A comprehensive approach to measuring the relation between systemic risk exposure and sovereign debt

Accepted Manuscript Title: A Comprehensive Approach to Measuring the Relation Between Systemic Risk Exposure and Sovereign Debt Author: Michael S. Pagano John Sedunov PII: DOI: Reference:

S1572-3089(16)00022-X http://dx.doi.org/doi:10.1016/j.jfs.2016.02.001 JFS 419

To appear in:

Journal of Financial Stability

Received date: Revised date: Accepted date:

1-7-2015 3-12-2015 2-2-2016

Please cite this article as: Pagano, M.S., Sedunov, J.,A Comprehensive Approach to Measuring the Relation Between Systemic Risk Exposure and Sovereign Debt, Journal of Financial Stability (2016), http://dx.doi.org/10.1016/j.jfs.2016.02.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights for “A Comprehensive Approach to Measuring the Relation Between Systemic Risk Exposure and Sovereign Debt”

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Systemic risk is positively related to sovereign debt yields in a crisis-driven, episodic manner A simultaneous relation suggests that sovereign debt models should include systemic risk metrics Shocks to domestic linkages are stronger and longer lasting than international risk spillovers The channel is indirect between domestic sovereign debt yields and another nation’s sovereign debt The model is useful for capital adequacy, liquidity risk, “too-big-to-fail,” and monetary policy

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A Comprehensive Approach to Measuring the Relation Between Systemic Risk Exposure and Sovereign Debt

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Michael S. Pagano* John Sedunov Villanova University

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Forthcoming, Journal of Financial Stability

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First Draft: January 15, 2013 This Draft: February 4, 2016

Abstract

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Using an integrated model to control for simultaneity, as well as new risk measurement techniques such as Adapted Exposure CoVaR and Marginal Expected Shortfall (MES), we show that the aggregate systemic risk exposure of financial institutions is positively related to sovereign debt yields in European countries in an episodic manner, varying positively with the intensity of the financial crisis facing a particular nation. We find evidence of a simultaneous relation between systemic risk exposure and sovereign debt yields. This suggests that models of sovereign debt yields should also include the systemic risk of a country’s financial system in order to avoid potentially important mis-specification errors. We find evidence that systemic risk of a country’s financial institutions and the risk of sovereign governments are inter-related and shocks to these domestic linkages are stronger and longer lasting than international risk spillovers. Thus, the channel in which domestic sovereign debt yields can be affected by another nation’s sovereign debt is mostly an indirect one in that shocks to a foreign country’s government finances are transmitted to that country’s financial system which, in turn, can spill over to the domestic financial system and, ultimately, have a destabilizing effect on the domestic sovereign debt market. Keywords: Systemic Risk, Banking Crises, Sovereign Debt, Contagion, Financial Institutions JEL Codes: G01, G21, G28, H63 *

This paper was formerly titled “What is the Relation Between Systemic Risk Exposure and Sovereign Debt?” Address correspondence to Michael Pagano, Villanova School of Business, Villanova University, 800 Lancaster Ave., Villanova, PA 19085; Phone: 610-519-4389; Fax: 610-519-6881; or e-mail: [email protected]. We thank two anonymous referees, as well as Giovanni Petrella and other participants at the 2013 Financial Engineering & Banking Society (FEBS) annual meeting, Paul Kupiec and other participants at the 2013 Southern Finance Association (SFA) annual meeting, Eliza Wu and other participants at the 2014 Eastern Finance Association (EFA) meeting, Xin Huang and other participants at the 2014 Financial Intermediation Research Society (FIRS) meeting, as well as Lamont Black, Bob DeYoung, Pankaj Jain, Steve Jordan, Loretta Mester, Sandra Mortal, Yoon Shin, Christine Xiang, and participants at the Villanova University seminar series, as well as seminar participants at the University of Memphis for helpful comments. We also greatly appreciate the capable research assistance of Jayneel Jadeja, Boby Katumkeeryil, Lauren Knight, Matthew Retzloff, Jason Kushner, and Alejandro Cuevas. Finally, we thank Moody’s for allowing us the use of their Expected Default Frequency data.

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1 Introduction The recent European crisis is fundamentally a sovereign debt crisis in which the governments of developed countries neared default. The crisis affected many of the European Union countries, several of

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which are bound together by the same currency (Hoffmann, 2013). As the 2007-2009 U.S. financial crisis has shown, problems in one market (e.g., subprime mortgages) can quickly create negative spillover

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effects to financial institutions and nations that were not thought to be be closely related. These spillover effects can lead to sudden, sharp spikes in a financial system’s overall risk, commonly referred to as

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systemic risk.* Several studies show that contagion and / or spillover exists during crisis periods (e.g., Bekaert, Ehrmann, Fratzscher, and Mehl (2014); Beirne and Fratzscher (2013); Keiler and Eder (2013)).†

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Our study builds upon this literature, and is the first to use a comprehensive simultaneous system in order to show not only that international risk spillovers exist, but also reporting that risk spillovers exist

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between governments and their domestic financial systems, both in terms of sovereign yields and exposure to systemic risk.‡ Moreover, we demonstrate that these spillovers occur simultaneously and thus

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existing sovereign debt models should include systemic risk as an important additional explanatory

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variable in order to avoid potential mis-specification errors.

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The goal of this study is to answer four questions in a holistic manner about the relation between the risks of a nation’s sovereign debt and its financial system, along with their impact on other nations’ sovereign debt and financial systems. As summarized in Figure 1, our first research question examines the inter-relationships between one country’s financial system and its sovereign yield (denoted in the diagram * Note that recent literature such as Bekaert, Ehrmann, Fratzscher, and Mehl (2014) and Beirne and Fratzscher (2013) make the distinction between spillover and contagion effects. For example, contagion occurs when a “sick” country or firm “infects” an otherwise-healthy country / firm whereas a spillover occurs when conditions within a country or firm influence another country / firm which may or may not be “healthy.” In our analysis, we are primarily focused on risk spillover effects. See Duarte and Eisenbach (2015) for another perspective on risk spillovers in the context of fire sales. † As noted in Bekaert, et al. (2014), contagion can be defined as “the change in the way countries’ own fundamentals or regional risk are priced during a particular period.” As Boyson, Stahel, and Stulz (2010), among others, show, contagion can also occur at the firm level. However, our focus is on how firm level risk-taking can, in the aggregate, affect systemic risk exposure and sovereign debt yields at the national level. ‡ There is an important distinction between exposure to systemic risk and contribution to systemic risk. Exposure to systemic risk estimates the sensitivity of a single financial institution to a negative shock within the entire financial system. In contrast, contribution to systemic risk estimates the sensitivity of the financial system to a negative shock within a single institution. We focus on the former type of risk measure in this study because systemic risk exposure is most relevant to an FI’s managers and shareholders since it measures the direct impact of a systemic risk event on the FI’s market value. In particular, we find that Conditional Value-at-Risk (CoVaR) and Marginal Expected Shortfall (MES) are the most direct and reliable measures of systemic risk exposure. CoVaR measures the sensitivity of bank assets to changes in the assets of the financial system while controlling for systematic risks. Marginal Expected Shortfall estimates the average bank return during the 5% worst return days of the market. These concepts are described in more detail in Section 2. See Bisias, et al. (2012) for a comprehensive review of systemic risk measurement and Black et al., 2013 and Engle et al., 2014 for European-centric measures of contribution to systemic risk.

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as Relation 1 between Government A and Financial System A). Second, we study the linkage between the riskiness of one nation’s financial system and another country’s financial sector (referred to as Relation 2 between Financial System A and Financial System B in Figure 1). Third, we analyze the potential relation

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between different nations’ sovereign debt risk levels (shown as Relation 3 between Government A and Government B in the diagram). Fourth, we study the possible inter-relations between the riskiness of one

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nation’s financial system and another country’s sovereign debt because the risks from one nation might spill over to another in an indirect manner (between one nation’s financial system and another country’s

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sovereign debt market via a “cross-market” effect as described by Relation 4 in Figure 1).

Our approach is the first comprehensive, integrated analysis of all four inter-relations outlined in

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Figure 1 whereas most existing research has primarily focused solely on one or two of these relations. For example, Relation 1 (i.e., the links between domestic FIs and a nation’s sovereign debt) is the primary

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focus of Acharya and Steffen (2013), Beirne and Fratzscher (2013), Battistini et al. (2014), Gennaioli, Martin, and Rossi (2014), and Acharya, Pierret, and Steffen (2016). In contrast, Kallestrup et al. (2013),

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Alter and Beyer (2014), Eichengreen et al. (2012), Degryse et al. (2010), among others, have explored

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Relation 2 (financial system spillovers). Relation 3 (sovereign debt spillovers) has been studied by Beirne

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and Fratzscher (2013), Caporin et al. (2015), Bai et al. (2012), Benzoni et al. (2015), Lucas et al. (2013), and Brutti and Saure (2015). Finally, Relation 4 (cross-market international effects) has been analyzed in Kallestrup et al. (2013), Bruyckere et al. (2013), Billio et al. (2014), Gunduz and Kaya (2014), and Manzo and Picca (2015), among others. Thus, although these papers mainly focus on subsets of the risks and relations noted in Figure 1, our study is able to test all four relations simultaneously in order to see which relations remain significant in this broader context. In particular, we find that Relation 3 is not as strong as previously thought when all four effects are estimated jointly. Thus, the channel in which domestic sovereign debt yields can be affected by another nation’s sovereign debt is an indirect one in that shocks to one country’s government finances are transmitted to that country’s financial system which, in turn, can spill over to the domestic financial system and, ultimately, have a destabilizing effect on the domestic sovereign debt market. This indirect channel suggests that an integrated, simultaneous model is required

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to estimate the true effect of system risk events on financial institutions and sovereign debt in an international setting.§ The intuition underlying these questions is that a nation with a risky financial system may be

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more likely to have higher sovereign yields because investors expect the government’s finances can become strained if the government is forced to bail out the nation’s major FIs. That is, countries which

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provide a bailout to systemically distressed financial firms (or are perceived to be willing to bail out these FIs) may increase the riskiness of their own sovereign debt. Conversely, a country’s financial system

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might grow more risky as the government’s financial condition becomes weaker if these FIs are expected to purchase large amounts of the nations’ (risky) sovereign debt (Gennaioli et al., 2014). Thus, the risks of

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both the country’s government debt and financial system might be inter-related and, due to geographic and trade linkages, the risks of one nation might also spill over and affect other nations.

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To test the four questions described above, we first estimate the systemic risk exposure to European-wide banking crises for each individual FI within a nation (i.e., via the CoVaR and Systemic

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Expected Shortfall methods) and then aggregate these exposures at the national level.** Building from this

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firm-level estimate of systemic risk, we extend the analysis to examine the aggregate exposure of one

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country’s financial institutions to a systemic event and / or sovereign default in other countries within the same region. These potential spillover effects are similar in spirit to those described in Bekaert and

§ As noted above, there are several studies that examine a subset of the four relations but, to conserve space, we describe just a few here that are most closely related to our study. For example, Manzo and Picca (2014) use CDS data and a custom system risk contribution measure to estimate spillovers between the sovereign debt of 24 European countries and 41 large financial institutions. However, this study, as well as Kallestrup et al. (2013), relies on CDS data and does not directly examine all four types of linkages across these countries’ sovereign debt and FIs. Alter and Beyer (2014) also use CDS data to study domestic and international linkages but the reliance on CDS information can be problematic because these data are more directly capturing an FI’s default risk (and liquidity risk) rather than the FI’s exposure to systemic risk. In contrast, we use two direct measures of systemic risk, CoVaR and MES. Billio et al. (2014) examines the interconnectedness of European sovereign and FIs using Granger causality and network analysis on a pairwise basis but does not jointly quantify the impact of all four relations that we describe in Figure 1. Beirne and Fratzscher (2013) develop a framework for studying the linkages between sovereign debt yields within an economically integrated region and their analysis implies that international connections between systemic risk and sovereign debt might also exist (although they do not perform such tests). Lastly, Lahmann (2012) investigates some aspects of these potential intra-regional linkages, although not in as comprehensive empirical framework as we describe here. ** It should also be noted that Danielsson et al. (2012) suggest that systemic risks such as CoVaR and SES may be essentially alternative measures of systematic (or investment) risk rather than FI-specific systemic risk. In addition, Zhang, Vallascas, Keasey, and Cai (2013) voice similar concerns about the relative rankings of different methods of measuring the contributions to systemic risk. To address these concerns, we perform robustness checks in Section 5 that demonstrate that CoVaR is not simply measuring systematic risk. However, even if Danielsson et al’s criticism of systemic risk measures is correct, the important point for our analysis is that our metric remains a statistically significant determinant of sovereign debt models (regardless of whether one interprets it as “systemic” or “systematic” risk). Moreover, recent work also suggests that the relation between banks and sovereigns may be unique. Bedendo and Colla (2015) show that risk from non-financial corporations does not spill over to sovereigns. This gives further evidence that the banking system has an important relation with sovereign governments. We thank Paul Kupiec for pointing out this possibility.

