Three Essays on Systemic Risk and Financial Contagion

Three Essays on Systemic Risk and Financial Contagion Dissertation zur Erlangung des akademischen Grades Doktor der Wirtschaftswissenschaften (Dr. rer. pol.) im Fachbereich Wirtschaftswissenschaften der Universität Konstanz vorgelegt von: Adrian Alter Tag der mündlichen Prüfung: 29.08.2013 Referenten: 1. Prof. Dr. Dr. h.c. Günter Franke 2. Prof. Dr. Almuth Scholl

To my family

Contents Contents.................................... I List of Figures................................. V List of Tables................................. VII Acknowledgements.............................. IX Summary................................... XI Zusammenfassung............................... XVII 1 Credit spread interdependencies of European states and banks 1 1.1 Introduction............................... 2 1.2 Related literature............................ 5 1.3 Hypotheses, data, and econometric methodology............................... 7 1.3.1 Hypotheses........................... 7 1.3.2 Bailout specific characteristics................. 9 1.3.3 Data and sub-sample selection................. 10 1.3.4 Econometric methodology................... 12 1.4 Results.................................. 14 1.4.1 Cross-country analysis..................... 15 1.4.2 Specific country analysis.................... 20 1.5 Conclusion................................ 31 Appendix 1.A Further issues on methodology............... 36 1.A.1 VEC-analysis - Selection of sub-stages............ 36 1.A.2 Pre-analysis of the data, model specification, and estimation 36 1.A.3 Interpretation of long-run relations in a VECM....... 37 Appendix 1.B Specific country analysis.................. 38 1.B.1 France.............................. 38 1.B.2 Germany............................. 39 1.B.3 Ireland.............................. 40 1.B.4 Italy............................... 41 1.B.5 The Netherlands........................ 42 1.B.6 Portugal............................. 43 I

1.B.7 Spain............................... 44 1.B.8 Cointegration graphs...................... 45 2 A Contagion Index for the Euro Area 47 2.1 Introduction............................... 48 2.2 Related Literature........................... 51 2.3 Econometric Methodology and Data Description............................ 53 2.3.1 Vector autoregressive model with exogenous variables (VARX) 54 2.3.2 Generalized impulse response functions (GIRF)....... 55 2.3.3 The spillover matrix...................... 56 2.3.4 Contagion indices........................ 59 2.4 Results.................................. 60 2.4.1 A static perspective....................... 60 2.4.2 The dynamics of potential spillover effects.......... 66 2.4.3 The euro area Contagion Index................ 68 2.4.4 The spillover and net spillover matrices............ 71 2.4.5 The systemic contribution of sovereigns............ 74 2.4.6 The impact of different economic/policy events on the contagion index............................ 74 2.4.7 Critical spillover thresholds for contagion........... 75 2.5 Robustness and motivation of setup parameters........... 78 2.5.1 Differences in distributions of residuals............ 78 2.5.2 Relaxing restrictions imposed on impulse responses..... 79 2.6 Conclusion and Outlook........................ 81 Bibliography................................. 85 Appendix 2.A Description of variables and events............. 87 Appendix 2.B The explicit VAR model with exogenous common factors 90 Appendix 2.C Other versions of the contagion indices and systemic contribution of sovereigns......................... 91 Appendix 2.D Spillover and Net Spillover Matrices............ 94 Appendix 2.E Optimal rolling window size................ 96 3 Centrality-based Capital Allocations and Bailout Funds 99 3.1 Introduction............................... 100 3.2 Data and methodology......................... 106 3.2.1 Methodology.......................... 106 3.2.2 Data sources........................... 107 II

3.3 Interbank network........................... 111 3.3.1 German interbank market................... 111 3.3.2 Centrality measures....................... 112 3.4 Credit risk model............................ 116 3.4.1 Modeling the returns of large loans.............. 116 3.4.2 Modeling the returns of small loans.............. 119 3.5 Modeling contagion........................... 120 3.5.1 Losses and bankruptcy costs.................. 121 3.5.2 Eisenberg and Noe - interbank contagion algorithm.... 122 3.6 Optimization.............................. 123 3.6.1 Capital allocations....................... 124 3.6.2 Target function(s)....................... 126 3.6.3 Setting capital allocation(s) procedure............ 127 3.6.4 Bailout fund mechanism.................... 128 3.7 Results................................. 129 3.7.1 Capital allocations....................... 129 3.7.2 Bailout fund mechanism.................... 135 3.8 Robustness checks............................ 138 3.8.1 Interbank liabilities....................... 138 3.8.2 Network structure........................ 139 3.8.3 Credit risk parameters..................... 140 3.9 Conclusion................................ 140 Appendix 3.A Risk and contagion mechanism............... 146 Appendix 3.B Centrality measures - technical details........... 150 3.B.1 Eigenvector centrality..................... 150 3.B.2 Betweenness centrality..................... 150 3.B.3 Closeness centrality....................... 151 3.B.4 (Local) Clustering coefficient.................. 151 Appendix 3.C Modeling returns of small loans.............. 152 3.C.1 Estimating the granularity of small-loans exposures (Herfindahl Index)............................ 154 Appendix 3.D Other target functions................... 155 Appendix 3.E Other results......................... 156 Appendix 3.F Liabilities and network properties............. 158 Complete Bibliography 163 Erklärung und Eigenabgrenzung 173 III

List of Figures 1.1 Effects of a Banking Sector Shock on Government Spreads: Before Government Interventions....................... 18 1.2 Responses on Day 1 after the Shock................. 19 1.3 Effects of a Sovereign Shock on Bank Spreads: After Government Interventions............................... 20 1.4 Generalized Impulse Responses for Germany: (Solid) Before, (Dotted) During & After Government Interventions........... 22 1.5 Generalized Impulse Responses for Ireland: (Solid) Before, (Dotted) During & After Government Interventions.............. 26 1.6 Generalized Impulse Responses for Italy: (Solid) Before, (Dotted) During & After Government Interventions.............. 29 1.B.1 France: CDS Level Series....................... 38 1.B.2 Germany: CDS Level Series...................... 39 1.B.3 Ireland: CDS Level Series....................... 40 1.B.4 Italy: CDS Level Series........................ 41 1.B.5 The Netherlands: CDS Level Series................. 42 1.B.6 Portugal: CDS Level Series...................... 43 1.B.7 Spain: CDS Level Series........................ 44 1.B.8 Cointegration Graph of Germany and Commerzbank (Before Government Interventions)........................ 45 1.B.9 Cointegration Graph of Ireland and Allied Irish Banks (During and After Government Interventions)................... 45 1.B.10 Cointegration Graph of Italy and Intesa Sanpaolo (During and After Government Interventions)...................... 45 2.1 Potential impact of a Spanish sovereign CDS shock on other sovereign CDS spreads.............................. 62 2.2 Potential impact on Spanish sovereign CDS from a shock in the other sovereign CDS spreads......................... 62 2.3 Potential impact of a shock in Spanish sovereign CDS on bank CDSs 63 2.4 Potential impact of a shock in bank CDSs on Spanish sovereign CDS 63 V

