Short-Term Drivers of Sovereign CDS Spreads

Abstract

This chapter presents large-scale estimated models, one for each country, representing factors driving changes in credit default swap (CDS) spreads of 35 sovereigns. I estimate the models and test their robustness using data from July 2005 to July 2016. The set of eligible explanatory variables comprises indicators of the state of the global economy and of the domestic economic conditions, and proxies for risk premia. I find that not only the S&P 500 variable is pervasive across the countries, but also that the estimated S&P 500 coefficients are higher in magnitude for emerging markets than developed countries.

1 Introduction

Given the size of the sovereign credit default swaps (CDS) market (currently at $1.6 trillion) and the valuable information it reveals about market expectations on the probability of default, there is great need for gaining understanding the determinants of CDS spreads (Alsakka and Gwilym 2010). CDS contracts are particularly useful for a wide range of investors, either for hedging existing exposures or for speculators who wish to take positions without the need to maintain the reference obligation on their books. This is one reason why the market of sovereign CDS is, in some cases, more liquid than the underlying sovereign bond market itself.¹ Moreover, CDS spreads may be monitored for gauging the market perception of the debt sustainability of specific governments, as they provide more timely and, arguably, within periods of crisis, more accurate, distress assessment than rating agencies, as conveyed by long-term ratings. Timely measures of credit risk are important, for example, to central banks concerned with the risk of their foreign reserves portfolios.

To account for model uncertainty, I fit all possible linear models using the chosen independent variables (which include both global and local factors), and choose the model specification with the best fit for 35 developed and emerging economies’ sovereign CDS spreads (please see Table 7.1 for the full list). Identifying the best model separately for each country might prove useful for risk assessment and, eventually, for forecasting purposes. This procedure also allows us to gain insights about the relative importance of each of the factors considered. The most important result I find is that the S&P 500 index is contemporaneously negatively related to the CDS spreads for most of the countries. Further, the coefficients of the S&P 500 are higher for emerging markets than they are for advanced economies. I also conduct multiple robustness checks, all of which confirm the main result of this chapter.

Table 7.1 Classification of sovereigns according to investment class

It must be stressed that the proposed framework is not necessarily meant to either predict crises or enhance financial investment efficiency; however, it might prove useful for supporting short-term sovereign risk assessment. This chapter is closely related to Westerlund and Thuraisamy (2016) and Longstaff et al. (2011), but differs from these studies in the following aspects: (1) focus on the short-term relationship between spreads and drivers, and (2) comparing the drivers of CDS spreads in developed and emerging economies.

This chapter is organized as follows: Sect. 7.2 revises the related literature; Sect. 7.3 presents a short description of the CDS market; Sect. 7.4 describes the data; Sect. 7.5 provides the empirical strategy, the results, and the robustness assessment; and finally Sect. 7.6 concludes this chapter.

2 Related Literature

In the spirit of Westerlund and Thuraisamy (2016), I test many models with different combinations of multiple drivers, instead of solely testing a specific model, for each sovereign. Applying a bootstrap-based panel predictability test, Westerlund and Thuraisamy (2016) find that the global drivers are the best predictors. In line with this analysis, I find that the S&P 500 is statistically significant across the board.

This chapter’s results are also closely in line with Longstaff et al. (2011), who find that sovereign credit spreads are primarily driven by global macroeconomic forces and that the risk premium represents about a third of the credit spread.³ Sixty-four per cent of the variations in sovereign credit spreads are accounted for by a single principal component which primarily loads on USA stock, high-yield markets and volatility risk premium (proxied by the VIX index). Instead of using principal components, this chapter tries to find the subsets of explanatory variables that can best explain short-term CDS spreads for each of the countries considered.

While this chapter focuses on the short-term determinants of sovereign risk, Remolona et al. (2008) are concerned with pricing mechanisms for sovereign risk and propose a framework for distinguishing market-assessed sovereign risk from its risk premia. They use a dynamic panel data model with a sample covering 16 emerging countries’ sovereign CDS spreads. In contrast, I believe that this chapter provides a more comprehensive understanding of the determinants of credit risk, since this chapter’s sample covers not only emerging countries but also advanced economies, summing up to 35 countries.