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Harvey (2005) and to bank-level contagion effects studied in Straetmans and Chaudry (2015) and Lahmann (2012). To answer these questions, we use data from a relatively well-integrated region as well as a new set of systemic risk metrics, as developed in Adrian and Brunnermeier (2015) and refined in

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Sedunov (2016). We use time series and panel regression methods to investigate the relations between a nation’s

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systemic risk exposure and the default risk of sovereign debt. Our study focuses on Europe during 20072013 and provides evidence that the aggregate systemic risk exposure of the financial institutions in a

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given European country is positively related to future changes in the yields on sovereign debt obligations. We show that, on average, a one-standard deviation increase in a nation’s contemporaneous systemic risk

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exposure can anticipate by one quarter a change in the country’s ten-year yield spreads of 39.00 bps, which is 12.04% higher than the mean ten-year spread in 2011. Further, we show that systemic risk

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exposure may spill over on a national level during a financial crisis. In doing so, we quantify the magnitude of the spillover effect between nations. For example, we find that the so-called GIIPS nations

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affect the systemic risk exposure of all other European nations and this effect is strongest during the

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2009-2011 European sovereign debt crisis.††

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We contribute to the literature in four ways. First, our paper examines the link between systemic risk exposure and sovereign yields within an integrated empirical framework which allows for potential endogeneity between systemic risk exposure and sovereign debt (i.e., Relation 1) and cross-border spillovers. We find that the aggregate systemic risk exposure of a country is positively related to sovereign yields, even after controlling for known determinants of sovereign yields and spreads. Moreover, we test for endogeneity and find support for a simultaneous relation between systemic risk exposure and sovereign debt yields. Second, our paper shows that systemic risk is an important determinant of sovereign yields. This has implications for modeling sovereign debt going forward. To this point, a comprehensive analysis of systemic risk exposure of a country’s financial system and its simultaneous inter-relations within a ††

The GIIPS acronym represents the following European countries: Greece, Ireland, Italy, Portugal, and Spain (e.g., Walker (2009)).

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country and across nations has been less extensively studied in the current sovereign debt literature. Our findings suggest that systemic risk is an important determinant of the riskiness of sovereign nations (especially during a crisis period) and thus this form of risk should be included in sovereign debt models

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in order to avoid potential mis-specification problems. Third, we address the issue of potential linkages across nations by estimating models via system

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generalized method of moments (GMM) and find that our initial results remain robust to this specification. In addition, we observe significant spillover effects that confirm Relations 1-4 within a

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jointly determined empirical specification. We also observe that the strength of these linkages and spillover effects vary over time with the strongest effects occurring during the 2009-2011 European

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sovereign debt crisis period.‡‡ In addition, we explore the time series dynamics of these relations and find that the domestic linkages between sovereign debt and the financial system are stronger and more

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persistent than international risk spillovers. For example, a one-standard deviation increase in domestic systemic risk can quickly increase sovereign debt yields by more than 118 bps and these yields will still

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remain over 40 bps higher 3 years after the initial shock to the domestic financial system. Thus, the

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channel in which domestic sovereign debt yields can be affected by another nation’s sovereign debt is

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mostly an indirect one in that shocks to a foreign country’s government finances are transmitted to that country’s financial system which, in turn, can spill over to the domestic financial system and, ultimately, have a destabilizing effect on the domestic sovereign debt market. This indirect channel suggests that an integrated, simultaneous model is needed to estimate the true effect of systemic risk events on financial institutions and sovereign debt in an international setting. Finally, we estimate robustness tests. First, we substitute the Marginal Expected Shortfall (MES) measure of systemic risk exposure (Acharya, et al., 2015) for the Adapted Exposure CoVaR method (defined in Section 2) in our GMM model. We find that our main GMM results are invariant to the choice of systemic risk exposure metric. This finding is observed even though MES may measure a ‡‡

This finding is consistent with Beirne and Fratzscher’s (2013) “wake-up call” effect where sovereign debt yields suddenly react to an increase in the riskiness of a nation’s fiscal condition.

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different aspect of risk than the CoVaR methodology. Thus, we have confidence in the Adapted Exposure CoVaR methodology as our primary measure of systemic risk exposure, and the supporting evidence by MES serves as an important robustness check. Moreover, we allow for the possibility that the CoVaR

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measure is correlated with sovereign risk, as both measures are likely to move simultaneously, particularly during a crisis period. To disentangle this possible confounding effect, we thus regress

regressions.

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CoVaR on the spreads of a European sovereign debt index and recover the residuals from these The residuals act as “clean,” orthogonalized estimates of exposure to systemic risk,

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independent of any co-movement with sovereign debt spreads. All of our results are robust to replacing CoVaR with these residuals and thus confirm that a nation’s systemic risk, independent of any crisis-

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related fluctuations in foreign debt spreads, can significantly affect the country’s sovereign debt yields. The answers to the above questions are of primary importance to bank regulators. Given the

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fragile nature of several European economies at this time, it is necessary for regulators to understand the role that financial institutions play in shaping the probability of further distress in European sovereign

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debt. Acharya, et al. (2009) also notes that one of the major issues in the U.S. financial crisis is that

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“current regulation is focused not on systemic risk but rather on the individual institution’s risk.”

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Additionally, these questions and our model’s findings are important for regulators in terms of addressing issues related to capital adequacy, liquidity risk management, “too big to fail” behavior, and monetary policy. For example, understanding the link between sovereign debt and systemic risk exposure may require a change in the risk-weighting of sovereign debt when risk-weighted assets are calculated for Basel III capital requirements. Thus, understanding how financial institutions influence aggregate sovereign default probabilities and what types of FIs are most likely to affect these outcomes can help regulators develop specific policies that mitigate some of the effects of a crisis situation or possibly prevent one altogether. Further, it would be of great use for investors (including banks, international money managers, and other central banks who hold large amounts of sovereign debt) to have an understanding of how the default of a single nation is related to the possible default of other nations. Extending our systemic risk measures to capture changes in, for example, the default probability of

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various nations, will allow for an understanding of which nations may be “too systemic to fail.” The remainder of this paper is organized as follows. Section two motivates and defines the systemic risk exposure measures used in the analysis. Section three describes the data, while section four

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presents our results. Section five presents a set of robustness checks. Section six concludes.

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2 Methodology

The issues described above are important to the finance literature. Carey, Kashyap, Rajan, and

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Stulz (2012) note that one of the key open questions about the recent crisis is what we can “learn from similarities and differences in the performance of banks across countries.” Our paper directly addresses

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this question, enhances our understanding of systemic risk on an international level, and also contributes to the burgeoning literature on systemic risk and its link to sovereign debt (e.g., Acharya, Dreschsler, and

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Schnabl, 2015; Bolton and Jeanne, 2011; Leonello, 2014, and others noted in the Introduction). Consistent with the intuition outlined in the Introduction, prior research has explored some of the

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relations noted in Figure 1. For example, Relation 1 has been partially examined and, during the 2007-

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2011 crisis period, bank holdings of the sovereign debt of several European nations are shown to be

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related to the systemic risk contribution of individual banks within the system (Acharya and Steffen (2013); Alter and Beyer (2014); Gennaioli et al. (2012), among others).§§ However, an important question which remains is what the effect of aggregate systemic risk exposure is on sovereign debt yields. A bank with high systemic risk exposure is susceptible to a tail event, such as the sovereign debt default of a given country or set of countries; or a systemic event within the financial system such as the failure of a large financial institution.*** If the financial institution is regarded as systemically important, then its national government may be forced to provide a bailout, so as to save the rest of the financial system (Acharya, Philippon, Richardson, and Roubini 2009). A similar situation may occur when many banks

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Unlike Acharya and Steffen (2013), who use hand collected, semi-annual data for 63 banks, we do not include bank holdings at the firm level. Our sample many more financial institutions over a longer time series, and utilizes quarterly data. We can thus not obtain data over this time period to include sovereign debt holdings by individual banks in our analysis. *** The systemic and sovereign debt risks may be inter-related because a sovereign default is an economy-wide event and thus will affect both the “real” and financial sectors of the macroeconomy.

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fail at once (Acharya and Yorulmazer, 2007). A bailout may then lead to some form of financial distress for the sovereign nation, particularly if the nation is already experiencing other macroeconomic difficulties. The literature referenced here suggests the importance of measuring the impact of a tail event

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financial institution, we use Adapted CoVaR as our primary metric.

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on a nation’s financial system, which we define as systemic risk. Thus, to measure this type of risk for a

2.1 Estimating Systemic Risk Exposure - Adapted Exposure CoVaR Beta

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We describe fully our primary measure of systemic risk exposure, CoVaR, in Appendix A. Here, we present some modifications we make to the traditional CoVaR methodology. As constructed, the

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estimation method of Exposure CoVaR incorporates all available past information. Thus, it is a useful tool to discern what institution-level variables are closely linked to systemic risk exposure over the full

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length of a sample period. However, it is not clear that the measure accurately reflects the systemic risk exposure of an institution at a specific time since there is no reason for this exposure to be constant over

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time for an institution. Thus, we follow the methodology of Sedunov (2016), and introduce two

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innovations for estimating Exposure CoVaR compared to the approach used by Adrian and Brunnermeier

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(2015).

The first modification relates to the estimation of  vary over time. We allow 

j| s

j| s

. As currently calculated, 

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does not

to vary over time by using stock return data available only over the two

years of daily data prior to the quarter of estimation.††† In all regressions that follow, Exposure CoVaRs are calculated using this modified process. This modification thus allows institution-level exposures to fluctuate over time. This is a beneficial change, since the drivers of systemic risk exposure may be timevarying. Thus, rather than use institution-level variables to indirectly forecast systemic risk exposure, the Exposure CoVaR measure may be utilized directly to determine which institutions have the highest levels of systemic risk exposure at a specific time. Despite this modification, however, the economic definition †††

Other short lags can be utilized, and produce similar results to those below. As shown in Sedunov (2016), this variable is problematic if the entire time-series of available data is used. It is important to update the data over time, as this allows the measure to capture the evolving nature of the financial system.

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of Adapted Exposure CoVaR does not change from its original meaning, as it measures the sensitivity of the performance of financial institutions conditional on a systemic event. As noted above, our second adaptation constructs the CoVaR measure using stock returns rather

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than asset returns. This is due in most part to the lack of quarterly banking data available from European banks for total assets and liabilities.‡‡‡ Further, the European Systemic Risk Board (ESRB) utilizes this

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equity-based method when constructing CoVaR for its systemic risk dashboard.§§§ We estimate the daily Exposure CoVaR beta of each bank in each country using regressions which roll over a 500-day window

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of previous equity returns. Then, on a daily basis, we compute a simple average using the Exposure CoVaR beta of all FIs within a country to calculate the aggregate country-level Exposure CoVaR beta. To

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calculate weekly or quarterly measures, we average the country-level Exposure CoVaR beta over the corresponding time period.