2.5 The dynamics of the cumulated potential impact on CDS spreads. 67 2.6 Average cumulated impact on European banks........... 68 2.7 Sovereign CDS series and the EA Contagion Index......... 69 2.8 EA Contagion Indices......................... 70 2.9 Average potential spillover effects................... 71 2.10 Systemic contributions of GIIPS countries (left axis) and the Total Net Positive (TNP) Spillover (right axis).............. 75 2.11 Impact on Contagion Index components at some specific news/policy events.................................. 76 2.12 Rejection of the Null hypothesis of the Kolmogorov-Smirnov (KS) test................................... 79 2.13 Moments of the sample distributions of residuals from the VAR model 80 2.14 The Contagion Index with restricted and unrestricted IRs..... 80 2.C.1 Different versions of the EA Contagion Index of sovereigns..... 93 2.E.1 Optimal size of the rolling window.................. 97 3.1 Individual bank balance sheet and benchmark capital....... 108 3.2 A comparison of different capital allocations across network measures 130 3.3 Expected system losses: All defaults, fundamental defaults and contagious defaults............................ 132 3.4 Frequency distributions of individual bank PDs........... 133 3.5 Occurrences of individual bank defaults............... 134 3.6 Comparison of different capital allocations based on: Total Assets, Opsahl and Weighted Eigenvector.................. 135 3.7 Pdfs of bank defaults AFTER contagion using a bailout fund mechanism with rules based on: Opsahl (Ops) versus VaR (upper level); Total Asstets (TA) versus VaR (lower level)............. 137 3.8 Bailout efficiency surface: Opsahl centrality............. 138 3.A.1 Risk model sketch........................... 147 3.B.1 Centrality measures.......................... 151 3.E.1 Unconditional distribution of total system losses.......... 156 3.E.2 Conditional distributions of losses for best capital allocation under rule based on: Total Assets (TA), Value-at-Risk (VaR), and Opsahl centrality (Opsahl)........................... 157 3.F.1 Power law vs log-normal diagnostics................. 158 3.F.2 Comparison between ranked interbank liabilities (by size)..... 159 VI

List of Tables 1.1 Government Support Measures for Financial Institutions (October 2008 - May 2010)........................... 9 1.2 Results of Granger-Causality Tests for all Countries......... 15 1.3 Percentage of Significant/Insignificant Responses in the Long Run (after 22 days)............................. 15 1.4 Results of Cointegration Analysis for all Countries.......... 16 1.5 Generalized Impulse Responses.................... 17 1.B.1 France: Bivariate Cointegration Tests................ 38 1.B.2 Germany: Bivariate Cointegration Tests............... 39 1.B.3 Ireland: Bivariate Cointegration Tests................ 40 1.B.4 Italy: Bivariate Cointegration Tests................. 41 1.B.5 The Netherlands: Bivariate Cointegration Tests........... 42 1.B.6 Portugal: Bivariate Cointegration Tests............... 43 1.B.7 Spain: Bivariate Cointegration Tests................. 44 2.1 The Spillover Matrix.......................... 57 2.2 The spillover matrix of EA sovereigns and banks (on 21 June 2012) 64 2.3 Net Spillover matrix of EA sovereigns and banks (on 21 June 2012) 65 2.4 Ranking of NET senders and receivers of spillover effects on the 18 July 2011................................ 72 2.5 Ranking of NET senders and receivers of spillover effects on the 21 June 2012................................ 73 2.6 Critical spillover levels......................... 78 2.A.1 Composition and description of bank-specific and exogenous variables.................................. 87 2.A.2 Descriptive Statistics......................... 88 2.A.3 Country-specific bank assets and the weight in the country bank index 89 2.A.4 Selected events and the cumulative returns of contagion indices.. 90 2.D.1 The spillover matrix of EA sovereigns and banks (on 18 July 2011) 94 2.D.2 Net spillover matrix (on 18 July 2011)................ 95 VII

3.1 Interbank (IB) market and network properties........... 113 3.A.1 Risk model (RM) sectors....................... 146 3.A.2 Model parameters........................... 146 3.A.3 Credit risk parameters......................... 148 3.A.4 S&P s credit ratings transition matrix, in percent.......... 149 3.F.1 Network properties - 2009 Q1..................... 160 3.F.2 Network properties - 2007 Q1..................... 161 3.F.3 Network properties - 2005 Q1..................... 162 VIII

Acknowledgements This thesis concludes four remarkable years in which I have been a Ph.D. student in Economics and Finance at the University of Konstanz. 1 It is time to thank everyone who helped me walk this path and shared with me great moments, interesting ideas, and thoughtful discussions. First, I would like to express my deepest gratitude to Professor Günter Franke, whose unconditional support and supervision has been invaluable. His thoughts and advice helped me develop most of my knowledge related to systemic risk, macroprudential regulation, and financial contagion. He also backed my research visits at the European Central Bank and Deutsche Bundesbank. His assistance has been clearly invaluable. I am very thankful to the members of my thesis evaluation committee: Professors Almuth Scholl and Heinrich Ursprung. Moreover, Professors Ralf Brüggemann and Winfried Pohlmeier have contributed with technical expertise in econometrics and I am very grateful to them. I am also indebted to my colleagues Moritz Heimes, Ferdinand Graf, Steffen Seemann, Matthias Draheim who provided me useful comments on my research papers. Elvira Grübel, Michal Marenčák and Angelina Jegel helped me with many administrative issues but the most important achievement is the successful organization of the Final Marie Curie Conference in April 2013. Second, I would like to thank my former colleagues at the ECB. My supervisor and co-author, Andreas Beyer, has been always committed to our joint work. I am also grateful to him for teaching me the first steps in central banking and financial stability policy. I had amazing moments and I am thankful to my colleagues and friends made during my internship at the ECB: Fiona, Jasmien, Jolyn, Nora, Valerie, Galen, Guillaume, Daniel, David, Marco, Nicollo, Nicola, and Wolf. I am sure the list should be much longer here, hence, I am also thankful to all omitted ones. During my research secondment at the Deutsche Bundesbank I have collaborated with Peter Raupach and Ben Craig. I am grateful for their research commitment and 1 Marie Curie Doctoral Fellowship in Risk Management from European Community s Seventh Framework Programme FP7-PEOPLE-ITN-2008 (grant agreement PITN-GA-2009-237984) is gratefully acknowledged. IX

