Determinants of Credit Default Swaps Implied Ratings during the Crisis: was Sovereign Risk mispriced?

This paper addresses the question of whether sovereign risk pricing was related to macroeconomic fundamentals, between 2007 and 2015, in a sample of OECD countries. The authors argue that the conflicting evidence in the literature is due to poor methodology options. The researchers innovate by modelling sovereign credit default swaps implied ratings as our sovereign risk proxy, instead of spreads, avoiding common pitfalls. Furthermore, the authors improve the variable selection, model specification and the econometric procedures used. A panel ordered probit model is chosen, assuring robust inference. The authors relax the parallel lines assumption, allowing for rating-varying coefficients of explanatory variables. The result is the first congruent model of sovereign risk during the years of the financial crisis and of the Euro Area crisis. Fiscal space variables, economic activity indicators, variables pertaining to external imbalances, and contagion proxies are relevant, with effects matching theory priors. The scientists clarify conundrums in the previous literature, posed by lack of significance of some macro fundamentals and by puzzling signs of some estimated coefficients. Moreover, this is the first paper to estimate not only the global risk premium, but also the impact of changing risk aversion. The authors find no support for claims of sovereign risk mispricing during the sample period. The results allow relevant policy conclusions, namely concerning the validity of different fiscal consolidation paths in financially distressed countries. Maria Alberta Oliveira (Portugal), Carlos Santos (Portugal) BUSINESS PERSPECTIVES LLC “СPС “Business Perspectives” Hryhorii Skovoroda lane, 10, Sumy, 40022, Ukraine www.businessperspectives.org Determinants of Credit Default Swaps Implied Ratings during the Crisis: was Sovereign Risk mispriced? Received on: 9th of April, 2018 Accepted on: 25th of June, 2018