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 t j|s estimates the exposure of the assets of an institution to a change in the assets of the financial

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system. Alternatively, Adapted Exposure CoVaR is the product of  t j|s and the difference between the

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median state and 1% worst state of the financial system’s assets at time t . Thus, Adapted Exposure CoVaR is a measure that increases during crisis periods due to the state of the economy. Rather, a

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measure of exposure should remain reflective of the institution’s state at a given time, rather than reflective of the state of the financial system. Therefore, we use Adapted Exposure CoVaR beta (  t j|s ) throughout the paper as the primary estimate of systemic risk exposure from the CoVaR family. This measure specifically relates the sensitivity of an institution’s equity, rather than the institution’s VaR, to changes in the value of the equity of the financial system. Because of this, Adapted Exposure CoVaR beta can be thought of as a measure of the exposure of the market value of an institution to a systemic crisis. Moreover, because we are not calculating a true Value-at-Risk measure, we need not worry about the possible non-normality of equity returns distorting a VaR calculation. In calculating Adapted Exposure ‡‡‡

Sedunov (2016) uses asset returns in the CoVaR methodology. Adrian and Brunnermeier (2015) calculate the market value of assets as market equity multiplied by book leverage, whereas Sedunov (2016) proposes (book assets - book equity + market equity), which is a standard definition. §§§ This report can be found at: http://www.esrb.europa.eu/pub/pdf/dashboard/121220_ESRB_risk_dashboard.pdf?7d675d1afebfe8d983401e6394314aa5

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CoVaR beta, we use quantile regressions, which allows us to estimate using the actual historical distribution of returns, rather than an assumed normal distribution. Thus, the Adapted Exposure CoVaR beta measure does not suffer from the distributional shortcomings that some traditional VaR metrics

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suffer from.

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2.2 Explaining Sovereign Yields

Our tests seek to understand the relation between exposure to systemic risk and sovereign debt

following form as an initial test of Relation 1 from Figure 1:

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yields. Using quarterly data aggregated at the national level, we run OLS panel regressions of the

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Yield Spread i ,t = y i ,t =    (Systemic Risk i ,t )   (CountryF.E.)  (Controls i ,t )   i ,t (2.1)

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Sovereign yield is estimated by using country i’s yield spread during period t ( y i ,t ), although our results are robust to the use of alternative forms of this variable, such as changes to the country’s yield

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spread, the actual yield level, as well as 5-year CDS levels on sovereign debt. We compute yield spreads

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relative to U.S. Treasuries with similar maturities. We use the Adapted Exposure CoVaR beta variable to proxy for systemic risk exposure in all regressions. We compute these aggregate measures of systemic

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risk by taking the individual firm-level CoVaR betas and averaging them on a daily basis for each country in our sample. We then calculate the average CoVaR beta over each quarter for each nation.**** The vector of control variables includes country-specific macroeconomic variables as well as global factors shown in prior literature to affect sovereign debt yields such as quarterly values for the debt-to-GDP ratio, inflation rate, national saving, change to real GDP (Beirne and Fratzscher (2013)), TED spread, and VIX (see e.g., Cantor and Packer (1996); Hauner, Jonas, and Kumar (2010); Hilscher and Nosbusch (2010); Longstaff, et al. (2011); and Beirne and Fratzscher (2013)).†††† An additional control is the lagged yield spread. Due to autocorrelation concerns, our results may be spurious (Granger

**** As we show later in Table 4, our systemic risk measure is robust to alternative ways of aggregating the daily FI-specific CoVaR beta estimates. †††† Because the TED spread and the VIX do not vary by country, we omit them in favor of quarterly fixed effects.

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and Newbold, 1974). By including lagged spread variables, we can account for this possibility. Moreover, we include dummy variables to capture the effects of the U.S. crisis and what we term the “wind-down” phase of the European crisis period (2007:Q3-2009:Q2, following Adrian, Colla, and

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Shin (2013), and 2012-13, respectively).‡‡‡‡ We also interact the dummy variables with the CoVaR beta. These interaction terms are included to allow for time-variation in our systemic risk measure’s impact on

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yield spreads. This allows the model to accommodate variations in the importance that investors place on a systemic risk event. For example, investors might be complacent about systemic risk and/or sovereign

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debt risk and then an unexpected shock such as the potential default on Greek government debt can create what Beirne and Fratzscher (2013) refer to as a “wake-up call” for investors. In such a situation, investors

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suddenly become highly sensitive to differences in systemic risk and sovereign credit risk and then, when the crisis subsides, investors become less concerned about such risks. By including interaction terms for

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both the U.S. crisis periods and the Euro crisis “wind down” period (i.e., 2007:Q3-2009:Q2 and 20122013), we can test to see if investors’ sensitivity to systemic risk exposure varies in accordance with such

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a “wake-up call” pattern.

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Finally, we include a set of country dummy variables to estimate country fixed effects (denoted as

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Country F.E. in the above equation). We expect that the systemic risk variable will have a positive and significant coefficient, signifying that aggregate systemic risk exposure has a strong, direct association with sovereign debt yields, especially during the 2009-2011 crisis period. We cluster all standard errors at the country level (Petersen, 2009). Our results are also robust to two-way clustering of standard errors, which cluster over time and country.

2.3 Examining All Relations Together As noted earlier in this section, findings from Acharya and Steffen (2013), Gennaioli et al. ‡‡‡‡ We consider the period from 2009:Q4-2011:Q4 as the heart of the Eurozone crisis. We arrive at this conclusion following several news outlets, which explain that the crisis begins at this time (see, e.g., BBC (2012) or Cadman, Minto, and Bernard (2011)). Moreover, while the crisis continued beyond 2011:Q4, it entered a distinctly different phase, as the TED Spread, an indicator of international risk, peaked in early January of 2012. Additionally, key bailout provisions and austerity provisions were agreed upon at this time, including the agreement on a “fiscal pact” in the EU (January, 2012), the passage of austerity measures in Greece (February 12, 2012), and a 130 billion Euro bailout of the Greek economy (March 13, 2012).

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(2012), and Alter and Beyer (2014), among others imply that sovereign debt holdings by banks can affect these institutions’ systemic risk exposure and, in turn, the banks’ systemic risk exposure can influence sovereign debt yields. Moreover, we want to examine the domestic government’s relation with domestic

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banks in the context of a fully international jointly determined model, allowing for cross-border activity. Thus, we examine all relations (including spillovers) between the sovereign debt yields and systemic risk

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exposure measures for our sample of countries and financial institutions in an alternative simultaneous empirical setting. Since the GIIPS nations were at the heart of the European sovereign debt crisis, we

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compute equally weighted averages of these nations’ systemic risk exposures and yield spreads in order to identify an intra-regional set of measures that can be used to quantify potential risk spillovers from these

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countries to the rest of Europe. To estimate the relations between ten-year spreads and average CoVaR estimates between each country and the GIIPS countries, we employ a two-equation System Generalized

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Method of Moments (GMM) framework. This allows us to account for the simultaneous and endogenous nature of yield spreads and systemic risk exposure. We instrument for systemic risk exposure with the

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size of the country’s financial system in the first regression.§§§§ This variable is reported in aggregate by

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the ECB in their Statistical Data Warehouse.

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To estimate this GMM model, we average the ten-year yield spreads and CoVaR estimates for the five GIIPS countries to create an aggregate GIIPS Spread and GIIPS CoVaR. As an instrumental variable for average CoVaR, we use the size of all bank assets in a country relative to the country’s GDP. This represents, to a degree, the nature of a too-big-to-fail financial system in a given sovereign nation because a large banking system (relative to GDP) suggests that a country’s FIs are an important component of the economy. We estimate F-tests and Wald tests to check the validity of using size as an instrument for Exposure CoVaR beta. Based on F-tests, the Size variable is statistically significant at the 1% level as an §§§§ We also employed a Seemingly Unrelated Regression (SUR) framework (Zellner, 1962). The SUR method is appropriate for this sample because it enables the errors from one model (e.g., the yield spread regression described below as Equation 2.2) to be correlated with the residuals from another model (e.g., the systemic risk regression of Equation 2.3). For example, if a nation’s systemic risk exposure was under-estimated by investors and regulators, then the systemic risk regression’s residual is most likely larger than expected which, in turn, would cause these market participants to react adversely to this unexpected “news” by causing sovereign debt yields to jump. This “chain reaction” between a large and positive residual in the systemic risk model and the country’s sovereign yield spread will then cause the yield spread regression’s error to also be positive, thus creating a significant correlation between the two model’s residuals. Consequently, a SUR econometric technique enables us to control for this potential correlation between the error terms of both models. Results below are robust to this specification although the SUR tests are not reported here to conserve space.

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instrument for Exposure CoVaR beta. The Wald test value for Size is 20.1073, which is above the critical value of 16.38 for rejection. Thus, we have confidence that Size is a valid instrument for the systemic risk exposure of a country’s financial system. Moreover, Size is an instrument which meets the exclusion

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restriction. In other words, Size should not affect sovereign spreads, but should be related to Exposure CoVaR beta. We believe that Size meets this restriction, as we do not see an obvious connection between

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the size of a country’s banking system and the spread on its sovereign debt. Meanwhile, the connection between system size and systemic risk is documented in the literature (see, e.g., Sedunov (2016)). While

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size may not necessarily be the cause of an institution’s systemic risk exposure, it is a determinant of systemic risk exposure.

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Moreover, we instrument for yield spreads by utilizing other macroeconomic variables in the second regression. These variables include the country’s Debt-to-GDP ratio, change in real GDP, and

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inflation rate. This set of variables is included in the first equation, but omitted in the second. The second equation in the GMM model is not part of a two-stage process involving the first equation, but

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rather, it is estimated simultaneously with the first equation, thus allowing us to use these variables as

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instruments. As noted above, this approach allows us to isolate the possible risk spillover / contagion

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effects of economically weaker countries on Europe’s financially stronger nations. When we compare the GIIPS countries to other GIIPS member nations, we calculate the GIIPS Spread and GIIPS CoVaR by omitting the particular GIIPS country that we are using as a dependent variable (e.g., we drop Italy from the GIIPS Spread and GIIPS CoVaR calculations when Italy’s values are used as the dependent variable in Equations 2.2 and 2.3 described below). Table 5 presents the results from the following GMM model (where the dependent variables represent the sovereign debt yield spread and systemic risk exposure measure for the i-th nation in the t-th quarter):

Spread i ,t =  1 (GIIPSSprea d t )  1 ( AverageCoVaR i ,t )   1 (GIIPSCoVaR t )   1 (Spread i ,t 1 )   1 (Controls )   i ,t (2.2)

Avg. CoVaR i ,t =  2 (GIIPSSprea d t )   2 ( AverageCoVaR i ,t 1 )   2 (GIIPSCoVaR t )   2 (Spread i ,t )   2 (Controls )   i ,t

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(2.3) Included in the vector of control variables are the same set of control variables used in the prior section. Furthermore, we control for country-level fixed effects and cluster standard errors by country.*****

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As described by Figure 1 and discussed in the Introduction, by examining these two equations, we are able to study the effect of domestic systemic risk exposure on domestic sovereign spreads (Relation 1);

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foreign systemic risk exposure on domestic systemic risk exposure (Relation 2); simultaneous effects of foreign spreads on domestic spreads (Relation 3); and domestic systemic risk exposure on a foreign

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country’s spreads (Relation 4).

In Equations 2.2 and 2.3 above, Relation 1 from Figure 1 can be tested by examining the

1 and  2 because these two parameters show how a nation’s systemic

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statistical significance of both

of

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risk exposure and sovereign yields are inter-related. Relation 2 can be tested via the statistical significance

 2 while Relation 3 can be confirmed by the significance of 1 . In addition, if both 1 and  2 are

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statistically significant, then the GIIPS country’s systemic risk exposure affects another nation’s

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sovereign debt while the GIIPS’ yield spread affects another country’s systemic risk exposure, respectively. This finding would support the concept of cross-market risk spillovers as outlined by

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Relation 4 in Figure 1. Thus, Equations 2.2 and 2.3 provide a comprehensive and econometrically sound method to test all four main research questions.

3 Data

FI-specific data, including stock prices, firm size, and industry classification are collected from Bloomberg on a daily basis for the 2007-2013 period.††††† Country-level bond yields and 5-year sovereign CDS levels are collected on a daily basis from Bloomberg, as well. As described by Equations 2.1 - 2.3

*****

As noted earlier, we also estimated this model with a number of other standard error strategies such as clustering by year or by both country and year. The model is also robust to clustering by quarter, adding quarterly fixed effects, and removing country-level fixed effects. Moreover, we estimate this model by bootstrapping, and find that the model is again robust. Regardless of specification, the coefficient on systemic risk exposure remains negative and statistically significant. ††††† We include all forms of publicly traded financial institutions, such as commercial banks, brokers, insurance companies, money managers, and financial conglomerates. By focusing on publicly traded entities, we are ignoring smaller, private firms and thus the effects of systemic risk on sovereign debt yield spreads we find here strictly apply only to larger, public financial institutions within the Euro zone system.