3 Description of the CDS Market

The sovereign CDS market grew from $0.17 trillion (in terms of notional amounts outstanding) in December 2004 to almost $2 trillion in December 2015.⁴ During the same period, the credit derivatives market increased from $6 trillion to $15 trillion. Fig. 7.1 shows that positions in sovereign contracts have become an increasing part of the CDS market since December 2004, while total notional amount outstanding in the credit derivatives market as a whole has been declining markedly since 2007.⁵

Fig. 7.1

Notional amount of CDS contracts outstanding: total versus sovereigns

CDS spreads indicate the cost of buying protection against the default of a reference entity. The protection buyer pays a premium or spread on a periodic basis and in exchange, upon the occurrence of a credit event (defined within the terms of a CDS contract), has the right to sell the bond to the protection seller at face value. CDS contracts are generally considered by market participants to be efficient and liquid instruments to mitigate credit risk. Further, they enable credit providers to diversify exposure and expand lending capacity. The protection seller, on the other hand, can take credit exposure over a customized term and earn the premium without having to fund the position. The spread is related to the expected loss of the bond: the higher the expected loss, the higher the spread. Since trades by market participants are more frequent than ratings (re)assessments by ratings agencies, CDS spreads are a more timely, though not necessarily a more accurate, way of gauging the market perception of credit conditions of specific entities.

Triggers for sovereign CDS contracts may be a failure-to-pay, a moratorium, or a restructuring. A failure-to-pay occurs when a government fails to pay part of its obligations in an amount at least as large as the payment requirement after any applicable grace period. A moratorium occurs when an authorized officer of the reference entity disclaims, repudiates, rejects, or challenges the validity of one or more obligations. A moratorium that lasts a pre-defined time period triggers a failure-to-pay event or a restructuring. Restructuring occurs when there is a reduction, postponement, or deferral of the obligation to pay the principal; when there is a change in priority ranking causing subordination to another obligation; or when there is a change in currency or composition of interest or principal payments to any currency which is not a permitted currency.

Upon default, there are two types of settlement: physical or cash. Both of them cause the termination of the contract. In the case of the physical settlement, the protection buyer delivers to the protection seller one of a list of bonds with equivalent seniority rights and the protection seller pays to the protection buyer the face value of the debt. In the case of cash settlement, the protection seller pays to the protection buyer the difference between the face value of the debt and its current market value.

4 Data

The dependent variable for each of the 35 investment-class markets listed in Table 7.1 is the change in its five-year CDS spreads, with the reference obligation being a deliverable senior dollar-denominated external debt of the sovereign. Table 7.2 shows descriptive statistics for the sovereign CDS spreads of the 35 selected countries.

Table 7.2 Descriptive statistics for CDS spreads

I select the set of global and local explanatory variables that could potentially be used by investors and risk-managers who take short-term views on sovereign risk. The focus of this chapter is on establishing statistical relationships, and not on identifying the economic content of the variables considered. The slope, for example, not only provides an indirect indication of future tax revenues, as they are related to growth prospects through the business cycle, but also captures the risk premia embedded in long-term yields. Alternatively, it could convey information about the state of the economy with respect to growth prospects, risk aversion, banking system vulnerability, and business cycle. In this chapter, I do not take a stand on which of these interpretations matters more for the results.

In the following, I use sp500, vix, Slope, and oil, respectively, to refer to the S&P 500 index, VIX index, USA slope factor, and Brent oil price index. The local factors that I consider as presumably providing information on specific aspects related to debt sustainability or overall risk premium are the local stock index level (stock_i), exchange rate (xr_i), local two-year yield (localTY_i), local slope factor (localSlope_i), and the average of banks’ CDS spreads (when available) of the banking system of the corresponding jurisdiction (bank_i). Given the reasonable assumption of persistence of CDS spreads, I include the lagged dependent variable in the regression. The description of the variables, the economic reasoning behind their inclusion, and data sources are described in detail in Table 7.3.