interesting discussions during my visit. I learned a lot from them. I am also thankful to Co-Pierre Georg, Kartik Anand, Rients Galema, Marcus Pramor, Benedikt Ruprecht, Klaus Düllmann, Thomas Kick, and Barbara Meller. The Marie Curie network and support has been very useful during my Ph.D. research. Special thanks to Professor Ser-huang Poon, Claire Faichnie, Fady Barsoum, Anton Golub, Eberhard Mayerhofer, Kyle Moore, Pengfei Sun, Zhen Guo, Yiran Zhang, Shibashish Mukherjee, Hossein Khatami, Heikki Seppala, Armin Eder, Kebin Ma, and Rachel Lidan. Third, I want to express my appreciation to Camelia Minoiu, who has been always supportive and contributed with enlightening comments and discussions to my research and career path. Thank you for being part of this success. I had a great time in Konstanz with two of my best friends Yves Schüler, with whom I wrote my first research paper, and Fabian Krüger. Moreover, I want to express my gratitude to my friends Bianca, Tudor, Denisa, Recca, Ruben, Tim, Anna, Daniel, Anca and Stefano, with whom I spent memorable moments. Finally, and most importantly, I am thankful to my family. Without the support of my parents, Iancu and Marilena, and my grandparents, things would have been much more difficult. They have always shown their love and encouragement and I am very grateful to them. Adrian Alter Konstanz, 19 June 2013 X

Summary One of the lessons that emerged from the global financial crisis 2007-2009 and the recent European sovereign debt crisis is that the institutional framework for supervising and regulating financial systems has to be reformed. One of the novel policy direction that gained interest and attention is macro-prudential supervision. The interaction with micro-prudential regulation and monetary policy, among others, adds to the complexity of the global financial system. This dissertation has at its core the concept of systemic risk. Seen as a feature of financial systems, systemic risk can be related to the likelihood of an institution, an asset class or a group of institutions to harm the financial stability with repercussions on the real economy (see e.g. Kaufman (1995)). The aim of this thesis is to tackle this concept from different angles. First, it sheds light on the implications of the nexus between the default risk of sovereigns and the financial sector. This direction is covered by an empirical analysis of the credit default swap (CDS, hereafter) market. The dynamics of interconnectedness between financial institutions and countries are at the roots of a novel feature observed during the last four years in the Eurozone: the feedback loop between the stability of the banking system and the macroeconomic health of sovereigns. Moreover, the phenomenon of financial contagion has attracted the attention of academia, policy makers and market participants. Constâncio (2012), the vice-president of the ECB, refers to contagion as one of the mechanisms by which financial instability becomes so widespread that a crisis reaches systemic dimensions.[... ] As a consequence, crisis management by all competent authorities should also focus on policy measures that are able to contain and mitigate contagion. Allen and Gale (2000) explain contagion as a consequence of excess spillover effects. For example, a banking crisis in one region may spread to other regions. Contagion in their view is the phenomenon of extreme amplification of spillover effects. Therefore, spillover effects are a necessary, but not sufficient, condition for contagion. Finally, this thesis is motivated by an acute need for policyrelevant methodologies and frameworks to deal with systemically important financial institutions (SIFIs hereafter), especially for large financial systems. Using measures XI

Summary of centrality derived from the interbank network, I intend to provide more insight to the too-big-to-fail versus too-interconnected-to-fail discussion. Capital allocations based on both, riskiness and size of individual bank assets combined with metrics of interconnectedness constructed from the entire banking network appear to improve the robustness of financial system. Let me give an overview of this dissertation. Chapter 1 presents an analysis of the interdependencies between the credit risk of Eurozone sovereigns and financial sector during the financial crisis. Generalizing Chapter 1, in Chapter 2 we propose a framework of tracking and monitoring financial contagion in the Eurozone. Furthermore, this chapter intends to provide a toolbox that allows policy makers to determine the impact of political/policy events on stemming or fueling financial contagion. Finally, Chapter 3 presents a tractable framework to deal with SIFIs. By proposing two policy directions, we show that network measures derived from the interbank market and the size of financial institutions could help to improve the resilience of large financial systems. In the rest of this summary I provide an overview of the main ideas and results of each chapter and highlight the contributions to the literature. Chapter 1 investigates empirically the relationship between the credit risk of several Eurozone countries (France, Germany, Italy, Ireland, the Netherlands, Portugal, and Spain) and their domestic banking sectors during the period 2007-2010, using daily CDS spreads. 2 Bank bailouts changed the composition of both banks and sovereign balance sheets and, moreover, affected the linkage between the default risk of governments and their local banks. Our main findings suggest that in the period before bank bailouts the contagion disperses from bank credit spreads into the sovereign CDS market. After bailouts, a financial sector shock affects sovereign CDS spreads more strongly in the short run. However, the impact becomes insignificant in the long term. Furthermore, government CDS spreads become an important determinant of banks CDS spreads. Yet, there exist clear-cut differences between strong and weak member states. The relationship between government and bank credit risk is heterogeneous across countries, but homogeneous within the same country. These findings help to better understand the interaction between bank and sovereign risks and shed light on the private-to-public risk transfer. Moreover, focusing on the effects of bank bailouts on the linkage between CDS spreads of governments and their local banks, we contribute to the literature in the following ways: i) relying on previous studies that emphasize the importance 2 Chapter 1 is a reprint of the published paper Credit spread interdependencies of European states and banks during the financial crisis, Journal of Banking and Finance, Volume 36, Issue 12, December 2012, pp. 3444-3468, joint work with Yves S. Schüler (University of Konstanz). XII

Summary of the domestic financial sector as a determinant of sovereign CDS spreads, we provide detailed empirical evidence for its influence during the financial crisis; ii) in contrast to other studies, we research on the credit risk interdependence of banks and governments during the last financial turmoil. Using this approach we highlight stark alterations of the latter linkage after bank bailouts and we contrast differences in the private-to-public risk transfer both within a country but also across the Eurozone. In Chapter 2, we develop an analytical and empirical framework for measuring spillover effects by extending the econometric setup proposed by Diebold and Yilmaz (2009; 2011). 3 We illustrate our method by an empirical application to the interlinkages between sovereigns and banks in the Eurozone. By analyzing daily CDS data, we quantify those spillover effects based on an 80-days rolling window. We combine sovereign and bank CDS spreads in a vector autoregressive framework, augmented by several control variables (i.e. in order to deal with common risk factors, omitted variables). In our model we focus on 11 sovereigns and nine country-specific banking groups from the euro area, over the period October 2009 - July 2012. Furthermore, we rely on a generalised impulse response approach to assess the systemic effect of an unexpected shock to the creditworthiness of a particular sovereign or countryspecific bank index. We aggregate this information into a Contagion Index. This index has four main components. Average potential spillover: i) among sovereigns, ii) among banks, iii) from sovereigns to banks and iv) vice-versa. Our measure can be used to highlight the potential contagion at a certain point in time or the time-dependent feature of the contagion index. This toolbox allows us to identify systemically relevant entities (i.e. country specific banking sectors and sovereigns) from the proposed set of sovereigns and banks in our system. Based on empirical distributions of CDS changes, we propose a simple method to compute thresholds for excessive spillovers. Excessive spillovers are a characteristic of dysfunctional markets and can be regarded as a source of contagion and systemic risk. When financial variables (e.g. markets, participants, intermediaries) are characterized by extreme dependence, financial systems become unstable. Furthermore, we show the dynamics of the nexus between banks and sovereigns, that represents a potential source of systemic risk. Euro area sovereign creditworthiness carries a growing weight in the overall financial market picture, with a subset of sovereigns that can potentially produce negative externalities to the financial system. We find that several previous policy interventions had a mitigating impact on spillover risks. A potential unexpected shock to Spanish sovereign CDS spread 3 Chapter 2 is a partial rewrite of the CFS Working Paper No. 2012/13 and ECB Working Paper No. 2013/1558 The dynamics of spillover effects during the European sovereign debt turmoil, joint work with Andreas Beyer (ECB). XIII