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above, we use these daily data to estimate, in a time series framework, the systemic risk exposure for individual FIs and then aggregate these daily estimates on a quarterly basis for each nation so that we can perform panel regression tests across our full 15-nation sample. Thus, other country-level control

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variables are collected on a quarterly basis from the International Monetary Fund’s World Economic Outlook (WEO) database. These variables include the debt-to-GDP ratio, inflation, national saving, and

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total saving. Finally, other quarterly macro-level data are collected from Bloomberg and the Federal Reserve (via the WRDS database). These variables include U.S. risk-free rates of return, the VIX, and the

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TED Spread (which is the three-month U.S. T-bill rate minus the three-month LIBOR rate). Also, in our robustness checks, we use Expected Default Frequency data for individual Financial Institutions from

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Moody’s CreditEdge database as a control variable for FI-specific default risk in order to distinguish this risk from an FI’s exposure to systemic risk.

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We have fifteen of the largest European Union countries in our sample: Austria, Belgium, Cyprus, Finland, France, Germany, Greece, Ireland, Italy, Norway, Poland, Portugal, Spain, Sweden, and

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the United Kingdom.‡‡‡‡‡ For each country in our sample, we include all publicly traded financial

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institutions within the country which have available data on Bloomberg. We also gather relevant quarterly

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information at the country level. Together, this provides 420 country-quarters of data for our analysis (15 nations x 7 years x 4 quarters per year).

Table 1 provides summary statistics, on an annual level for the sample period 2007-2013, for key variables used in our analysis. As the crisis deepened, the average 10-year sovereign debt yield for the sample countries increased. For example, in 2007, the average yield was 4.59%, and increased to 5.87% by 2011. The average debt-to-GDP ratio also increases by 49.72% during the sample period, while national saving (normalized by GDP) decreased by 9.10%. The VIX and TED spread, which proxy for global risk, both peak earlier in the sample period, most likely reflecting the height of the U.S. financial crisis. Finally, the average Adapted Exposure CoVaR beta aggregated across all banks within a country

‡‡‡‡‡

We collect data for The Czech Republic, Estonia, Luxembourg, Malta, The Netherlands, and The Slovak Republic as well. However, these countries have fewer than five publicly traded financial institutions. Thus, they are excluded from the analysis below.

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rises by 136.01% to a level of 0.502 during the height of the European crisis in 2011. Average CoVaR beta then decreased to 0.448 in 2013, as the crisis eased. Figure 2 presents aggregate yields for GIIPS countries against the aggregate yields for non-GIIPS

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countries in our sample. While non-GIIPS countries experienced a decrease in sovereign yields from 2007-2013, GIIPS countries experienced a large increase in rates, which peaked in 2011. On a country-

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by-country level, the positive relation between CoVaR beta and sovereign debt yields is clear.§§§§§ Figure 3 presents the relation between aggregated average CoVaR beta and the average ten-year yield for the

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GIIPS countries on a weekly basis over the sample period. The two series tend to move together with a correlation of 81.6%, peaking in the middle of 2011, as investors feared that other GIIPS nations might

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follow the same path as Greece (See Bartha and Chaturvedi, 2011).

Table 2, panel A provides the correlations between sovereign debt yield levels and yield spreads,

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as well as for 5-year CDS levels and CoVaR beta over the sample period. The yield spreads are calculated by subtracting the U.S. Treasury rate from the country’s sovereign debt yield for comparable maturities.

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As expected, the yields, spreads, and year-to-year changes in these variables are highly correlated.

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Notably, the CoVaR beta variable is positively correlated with the yield variables. For example, the

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CoVaR variable has a 46.9% correlation with the ten-year spread. Panel B presents the correlations among CoVaR beta and the independent variables we use in our analysis. Note that most independent variables have a relatively low correlation with each other and thus multi-collinearity does not appear to be a problem in our sample. The highest correlation is between the Debt-to-GDP ratio and CoVaR beta (52.1%).

4 Results 4.1 Estimating Sovereign Debt Yields

§§§§§

Appendix B presents annual average CoVaR beta estimates by country. Cyprus had less than 5 publicly traded financial institutions in 20122013 and thus we do not report CoVaR betas for these years in Appendix A.

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Table 3 presents results in which the quarter-end yield spread is used as the dependent variable. All models feature the CoVaR beta variable as the key independent variable. Models (1)-(3) examine the three-, five-, and ten-year yield spreads. For all maturities, the coefficient on CoVaR beta is significant at

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the 10% level****** When we restrict the sample to the 2009:Q4-2011:Q4 subsample in models (5)-(7), we find that the coefficient on CoVaR beta is positive and significant at the 10% level for three-year

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maturities and at the 5% level for five- and ten-year maturities. Thus, the exposure CoVaR variable is best at explaining variations in the five- and ten-year yield spreads. According to model (3), a one-

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standard deviation increase in a country’s aggregate CoVaR beta during 2011 is related to a 11.87 bps increase in the ten-year spread during 2011 for Germany, and a 34.70 bps increase in the ten-year spread

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during 2011 for Greece. This corresponds to a 75.13% increase above the sample average of -0.158% for Germany and a 1.81% increase above the sample average of 19.14% for Greece. For the aggregate

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sample, model (3) shows that a one-standard deviation increase in CoVaR beta is related to a 39.00 bps increase in the ten-year spread, which is 12.04% above the sample mean of 3.24% in 2011. Note that

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several control variables are statistically significant. The debt-to-GDP ratio and inflation variables are

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macroeconomic factors.

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statistically significant and positively related to yields. This shows that yields are positively related to

The U.S. Crisis and Euro Crisis “Wind Down” interaction terms are also negative and statistically significant. Combining the U.S. Crisis interaction term’s parameter value with the coefficient on CoVaR beta shows that the net effect of systemic risk exposure on sovereign yield spreads during the U.S. Crisis period is still positive, although not as dramatic as during the 2009:Q4-2011:Q4 period (e.g., +0.236 in model 3). The combined effect of the 2012-13 interaction term and CoVaR beta is negative (-0.152 in model 3). We again implement an F-test to check the joint significance of the interaction terms and the CoVaR beta variable. In this case, the combined parameters are not jointly significant in models (2) and (3). As noted in the Introduction, these results are consistent with Beirne and Fratzscher’s (2013) notion ******

All results in Table 3 are robust to standard errors clustered by both quarter and country. We do not report results with double-clustered standard errors throughout the paper, as we have a limited sample size with a small amount of clusters. As in Petersen (2009), clustering with an insufficient number of clusters will not properly reduce the bias of the standard errors. Accordingly, we control for time parametrically while clustering by country throughout the paper. This method is in accordance with guidance provided in Petersen (2009).

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of a “wake-up call” where investors suddenly become more sensitive to some nations’ systemic risk and government finances. After the crisis is perceived to be resolved, then investors once again become less sensitive to a country’s systemic risk. Thus, systemic risk’s effect on sovereign debt yields is episodic in

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nature and varies positively with the intensity of the financial crisis the nation is facing. In addition to using the yield spread as the dependent variable, Table 3 incorporates the level of

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the five-year sovereign debt CDS spread. Models (4) and (8) include control variables along with the fiveyear CDS spread, and we find that the CoVaR beta variable is positively related to the CDS spreads at the

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5% significance level. In addition, we find that a one-standard deviation increase in CoVaR beta is related to an increase of 48.52 bps in CDS levels during 2011, which is 14.56% higher than the sample mean.

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We also investigate the yield levels (rather than the yield spread) and the change in the yield spread as alternative forms of the dependent variable. These results are not reported below to conserve

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space. Similar to the above tables, we find that CoVaR beta is significantly related to changes in yield spreads and yield levels at the 5% and 10% level, respectively. For example, a one-standard deviation

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change in CoVaR beta is related to a 38.08 bps change in a country’s ten-year yield spread in 2011. This

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is a 49.17% increase over the mean change of 0.775%.

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As noted in the Introduction, we also acknowledge the possibility that the CoVaR measure may not be a pure measure of a financial system’s riskiness due to its possible contemporaneous co-movement with sovereign yield spreads, especially during crisis periods. In this case, CoVaR could actually reflect sovereign risk rather than exposure to systemic risk. As such, we address this possibility by regressing CoVaR on a European sovereign debt index and replace CoVaR in our main empirical models with the residuals from this regression. In this way, we thus obtain a clean, orthogonalized estimate of systemic risk exposure. We find that all of our results remain robust to this change and thus the possible comovement of systemic risk with foreign debt yields does not alter our main conclusions. We report the results of this robustness check later in Section 5 below. These results show that exposure to systemic risk, on an aggregate level, is positively related to sovereign debt yields in Europe and are not influenced by the form of the dependent variable. Further, the

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results show that the effect is not only statistically significant but also economically meaningful. Changes to the systemic risk exposure of a country can therefore result in large shifts in sovereign debt yields,

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particularly during times when systemic risk most relevant (i.e., during crisis periods).

4.2 The Aggregation of CoVaR beta

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We also seek to verify that our aggregation method for our main independent variable, CoVaR beta, is not affecting our results. It is important to note that although we are using a CoVaR methodology,

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we are using a coefficient from the methodology (CoVaR beta), rather than the CoVaR value itself. Thus, although one can add CoVaR or VaR values to aggregate them, it is not a proper approach to sum the

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CoVaR beta terms as they are measures of sensitivity rather than dollar value change. This is actually a positive feature of our coefficient-based methodology, as it allows us to avoid the sub-additivity problem

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that VaR and CoVaR value-based methodologies suffer from when there is not perfect correlation among the assets in a portfolio (Hull, 2012).

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Our approach thus far has been to find an equally weighted average of the CoVaR betas of all

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financial institutions within a country and quarter. Table 4 includes our baseline estimate from Table 3 as

Ac ce p

well as four alternative methods for aggregating CoVaR beta, and replicates Equation (7) of Table 3. To conserve space, we only report the coefficients and t-statistics from the CoVaR beta variable for each replication. In addition to equally weighting the CoVaR beta variable, we also construct: a value-weighted average by bank assets††††††, the average of only institutions within the banking and financial services sectors, the average of the CoVaR beta values on only the last day of the quarter, and the CoVaR beta average for the largest bank in each country and quarter. We find that our results are robust to all specifications listed above. Moreover, the final column of the table provides an estimate of the economic impact forecasted by each methodology. We calculate this as the percentage change in the average ten-year spread which is related to a one-standard deviation increase in aggregate systemic risk exposure over the entire sample period and for all countries. We find ††††††

Bank assets are available annually from Bloomberg. We use the year-end value of bank assets to create this value-weighted index.

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that our results are quantitatively and qualitatively similar regardless of the aggregation method we choose. Accordingly, the subsequent sections will continue to present results using an equally weighted

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aggregation approach.

4.3 Estimating All Relations Together

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Panel A of Table 5 reports the outcome for the first GMM regression based on Equation 2.2.‡‡‡‡‡‡ Regression (1) omits the CoVaR and GIIPS CoVaR beta measures and examines both the full 2007-2013

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period, as well as the 2009:Q4-2011:Q4 sub-period associated with the European crisis. When we exclude the domestic CoVaR betas from the specification, we find in model (1) that the yield spread on GIIPS

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countries is positive and significantly related to the domestic ten-year yield spread.§§§§§§ However, when we include CoVaR beta estimates, models (2), (3), and (4) show that the domestic average CoVaR beta’s

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parameters have a positive and statistically significant relation with the domestic yield spreads while the GIIPS spread variable now becomes insignificant during the full sample period and the 2009-11 crisis

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period. Our results are consistent with the OLS results presented earlier. Additionally, we estimate

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Hansen’s J test for models (2)-(4), as they are the main models in our analysis. We find that the Hansen’s

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J statistics are 1.43, 0.13, and 1.36, respectively. In all cases, the corresponding p-value is larger than 23%, meaning that we fail to reject the null hypothesis that our GMM model is valid. Moreover, the above finding provides evidence of an omitted variable problem for existing models that estimate sovereign yield spreads. We consider this to be evidence of model mis-specification because when domestic CoVaR beta is included in the regressions, the coefficient on the GIIPS spread variable is no longer statistically significant. Thus, the inclusion of a measure of systemic risk (proxied here by CoVaR beta) is an important determinant of sovereign debt yields, especially during crisis periods. The CoVaR beta coefficient in the third regression, 2.551, suggests that, for all sample countries,

‡‡‡‡‡‡

We also estimate this GMM model using the countries which comprise the GIIPS individually. In other words, we estimate one model for each of the five constituent nation of the GIIPS cohort. We find that the results are similar to those presented for the general model where we use a simple, equally weighted average of all five countries’ yield spreads. §§§§§§ To streamline and focus the analysis, we report the GMM results for only the 10-year yield spreads, as the results based on the 3- and 5-year yield spreads are qualitatively similar, albeit somewhat statistically weaker.