Table 7.3 Description of explanatory variables

To avoid potential problems of non-stationarity of the variables in our study, I analyse the first differences of all the variables at the weekly frequency from July 2005 to July 2016. I perform the analysis at the weekly frequency to get a sufficient sample size. This, however, has the drawback of making it infeasible to use other macroeconomic sovereign credit-related factors, such as deficit/GDP, debt/GDP ratios, or foreign reserves, as explanatory variables. These variables are available at best at a monthly frequency. I test as many as possible econometric models for a time period encompassing the period July 2005 to October 2012. The last 45 months (from November 2012 to July 2016) are set apart for calculating out-of-sample goodness-of-fit statistics.

5 Empirical Strategy and Results

First, in order to mitigate potential multicollinearity issues, I orthogonalized the variables most usually associated to the general economic conditions (vix, oil, and stock) to the S&P 500.

I begin the empirical analysis by attempting to narrow down the set of variables that could be included in the regressions, by means of the Granger-causality test (Granger 1969). This step is useful to reduce the computational time required for the analysis. I limit the set of eligible local explanatory variables to only endogenous and weakly exogenous ones, as given by the Granger-causality test. I narrow the set of variables because when estimating models with contemporaneous independent variables, a primary concern is the endogeneity of the regressors. For example, while weekly changes in the exchange rate may anticipate changes in CDS spreads, it could also be argued that currency changes might arise as a consequence of changes in CDS spreads. When associated with a negative outlook of government debt sustainability, increases in CDS spreads might lead currency depreciation as net capital outflows ensue. In order to mitigate such endogeneity issues, I run Generalized Method of Moments (GMM) estimations with instrumental variables for the endogenous variables. When the variable is set as exogenous a priori (this is the case for the global variables and the lagged dependent variable), I simply use it as instrument for itself; for the endogenous ones, I use their first lags as instruments. Non-exogenous and non-endogenous variables are not considered in the model specification. Therefore, by constraining the testable model specifications to a subset of only endogenous and exogenous variables, I can save computational cost. Parts A and B of Table 7.4 show chi-squared statistics for the Granger-causality test, respectively: (1) whether local variables anticipate changes in CDS spreads, and (2) whether the opposite holds true. A variable is deemed eligible when it is weakly exogenous or endogenous. Table 7.5 shows the subset of eligible variables for each country, that is, the weakly exogenous and endogenous variables marked with the labels “*” and “&”, respectively. Let’s take the case of Italy. Their eligible variables are the global variables (sp500, vix, Slope, and oil) and the local variables spread_i − 1, localTY_i, localSlope_i, and bank_i. The first five variables are assumed to be exogenous a priori. Weak exogeneity is attributed to localTY_i and localSlope_i, as their chi-squared statistics are significant at the 10% level in Part A (Table 7.4), while their Part B’s (Table 7.4) chi-squared statistics are non-significant at the 10% level. bank_i is set as endogenous, as their chi-squared statistics are significant at the 10% level in both Part A and Part B. When there is no label, the corresponding variable is not taken as eligible. Variables labelled as “(*)” in Table 7.5 are set as exogenous by assumption, that is, the global variables and the first lag of the dependent variable are not expected to be affected by the dependent variable in any sense.

Table 7.4 Granger-causality test

Table 7.5 Set of eligible explanatory variables

I run the change in the weekly CDS spread over the four global factors (sp500, vix, Slope, and oil), the lagged first difference of the corresponding CDS spread, and the local factors chosen following Granger-causality test results. Second, I run the large-scale engine in Stata (Baum 2003) for choosing the best-fit model for each country i, testing as many econometric models as possible, according to Eq. (7.1):

$$ \varDelta {\mathrm{spread}}_{i,t}={\alpha}_i+\sum \limits_{j=1}^4{\beta}_{i,j}.\varDelta {X}_{j,t}+{\lambda}_i.\varDelta {\mathrm{spread}}_{i,t-1}+\sum \limits_{k=1}^5{\gamma}_{i,k}.\varDelta {Z}_{i,k,t}+{\varepsilon}_{i,t} $$

(7.1)

where α_i = constant term for country i, X_{j, t} = set of global factors for week t: sp500, vix, Slope, or oil, Z_{i, k, t} = set of local factors for country i and week t: stock_i, xr_i, localTY_i, localSlope_i, or bank_i, ε_{i, t} = error term for country i and week t.