INTRODUCTION
Understanding the fluctuations of credit risk is of the utmost relevance both for policy-makers and for investment managers, particularly since the onset of the financial crisis in 2007. The Euro Area (EA) debt crisis has further increased this relevance. If earlier academic research on credit risk mispricing was focused on US corporate bonds, and on sovereign credit default swaps (SCDSs) for emerging economies, Heynderickx et al. (2016) argue the EA is now at the core of the credit spreads puzzle. Feldhüter and Schaefer (2018) restrict the dimension of the puzzle to sovereign securities. As pointed out, inter alia, by Bannier et al. (2014), the surge of SCDSs in recent years is mainly due to the European debt crisis. In this journal, Oliveira and Santos (2015) have extensively discussed these OTC derivatives, while providing evidence of the vast related research propelled by the EA crisis.
The relevance of this topic for policy-makers is easy to understand. During the EA crisis, fluctuations in sovereign risk premia account for 30 to 50% of the forecast errors in unemployment, and for 20 to 40% of the increase in private borrowing costs (Bahaj, 2014). The transmission mechanism from SCDSs spreads to the real economy rests on their leading role on the price discovery process in bond markets (Delatte et al., 2012), and on the upper bounds sovereign ratings still pose on corporate ratings (Borensztein et al., 2013) 1 . Policy-makers are aware of the role of country ratings in financial stability (Klinger & Lando, 2018), since the linkage between sovereign and banking risk is well documented (Bruneau et al., 2014). Furthermore, access to the ECB Asset Purchasing Program is contingent on the existence of at least one major rating agency grading such debt securities above a minimum threshold 2 .
From the perspective of an investments manager, the ability to assess credit risk is also of paramount importance, since portfolios usually contain corporate and / or sovereign bonds. A correct hedging strategy entails assessing the likelihood of default, namely to decide the amount of protection to buy in the form of Credit Default Swaps (CDSs). Moreover, if the investment manager wishes to buy CDSs for trading, the ability to anticipate changes in spreads allows significant profit opportunities 3 .
Irrespective of whether the motivation is policy design or building trading and hedging strategies, understanding the relationship between sovereign risk and economic fundamentals has become a part of the research agenda in finance. Notwithstanding, the literature is far from reaching sound conclusions. As we shall debate in section 1, this is largely due to poor methodology options. Afonso et al. (2007) had argued that modelling sovereign spreads is difficult, advising the usage of ratings as latent dependent variables in ordered probit models. A panel approach was also strongly recommended to increase the robustness of statistical inference. However, the empirical literature has neglected proxies for sovereign risk other than spreads and has paid no attention to the authors' recommendation on econometric methods.
The research question motivating this paper is whether there is a role for economic fundamentals in sovereign risk pricing. We improve on the literature in different ways. Firstly, this is the first paper to use SCDSs implied ratings, constructed using spread implied credit default probabilities (CDPs) 4 as a proxy of sovereign risk. Secondly, we use a panel ordered probit model, as recommended by Afonso et al. (2007). Thirdly, we explore the implications of relaxing the parallel lines assumption, which had never been discussed in this literature. As such, instead of simply including time-varying coefficients, we also allow rating-varying coefficients. We do not assume that different crisis stages have similar cross-sectional impacts on sovereign risk, irrespective of each country's rating at the time. Rather, the no parallel lines hypothesis allows to assess the impact of different crisis periods per rating class. We also innovate by including in our model a proxy for time-varying risk aversion. Our estimation results improve on the literature: the first congruent model relating macro-financial variables to sovereign risk is achieved. We have tested the inclusion of proxies for all the relevant dimensions suggested in earlier papers. They proved to be significant and their estimated impact on sovereign risk matches theory priors. Thus, previous empirical conundrums were solved. Finally, this paper also innovates by exploring a novel data set on SCDSs.
The paper is organized as follows. Section 1 provides a critical overview of the relevant literature. Section 2 explains our methodology. Section 3 discusses the research hypotheses. Section 4 describes the data. Section 5 discusses estimation results. Final section concludes the paper. 1 Although rating agencies claim to have moved away from the "sovereign ceilings" policy, evidence shows that sovereign ratings are still a major determinant of corporate ratings (Borensztein et al., 2013). 2 his is of special concern in the financially distressed EA periphery (De Santis, 2016). In the Portuguese case, until early 2017, financial stability was dependent on the Canadian rating agency DBRS, the only one classifying the country's sovereign debt just above "speculative grade" (as BBB). 3 Oliveira and Santos (2015) discuss profitable trading strategies for investors holding SCDSs. 4 Research on CDPs and implied ratings has been conducted in Finance, but not with respect to the macroeconomic determinants of sovereign risk. For details on filtering CDPs from CDSs spreads see, inter alia, Elkamhi et al. (2014).

LITERATURE REVIEW
The conclusions emerging from the empirical literature on sovereign risk and fundamentals are largely contradictory. Indeed, not only do candidate explanatory variables vary across papers, but also even papers including similar covariates reach opposite conclusions regarding their significance and impact. Furthermore, poor choices of the proxy for sovereign risk are common. Finally, the econometric methods chosen are misleading. We will divide our critical overview of the literature in 3 subsections, each pertaining to one of the referred problems.

Candidate covariates
It is possible to arrange the variables assessed in the literature into five main groups: fiscal space; external imbalances; risk and contagion; economic activity; less common covariates.

Fiscal space
The and Paniagua et al. (2017). Santos (2011) has concluded that the public debt to GDP ratio was only significant for the top 10% of the CDPs distri-bution. Oliveira et al. (2012) find their classes of government expenditure to be relevant, but only before the EA crisis. Differently, the taxes to GDP ratio is relevant throughout their entire sample period. Afonso et al. (2015) conclude against the significance of the public debt to GDP ratio. This is unexpected, since their sample contains only the EA countries. Notwithstanding, the authors find the government balance to be relevant. Beirne and Fratzscher (2013) achieve even more puzzling results: the public debt to GDP ratio is always irrelevant for EA countries, and the government balance ratio matters only before the crisis period. Yuan and Pongsiri (2015) conclude that the government balance is irrelevant, although the expected government balance is significant. The authors acknowledge that multicollinearity is affecting their results. Cantor and Packer's (1996) seminal work provides the expectation of a positive correlation between a country's current account balance and its sovereign spreads. However, Beirne and Fratzscher (2013) find that the current account to GDP ratio is not significant for the EA countries during their sample period, although it is relevant for other advanced economies. Furthermore, Aizenman et al. (2013) conclude that the external debt to GDP ratio is not significant. Albeit concluding against the relevance of the current account, Yuan and Pongsiri (2015) find that the ratio of external debt to GDP increases sovereign spreads.