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a one-standard deviation shift in average CoVaR beta during 2011 is related to a 26.98% increase in the ten-year domestic spread over its 2011 mean level of 3.24%. For reference, this same relation suggests a 4.06% increase in the ten-year spread for Greece relative to its mean level of 19.14% in 2011.

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The coefficient on GIIPS CoVaR is statistically significant and negative at the 1% level in models (2) and (4) and at the 5% level in model (3). A one-standard deviation increase of GIIPS CoVaR is related

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to a decrease in domestic sovereign debt spreads of 6.25% below its mean level in 2011. This suggests a flight-to-quality away from poorly performing GIIPS countries as the systemic risk in these nations

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increases. Finally, the coefficient on the lagged ten-year domestic yield spread is positive and statistically significant, thus confirming that interest rates are strongly related to past rates. We also include the

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average value of Moody’s expected default frequency (EDF) for financial institutions in each country as an additional control variable in regression (4). By including this variable, we can rule out the possibility

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that systemic risk exposure measures are simply a proxy for the probability of the banks’ default, and are instead a true estimate of systemic risk. Our GMM results remain qualitatively and quantitatively similar

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when this average EDF variable is included.******* This finding in regression (4) highlights the fact that it

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can be difficult to distinguish between FI-specific default risk and a firm’s exposure to systemic risk since

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these two factors tend to be positively correlated. Panel B of Table 5 reports the outcome of the second GMM regression based on Equation 2.3. Here, we find that foreign systemic risk exposures (GIIPS CoVaR) are related positively to domestic systemic risk exposures at the 1% level. A one-standard deviation increase in the GIIPS CoVaR variable corresponds to an increase of 8.32% in domestic exposure CoVaR over 2011 mean levels of 0.502. Thus, we have evidence that exposure to systemic risk spills over from the financial system of one country to that of another. Moreover, the relation between GIIPS Spread and domestic systemic risk exposure is positive in regressions (1), (3), and (4), but not statistically significant in any of the three models. Finally, the domestic yield spread is positive and statistically significant at the 1% level in regressions (1), (2), and (4), and at the 10% level in regression (3), and shows that sovereign yields can influence a nation’s *******

Results are also robust to the median EDF.

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systemic risk exposure (as well as vice versa, based on Panel A’s earlier results). For example, a onestandard deviation increase in domestic spreads is related to an increase in domestic CoVaR beta of 6.55% over mean levels in 2011.

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In Figure 4 we explore the time series dynamics of how a one-standard deviation increase in CoVaR beta can impact average sovereign debt yields and domestic systemic risk over a 12-quarter

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period. Panel A of Figure 4 simulates the effect of an immediate increase in domestic CoVaR beta on sovereign debt yield spreads and domestic systemic risk over the next 12 quarters. These estimates are

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based on an initial increase of 0.366 in CoVaR beta which then affects future sovereign debt yields via the statistically significant coefficient of 2.551 for CoVaR beta from model (3) in Panel A of Table 5. For

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example, the initial shock to CoVaR beta leads to a 93 bps increase in sovereign debt yields during the first quarter and ultimately peaks at 118 bps in the third quarter before gradually declining to 41 bps at the

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end of the 12-quarter simulation horizon.††††††† Thus, an increase in domestic systemic risk can have large and long-lasting effects on sovereign debt yields. Panel A of Figure 4 also shows the impact of an

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increase in CoVaR beta on future systemic risk in the average country’s financial system based on the

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parameter estimate of 0.875 for the lagged CoVaR beta variable from Panel B of Table 5. This graph

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shows that CoVaR beta also spikes within one quarter and then gradually declines over the 12-quarter forecast period. So, future levels of both sovereign debt yields and domestic systemic risk remain elevated several years after an initial surge in a nation’s CoVaR beta. In contrast, Panel B of Figure 4 displays graphs for a one-standard deviation increase in foreign systemic risk (proxied for by the GIIPS CoVaR beta variable). These graphs show that the impact of greater foreign systemic risk is much smaller and short-lived than a nation’s own systemic risk. Thus, although the cross-market effect of GIIPS CoVaR beta is statistically significant, its economic significance is relatively small in comparison to changes in the riskiness of a nation’s own financial system. ††††††† Regression (3) is estimated for the 2009-2011 crisis period and thus the coefficient for CoVaR beta is larger during this period compared to the full 2007-2013 period which was used to estimate regression (2) (i.e., 2.551 vs. 1.146). Thus, even though the impact of CoVaR beta on yield spreads would be lower during the non-crisis periods, it still is relatively large and persistent (e.g., 42 bps vs. 93 bps in the first quarter). Also, for the second quarter and beyond, the lagged 10-year yield spread coefficient of 0.477 in regression (3) is included in the above simulation because the increased yield spread in the first quarter can impact future yield spreads according to our model. Similar logic also applies to our simulations of the impact of CoVaR beta on future domestic systemic risk using coefficients from Panel B of Table 5.

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Overall, these results suggest that domestic yield spreads are positively related to domestic systemic risk and negatively related to foreign systemic risk exposures (the latter appears to represent a “flight-to-quality” effect). However, in the presence of these systemic risk effects, we find that domestic

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yield spreads are not strongly related to foreign yield spreads. Further, we find that domestic exposures to systemic risk are related positively to foreign systemic risk exposure and to domestic yields, but not to

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foreign yields. Thus, the cross-market effects described by Relation 4 in Figure 1 are not as strong as the effects between a nation’s sovereign debt and its domestic financial system. These findings are also

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episodic in nature, as the results vary depending on whether the Euro zone is experiencing a financial crisis. For example, the effect of both domestic and foreign systemic risk on sovereign debt yields is

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strongest during peak of the Eurozone crisis period of 2009:Q4-2011:Q4.

Taken together, the results reported in Table 5 show strong support for three of the four relations

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noted in Figure 1 (Relations 1, 2, and 4). In addition, no consistent support for Relation 3 can be found due to the statistically insignificant parameter estimates for GIIPS Spread in Table 5’s Panel B. As can be

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seen by the significant parameter estimates for GIIPS CoVaR in Panel A of Table 5, increased systemic

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risk in GIIPS nations can create a flight-to-quality shift into non-GIIPS sovereign debt instruments (thus

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lowering their yields) while also increasing the systemic risk exposure of the rest of Europe. In general, the results shown in Table 5 confirm that the risks associated with a nation’s sovereign debt and financial system are simultaneously determined. In addition, there are significant international risk spillovers although the domestic spillovers between sovereign debt and systemic risk (Relation 1 and 2) are stronger and more persistent than the international cross-market effects. However, the linkage between foreign and domestic sovereign debt yields (Relation 3) is not that strong once we control for the effects of systemic risk. This result suggests that systemic risk is an important factor that should be incorporated into sovereign debt risk models. 5 Robustness We modify our primary model outlined in Sections 2 and 4 in two ways: first, we replace the CoVaR measure with the residuals from the regression of CoVaR on GIIPS spreads; and second, we use

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an alternative measure of systemic risk exposure. In our first robustness test, we acknowledge that the increase in a country’s systemic risk may be driven by changes to the aggregate risk of sovereign debt, thus possibly confounding our measure of

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systemic risk exposure. Thus, we estimate the following regression by country over a rolling estimation window, using all available data up to the quarter of interest:

(5.1)

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Average CoVaR Betai ,t   i   i  Sovereignt   i ,t

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The variable Sovereign represents the Barclays Euro Aggregate Government index, which proxies for the combined sovereign risks of European governments.

We recover the residuals from this

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regression, and use them as an orthogonalized measure of a country’s systemic risk exposure, which is not related to sovereign debt risk from foreign nations known to have had an impact on yields throughout the

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European region. We then replace the CoVaR measure with the residuals in Equations (2.2) and (2.3) in order to re-estimate the models first reported in Table 3. The results of this modified test are reported in

d

Table 6. We find that our results are robust to the inclusion of the residuals from Equation (5.1), thus

sovereign debt risk.

te

allaying concerns that our systemic risk measure is a statistical artifact of potential co-movements with

Ac ce p

Table 7 presents results which use an alternative measure of systemic risk exposure. Acharya, et al. (2015) propose the Systemic Expected Shortfall (SES) methodology for calculating the systemic risk exposure of financial institutions. One of the key innovations of this methodology is the Marginal Expected Shortfall (MES) variable. This variable is the average institution return during the 5% worst return days of the market.‡‡‡‡‡‡‡ Note that the MES measure is negative. Thus, MES estimations which are more negative suggest relatively higher exposure to systemic risk. We replicate the GMM methodology used above. Similar to the GMM model reported in Table 5, regressions (1) and (2) examine the entire 2007-2013 sample period, while regression (3) examines the 2009:Q4-2011:Q4 subperiod. Given the concerns of Danielsson et al. (2012) that systemic risk measures such as MES may actually be simply

‡‡‡‡‡‡‡

We again proxy for the market returns by using the STOXX 600 Europe index.

26 Page 26 of 51

capturing systematic risk, we estimate an additional regression, (4), which adds the CAPM beta to the estimation. Including the CAPM beta allows us to examine whether our measures of systemic risk can simply be replaced by a standard estimate of systematic risk.

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Panel A of Table 7 provides results of the first regression, which uses the ten-year yield spread as the dependent variable. The domestic MES coefficient is negative and significant in regressions (2) and

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(3), suggesting that greater systemic risk exposure is related to larger yield spreads. However, when we incorporate the CAPM beta into the model, MES is not statistically significant in regression (4).§§§§§§§

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This result suggests that the MES variable may more closely estimate systematic risk rather than systemic risk. Thus, regressions (2) and (3) support our earlier finding that domestic systemic risk exposure can

an

affect domestic yield spreads (Relation 1), but regression (4) casts doubt on the ability of MES to distinguish between systematic and systemic risk. The results in Table 8 differ from the CoVaR

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methodology in that we do not find support for spillover effects from foreign financial institutions to domestic governments in terms of sovereign debt yields (Relation 4). Here, the coefficient on GIIPS MES

d

is not statistically significant in regressions (2) or (3), and switches signs between regressions. We further

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find that the GIIPS Spread is positive in all regressions and significant in regressions (1) and (3), giving

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support for spillover from foreign governments to domestic governments (Relation 3). Panel B presents results of our second set of regressions, based on Equation 2.3, which uses the domestic MES estimate as the dependent variable. We find that the GIIPS Spread variable is a negative and significant determinant of domestic MES for both sample periods, but that the sign switches depending on the regression specification. This provides some evidence that foreign government risk spills over to domestic institutions. This result is different from that found in Table 5. We find that, like CoVaR beta, GIIPS MES is a statistically significant determinant of domestic MES. These cross-market linkages support Relations 2 and 4. Finally, we see that the domestic ten-year yield spread is negatively related to domestic MES, once again providing support for Relation 1. §§§§§§§ We estimate the same set of regressions, replacing MES with CoVaR. In contrast to MES, we find that the CoVaR variable remains statistically significant while CAPM beta is not significant. Thus, we interpret this finding as evidence that CoVaR might be a reasonable measure of systemic risk exposure.

27 Page 27 of 51

While we observe that the results of this robustness check support our previous results, there are some differences, as noted above. These differences are not surprising given that MES and CoVaR beta are not perfectly correlated. First, using the time series of daily MES and Exposure CoVaR beta

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estimates, we find that the correlation between MES and CoVaR beta is 21.18%, suggesting that the two variables are measuring different things, even though they are both designed to measure systemic risk

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exposure. However, there appears to still be enough similarity between MES and CoVaR beta because both measures support Relations 1-4, with more support for Relation 3 when MES is used.