Summary reveals an elevated impact on both spreads of euro area sovereigns and banks during the first half of 2012, compared to 2011. Moreover, spillover effects from a shock to Spanish sovereign CDS to Eurozone core countries and to non-core countries become more similar in magnitude during 2012. We also highlight the stark amplification of the nexus between sovereigns and banks until the end of June 2012, the announcement of the Banking Union. Focusing on policy relevant interventions, we observe that the systemic contributions of Greece, Portugal and Ireland decrease remarkably after the implementation of IMF/EU programs. Moreover, the setup of the European Financial Stability Facility (EFSF) and the decision of the two Long-Term Refinancing Operations (LTRO) in December 2012 have a mitigating impact on all four contagion index components. This chapter suggests a macro-prudential toolbox for measuring the potential contagion in the euro area using market data. 4 It can be adapted to the needs of policy makers by integrating other banks or sovereigns or extending it to real economy variables. Furthermore, we attempt to show its usefulness in quantifying the potential effects of different policy measures on containing spillovers across the system. Applying network theory and analysis, we determine in Chapter 3 different capital rules with the scope of minimizing total system losses. 5 Using the German Credit Register database, several measures of centrality are constructed from the network topology of the interbank market that help us designing systemic capital buffers. Capital is reallocated among banks based on network centrality measures in order to minimize the expected losses in the banking system. The so-called Opsahl centrality turns out to dominate any other centrality measure tested, apart from total assets. Furthermore, we use centrality measures to implement a bailout fund mechanism. The bailout fund offers insurance against the default of certain banks, however with priorities depending on banks size and centrality. Finally, we compare the total system loss across different types of capital allocation and sizes of the bailout fund. We attempt to draw policy conclusions related to too-interconnected-to-fail versus too-big-to-fail discussion. We show that there are certain capital allocations that are able to improve financial stability. Focusing on the system as a whole and assigning capital allocations based on network metrics yields better results than the benchmark capital allocation that is based solely on the individual bank balance sheet. The improvement comes from getting the big picture of the entire system where interconnectedness and centrality play a major role in triggering and amplifying contagious defaults. What is interesting is that capital allocations based on 4 This toolbox has been applied also in ECB 2012, pg. 73, Box 5. 5 Chapter 3 has been partially written together with Peter Raupach and Ben Craig, both from the Deutsche Bundesbank. XIV

Zusammenfassung total assets dominate any other centrality measure tested. These results strengthen previous findings that systemic capital requirements should depend mainly on total assets as proposed by Tarashev et al. (2010). One could improve even further the system s stability, by combining total assets and network metrics on top of individual bank asset riskiness (measured for example by the individual bank Value-at-Risk). In this last chapter, we propose a tractable framework to assess the impact of different capital allocations on financial stability. We integrate a sound credit risk engine (i.e. CreditMetrics) to generate correlated shocks to credit exposures of the entire German banking system, where about 1750 banks are active in the interbank market. This engine gives us the opportunity to focus on correlated tail events, endogenously determined by the composition of bank balance sheets. Moreover, we model interbank contagion based on a clearing mechanism, as described firstly by Eisenberg and Noe (2001), and extend it to include bankruptcy costs as proposed by Elsinger et al. (2006). This feature allows us to measure expected contagion losses and to observe the propagation process in the interbank market. To empirically exemplify our framework, we use several sources of information: German central credit register (for large exposures), aggregated credit exposures (for small loans), balance sheet data (i.e. total assets, total sector exposures), and market data (to compute correlations between real economy sectors or credit spreads). We focus on capital reallocations and try to minimize a target function with the scope of improving financial stability. We intend to use several target functions: total system losses, approximated by total bankruptcy costs, second-round contagion effects (i.e. contagious defaults) or losses from fundamental defaults (i.e. banks which default due to real-economy portfolio losses). Furthermore, we determine capital allocations that improve the resilience of the financial system based on interconnectedness measures constructed from the interbank network or associated with the size and riskiness of bank balance sheets (e.g. total assets, total interbank liabilities, eigenvector centralities, Opsahl centrality, closeness or the clustering coefficient). Our method which deals with interconnected financial systems is an alternative to market-based systemic measures (e.g Acharya et al. (2010); Adrian and Brunnermeier (2011); Gauthier et al. (2012)) when tackling the too-interconnected-to-fail externality. The main advantage of our framework is that policy makers can deal with large banking systems where market data is not available for most of the institutions. To sum up, this dissertation intends to familiarize the reader with several important concepts related to macro-prudential supervision and financial stability. Moreover, it provides empirical applications to show case these concepts and ignite further research on these topics. XV

Zusammenfassung Keywords: interdependencies, systemic risk, financial contagion, interconnectedness, private-to-public risk transfer, sovereign - financial sector feedback loop, SIFIs, large financial system, credit default swap (CDS), systemically important market, contagion index, systemic contribution, liquidity risk, credit risk, macroprudential supervision, regulation, mutual exposures, interbank network, common shocks, collateral, bailout fund, resolution mechanism, lender-of-last-resort, transparency, moral hazard, uncertainty, stress tests, cointegration, externalities, too-bigto-fail, degree, betweenness, closeness, eigenvector centrality. XVI