Variable transformations are such that “rate” variables are transformed first into absolute values, that is, CDS spreads, originally in basis points, are divided by 10,000; the other “rate” variables are divided by 100, when originally obtained in percentage format (USA slope factor, Local Short-Term Yield, and Local slope factor). “Price” variables are transformed into their logarithms: S&P 500 index, VIX index, Oil price, Local Stock Index, and Exchange Rate. I take the first differences of the resulting variables.

In the second step, I let the algorithm selects the model specification for each country constrained by the following pre-defined set of criteria.⁶ First, I require that at least one variable with significance at the 10% level has the expected sign as in Table 7.3 is included in the model. Within the space of such models, I select the one with the highest Adjusted R² which is statistically superior to all possible nested models.⁷ After testing 255 model specifications for Italy, for instance, the engine comes out with a model comprising S&P500, Slope, spread − 1, and localTY factors, as shown in Table 7.6. The Italy’s S&P 500 estimator value of −0.025 means that a 1% weekly variation of the S&P500 index would be consistent, ceteris paribus, with a 2.5 basis points contemporaneous reduction in the Italy’s CDS spreads. Blank cells in Table 7.6 mean that models including the corresponding factor are superseded by the prevailing model specification as presented in the table; or simply that this variable is not selected in the selection procedure. Finally, I assess the goodness-of-fit of the estimations and their forecast accuracy.

Table 7.6 GMM results

5.1 Results

The most striking result of Table 7.6 is that the sp500 estimator not only shows up as significant for most of the countries (22 out of 35), but one can also notice a remarkable difference in sensitivity magnitudes to this global factor between emerging markets and advanced economics. For countries where sp500 doesn’t show up as statistically significant in the specification (Germany, the Netherlands, Austria, Portugal, Denmark, Poland, Turkey, Australia, Hong Kong, Korea, China, Mexico, and Chile), different combinations of global and local factors (oil, spread − 1, xr, localTY, and bank) are found by the algorithm to be their best-fit models. Quite noticeably, vix, oil, and stock, which are exactly the variables orthogonalized against sp500, barely show up as significant for any country’s model specification.⁸ In line with the usual finding that most emerging markets and advanced economies are typically well integrated into the global markets, no local variable shows up as a significant driver of sovereign CDS spreads for 16 out of the 35 countries.⁹

The pervasiveness of sp500 is consistent with the results reported by other authors (Longstaff et al. 2011; Pan and Singleton 2008). The results in Table 7.6 also confirm the intuition that CDS spreads of emerging market sovereigns are more sensitive to global factors than spreads of developed countries.

That the CDS spreads of Israel, Malaysia, South Africa, Mexico, Peru, Chile, and Colombia are significantly sensitive to the exchange rate is in line with the evidence (Broner et al. 2013; Broto et al. 2011; Calvo 2007) that emerging markets’ debt riskiness is tightly linked to the dynamics of global capital flows or commodity prices.

Another interesting finding is that Portugal, Italy, Russia, Poland, Hungary, Turkey, and Colombia appear in Table 7.6 with local two-year yields being significant. While Portugal’s and Italy’s short-term debts might have been eventually under rollover risk between 2010 and 2012, as per the Eurozone debt crisis, the CDS spreads and yields co-movements of Russia, Poland, Hungary, Turkey, and Colombia are consistent with the usual view that a large part of their higher yields is presumably related to credit risk itself. In any case, these dynamics are arguably consistent with protection-sellers charging higher premiums on CDS contracts with those debts as reference obligations.