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In unreported tests, we find that our results are robust to estimating yield spreads using an alternative definition of the benchmark risk-free rate. Due to Germany’s economic strength within the

an

European region, we use the German bond rate rather than the U.S. Treasury rate as the benchmark and find that results of our tests remain unchanged. Moreover, we find that incorporating a dummy which

M

accounts for whether a country is a member of the Euro zone currency union does not affect the results. We also find that accounting for a country’s private debt (as a proportion of GDP), total foreign

d

investment (as a proportion of GDP), foreign exchange rates, foreign exchange rate volatility, the

te

VSTOXX, or currency reserves (as a proportion of GDP) also does not alter the results. Thus, the

Ac ce p

possibility of economic distortions and / or spillovers driven by rapid growth in private credit or foreign investment (in contrast to public debt) does not affect our main findings. Lastly, we address the possibility that our results may be the product of a smooth, cointegrated time series of data. Both the CoVaR and spread variables may be driven by a common, unobserved factor over time, meaning that they could be unit root variables. We examine this possibility in two ways. First, we test each time series using a Perron-Phillips test. Neither spreads nor CoVaR are shown by this test to follow a unit root. Moreover, we estimate Johansen’s maximum likelihood cointegration rank test, and Westerlund’s error-correction-based panel cointegration test to check for cointegration. Neither test provides evidence of cointegration of our time-series. Second, we replace the level of spread and CoVaR in the GMM regressions with their quarterly change. If the variables truly are cointegrated, then their quarterly changes, rather than their levels, can provide an estimate of any unique or novel information

28 Page 28 of 51

contained within these variables. After running the GMM tests with the quarterly change variables, we observe that the results remain qualitatively similar to those discussed above. Consequently, the possibility that the spread and CoVaR variables are unit root variables is not confirmed by these

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additional tests and therefore this potential econometric problem does not affect the outcomes we present. 6 Conclusion

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This study is the first comprehensive analysis of cross-border and domestic relations between sovereign debt and systemic risk exposure. We find evidence that, within this framework, the aggregate

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exposure to systemic risk can affect the probability of a country’s default, as proxied for by sovereign debt yield spreads, and this effect is strongest during a crisis period. We report that the relation between

an

these variables is both statistically and economically meaningful. This relation holds for three estimates of sovereign yield: yield spreads, changes in yield, and changes in yield spreads. Thus, we conclude that

avoid a potential omitted variable problem.

M

sovereign debt risk models should include a measure of systemic risk (such as CoVaR beta) in order to

d

We also find evidence of simultaneity between systemic risk exposure and sovereign yields. We

te

further investigate this issue by estimating our models via generalized method of moments. Our results

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are robust to this specification, thus confirming our main results remain intact despite the presence of a simultaneous relation between systemic risk exposure and sovereign debt yields. In addition, the evidence of simultaneity shows that there are multiple ways for risk spillovers to occur (e.g., not only from a nation’s government debt yields to the country’s financial institutions, and vice versa, but also from one nation’s financial systemic risk to another country’s systemic risk, or from a country’s systemic risk to another nation’s sovereign debt, as described by the four relations in Figure 1). These spillover effects are also dynamic in nature and show that increases in domestic systemic risk lead to larger and longer lasting changes in yield spreads relative to increases in foreign (GIIPS) systemic risk. We find that our results are robust to numerous modifications. Most importantly, we see that using MES rather than CoVaR beta as a measure of systemic risk does not alter our main results. The differences between the two risk measures we observe are most likely due to methodological differences

29 Page 29 of 51

between the measures. These methods lead to non-trivial differences in the estimation of systemic risk exposure by each measure but our primary conclusions remain the same. This research contributes to the finance literature by answering an open question on the country-

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by-country impact of systemic risk exposure. Moreover, it quantifies the time-varying effects that systemic risk exposure have on sovereign yields, and measures the dynamic inter-relations between

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different countries’ financial systems and sovereign debt. This analysis can provide assistance to regulators who are attempting to understand the relationships between sovereign yields and country-level

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systemic risk exposure, and to investors who may hold large quantities of sovereign debt.

In particular, our model of sovereign debt indicates that regulators should consider the condition

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of a nation’s financial system when estimating the riskiness of a nation’s debt. This, in turn, can affect the risk-weighting of a nation’s sovereign debt holdings and the capital adequacy of any FI that owns

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these bonds. In addition, our model’s assessment of sovereign debt can affect whether a certain country’s bonds are deemed “high quality liquid assets” and thus impact a FI’s liquidity coverage ratios and overall

d

liquidity risk. To the extent that our model helps identify “high risk” nations / regions prior to a crisis, a

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regulator can also proactively monitor “too big to fail” and moral hazard incentives at globally important

Ac ce p

FIs. One last area that highlights the usefulness of the model is monetary policy. As shown in Figure 4, a large increase in systemic risk can cause a spike in sovereign debt yields that lasts for up to three years. This spike can then work against any easing monetary policy that a central bank might want to pursue. In sum, our approach provides a useful description of the inter-relationships between the riskiness of sovereign debt and financial systems, and provides guidance in terms of policies related to capital adequacy, liquidity risk, “too big to fail,” and monetary policy.

30 Page 30 of 51

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Adrian, T., Brunnermeier, M. 2015. CoVaR. American Economic Review, Forthcoming.

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Alter, A., Beyer, A., 2014. The dynamics of spillover effects during the European sovereign debt turmoil. Journal of Banking and Finance 42, 134-153. Bai, J., Julliard, C., Yuan, K., 2012. Eurozone sovereign bond crisis: Liquidity of fundamental contagion, Working Paper. Bartha, E. Chaturvedi, N., 2011. Italian yields jump after poor auction. WSJ.com. Wall Street Journal, November 25, 2011. Web. January 11, 2013. < http://online.wsj.com/article/SB10001424052970204630904577059702484791324.html > . Battistini, N., Pagano, M., Simonelli, S., 2014. Systemic risk, sovereign yields, and bank exposures in the Euro crisis. Economic Policy 29, 203-251. BBC 2012. Timeline: The unfolding Eurozone crisis. www.BBC.com. BBC News, June 13, 2012. Web. November 11, 2015. . Bedendo, M., Colla, P., 2015. Sovereign and corporate credit risk: Evidence from the Eurozone, Journal of Corporate Finance 33, 34-52. Beirne, J., Fratzscher, M., 2013. The pricing of sovereign risk and contagion during the 31 Page 31 of 51

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Boyson, N.M., Stahel, C.W., Stulz, R., 2010. Hedge fund contagion and liquidity shocks, Journal of Finance 65, 1789-1816. Brutti, F., Sauré, P., 2015. Transmission of sovereign risk in the Euro crisis. Journal of International Economics 92, 231-248.. Bruyckere, V.D., Gerhardt, M., Schepens, G., Vennet, R.V., 2013. Bank/Sovereign Risk Spillovers in the European Debt Crisis. Journal of Banking and Finance 37, 4793-4809. Cadman, E., Minto, R., Bernard, S., 2011. Interactive timeline: Greek debt crisis. www.ft.com. Financial Times, October 21, 2011. Web. November 11, 2015. . Cantor, R., Packer, F., 1996. Determinants and impact of sovereign credit ratings. FRBNY Economic Policy Review, October, 1996, 37-54. Caporin, M., Pelizzon, L., Ravazzolo, F., Rigobon, R., 2015. Measuring sovereign contagion in Europe. NBER Working Paper 18741.

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Year

0.213 0.192 0.332 0.381 0.502 0.528 0.448 0.369 0.366 -0.680 0.353 1.519

60.722 59.663 69.352 76.073 81.448 85.241 90.910 73.919 30.983 24.500 68.900 171.800

2.255 3.540 0.777 2.110 2.875 2.255 1.177 2.150 1.470 -3.000 2.200 5.800

cr

Inflation

National Saving GIIPS 10-Year Spread 21.603 -0.055 20.537 1.232 17.440 1.216 18.175 2.990 18.56 8.324 19.283 8.131 19.635 3.435 19.331 3.568 8.458 3.532 -17.200 -0.422 18.750 2.236 40.700 16.587

Ac ce p

te

2007 2008 2009 2010 2011 2012 2013 Sample Mean Sample Std. Dev. Sample Minimum Sample Median Sample Maximum

Debt-to-GDP

us

4.594 4.456 4.169 4.448 5.871 4.706 3.711 4.559 3.16 1.289 4.132 34.963

CoVaR Beta

an

2007 2008 2009 2010 2011 2012 2013 Sample Mean Sample Std. Dev. Sample Minimum Sample Median Sample Maximum

10-Year Yield Spread 0.027 1.071 0.819 1.288 3.243 2.874 1.193 1.495 1.495 -1.084 0.531 33.073

M

10-Year Yield

d

Year

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Table 1: Summary Statistics: This table presents summary statistics for key variables based on data for all fifteen European Union countries. Variables include the average annual ten-year bond yield for sample countries and average aggregate CoVaR Beta, which is the coefficient from the CoVaR methodology that predicts the sensitivity of bank stock prices relative to changes in the aggregate stock price of the financial system. Moreover, the Debt-toGDP ratio describes the ratio of a country’s debt to its annual GDP, Inflation is the year-end rate of inflation, National Saving is gross disposable income less final consumption expenditures normalized by GDP.

GIIPS CoVaR 0.317 0.353 0.430 0.460 0.826 0.869 0.689 0.559 0.230 0.129 0.479 1.010

35 Page 35 of 51

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Panel A: 10 Year Spread

0.960 (0.000) 0.337 (0.000) 0.241 (0.000) 0.229 (0.000) 0.402 (0.000)

1.000

10 Year Spread Δ 5 Year CDS Δ 10 Year Yield Δ 10 Year Spread

Panel B:

0.337 (0.000) 0.168 (0.001) 0.217 (0.000) 0.469 (0.000)

ce pt

CoVaR Beta

CoVaR Beta

Ac

Δ Inflation

Debt-to-GDP

National Saving

Δ Real GDP

Δ 5 Year CDS

M an

10 Year Yield 1.000

Δ 10 Year Yield Δ 10 Year Spread

CoVaR Beta

1.000

ed

10 Year Yield

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Table 2: Cross-Correlation Table: This table presents the cross-correlation of some key variables in the analysis. Panel A presents correlations between CoVaR beta and the dependent variables used in the analysis. We compare the ten-year yield, ten-year spread (over the ten-year treasury rate), five-year sovereign debt CDS level, change in the ten-year yield and spread, and CoVaR Beta. Several of these variables are used as dependent variables in the analysis, and CoVaR Beta is used as the key independent variable. These results suggest a univariate link between sovereign yields and systemic risk exposure. Panel B presents correlations between CoVaR beta and other independent variables in the analysis.

CoVaR Beta 1.000

Δ Inflation

-0.120 (0.015) 0.521 (0.000) -0.257 (0.000) -0.183 (0.000)

1.000 -0.063 (0.211) -0.051 (0.306) 0.007 (0.893)

0.282 (0.000) 0.492 (0.000) 0.084 (0.107)

1.000 0.488 (0.000) 0.012 (0.815)

Debt-to-GDP

1.000 -0.010 (0.847)

National Saving

1.000

Δ Real GDP

1.000 -0.471 (0.000) -0.129 (0.013)

1.000 0.132 (0.011)

1.000

36 Page 36 of 51

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Table 3: Explaining Sovereign Yield Spreads and CDS Levels with Average CoVaR Beta: This table presents a set of regressions which feature the yield spread (over the equal length U.S. Treasury rate), as week as the 5-year CDS level, as the dependent variable. Independent variables include the average annual aggregate CoVaR Beta, which is the coefficient from the CoVaR methodology that estimates the sensitivity of bank stock prices relative to changes in the aggregate stock price of the financial system. Control variables include dummy variables to control for the sub-period effects of 2007:Q3-2009:Q2 and 2012-2013; an interaction term between CoVaR beta and the 2007:Q3-2009:Q2 and 2012-2013 dummies (to control for changes in the effect of CoVaR beta during each subperiod); the Debt-to-GDP ratio, which describes the ratio of a country’s debt to its annual GDP; Inflation, which is the quarter-end rate of consumer inflation; and National Saving, which is gross disposable income less final consumption expenditures normalized by GDP. Finally, we include time fixed effects to proxy for global macroeconomic events. All regressions include country fixed effects. Standard errors are clustered at the country level.