Zusammenfassung Eine der Lektionen aus der globalen Finanzkrise 2007-2009 und der Europäischen Staatsschuldenkrise, die Anfang des Jahres 2010 begann, ist, dass eine Reformierung des institutionellen Rahmens für die Überwachung und Regulierung des Finanzsystems notwendig ist. Eine neue politische Strategie, die bereits auf grosses Interesse stiess, ist die makroprudentielle Aufsicht. Die Interaktion zwischen der Geldpolitik und der unter anderem mikroprudentiellen Regulierung verstärkt die Komplexität des globalen Finanzsystems. Der Kern dieser Dissertation ist das Konzept des systemischen Risikos. Das systemische Risiko, das als Eigenschaft des Finanzsystems gesehen wird, stellt die Wahrscheinlichkeit einer Institution, einer Anlagenklasse oder einer Gruppe von Institutionen dar, die Finanzmarktstabilität zu gefährden, was wiederum Auswirkungen auf die Realwirtschaft hat (z.b.kaufman (1995)). Das Ziel der Dissertation ist es das systemische Risiko von mehreren Seiten zu betrachten. Zuerst werden die Auswirkungen der Verbindung des Ausfallrisikos staatlicher Organe mit dem Finanzsektor analysiert. Diese Analyse umfasst eine empirische Auswertung des Credit-Default-Swap Marktes. Die Dynamiken der Vernetzung der Finanzinstitutionen mit den Ländern sind die Ursache für eine neuentdeckte Eigenschaft: eine Rückkopplungsschleife zwischen den Problemen des Bankensystems und der makroökonomischen Stabilität der staatlichen Organe. Diese Eigenschaft wurde während der letzten vier Jahre in der Eurozone beobachtet. Zudem hat der finanzielle Contagion die Aufmerksamkeit von Akademikern, Politikern und Marktteilnehmern während der jüngsten Europäischen Staatsschuldenkrise auf sich gezogen. Constâncio (2012), der Vize-Präsident der EZB, beschreibt Contagion als einen der Mechanismen, durch die die finanzielle Instabilität so weit verbreitet wird, dass eine Krise systemische Dimensionen erreicht [... ] Folglich sollte das Krisenmanagement durch alle kompetenten Behörden auch politische Massnahmen beachten, die in der Lage sind, den Contagion- Effekt einzugrenzen und abzuschwächen. Nach Allen and Gale (2000) ist Contagion eine Konsequenz von übermässigen Spillover - Effekten. Zum Beispiel könnte die Bankenkrise einer Region auf andere Regio- XVII

Zusammenfassung nen übergehen. Ihrer Ansicht nach ist Contagion daher die extreme Verstärkung der Spillover - Effekte. Deshalb sind Spillover - Effekte notwendige - jedoch keine hinreichenden - Bedingungen für den Contagion- Effekt. Letztlich wurde die Thesis motiviert durch einen akuten Bedarf an politisch relevanten Methoden und Rahmenbedingungen, um mit systemisch wichtigen Finanzinstitutionen - insbesondere mit den grossen Finanzsystemen - umzugehen. Ich beabsichtige, unter der Verwendung der Network Theorie und der Analyse mehr Einsicht für Diskussionen über die Auswirkungen der Theorien Too-Big-to-Fail und Too-Interconnected-to-Fail zu geben. Die Kapital-Allokation, die von der Grösse und dem Risikogehalt einer Anlage einer individuellen Bank abhängt, verknüpft mit Massen für die finanzielle Vernetzung, die von dem gesamten Banken-Netzwerk konstruiert wurde, scheint die Widerstandsfähigkeit des Finanzsystems zu verbessern. Im Folgenden gebe ich Ihnen einen Überblick über meine Dissertation. Im ersten Kapitel präsentieren wir eine Analyse der Interdependenzen des Kreditrisikos eines europäischen Staates mit dem Finanzsektor während der Finanzkrise 2007 2010. Den ersten Teil verallgemeinernd, stellt das zweite Kapitel einen Rahmen für die Nachverfolgung und Beobachtung des finanziellen Contagion- Effekts in der Eurozone auf. Weiterhin stellt es eine Toolbox bereit, die es den Politikern ermöglicht, die Auswirkungen von politischen Ereignissen auf das Verringern oder Verstärken des finanziellen Contagion- Effekts zu ermitteln. Schlussendlich präsentiert das dritte Kapitel lenkbare Rahmenbedingungen, um mit SIFIs umzugehen. Wir zeigen, dass Network - Masse des Interbankenmarktes und die Grösse der Finanzinstitution dabei helfen könnten, die Widerstandsfähigkeit grosser Finanzsysteme zu verbessern, indem wir zwei Politikrichtungen vorschlagen. Die wichtigsten Ideen und Ergebnisse jedes Kapitels werden im Folgenden kurz zusammengefasst. Im ersten Kapitel untersuchen wir die Wechselbeziehung zwischen dem Ausfallrisiko einiger europäischen Länder (Frankreich, Deutschland, Italien, Irland, Niederlande, Portugal und Spanien) und deren inländischen Bankensektoren im Zeitraum 2007 2010. Dabei nutzten wir die täglichen CDS-Spreads. Banken Bailouts veränderten die Zusammensetzung der Bilanzen sowohl von Banken als auch von Staatsorganen. Zudem wirkten sich die Banken-Bailout-Programme auf die Koppelung des Ausfallsrisikos von Staaten und deren lokalen Banken aus. Unsere wichtigsten Ergebnisse deuten darauf hin, dass der Contagion- Effekt in der Zeit vor den Banken- Bailouts auf den CDS- Markt überging. Nach den Bailouts beeinträchtigt ein Schock in den Finanzsektoren die staatlichen CDS-Spreads kurzzeitig sogar noch stärker. Langzeitig hatte das jedoch keine signifikanten Auswirkungen. Darüber hinaus wurden staatliche CDS-Spreads ein wesentlicher Bestandteil in den CDS- XVIII

Zusammenfassung Reihen der Banken. Noch immer existieren deutliche Unterschiede zwischen den starken und schwachen Mitgliedsstaaten. Zwischen verschiedenen Ländern sind die Interdependenzen der Kreditrisiken von Regierungen und Banken heterogen, aber homogen innerhalb eines Landes. Diese Ergebnisse führen zu einem besseren Verständnis der Interaktion zwischen Banken und staatlichen Risiken und geben Aufschluss über den Private-to-Public Risikotransfer. Wir konzentrieren uns auf die Effekte der Banken-Bailout- Programme auf die Verbindungen zwischen staatlichen CDS-Spreads und ihren lokalen Banken. Dabei verwenden wir den Beitrag der Literatur folgendermassen: i) Indem wir uns auf frühere Studien, die die Bedeutung von heimischen Finanzsektoren als einen Bestandteil der staatlichen CDS-Spreads hervorheben, stützen, liefern wir detaillierte empirische Nachweise für ihren Einfluss während der Finanzkrise. ii) Im Gegensatz zu anderen Studien erforschen wir die Interdependenz des Kreditrisikos von Banken und Staaten während der letzten Finanzkrise. Unter Verwendung dieses Ansatzes heben wir reine Änderungen der letzteren Verbindung nach Banken- Bailouts hervor. iii) Wir stellen die Unterschiede in Private-to-Public-Risikotransfers innerhalb eines Landes und innerhalb der Eurozone gegenüber. Durch die Erweiterung des ökonometrischen Aufbaus von Diebold and Yilmaz (2009; 2011) stellen wir im zweiten Kapitel analytische und empirische Rahmenbedingungen für die Messung von Spillover- Effekten vor. Durch eine empirische Anwendung von Verknüpfungen zwischen Staatsorganen und Banken innerhalb der Eurozone veranschaulichen wir unsere Methode. Bei der Analyse täglicher CDS- Daten quantifizierten wir diese Spillover- Effekte basierend auf einem 80 Tagen langen Zeitfenster. Wir kombinierten die CDS- Spreads von Staatsorganen und Banken in einem autoregressiven Vektorsystem. Dieser Rahmen wurde durch einige Kontrollvariablen erweitert (z.b. um gewöhnliche Risikofaktoren oder weggelassene Variablen zu handhaben). Der Fokus unseres Modells lag auf elf Staatsorganen und neun länderspezifischen Bankengruppen der Eurozone im Zeitraum Oktober 2009 Juli 2012. Um den systemischen Effekt von unerwarteten Schockzuständen auf die Kreditwürdigkeit eines bestimmten Staatsorganes oder einen länderspezifischen Bankenindex zu bewerten, berufen wir uns auf den Impulse-Response Ansatz. Die Informationen sammelten wir in einem Contagion-Index. Dieser Index beinhaltet vier Komponenten. Er kann in durchschnittliche potenzielle Überschüsse aufgesplittet werden: i) unter Staatsorganen, ii) unter Banken, iii) von Staatsorganen zu Banken und iv) umgekehrt. Unser Mass kann genutzt werden, um den Zustand des potenziellen Contagion zu einem bestimmten Zeitpunkt oder die zeitabhängige Eigenschaft des Contagion-Index hervorzuheben. Diese Toolbox ermöglicht XIX