The fact that bank barely shows up as significant might be due to the general assessment that the transmission of distress from the banking sector to sovereign credit may occur more like a structural break than gradually over time.¹⁰ It could perhaps have been expected that increases in bank, as a stress indicator of the banking sector, could have gradually spilled over into the risk perception of sovereign bonds. Thus, the apparent underpricing of the spillover effect from the financial stability stance to the sovereign debt risk during the period leading to the 2010–2012 European sovereign debt crisis can be tentatively explained by the expectation that governments would: (1) monetize their debts (perhaps more in the case of the USA than for Eurozone countries), (2) wipe out defaulted bank’s shareholders and subordinated debtholders, or (3) be simply bailed out by economically stronger sovereigns. While not having been noticeably impacted by the global financial crisis, Hong Kong, Korea, and China are three jurisdictions where the banking sector remained relatively stable during the 2005–2012 period and where the governments are perceived to be very supportive of their domestic big banks. This may be the reason why, in these three cases, the sovereign and their banking system CDS spreads tend to co-move, that is, why their coefficients of the bank variable showed up as significant.

Next, I perform a goodness-of-fit analysis and compare the contemporaneous-variable model estimation outcomes with those of Autoregressive Moving Average (ARMA) structural models and lagged-explanatory variables specifications.

The goodness-of-fit of the GMM estimations is evaluated by means of Adjusted R², Theil’s U₁, Theil’s U₂, and percent hit misses (PHM) statistics. I calculate Adjusted R²s for the in-sample period, whereas for calculating Theil’s U₁, Theil’s U₂, and PHM out-of-sample statistics, I use the first two-thirds of the data for estimation and perform out-of-sample tests on the remaining sample. Normalizing the root mean squared error by the dispersion of actual and forecasted series or calculating the root mean squared percentage errors relative to naive forecast (random walk), Theil’s U₁ and Theil’s U₂ stand, respectively, as intuitive assessments of forecast accuracy. PHM assesses whether the direction of the prediction is accurate or not, that is:

$$ PHM=\raisebox{1ex}{$\# HitMisses$}\!\left/ \!\raisebox{-1ex}{$N$}\right. $$

where #HitMisses = number of times the prediction does not have the same sign as the realized value and N = total number of observations.

It is well known that higher values of Adjusted R² imply better model fit; however, lower Theil’s U₁, Theil’s U₂, and PHM values indicate better forecasting ability.

The goodness-of-fit statistics of Table 7.6 suggest that emerging market economies’ models presumably show more forecasting power than the developed countries’. Sorting into ascending (Adjusted R²) or descending order (Theil’s U₁, Theil’s U₂, and PHM), these statistics confirm that countries at the bottom rows of the table, broadly composed of emerging market economies, are associated with better goodness-of-fit measures.

As a benchmark for this chapter’s GMM estimations, ARMA model specifications are also estimated. The ARMA(p,q) process is estimated by full-information maximum likelihood estimation (FIMLE), following Box et al. (1994) and Enders (2004). I select the best model according to the following criteria: (1) the AR and MA terms are significant at the 10% level; (2) the residuals behave as a white-noise process (all autocorrelations of the residuals should be indistinguishable from zero), (3) the model has to have the lowest Bayesian Information Criteria (BIC) statistic, (4) it is non-degenerate, that is, there are no gaps within AR or MA terms, and (5) when (1) and (2) don’t hold, then I only take criteria (3) and (4) into account. I use Ljung and Box (1978) Q-statistic in eq. (2) at 10% significance level for testing (2).

$$ Q=T\left(T+2\right)\sum \limits_{k=1}^s\raisebox{1ex}{${r}_k^2$}\!\left/ \!\raisebox{-1ex}{$\left(T-k\right)$}\right. $$

(7.2)

If Q exceeds the critical value of χ² with s − p − q degrees of freedom, then at least one value of r_k, which is the sample autocorrelation coefficient of order k, is statistically different from zero (I set s to 10).

Table 7.7 shows that the goodness-of-fit statistics (Adjusted R², Theil’s U₁, Theil’s, U₂ and PHM) of are noticeably worse than the respective contemporaneous model statistics (Table 7.6).