Debt to GDP t Inflationt National Savingt Δ Real GDP t

US Crisis Dummy (2007:Q3-2009:Q2)

Euro Crisis "Wind Down" Dummy (2012-2013) "Wind Down" Interaction

5 Year Spreadt-1 10 Year Spreadt-1 5 Year CDSt-1

Constant

Qtr FE Country FE Country Cluster Observations R-squared

1.138* (1.835) 0.00599 (1.768) 0.0878 (1.650) -0.00609 (-0.743) -0.0193 (-0.474)

137.0** (2.699) 0.872* (1.847) 12.09* (1.948) -2.000* (-2.079) -3.836 (-0.863)

0.0583 (0.138) -1.853** (-2.196)

-0.130 (-0.359) -1.172 (-1.755)

-0.368* (-1.844) -0.902** (-2.268)

97.38*** (4.051) -114.6** (-2.678)

0.888 (1.545) -2.674* (-1.892)

0.847* (1.935) -2.054* (-1.994)

0.165 (0.687) -1.290* (-1.968)

40.14 (1.766) -126.6** (-2.429)

0.804*** (12.52)

Ac

3 Year Spreadt-1

1.882* (1.948) 0.00710* (1.871) 0.174* (2.069) 0.00259 (0.218) 0.0113 (0.128)

ce pt

US Crisis Interaction

2.387* (1.945) 0.0133* (2.069) 0.154 (1.633) -0.00755 (-0.536) 0.0214 -0.137

ed

CoVaR Betat

M an

(1) (2) (3) (4) 3 Year Spread 5 Year Spread 10 Year Spread 5 Year CDS

(5) (6) (7) (8) 3 Year Spread 5 Year Spread 10 Year Spread 5 Year CDS 2009:Q4 - 2011:Q4 3.995* 3.115** 2.094** 148.5** (2.092) (2.212) (2.712) (2.427) 0.129** 0.0559 0.0289 5.085* (3.048) (1.646) (0.864) (1.915) 0.661** 0.375* 0.241* 17.73* (2.759) (1.984) (1.783) (1.997) -0.00856 0.0257 0.0198 1.387 (-0.274) (0.862) (0.939) (0.956) 0.0227 -0.0572 -0.0435 -2.211 (0.143) (-0.441) (-0.659) (-0.297)

0.485** (2.969) 0.815*** (15.37)

0.574*** (4.002) 0.861*** (21.00)

0.619*** (4.262) 0.827*** (32.27)

0.679*** (4.997)

-2.033* (-1.997)

-1.740** (-2.352)

-0.772* (-1.780)

-91.40 (-1.654)

-12.23** (-2.987)

-7.422** (-2.316)

-4.830* (-1.782)

-527.2** (-2.296)

YES YES YES 313 0.890

YES YES YES 330 0.917

YES YES YES 345 0.936

YES YES YES 330 0.930

YES YES YES 109 0.928

YES YES YES 113 0.937

YES YES YES 122 0.949

YES YES YES 123 0.936

37 Page 37 of 51

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Table 4: Alternative Methods of Aggregating CoVaR Beta: This table presents results which replicate regression (7) of Table 3 for alternative ways to measure CoVaR beta. In these regressions, the ten-year yield spread is the dependent variable. We report the coefficient and t-statistic on average CoVaR beta using a variety of aggregation methods (including our original measure reported in the first row), in addition to equally weighting the CoVaR beta measures across only banks within a country and over a quarter. Also, we report the economic impact implied by each coefficient. This figure estimates the percentage change in the average yield spreads over the entire sample period given a one-standard deviation increase in systemic risk exposure, as estimated by CoVaR beta. Coefficient Value

T-statistic

Economic Impact

Equally Weighted

Equally weighted average CoVaR beta for all banks in a country over the quarter.

2.094***

2.712

29.79%

Value Weighted

Value weighted, by assets, average CoVaR for all banks in a country over the quarter.

1.686***

Last of Quarter

Equally weighted average CoVaR beta using only the last observation in each quarter.

Largest Bank

Average over time of the CoVaR beta of the largest bank in each country and quarter.

Banks Only

Equally weighted average CoVaR beta of institutions in the Banking or Financial Services sectors.

cr

Description|

us

3.411

39.63%

2.694

24.80%

1.07***

4.009

27.06%

2.707

33.16%

an

1.657**

Ac ce p

te

d

M

2.161**

38 Page 38 of 51

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Table 5: Examining All Relations in a System GMM Setting: We examine all relations by estimating two regressions simultaneously using a Generalized Method of Moments methodology. The first equation uses the 10-year Spread as the dependent variable. The second equation uses the Average CoVaR beta of a country as the dependent variable. Aggregate CoVaR Beta is the coefficient from the CoVaR methodology that estimates the sensitivity of bank stock prices relative to changes in the aggregate stock price of the financial system. Control variables include the Debt-to-GDP ratio, which describes a the ratio of a country’s debt to its annual GDP; Inflation, which is the quarter-end rate of inflation; National Saving, and which is gross disposable income less final consumption expenditures normalized by GDP. Finally, we include time fixed effects to proxy for global macroeconomic events. All regressions include country fixed effects. Standard errors are clustered at the country level. Panel A: Dependent Variable - 10-year Spread

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CoVaR Beta

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Debt-to-GDP Inflation

an

Δ Real GDP

M

National Saving U.S. Crisis Dummy

te

Euro-Crisis "Wind Down" Dummy

d

U.S. Crisis Dummy * CoVaR Beta

Ac ce p

Euro-Crisis "Wind Down" Dummy * CoVaR Beta 10 Year Spread t-1 GIIPS CoVaR GIIPS Spread

2007-2013 2009:Q4-2011:Q4 (1) (2) (3) 1.146** 2.551*** (2.07) (3.93) 0.00710** 0.0166*** 0.0597 (2.25) (3.68) (1.61) 0.0974*** -0.0150 0.309*** (3.02) (-0.48) (2.62) -0.0810* -0.0590 0.00939 (-1.81) (-1.09) (0.16) 0.0186*** -0.000952 0.0453* (4.64) (-0.19) (1.82) 0.0479 0.555*** (0.71) (3.57) -0.441 (-1.18) -0.249** 0.223 (-2.51) (1.11) -1.200** (-2.16) 0.739*** 0.790*** 0.477*** (15.43) (15.34) (3.85) -0.217*** -0.162** (-6.42) (-2.13) 0.131*** 0.00233 0.0384 (2.80) (0.04) (0.41)

Expected Default Frequency Constant

Country Fixed Effects Time Fixed Effects

-0.988*** -1.569*** (-3.29) (-3.19) YES YES YES YES

-4.759*** (-3.18) YES YES

2007-2013 (4) 1.020** (2.08) 0.0196*** (3.45) 0.0246 (0.67) -0.0371 (-1.09) 0.000270 (0.06) 0.701*** (5.02) -0.672 (-1.51) 0.163 (0.76) -1.193** (-2.50) 0.638*** (9.19) -0.170*** (-4.13) -0.0414 (-0.69) 0.317*** (4.17) -1.946*** (-3.52) YES YES

39 Page 39 of 51

Panel B: Dependent Variable - Domestic CoVaR Beta

Ac ce p

te

d

M

an

us

cr

ip t

2007-2013 2009:Q4-2011:Q4 2007-2013 (1) (2) (3) (4) CoVaR Beta t-1 0.862*** 0.816*** 0.875*** 0.828*** (31.37) (22.27) (12.35) (25.31) U.S. Crisis Dummy 0.0428 0.00179 0.0146 (1.39) (0.06) (0.48) Euro-Crisis "Wind Down" Dummy 0.0210** -0.0191 -0.00538 (2.09) (-0.78) (-0.22) 10 Year Spread t-1 0.0201*** 0.0309*** 0.00824* 0.0276*** (5.28) (5.59) (1.69) (5.40) GIIPS CoVaR 0.0205** 0.0221* 0.0334*** 0.0173 (2.46) (1.74) (4.26) (1.42) GIIPS Spread 0.00850 -0.000424 0.00288 0.00213 (0.90) (-0.04) (0.30) (0.18) Constant -0.00637 0.0481** 0.0294* 0.0360* (-0.34) (2.16) (1.95) (1.66) Observations 345 319 113 319 Country Fixed Effects YES YES YES YES Time Fixed Effects YES YES YES YES

40 Page 40 of 51

ip t cr

M an

us

Table 6: Explaining Sovereign Debt Yield Spreads with Orthogonalized Estimates of CoVaR: This table presents a set of regressions which feature the residuals of the regression of CoVaR on the Barclays Euro Aggregate Government debt Index as the key independent variable (CoVaR Residual). Dependent variables include quarterly yield spreads of 3-, 5-, and 10-years. Control variables include dummy variables to control for the sub-period effects of 2007:Q3-2009:Q2 and 2012-2013; an interaction term between the CoVaR beta residual and the 2007:Q3-2009:Q2 and 2012-2013 dummies (to control for changes in the effect of CoVaR beta residual during each sub-period); the Debt-to-GDP ratio, which describes the ratio of a country’s debt to its annual GDP; Inflation, which is the quarter-end rate of consumer inflation; and National Saving, which is gross disposable income less final consumption expenditures normalized by GDP. Finally, we include time fixed effects to proxy for global macroeconomic events. All regressions include country fixed effects. Standard errors are clustered at the country level. (1) (2) (3) (4) 3 Year Spread 5 Year Spread 10 Year Spread 5 Year CDS

Debt to GDP

t

Inflation t National Saving t Δ Real GDP

t

U.S. Crisis Interaction t

Euro Crisis "Wind Down" Dummy t

3 Year Spread t-1 5 Year Spread t-1 10 Year Spread t-1 5 Year CDS t-1 Constant

Observations R-squared

Ac

"Wind Down" Interaction t

0.926* (2.144) 0.00185 (0.366) 0.157** (2.177) 0.00111 (0.0956) 0.00307 (0.0372) -0.0240 (-0.0758) 0.247 (0.591) -0.389 (-1.504) -1.046* (-2.026)

ce pt

U.S. Crisis Dummy (2007:Q3-2009:Q2) t

1.015 (1.681) 0.00762 (0.769) 0.117 (1.341) -0.00979 (-0.665) -0.00344 (-0.0231) 0.267 (0.551) 0.359 (0.649) -0.597** (-2.220) -1.282 (-1.756) 0.843*** (18.48)

ed

CoVaR Residual t

0.557* (2.027) 0.000501 (0.114) 0.0942* (1.776) -0.00467 (-0.544) -0.0167 (-0.463) -0.108 (-0.557) -0.104 (-0.347) -0.462*** (-3.226) -0.714* (-1.827)

92.81** (3.006) 0.434 (0.792) 10.91 (1.702) -2.041** (-2.164) -3.451 (-0.671) -79.98*** (-3.346) -67.92** (-2.682) -74.02** (-2.671) -67.42* (-1.908)

(5) (6) (7) (8) 3 Year Spread 5 Year Spread 10 Year Spread 5 Year CDS 4.000** (2.470) 0.141*** (3.991) 0.558*** (4.136) -0.00874 (-0.293) -0.115 (-0.718)

3.237** (2.309) 0.0689** (2.177) 0.334** (2.189) 0.0253 (0.862) -0.163 (-1.302)

2.133** (2.665) 0.0380 (1.195) 0.244** (2.323) 0.0189 (0.930) -0.0917 (-1.671)

169.6*** (3.037) 5.453* (2.138) 17.56*** (3.084) 1.324 (1.056) -5.728 (-0.818)

0.469*** (3.343)

0.853*** (24.72)

0.549*** (3.949) 0.894*** (34.00)

0.592*** (3.962)

-0.192 (-0.211)

-0.0782 (-0.162)

0.278 (0.980)

0.862*** (30.56) 99.77** (2.232)

300 0.881

319 0.912

332 0.932

320 0.927

-10.98*** (-4.045)

-6.741** (-2.890)

-4.439* (-1.901)

0.662*** (5.039) -481.8** (-2.422)

109 0.928

113 0.937

122 0.949

123 0.938

41 Page 41 of 51

2007-2013

-1.460*** (-3.84) YES YES

-0.957*** (-2.72) YES YES

MES Debt-to-GDP

0.0107*** (3.46) 0.0865*** (2.75) -0.0684* (-1.82) 0.0240*** (4.43) 0.106 (1.30)