Zusammenfassung es uns, systemrelevante Einrichtungen (z.b. länderspezifische Bankensektoren und Staatsorgane) der in unserem System befindlichen Staatsorganen und Banken zu identifizieren. Wir stellen eine einfache Methode bereit, um die Schwelle der exzessiven Überschüsse zu berechnen. Diese Methode basiert auf empirischen Verteilungen der CDS-Veränderungen. Exzessive Überschüsse sind ein Charakteristikum von dysfunktionalen Märkten und können als eine Quelle des Contagion und des systemischen Risikos betrachtet werden. Finanzsysteme neigen zur Instabilität, wenn Finanz-Variablen (z.b. Märkte, Marktteilnehmer, Finanzvermittler) durch eine extreme Abhängigkeit ausgezeichnet sind. Eine solche extreme Abhängigkeit kann während ruhiger Zeiten nicht beobachtet werden. Ausserdem zeigen wir die Dynamiken der Verknüpfung zwischen Banken und Staatsorganen, die eine potentielle Quelle des systemischen Risikos darstellen. Die staatliche Kreditwürdigkeit in der Eurozone gibt dem Gesamtbild des Finanzmarktes zusätzliches Gewicht, mit einem Teil der Staatsorgane, die möglicherweise negative externe Effekte auf das Finanzsystem haben. Wir fanden heraus, dass einige der früheren politischen Interventionen einen mildernden Einfluss auf das Spillover- Risiko hatten. In unserer Anwendung bemerkten wir, dass ein Schock in den staatlichen CDS Spaniens während des ersten Halbjahres 2012 einen erhöhten Einfluss auf Staaten und Banken der Eurozone hatte, verglichen mit dem Jahr 2011. 2012 waren zudem die Auswirkungen der Spillover, die aus einem Schock in den staatlichen CDS Spaniens resultierte, auf die Kernländer der Eurozone ähnlich zu den Auswirkungen auf die Nicht-Kernländer der Eurozone. Wir fanden auch einen erheblichen Hinweis dafür, dass die Verknüpfung zwischen Staatsorganen und Banken bis Ende Juni 2012 verstärkt wurden. Jedoch verringerte sich der systemische Beitrag von Griechenland, Portugal und Irland nach der Einführung des IMF/EU Programms beachtlich. Das Einführen der EFSF und die Beschlüsse der beiden LTROs im Dezember 2012 haben einen mildernden Einfluss auf alle vier Contagion-Index-Komponenten. Dieses Kapitel präsentiert eine makroprudentielle Toolbox, um den potentiellen Contagion- Effekt in der Eurozone unter Verwendung von Marktdaten zu messen. Dies kann den Bedürfnissen der Politiker angepasst werden, indem man andere Banken und Staatsorgane integriert oder es zu realwirtschaftlichen Variablen erweitert. Ausserdem versuchen wir, ihre Nützlichkeit darzustellen, indem wir die potenziellen Effekte von verschiedenen politischen Massnahmen, die Spillovers im System mit sich bringen, quantifizieren. Im dritten Kapitel bestimmen wir verschiedene Kapitalregeln mit der Absicht, den Totalverlust des Systems zu minimieren. Dabei verwendeten wir die Network- Theorie und -Analyse. Aus der Network- Struktur des Interbankenmarktes wurden einige Zentralitätsmasse konstruiert, die uns dabei helfen, systemische Kapitalre- XX

Zusammenfassung serven zu kreieren. Als Quelle nutzten wir die Deutsche Kreditregister- Datenbasis. Unter Verwendung der Netzwerk-Zentralitätsmasse ist das Kapital unter den Banken neu verteilt worden, um die erwarteten Verluste im Bankensystem zu minimieren. Abgesehen von der Bilanzsumme dominiert die sogenannte Opsahl- Zentralität jedes andere getestete Zentralitätsmass. Ausserdem nutzen wir Zentralitätsmasse, um Bailout-Fond-Mechanismen einzuführen. Der Rettungsfond bietet Versicherungsschutz gegen den Ausfall bestimmter Finanzinstitutionen, jedoch werden die Finanzinstitute abhängig von ihren Ratings bezüglich der Bankengrösse und Zentralität bevorzugt. Schliesslich vergleichen wir den Gesamtsystemverlust in Bezug auf die verschiedenen Arten der Kapitalverteilung und die verschiedenen Grössen des Bailout-Fonds. Wir versuchen politische Schlussfolgerungen bezüglich der externen Effekte, Too-Interconnected-to-Fail und Too-Big-to-Fail, zu ziehen. Wir zeigen, dass es gewisse Kapitalallokationen gibt, die die Finanzstabilität verbessern. Diese gewissen Kapitalallokationen sind in dieser Thesis definiert. Mit Fokus auf das System als ein ganzes und zuordnendes System produzieren Kapitalallokationen auf Basis der Network -Masse hervorragende Ergebnisse, verglichen mit der Bezugs-Kapitalallokation, die nur auf den individuellen Bankenbilanzen beruht. Die Ähnlichkeiten der Portfolios machen das Finanzsystem gegenüber normalen Makro- Schocks anfällig. Bekommt man einen grossen Überblick des gesamten Systems, in dem Vernetzung und Zentralität eine wesentliche Rolle des Contagion-Effekts übernehmen, so kann eine Verbesserung erzielt werden. Das Interessante daran ist, dass Kapitalallokationen, die auf dem Gesamtvermögen basieren, jedes andere getestete Zentralitätsmass dominieren. Diese Ergebnisse verstärken die Untersuchungsergebnisse von Tarashev et al. (2010), dass die systemischen Kapitalerfordernisse hauptsächlich von dem Gesamtvermögen abhängen sollten. Indem man das Gesamtvermögen zusätzlich zum individuellen Risiko des Bankenvermögens mit den Network-Massen kombiniert, könnte die Systemstabilität sogar weiter verbessert werden (das z.b. durch das VaR individueller Banken gemessen wird). Des Weiteren schlagen wir lenkbare Rahmenstrukturen vor, um den Einfluss von den verschiedenen Kapitalallokationen auf die Finanzmarktstabilität zu bewerten. Wir integrieren ein gut fundiertes Kreditrisikomodell (z.b. CreditMetrics), um korrelierende Schocks von Kreditrisiken auf das gesamte deutsche Bankensystem zu generieren (1764 Sind Monetäre Finanzinstitute (MFIs) im Interbankenmarkt (IB) aktiv). Diese Modelle ermöglichen, dass wir uns auf korrelierende Nacheffekte fokussieren können (endogen bestimmt durch gewöhnliche Risiken in der Realwirtschaft). Zudem modellieren wir auf Basis von Eisenberg and Noe (2001) den Interbank-Contagion und erweitern ihn, indem wir die Bankrottkosten von XXI