Risk and contagion
The VIX index 5 is the standard proxy for global risk in this literature. It is significant in explaining country-specific sovereign risk in Paniagua et al. (2017) and Afonso et al. (2015). However, Arghyrou and Kontonikas (2012) do not find a role for global risk in their first sample period (2001)(2002)(2003)(2004)(2005)(2006)(2007). The authors claim that relevance of global risk occurs during the financial crisis alone. Surprisingly, during the EA crisis, they don't find the VIX to be significant.
Beirne and Fratzscher (2013) use the first difference of the VIX as a proxy of global risk 6 . They reach the unexpected conclusion that an increase in global risk decreases the EA sovereign spreads. Beirne and Fratzscher (2013) use regional dummies to test for shift-contagion, concluding in favor of that hypothesis. Caceres et al. (2010) had also found evidence of contagion within the EA periphery.

Economic activity
The real growth rate of GDP is relevant in the models of Kriz et al. (2015) and Yuan and Pongsiri (2015). Beirne and Fratzscher (2013) find that, for the EA periphery, real GDP growth does not explain sovereign risk. Adding to the authors' surprise, they find that, for other advanced economies, increases in real GDP growth are estimated to significantly increase sovereign spreads. Arghyrou and Kontonikas (2012) use output growth differ- 5 Obtained using call and put implied volatilities from the S&P 500 index. 6 In section 4, we shall provide a different interpretation for this difference. entials between countries as a proxy for the space of growth related variables, but only in single equation models (not in their panel setting). They conclude that the variable is significant in only one of the sample countries.
The growth rate of industrial production has been used by Oliveira et al. (2012). A negative relationship between industrial production and sovereign spreads is found, although only for the period before the EA crisis. The differential between each country's industrial production growth and the German one is significant in Boffelli et al. found the variable to be significant. Notwithstanding, the authors do not clarify whether they are referring to inflation or to changes in inflation. None of the other papers has discussed the relevance of inflation in sovereign risk models.

Other variables
Yuan and Pongsiri (2015) (2012) found bond markets liquidity to be relevant, but with an unexpected positive estimated coefficient, implying lower spreads for less liquid markets.

Explained variable
The most common sovereign risk proxy is the spread between the interest rate on a country's government bonds and that on bonds of some other reference country for the same maturity. In the recent literature, the reference is usually the 10 years maturity German bonds. This is the case in