Table 7.7 ARMA results

As for the lagged-factor specifications, Table 7.8 shows that they are noticeably less robust than those comprising contemporaneous factors. Except for a few occurrences (10 out of 124), the lagged-variable models’ goodness-of-fit metrics are worse than those of contemporaneous-variable models (Table 7.6). Besides, the “best-fit” lagged-variable model specifications (which I am able to obtain for all but France, Italy, Spain, and Ireland) are even worse than those of ARMA models (Table 7.7).¹¹

Table 7.8 GMM results with lagged-explanatory variables

5.2 Robustness Check

This subsection shows that even altering the algorithm criteria significantly (changing the significance level of the Granger-causality test at which variables are included in the analysis, or substituting other goodness-of-fit statistics for the Adjusted R²) or repeating the analysis across different sub-periods does not give rise to results substantially challenging this chapter’s two main claims, that is, that the S&P 500 index is statistically significant and contemporaneously negatively related to the CDS spreads for most of the countries, and that emerging market’s coefficients on the S&P 500 variable are higher in magnitude than those of advanced economies. To be sure, the S&P 500 coefficient’s statistical significance and its magnitude do change when modifying the algorithm criteria or the sample period, leading to different country ranking orders. The coefficient on the S&P 500 for Russia (statistically significant and with the expected negative sign in Table 7.6), for instance, is not available in the July 2005–June 2010 and January 2008–December 2010 sub-periods’ models, while ranging from −0.073 to −0.028 as for the other four sub-periods (Tables 7.15 and 7.16). Although the individual coefficient estimates somewhat vary between the different specifications, those of the S&P 500 remain higher (in absolute terms) for emerging markets.

Interestingly, eliminating the criterion (1) (choosing models with at least one coefficient significant at the 10% level with the expected sign) altogether from the algorithm, or modifying the restriction (2) (choosing models with the highest Adjusted R²), the engine still generates models (see Tables 7.9, 7.10, 7.11, and 7.12) with statistically significant negative coefficients on the sp500 variable, higher in absolute terms for emerging market countries than for advanced economies. Table 7.9 shows that the characteristics of the sole 6 (out of 35 models; highlighted in bold) models which happen to be distinct from those of Table 7.6 don’t lead to a different assessment regarding the coefficient of the sp500 variable. By the same token, no dramatic changes take place regarding the quantity and the magnitude of statistically significant sp500 coefficients. It continues to play a dominant role in explaining the CDS spreads in nearly all of our sample countries, and the higher sensitivity of emerging markets to this variable, when substituting other goodness-of-fit statistics for the Adjusted R² as a criterion for selecting the best-fit models (Tables 7.10, 7.11, and 7.12).

Table 7.9 GMM results without the criterion “with at least one 10%-significant coefficient with expected signs according to Table 7.3”

Table 7.10 GMM results substituting Theil’s U₁ for Adjusted R² in criteria (2) “with the highest Adjusted R²”

Table 7.11 GMM results substituting Theil’s U₂ for Adjusted R² in criteria (2) “with the highest Adjusted R²”

Table 7.12 GMM results substituting percent hit misses (PHM) for Adjusted R² in criteria (2) “with the highest Adjusted R²”

Aiming to evaluate, to a fairly large extent, whether changing the Granger-causality test significance level from 10% to 5% would lead to the rejection of this chapter’s main claims, I ran the algorithm over the six sub-periods: (1) July 2005 to October 2012, (2) July 2005 to June 2010 (Before Jul 2010), (3) July 2010 to June 2014 (After Jul 2010), (4) July 2005 to June 2008 (Before Jul 2008), (5) January 2008 to December 2010 (Subprime Crisis), and (6) July 2010 to June 2013 (Euro Crisis). As it turns out, had I imposed a stricter cutoff (a 5% significance level, instead of 10%), it wouldn’t materially have changed this chapter’s main outcomes (Table 7.13).