Zusammenfassung Elsinger et al. (2006) einbeziehen. Dieses Element erlaubt uns, die erwarteten Contagion Verluste zu messen und den Verbreitungsprozess zu beobachten. Um unsere Rahmenbedingungen empirisch zu belegen, nutzen wir einige Informationsquellen: Die Gross- und Millionenkreditstatistik der Deutschen Bundesbank (Grosse Kredite), die Kreditnehmerstatistik der Deutschen Bundesbank (Kleine Kredite), Bilanzdaten (Kapital, Gesamtvermögen) und Marktdaten (z.b. um die Korrelation zwischen realwirtschaftlichen Sektoren, Ratingtabellen oder Credit Spreads zu berechnen). Wir fokussieren uns auf die Kapital-Neuverteilungen und versuchen, die verschiedenen Zielfunktionen in der Absicht die Finanzmarktstabilität zu verbessern, zu minimieren. Wir beabsichtigen einige Zielfunktionen zu nutzen: Gesamtsystemverlust, Contagion Effekte der zweite Runde (z.b. Ausfällen durch das Contagion) oder Verluste von fundamentalen Ausfällen (z.b. Banken, die aufgrund von realwirtschaftlichen Portfolioverlusten ausfallen). Zum Beispiel können Gesamtsystemverluste als Gesamtkosten des Bankrotts ausgefallener Banken definiert werden. Ausserdem bestimmen wir Kapitalallokationen, die die Belastbarkeit des Finanzsystems verbessern (wie durch unsere Zielfunktionen definiert ist) auf Basis der Verknüpfungsmassnahmen des IB Network. Um neue Kapitalregeln zu bestimmen und diese mit unseren Rahmenbedingungen zu testen, verwenden wir einige Risikound Network- basierende Konnektivitätsmasse: Gesamtvermögen, die gesamte Interbank Aktiva und Passiva, den Grad, den Eigenvektor und die gewichteten Eigenvektor- Zentralitäten, das gewichtete Betweenness -Mass, die Opsahl- Zentralität, der Näheund der Clusterkoeffizient. Diese Rahmenbedingungen können auf jedes Land oder auf jede Gruppe von Ländern, in denen solche Informationen verfügbar sind, angewendet werden. Diese Methode ist eine Alternative zu marktbasierenden systemischen Massen, um die Verknüpung von Finanzsystemen zu handhaben (z.b. Acharya et al. (2010); Adrian and Brunnermeier (2011); Gauthier et al. (2012)). Der hauptsächliche Vorteil unserer Rahmenbedingungen ist, dass Politiker mit grossen Bankensystemen, in denen Marktdaten für den grössten Teil der Institutionen - auch einigen sehr grossen Einrichtungen - nicht verfügbar sind, umgehen können. XXII

Summary Bibliography Acharya, V., L. H. Pedersen, T. Philippon, and M. Richardson (2010). Measuring systemic risk. Mimeo. Adrian, T. and M. K. Brunnermeier (2011). Covar. Federal Reserve Bank of New York Staff Reports No. 348. Allen, F. and D. Gale (2000). Financial contagion. Journal of Political Economy 108, 1 33. Constâncio, V. (2012). Contagion and the european debt crisis. Banque de France, Financial Stability Review No. 16, 109 121. Diebold, F. X. and K. Yilmaz (2009). Measuring financial asset return and volatility spillovers, with application to global equity markets. Economic Journal 119, 158 171. Diebold, F. X. and K. Yilmaz (2011). On the network topology of variance decompositions: Measuring the connectedness of financial firms. PIER Working Paper, 11 031. ECB (2012). Financial stability review. December. Eisenberg, L. and T. Noe (2001). Systemic risk in financial systems. Management Science 47(2), 236 249. Elsinger, H., A. Lehar, and M. Summer (2006). Risk assessment for banking systems. Management Science 52, 1301 1314. Gauthier, C., A. Lehar, and M. Souissi (2012). Macroprudential capital requirements and systemic risk. Journal of Financial Intermediation 21, 594 618. Kaufman, G. (1995). Research in Financial Services: Banking, Financial Markets, and Systemic Risk, Chapter "Comment on Systemic Risk", pp. 47 52. JAI Press. Tarashev, N., C. Borio, and K. Tsatsaronis (2010). Attributing systemic risk to individual institutions. BIS Working Papers No. 308. XXIII