ANALYSIS METHODS
Credit ratings provide a natural field of application for ordered probit models (e.g. Cantor & Packer, 1996). The nature of ratings data fits in a framework where the difference between the ordinal scores of, say, 4 and 3, is not equivalent to the difference between the cardinals 4 and 3. For the latter, multinomial probits and logits are better suited. Differently, albeit being associated with differences in credit worthiness, variations in rating scores are not quantitatively equal to those.
In Corporate Finance, selection bias is common, when modelling ratings with ordered probits. This is attributed to privileged information managers possess about their firms. When choosing to solicit ratings, managers anticipate good scores. Hence, firms receiving unsolicited ratings are likely to be subject to downward biased rating estimators (e.g. Poon, 2003).
The methodology framework in which this paper studies sovereign risk avoids the selection bias problem, as data provided by rating agencies is avoided. Instead, ratings are derived from market information (SCDSs spreads and their implied CDPs). This is the case for every country in the sample in every period. Self-selection is prevented, since the decision to trade SCDSs on a country's debt depends on market participants alone, without interference from the country's government. All SCDSs implied ratings may be viewed as "unsolicited".
, it x is a vector of explanatory variables, and * β s the vector of coefficients. As expected for a panel data setting, equation (1) contemplates two random errors: i µ and , . it ε At the estimation level, we shall cope with this through the assumption that they are both normally distributed. Hence, we shall work with the Random Effects ordered probit model, using Maximum Likelihood (ML) estimation (see, inter alia, Frechette (2001) for implementation in STATA). Furthermore, we allow the coefficients to vary according to a country's risk class. This option is known as relaxing the parallel lines assumption in ordered probit theory (Williams, 2006 The probability that the market assigned the rating , j s 1, 2,..., jS = to country , i in period , t is: denotes, as usual, the cumulative distribution for a multivariate normal evaluated at some vector . w We choose to assign 1 to the best rating class and S to the worst. A rating order increase implies a higher sovereign CDP. Furthermore,  (Doornik, 2009). Notice further that, in equation (4) , SS ′ ≤ since the number of rating classes acceptable for efficient estimation may need to be reduced, when considering the subset of rating-varying coefficients, in the no parallel lines setting. It is usual that , SS ′ < as discussed in Pfarr et al. (2011). Finally, time specific dummies and the candidate macro covariates are subject to the same congruency and significance criteria for inclusion in the final model (for a detailed discussion of congruency and congruent models, see Bärdsen et al., 2005).
A note should be made on the construction of rating classes. Following the advice in the literature 8 , we were concerned that an excess number of rating classes might result in imprecise pa- 8 Cantor and Packer (1996) observe that a bigger number of classes combined with few to none rating observations in some, would induce failures of the ML estimates to converge. Afonso et al. (2007) also discuss the need to reduce the number of rating classes to increase estimation precision.  (Table A1). For the first 5 classes, the lower cut-off is included in the estimated interval. However, for the others, intervals nearly overlap. This is due to few observations for very high CDPs. Hence, it supports our choice to estimate the subset of ratingvarying coefficients with

HYPOTHESES DEVELOPMENT
Our research question pertains to the possibility of building a congruent model of sovereign risk based on macro fundamentals. The empirical evidence discussed in subsection 1.1 suggests 14 research hypotheses. The first 12 refer to the possible relevance of specific variables in explaining sovereign risk, the 13 th hypothesis refers to time-specific effects, and the 14 th to regional contagion: H1: Higher real GDP growth improves sovereign ratings.
H2: Higher public debt to GDP ratios worsen sovereign ratings.
H3: Higher government revenue to GDP ratios worsen sovereign ratings. H4: Higher external debt to GDP ratios worsen sovereign ratings.
H5: Higher government deficit to GDP ratios worsen sovereign ratings.
H7: Changes in inflation affect sovereign ratings.
H8: Higher global risk worsens sovereign ratings.
H9: Changes in risk aversion affect sovereign ratings.
H11: The current account balance to GDP ratio affects sovereign ratings.
H12: Changes in the current account balance to GDP ratio affect sovereign ratings.
H13: Year-specific events affect Sovereign ratings.
H14: There are regional specific effects in the EA periphery.