Table 7.13 5%-significant level Granger-causality test

Changing the significance level to 5% reduces the set of eligible variables either by excluding previously selected variables, or by switching previously endogenous variables to weakly exogenous ones. As expected, supressing previously elected variables from the set of eligible variables leads to the algorithm generating a different model. For instance, when excluding the LocalTY factor from the set of eligible variables, Portugal’s alternative model (Table 7.14) ends up presenting a statistically significant S&P 500 estimator, when it was not the case previously (Table 7.6). Less obviously, when the changed cutoff of the level of significance switches a previously endogenous variable into a weakly exogenous one using the Granger-causality test, the algorithm may prefer a different model. The Netherlands’ alternative model (Table 7.14), for example, shows a statistically significant coefficient on the S&P 500, when the previously endogenous variable localSlope (at the 10% significance level) turns into a weakly exogenous variable (at the 5% level) and further excluding xr and localTY from the set of eligible variables, even though none of these three variables were part of the originally selected model (see Table 7.6). As it turns out, this unintended consequence is due to the change in the instrumental variables setting: endogenous variables are transformed into lags when running the GMM regressions, while weakly exogenous ones are not.

Table 7.14 GMM results—5%-significant level Granger-causality-test set of eligible variables

Jointly, the results of Tables 7.15 and 7.16 show that the net effect of reducing the significance level from 10% to 5% in the Granger-causality test is almost neutral in terms of the quantity of statistically significant coefficients of the S&P 500 within each sub-period. What is more, the algorithm’s outcomes still provide support to this chapter’s two main findings. Tables 7.15 and 7.16 also show that the differences between the quantities of statistically significant S&P 500 estimators across the six sub-periods aren’t large: 5, 1, 0, 0, 0, and 2 out of 35 countries, respectively, for the sub-periods July 2005–October 2012, Before July 2010, After July 2010, Before July 2008, Subprime Crisis, and Euro Crisis. Overall, whether or not the S&P 500 is selected by the algorithm does depend on the specific setting. Let’s take the models for New Zealand and the Colombia models for the July 2005–June 2010 period (“Before Jul 2010” column in Table 7.16).¹² Supressing localSlope from the set of eligible variables for New Zealand gives rise to an alternative model where the previously non-significant coefficient of the S&P 500 (see the corresponding column in Table 7.15) now becomes statistically significant. In contrast, the S&P 500 is no longer selected by the algorithm for Colombia, when the Granger-causality test leads to the exclusion of the variable stock from the set of eligible variables. Quite conspicuously, apart from slight differences in other factor estimators for just three countries, the statistical significance of the coefficients of the S&P 500 is pretty much the same for the July 2005 to June 2008 (“Before Jul 2008” column in Tables 7.15 and 7.16).¹³

Table 7.15 Coefficient estimators for sp500_t across different sub-samples

Table 7.16 Coefficient estimators for sp500_t across different sub-samples 5%-significant level Granger-causality-test set of eligible variables

Ordering Adjusted R² statistics from low to high values and the other goodness-of-fit statistics (Theil’s U₁, Theil’s U₂, and PHM) the other way around (descending) according to the column “After Jul 2010”, Tables 7.17, 7.18, 7.19, and 7.20 support the finding that emerging markets model specifications (mostly at the bottom rows of the tables) tend toshow better goodness-of-fit and forecast accuracy statistics as a group than advanced economies across all the different sub-periods.

Table 7.17 Adjusted R² across different periods

Table 7.18 Theil’s U₁ across different periods

Table 7.19 Theil’s U₂ across different periods

Table 7.20 PHM across different periods

Tables 7.21 and 7.22 show respectively that ARMA models’ and lagged-variable models’ goodness-of-fit statistics are mostly superseded by the contemporaneous models across the other five sub-periods as they are for the July 2005–October 2012 period.¹⁴ However, comparing Table 7.21 values particularly with those of Tables 7.18 and 7.19, we find a couple of better ARMA Theil’s U₁ values (highlighted in bold in Table 7.21, column “Before Jul 2008”) and Theil’s U₂ values (highlighted in bold in Table 7.21, columns “After Jul 2010” and “Euro Crisis”); yet this is the case for just less than half the number of countries. Showing mixed results in comparison to the corresponding ARMA-model statistics (Table 7.21) for the periods “Before Jul 2010”, “After Jul 2010”, “Before Jul 2008”, “Subprime Crisis”, and “Euro Crisis”, Table 7.22 indicates that the lagged-variable model statistics are worse than those of the ARMA models for the July 2005–October 2012 period and noticeably worse than the corresponding contemporaneous model statistics (Tables 7.17, 7.18, 7.19, and 7.20). In addition, one can also notice that no coefficient of the S&P 500 appears to be statistically significant for the two overlapping sub-periods “After Jul 2010″ and “Euro Crisis”.

