validate the predictive power of the o-recursive regressio model, we use a resamplig techique kow as cross-validatio, ad more specifically, a popular variat of it called k- foldig (e.g., Shao, 993, Shao ad Tu, 995, Efro, 982, Hurvich ad Tsai, 989, Hjorth 994, Breima ad Spector, 992). I k-foldig, observatios are divided ito k subsets of approximately equal size. The regressio model is traied k times, each time leavig out from traiig oe of the k subsets, ad usig the omitted subset to test the regressio-predicted coutry risk ratig. I this paper, based o the relatively small size of the sample, we have selected k to be 0, ad partitioed the sample ito 0 groups of 6 or 7 coutries each. The groups were selected usig stratified radom samplig, i.e. assurig that each group cotais about the same umber of ivestmet-, speculative- ad default-grade coutries (see S&P s classificatio, Table 5). I Appedix (Table 7, Colum 3) we preset the i-the-sample predictios of the orecursive multiple regressio model obtaied i the precedig Sectio, ad the out-of-the-sample predictios obtaied usig the 0-fold cross-validatio. The major results are the followig: the correlatio betwee the i-the sample ad the out-of-the sample predictios is 99.%, the correlatio betwee the Stadard ad Poor ratigs ad the out-of-the sample predictios is 95.6%. The very high correlatio levels demostrate clearly that the impressive results of Sectio 3.. are ot due to chace or overfittig Ratig discrepacies betwee S&P ad the proposed model I this sectio, we shall idetify the few coutries for which the predictios of the orecursive regressio model disagree with the Stadard & Poor ratigs. I order to accomplish this, we shall costruct cofidece itervals for our predicted ratigs. Let us itroduce some otatios. Let ad p refer to the umber of observatios ad predictors, respectively. The expressio t( α / 2, p) refers to the Studet test with ( p) degrees of freedom, ad with upper ad lower tail areas of α /2. Let X j be the p- dimesioal vector of the values take by the observatio Y j o the p predictors, while ' X p be the trasposed of X j. Let the expressio ( X ' X) refer to the variace-covariace matrix, i.e. the iverse of the [ p p] -dimesioal matrix ( X ' X ). Deotig by MSE the mea square of errors i the regressio, the estimated variace while the ( α) ^ s 2 [ Y j ] of the predicted ratig is: ^ 2 ' j j j s [ Y ] = MSE*[ X ( X ' X) X ], (.2) -cofidece iterval for the predicted ratig Y ^ is: j ^ ^ ^ ^ j α j j α j { Y t( /2, p)* s[ Y ], Y + t( /2, p)* s[ Y ]} (.3) All formulae give i this sectio as well as those i Sectio are from Neter et al. (996)

19 RRR PAGE 5 SP We say that there is a discrepacy betwee the Stadard & Poor ratig R j of a coutry j ad ours, if the Stadard & Poor ratig is ot i the cofidece iterval, i.e.: ^ ^ ^ ^ SP Rj { Yj t( α/2, p)* s[ Yj], Yj+ t( α/2, p)* s[ Yj]} for α= 0. (.4) Takig α equal 5%, this formula idetifies four discrepacies. Three coutries (Icelad, Pakista ad Argetia) are rated higher by the o-recursive regressio model tha by Stadard & Poor, while Columbia is rated higher by Stadard & Poor. It is remarkable that subsequetly the Stadard & Poor ratigs for two of these four coutries (Columbia ad Pakista) have bee modified i the directio suggested by the regressio model. More precisely, Columbia has bee dowgraded by Stadard & Poor twice, movig from BBB- i December 998 to BB+ i September 999, ad the to BB i March After beig dowgraded i Jauary 999 (SD), Pakista was upgraded to B- i December 999. O the other side, Icelad s ratig has remaied uchaged, ad Argetia s ratig has edured sigificat dowgrade, which started however oly i November Are political variables ecessary? I this sectio, we test the predictive power of the o-recursive regressio model, from which the three political variables are omitted. The R-square as well as the adjusted R-square of this model are equal to 88.6 % ad 86.9 % respectively. These values are lower tha the correspodig values for the origial o-recursive regressio model, idicatig a loss i predictive power resultig from the omissio of the three political variables. The predicted ratigs are give i Appedix (Table 7, Colum 4). Variables Ustadardized coefficiets Table 3: Regressio coefficiets Stadard error Stadardized coefficiets t-statistic p-value Itercept FDE 2.20E RES IR.22E TB -5.85E EGR 2.75E GDPC 4.38E ER FB DGDP It appears that five of the idepedet variables are statistically sigificat at a 95% level. These variables are fiacial ad depth efficiecy (FDE), gross domestic product per capita (GDPc), debt to gross domestic product ratio (DGDP), exchage rate (ER) ad fiscal balace (FB). The correlatio coefficiet betwee the predicted ratigs ad those of Stadard & Poor is equal to 94.4 % ad is lower tha i the origial model. Moreover, the iferior fit of this model results i wider cofidece itervals as compared to the origial model. 5