DATA
Our panel is strongly balanced. It comprises the periods between the final quarter of 2007 and the 1 st quarter of 2015 (T = 30 quarters), and 26 OECD countries (N = 26) 9 . Hence, the analysis was conducted with 780 observations per variable. As explained in section 2, the rating classes were derived from CDPs. We have built a unique data set for this purpose. From 2007 to 2013, CDPs were collected from Credit Market Limited (CMA) Datavision® quarterly sovereign risk reports. Given that these became unavailable, with the necessary level of detail, from 2013 onwards, we have used, for the subsequent periods, CDPs computed similarly by Markit® 10 . To ensure consistency with CMA 9 10 of the original EA countries (except for Finland), Australia, Czech Republic, Denmark, Estonia, Hungary, Iceland, Israel, South Korea, New Zealand, Norway, Poland, Slovak Republik, Slovenia, Sweden, UK and US. 10 For detailed information on Markit ® data see, in this journal, Oliveira and Santos (2015). 11 It should be noticed that, in our sample, the mean of ΔX8 is negative, further supporting the need to estimate the impact of a changing risk aversion on sovereign ratings (as shall be done in section 5).
Datavision® data, we have chosen end of quarter Markit® CDPs, for each relevant period.
With respect to the macro-financial covariates, we have collected data for all the dimensions referred to in subsection 1.1. Hence, we define the following variables: • Fiscal Space: government revenue to GDP (X 5 ); government balance to GDP ( ) 6 ; X public debt to GDP ( ) 3 ; X • External Imbalances: external debt to GDP (X 4 ); current account to GDP (X 10 ); changes in the current account to GDP ( ) 10 ; X ∆ It should be noticed that Beirne and Fratzscher (2013) use the change in the VIX as a proxy for global risk, while we use the VIX index for that. Hence, 8 X ∆ has a different role in our model: it is a proxy for global risk aversion. Our hypothesis of a time-varying risk aversion is in accordance with the behavior anticipated in expected utility theory, in Financial Economics, matching preposition 6.C.4 in Mas-Colell et al. (1995). Furthermore, Heinz and Sun (2014) had provided empirical evidence of non-constant risk aversion, following the financial crisis 11 . Ours is the first model in this literature to include both risk and risk aversion as covariates explaining sovereign risk.
All macroeconomic and financial variables were obtained from DataStream, except for 3 X and 4 X (retrieved from OECD statistics) 12 .
Despite the discussion in subsection 1.1.5, no proxy for liquidity is included in our model, since we are working with SCDSs instead of bonds. For the latter, meaningful liquidity measures are easy to obtain. For the former, the opacity of OTC derivatives renders any liquidity proxy imprecise (e.g. Markit ® does not have bid-ask spreads neither for all sovereign entities, nor for the entire sample period). Table 1 reports the estimation results. The 1 st column lists the explanatory variables, the 2 nd the 12 Given the lack of availability of data, for some covariates, at a quarterly frequency, we follow the literature consensus, using standard interpolation (e.g. Beirne & Fratzscher, 2013). 13 ΔX7i,t is maintained in order to draw a conclusion regarding H7.

RESULTS AND DISCUSSION
coefficients' estimates, and the 3 rd the t-ratios. Non-significant year-specific indicators, macrofinancial covariates and cross-product dummies were omitted from the final model 13 , as outlined in section 2. The likelihood ratio test for global significance rejects the null hypothesis (at 0.1%): LR obs = -315.96357. Furthermore, the test of a pooled ordered probit against a panel model rejects the hypothesis of no gains from using a panel at 0.1% (LR obs = -166.63). Thus, congruency of our model is assured. Table 1 translate to relevant improvements over the previous literature. These improvements are robust to multivariate normality of the random errors (results for the panel ordered logit, provided in Table A2 in Appendix, do not change the conclusions of this section). Note: *** Refers to 1% significance, ** to 5% significance, * to 10% significance. Table 1 clarifies the relevance of the fiscal space covariates. X 3 (at 1%) and X 6 (at 5%) are individually relevant, confirming H2 and H5. Both variables have the expected impact: a better government balance to GDP ratio decreases the probability of a worse rating; a greater weight of public debt in GDP increases that probability. Notwithstanding, both X 5 and its associated cross-product dummies ( ) for 3 S′ ≥ are significant at 1%. The impact of an increase in the government revenue to GDP ratio on the probability of a worse sovereign risk differs per rating class. The parallel lines assumption is not imposed. As such:

Fiscal space
• for countries in the two best rating classes, the greater the government revenue to GDP, the lower the probability of a worse sovereign risk Hence, validity of H3 is rating contingent. This result merits the attention of policy-makers. Firstly, fiscal consolidation on high risk countries should favor lower government spending instead of higher taxes. Secondly, the negative impact of higher taxes worsens as sovereign risk increases.