Inflation Δ Real GDP

M

National Saving U.S. Crisis Dummy

-0.302*** (-2.69)

te

Euro-Crisis "Wind Down" Dummy

d

U.S. Crisis Dummy * MES

Ac ce p

Euro-Crisis "Wind Down" Dummy * MES 10 Year Spread t-1

0.752*** (14.36)

GIIPS MES

GIIPS Spread CAPM Beta

CAPM Beta t-1

GIIPS CAPM Beta Constant Country Fixed Effects Time Fixed Effects

2009:Q4-2011:Q4 2007-2013 (3) (4) -47.96** 1.511 (-2.15) (0.14) 0.0324** 0.0132** (2.14) (2.31) 0.260*** 0.0255 (2.95) (0.76) -0.0387 -0.0633 (-0.94) (-0.98) 0.0174 0.00907 (0.93) (1.47) -0.0404 (-0.21) -4.457 (-0.63) 0.134 (0.67) 15.84*** (3.07) 0.788*** 0.753*** (9.54) (14.51) 19.11 -29.94*** (0.57) (-3.37) 0.0553*** 0.0227 (2.75) (1.14) 1.887*** (2.65) 0.158 (0.24) 3.793*** (3.21) -4.634*** -5.828*** (-3.17) (-5.12) YES YES YES YES

us

0.0378** (2.39)

(2) -17.52* (-1.87) 0.00896*** (2.62) -0.0160 (-0.54) 0.00250 (0.04) 0.00251 (0.33) 0.0969 (0.69) -6.108 (-0.90) -0.154 (-0.71) 13.06* (1.89) 0.824*** (16.93) 2.233 (0.23) 0.0256 (1.51)

an

(1)

cr

Panel A: Dependent Variable - 10-year Spread

ip t

Table 7: Explaining Yield Spreads using Marginal Expected Shortfall (MES) in a System GMM Setting: This table presents a set of regressions which feature the yield spread (over the equal maturity U.S. Treasury rate) as the dependent variable. Independent variables include the average annual aggregate Marginal Expected Shortfall (MES, Acharya, et al. (2015)), the average return of banks in the country when the financial system is in the 5% tail of its return distribution. Control variables include the Debt-to-GDP ratio, which describes a the ratio of a country’s debt to its annual GDP; Inflation, which is the quarterend rate of inflation; and National Saving, which is gross disposable income less final consumption expenditures normalized by GDP. Finally, we include time fixed effects to proxy for global macroeconomic events. All regressions include country fixed effects. Standard errors are clustered at the country level.

42 Page 42 of 51

Panel B: Dependent Variable - Domestic MES

GIIPS MES GIIPS Spread GIIPS CAPM Beta

M

0.00236 (0.99) 319 YES YES

Ac ce p

te

Observations Country Fixed Effects Time Fixed Effects

0.00112 (0.60) 345 YES YES

d

Constant

an

10 Year Spread t-1

us

Euro-Crisis "Wind Down" Dummy

ip t

U.S. Crisis Dummy

2009:Q4-2011:Q4 2007-2013 (3) (4) 0.510*** 0.595*** (7.06) (9.68) 0.00239*** (2.61) 0.00387*** (5.17) -0.000158 -0.000153 (-0.47) (-0.80) 0.963*** 0.748*** (7.54) (9.78) -0.000561*** 0.000325*** (-7.30) (4.04) -0.00501 (-0.63) 0.0204*** 0.00747 (7.65) (1.06) 152 319 YES YES YES YES

cr

MESt-1

2007-2013 (1) (2) 0.503*** 0.474*** (11.27) (5.41) -0.00146** 0.00159 (-2.08) (1.61) 0.00123* 0.00331*** (1.86) (4.02) -0.000153 -0.000342* (-0.72) (-1.72) 0.572*** 0.753*** (8.16) (11.01) -0.0000266 0.000274*** (-0.46) (3.66)

43 Page 43 of 51

ip t

Ac

ce pt

ed

M an

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cr

Figure 1: Relations Examined in this Paper: This figure graphically presents the relations we study. Relation 1 represents the spillover of risk from financial systems to governments (and vice-versa). Some literature already examines this type of risk spillover, however, we are the first study to examine how systemic risk exposure affects sovereign yields. Relation 2 examines the spillover of risk from country to country in terms of financial systems while Relation 3 examines the spillover of risk from country to country in terms of governments. We are the first study to examine these types of relations. Finally, Relation 4 examines how risk spills over from governments to the financial systems of other countries (and vice versa). Again, we are the first study to examine this relation.

44 Page 44 of 51

ip t

Ac

ce pt

ed

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Figure 2: 10 Year Average Non-GIIPS Yield vs. 10 Year Average GIIPS Yield, 2007-2013: This figure plots the ten-year sovereign debt yield for non-GIIPS countries against the ten-year sovereign debt yield for GIIPS countries (Greece, Ireland, Portugal, Spain, Italy) over the period 2007-2013.

45 Page 45 of 51

ip t

Ac

ce pt

ed

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Figure 3: GIIPS CoVaR vs. 10 Year Average GIIPS Yield, 2007-2013: This figure plots the ten-year sovereign debt yield against the Adapted Exposure CoVaR beta for the GIIPS countries (Greece, Ireland, Portugal, Spain, Italy) over the period 2007-2011. The Adapted Exposure CoVaR beta is the average beta of all financial institutions calculated on a weekly basis. This variable represents the sensitivity of bank stock prices with respect to changes in system-wide stock prices.

46 Page 46 of 51

Figure 4: Time Series Dynamics of CoVaR and Yield Spreads: This figure plots the time series dynamics of how changes in CoVaR beta impact the average sovereign debt yields and domestic systemic risk over a 12-quarter period.

te

d

M

an

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cr

ip t

Panel A: Effects of Domestic CoVaR beta:

Ac ce p

Panel B: Effects of GIIPS CoVaR beta:

47 Page 47 of 51

Appendix A – Exposure CoVaR

Adapted Exposure CoVaR is based on Adrian and Brunnermeier (2015). The authors

ip t

provide two key measures for determining the systemic risk of an institution. Each measure captures a different aspect of an institution’s systemic risk. Contribution CoVaR estimates the

cr

contribution of a single institution to the overall losses suffered by the financial system, given a

us

crisis event. Exposure CoVaR provides an estimate of the change in an institution’s VaR given an industry-wide systemic crisis.

an

Adrian and Brunnermeier (2015) define Exposure CoVaR (specifically, CoVaRqj|s ) as

M

“institution j ’s increase in VaR in the case of a financial crisis.” We denote the financial system as s . Formally, Exposure CoVaR is given by the q th -quantile of the conditional probability

te

d

distribution:

s

Ac ce p

Pr ( X j  CoVaRqj|C( X ) | C( X s )) = q

(A.1)

where X j is the variable for which the value-at-risk of institution j is defined, C( X s )

is a tail event within the system, and CoVaRqj|C ( X

s)

is the VaR of an institution conditional on the

state of the financial system. The variable q denotes a probability level corresponding to the left tail of the distribution of institution-level asset returns. This value is typically set to 1%. Further, the system’s contribution to firm j , which is in turn j ’s exposure to the system, is given by:

j | X s =VaRqi

CoVaRqj|s = CoVaRq

 CoVaRqj| X

s = Median s

(A.2)

49 Page 48 of 51

Empirically, Adrian and Brunnermeier (2015) estimate exposure CoVaR on a weekly basis using quantile regressions (Koenker and Bassett, 1978), which estimate coefficients at the

ip t

1% quantile rather than at the mean. First, the authors calculate the week-to-week change in the

cr

market value of institution and industry assets. X j denotes the change in the assets of a financial institution and X s denotes the change in the assets of the entire financial system. In our case,

us

X j and X s represent daily equity returns. Adrian and Brunnermeier (2015) note that

an

constructing CoVaR using equity can provide information about the bank’s asset-liability mismatch. We use the MSCI Europe Financials Index as our proxy for financial system returns.*

M

Following Adrian and Brunnermeier (2015), we also denote M t 1 as a set of macroeconomic conditioning variables including the VIX†; liquidity spread measured by the

d

difference between the three-month U.S. repo rate and the three-month U.S. T-bill rate; change

te

in the three-month Treasury bill rate; change in the slope of the yield curve measured by the

Ac ce p

yield spread between the ten-year U.S. Treasury rate and the three-month U.S. Treasury bill rate; change in the credit spread measured by the difference between Moody’s Baa-rated bonds and the U.S. Treasury rate; weekly equity market return measured by the STOXX 600 Europe Index; and the one-year cumulative real estate sector return proxied for by the FTSE EPRA/NAREIT Index, which is an index of the 83 most heavily traded real estate stocks in Europe. Adrian and * This is a value-weighted index. The use of one financial company’s returns as the dependent variable as well as a small component of the index does not materially change the calculated CoVaR for that given bank. For example, we estimate a simple value-weighted index of Greek banks, and calculate CoVaR based on the index with and without each FI. The time series correlation of CoVaR estimates including (vs. omitting) the individual FI returns from the index is 98.84%. Due to this very high correlation, we use the MSCI Europe Financials Index without omitting the relevant FI’s returns when estimating the individual time series regressions for each firm. † This represents the implied volatility of a set of S&P 500 options. The VIX and the other variables employed here are meant to control for factors that have been used in the literature (e.g., Adrian and Brunnermeier (2015) and Beirne and Fratzscher (2013)) and proxy for various aspects of market-wide conditions in the economy and asset markets (e.g., stock market volatility, inflation and economic growth expectations, credit risk, and growth in equity and real estate markets). Moreover, yields on the left-hand side of the CoVaR regressions are not the same yields as used on the right-hand side of the yield spread regressions shown later. The CoVaR regressions use U.S.-based yields as macroeconomic controls, while the yield spread regressions use European sovereign debt yields. As such, our tests should not suffer from a “built-in” significance problem. This problem is further ameliorated in our robustness section, where we utilize German yields as a base from which to calculate yield spreads.

50 Page 49 of 51

Brunnermeier (2015) then estimate:

X j =  j|s X s   j|s M t 1   j|s

ip t

(A.3)

cr

The generated coefficients are then used to estimate the VaR and CoVaR of the institution and the system at the median and q = 1% levels. Finally,  j|s is used to calculate

an

us

Exposure CoVaR:

(A.4)

Ac ce p

te

d

M

CoVaRqj|s =  j|s (VaRts (q)  VaRts (50%))

51 Page 50 of 51

ip t cr

Appendix B - Adapted Exposure CoVaR Beta by Country and Year

2010 0.797 0.742 -0.013 0.341 0.361 0.079 0.582 0.654 0.351 0.263 0.054 0.404 0.466 0.229 0.420

M an

2009 0.645 0.691 -0.148 0.215 0.312 0.119 0.507 0.866 0.259 0.315 0.042 0.284 0.316 0.136 0.392

ed

2008 0.077 0.712 0.087 -0.058 0.557 0.244 0.360 0.848 0.209 -0.191 -0.249 0.206 0.452 0.002 0.376

ce pt

2007 -0.043 0.253 0.843 0.056 0.306 -0.154 0.127 0.420 0.364 -0.563 0.047 -0.158 0.353 -0.097 0.320

2011 0.467 0.773 0.396 0.230 0.717 0.186 1.376 0.608 0.706 0.116 0.082 0.950 0.744 0.176 0.245

2012 0.700 0.792 0.384 0.707 0.222 1.322 0.485 0.824 0.132 -0.078 1.070 0.642 0.065 0.122

2013 0.824 0.401 -0.300 0.867 0.269 0.640 -0.104 1.061 0.422 -0.058 0.969 0.879 0.062 0.335

Num. FI 5 9 9 6 17 36 11 8 42 9 44 5 14 23 54

Ac

Austria Belgium Cyprus Finland France Germany Greece Ireland Italy Norway Poland Portugal Spain Sweden United Kingdom

us

This table presents the annual average Adapted Exposure CoVaR beta for each country and year in our sample, as well as the average number of FIs used to estimate these parameters. The CoVaR beta term describes the sensitivity of bank equity to changes in the equity of the financial system. We calculate the aggregate measure below by averaging the weekly CoVaR betas of each financial institution within a given country over a one-year period.

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