Table 7.21 ARMA models’ goodness-of-fit statistics

Table 7.22 Lagged-explanatory variable models’ S&P500 estimators and goodness-of-fit statistics

6 Conclusion

I find that the S&P 500 is significant in explaining CDS spreads across a range of countries, especially emerging markets. Moreover, the coefficients of Exchange Rate and Local Two-Year Yield variables have the expected sign, and are also significant for some important investable markets. On the other hand, variables such as VIX, Oil, Local Stock index, Slope, Local Slope, and Banking System are rarely found to be statistically significant in explaining sovereign CDS spreads. Strikingly, goodness-of-fit and forecast accuracy are much better for emerging markets than for developed countries. Models with contemporaneous variables provide better statistical fitness than lagged-variable models. As for ARMA models, except for a few occurrences, their goodness-of-fit and forecast accuracy statistics are worse than for contemporaneous fundamental models across the board. When generating fundamental models with lagged variables, however, the engine comes up with goodness-of-fit statistics even worse than those of pure time series-generated models (ARMA).

If the past is any guide (so far I still believe it is!) and risk assessments are to be made on a weekly basis, the proposed large-scale, econometric-based framework can be used as part of an early warning tool. While using this framework in practice, however, some caveats should be kept in mind. Models with contemporaneous variables need one-week-ahead predictions as inputs. Accordingly, the results point out that forecasting initiatives should be focused on global variables, particularly those conveying the overall risk aversion or the general state of the global economy, like the VIX or the S&P 500 factors. Not least, Longstaff et al.’s (2011) advice is worth considering: as the estimation period is “characterized by excess global liquidity, prevalence of carry trades and reaching for yield in thesovereign market”, approaches like the one proposed in this chapter should be taken with a grain of salt when applied to periods not subject to those market forces. In addition, models based on historical information do not necessarily unveil the true relationship between variables under unusual circumstances, regardless of how sophisticated they are.

As for additional robustness assessments, I recommend applying randomization tests on a selected set of explanatory variables and compare the forecast accuracy ex-post. For example, if 60% of predictions of changes in S&P 500 had been correct, what would have been the value for PHM? Besides, while this chapter provides some evidence for the overall neutrality in terms of the quantity of statistically significant S&P 500 coefficients, there is an opportunity to more extensively check the robustness of the algorithm to potential unintended consequences when modifying the set of instrumental variables in the GMM estimation.

Finally, for future research, one could test other banking sector-related variables. While the well-functioning of the banking sector is key to fostering the economic development of any country, the opposite has proved so far to hold true: banking crisis can lead to economic recession. Not as a coincidence, the factor bank_{i, t} strikes as indicating double causality between the sovereign and its corresponding banking system CDS spreads in almost all cases for which I could achieve data for banks’ CDS spreads, as shown in Table 7.5.¹⁵ As it turns out, distresses in the banking sector, when pervasive and impacting too-systemic-to-fail banks, as for the 2007–2009 crisis and the European debt crisis, might lead to negative views on the debt sustainability of the corresponding jurisdiction, which would presumably manifest themselves by increasing CDS spreads. Playing a pivotal role in paving the way for economic growth or where having a specific mandate for guaranteeing financial stability, central banks, as lenders of last resort, have an incentive to bailing the banking sector out. In this chapter, although using the average of banks’ CDS spreads as a proxy for the distress in the banking sector, it didn’t show up as significant in most of the cases.¹⁶ I conjecture that movements in sovereign CDS spreads might not have fully captured the dynamics of the banking sector risk, as its transmission to sovereign credit deterioration may occur more like a structural break than continuously in time.