External imbalances
Both the external debt to GDP ratio and the associated cross-product dummies for 4 S′ ≥ are significant (at 5%). Conclusions with respect to H4 are rating contingent, since the parallel lines hypothesis fails. Our results imply that: • for countries in the 3 best rating classes, a decrease in X 4 augments the probability of a worse credit rating With respect to the current account balance to GDP ratio, the simultaneous significance of X 10 and Drat 5 X 10 (both at 1%) needs to be considered. As such: • for countries in the first four rating classes, an increase in X 10 augments the probability of worsening sovereign risk βδ += − < In conclusion, H11 is confirmed. With respect to changes in the current account to GDP ratio, ΔX 10 is found to be significant at 10%, with an estimated negative coefficient. Research hypothesis H12 is confirmed.
A final comment should be made on the results of this subsection. Macroeconomic theory supports the seemingly puzzling results for some estimated coefficient signs. Eliasson (2002) argues that external imbalances could serve as an indicator for the willingness of foreigners to cover the current account gap through loans and foreign investment. Hence, a higher current account deficit would be associated with higher creditworthiness or good economic prospects, consequently, a higher sovereign rating. Table 1 confirms that X 8 is significant (at 1%), and that its estimated coefficient is positive. A higher global risk increases the probability of a country moving to a worse rating class. With respect to risk aversion (ΔX 8 ), we conclude in favor of its significance at 5%, but with a negative estimated coefficient. Thus, although agents react adversely to risk, they ask for smaller increases in the risk premia. We estimate that a higher change in risk aversion lowers the probability of moving to a worse rating. This is consistent with the decline in risk aversion over the sample period, referred to in section 4, when discussion the behavioral basis for this variable (and in footnote 11). Furthermore, H8 and H9 are confirmed. Table 1 corroborates H14. The regional dummy for the EA periphery is significant at 5%, and 14 1.715823 0.

Risk and contagion
β ′

= >
The probability of an EA periphery country experiencing a deterioration in credit worthiness is higher than for other advanced economies in our sample. This common effect is interpreted as shift contagion.

Economic activity space
Research hypothesis H1 is confirmed: X 2 is significant at 1%, and its estimated coefficient is negative. An increase in the real growth rate of GDP diminishes the probability of a worse sovereign risk. Table 1 shows that a higher inflation rate augments the probability of a worse rating. There is no support for claims regarding the relevance of changes in inflation. ΔX 7 is not significant (at 10%), rejecting H7. Table 1 indicates that the estimated coefficient of the unemployment rate is positive and significant at 1%. A country with a higher unemployment rate has a higher probability of moving to the worse rating class. H10 is confirmed.

Year-specific dummies
Year-specific indicators are included in our model to account for episodes in the sample period, not controlled for by other variables. Table  1  The indicators' estimated coefficients are increasing from 2010 to 2012 and decrease in 2013. This is compatible with the evolution of the EA crisis: the 1 st rescue package for Greece occurred early in 2010; 2011 witnessed the Irish and Portuguese bail-outs, as well as the inversion in Italy's yield curve; in early 2012, Greece's 2 nd rescue package was implemented, and the EU bailed-out the Spanish banking system. From 2013 onwards, the crisis seems to have been softened, most likely due to regulatory changes and to a more pro-active ECB policy in favor of financial stability (De Santis, 2016).

CONCLUSION
This paper improved on the econometric methods used in the literature on the macro-financial foundations of sovereign risk. A congruent model, including covariates for all dimensions suggested by earlier authors, was achieved. The panel ordered probit, without the parallel lines assumption, using SCDSs implied ratings as the sovereign risk proxy, clarified the puzzles in earlier empirical papers. Thus, SCDSs implied ratings match economic expectations based on fundamentals, showing no evidence (at a quarterly frequency) of credit risk mispricing.
In particular, we have shown that a higher real growth rate of GDP decreases sovereign risk (improving on, e.g., Beirne & Fratzchser, 2013), a lower public debt to GDP ratio decreases sovereign risk (contrary to, e.g., Afonso et al., 2015), a higher government budget surplus benefits ratings (improving on, inter alia, Yuan & Pongsiri, 2015), and that lower inflation and unemployment rates diminish sovereign risk (improving on Kriz et al., 2015) and on Aizenman et al. (2013). Relaxing the parallel lines assumption allowed us to conclude that a worsening of the ratios of the external debt or the current account to GDP only deteriorate ratings for countries in high risk classes. Such risk class-contingent conclusions had not been addressed in the previous literature. Similarly, we improve on Kriz et al. (2015) by concluding the role of the ratio of government revenue to GDP is also varying with a country's rating group. Moreover, we have shown the relevance of controlling for risk aversion and global risk simultaneously, a procedure no other paper had followed before in this literature.