Chapter 1 Credit spread interdependencies of European states and banks

Chapter 1: Credit Spread Interdependencies of European states and banks The scope and magnitude of the bank rescue packages also meant that significant risks had been transferred onto government balance sheets. This was particularly apparent in the market for CDS referencing sovereigns involved either in large individual bank rescues or in broad-based support packages for the financial sector. (BIS, 2008, p. 20) 1.1 Introduction During the recent financial crisis extraordinary measures were taken by central banks and governments to prevent a potential collapse of the financial sector that threatened the entire economy. 1 However, it was widely unknown what the effects would be on the interdependence of the financial and the sovereign sector. Gray (2009, p. 128) argues that regulators, governments, and central banks have not focused enough on the interconnectedness between financial sector risk exposures and sovereign risk exposures and their potential interactions and spillovers to other sectors in the economy or internationally. The lack of theoretical macroeconomic models that are able to incorporate contagion mechanisms between government and financial sectors have amplified the uncertainty related to the implications of government interventions. Nevertheless, regulators and policy makers need to understand the complex dynamics of risk transmission in order to be able to formulate effective policies and be aware of the risk that may be transferred from the financial sector to the government. This chapter proposes a framework for investigating in detail the interdependence of banks and sovereign credit risk in the Eurozone. Our setup highlights the important changes that have occurred due to the bank bailouts. As pointed out by Gray et al. (2008), using arguments from contingent claims analysis (CCA) 2, there are several channels linking the banking and sovereign sectors, which are affected by implicit as well as explicit guarantees. A systemic banking crisis can induce a contraction of the entire economy, which will weaken public finances and transfer the distress to the government. This contagion effect is amplified when state guarantees exist for the financial sector. As a feedback effect, risk is further transmitted to holders of sovereign debt. An increase in the cost of sovereign debt will lead to a devaluation of government debt, which will impair the 1 This chapter is a reprint of the published paper Credit spread interdependencies of European states and banks during the financial crisis, Journal of Banking and Finance, Volume 36, Issue 12, December 2012, pp. 3444-3468, joint work with Yves S. Schüler. 2 This approach is based on Merton s and Black-Scholes (1973) option pricing work. It can also be employed for measuring sovereign-bank interaction, taking into account the implicit and explicit contingent liability for the financial system. 2

Chapter 1: Credit Spread Interdependencies of European states and banks balance sheets of banks holding these assets. Acharya et al. (2011) have recently used the term two-way feedback to describe these interdependencies. The authors construct a novel theoretical framework to model the link between bank bailouts and sovereign credit risk. In this chapter, we empirically study this feedback effect and show how the linkage between the sovereign and financial sectors was affected during the recent period of turmoil. The interconnectedness through balance sheets of governments and banks has been described in the context of the financial crisis in other recent empirical studies. For instance, Gerlach et al. (2010) find that, as a consequence of macroeconomic imbalances, especially in peripheral European countries (e.g. Greece, Ireland), a jump in sovereign bond and credit default swap (CDS) spreads may be transmitted from the banking sector. The authors claim that systemic and sovereign risk became more interwoven after governments began to issue guarantees for banks liabilities. This result is supported by Ejsing and Lemke (2011), who argue that the sensitivity of sovereign CDS spreads to the intensifying financial crisis increased after the bailout of the financial sector. Dieckmann and Plank (2011) also present evidence of a private-to-public risk transfer in the countries where governments stabilized the financial system after the Lehman Brothers event. Banks and sovereign CDS became closely linked, with financial institutions holding significant amounts of government debt and states bearing vital contingent liabilities from the financial system. Furthermore, Acharya et al. (2011) provide empirical evidence of the interconnection of financial and sovereign sector credit risk as a result of bailout programs. Our study contributes to the literature in three ways: First, relying on previous studies that emphasize the importance of the domestic financial sector as a determinant of sovereign CDS spreads, we provide detailed empirical evidence of the influence of the domestic financial sector during the financial crisis. Second, in contrast to other studies, we research the credit risk interdependence of banks and governments during the recent turmoil. Using this approach we highlight stark changes that occurred in that interdependence after bank bailouts. Third, we study differences in the private-to-public risk transfer both within countries and across the Eurozone. In more detail, we study the lead-lag relation between governments and banks default risk, with a focus on the effect of the bank bailouts in the midst of the recent financial crisis. First, we investigate whether, prior to the government interventions, an increase in the default risk of banks and states originates mainly from the financial sector. Second, we assess whether public contingent liabilities for the financial sector affected governments default risk. In tandem, this study examines whether 3

Chapter 1: Credit Spread Interdependencies of European states and banks the default risk of the banking sector is influenced by the sovereign default risk. Finally, we investigate the following two questions: i) Does the perceived degree of a bank s participation in a national rescue scheme influence its dependency on the development of the sovereign spread? ii) Are country-specific bailout characteristics reflected in the impact of government bailout programs? Methodologically, we consider the relationship between government and banks CDS spreads, as they provide a proxy for default risk. 3 We conduct this analysis by applying the theory of cointegration, Granger-causality, and impulse responses to daily CDS series, which are able to capture changes in the dynamic relation between government and bank credit risk. We consider sovereign CDS from seven EU member states (France, Germany, Italy, Ireland, the Netherlands, Portugal, and Spain) together with a selection of bank CDS from these states. We divide the analyzed period, i.e. June 2007 until May 2010, into the time before and after bank bailout programs were implemented. Our main findings suggest that in the period preceding government intervention, the contagion from bank credit spreads disperses into the sovereign CDS market. This finding can be interpreted as evidence of the systemic feature of the recent financial crisis. The default risk spills over from the financial system to the entire economy and calls into question the government s capacity to repay its liabilities. After government interventions, due to changes in the composition of both banks and sovereign balance sheets, we find that the government CDS spreads have increased importance in the price discovery mechanism of the banks CDS series. Furthermore, a financial sector shock affects the sovereign CDS spreads more strongly in the short run. However, the impact becomes insignificant in the long term. Based on a bank s dependency on future government aid, we are able to capture differences and similarities in the outcomes of bank bailouts within the same country. Finally, our cross-country analysis reveals noticeable differences in the outcomes of state interventions. From a policy perspective, our results imply an elevated financing cost for countries with contingent liabilities from the financial sector and a higher volatility in sovereign yield spreads. In assessing the total cost of bank bailouts, governments need to include increased interest payments due to augmented spreads. Furthermore, the banking system is sensitive to the economic health of the host country 3 The objective of this chapter is not to investigate the accuracy of this proxy. Our research design takes this link as given, even though there might have been distortions in this proxy during the recent turmoil. 4

Chapter 1: Credit Spread Interdependencies of European states and banks and the credibility of the support measures. This chapter is organized as follows. In Section 2 we discuss studies related to our research. Section 3 presents our hypotheses, the data, our sub-sample selection procedure, and the methodology. In Section 4 we present our results and Section 5 concludes. 1.2 Related literature Our study contributes to, at least, two strands of literature: On the one hand, it is linked to the literature that investigates the determinants of bond and CDS spreads and their returns, especially in the midst of financial crisis. On the other, it is related to the analysis of the effects of bank bailouts on the credit risk of governments and banks. Tied to the first strand and relying on a structural model, Schweikhard and Tsesmelidakis (2009) conclude that credit and equity markets were decoupled during the financial turmoil. They find support for the too-big-to-fail hypothesis, as some companies debt holders benefited from government interventions, and a shift of wealth took place from taxpayers to creditors after the bailout programs. During the crisis, some other factors might have influenced CDS prices (e.g. counterparty or liquidity risk). Collin-Dufresne et al. (2001) find that changes in credit spreads are mostly driven by a systematic factor; however, they are not able to identify it. Berndt and Obreja (2010) study determinants of European corporate CDS returns and identify the common factor, which explains around 50% of the variation, as the super-senior tranche of the itraxx Europe index, referred to as the economic catastrophe risk. Similar to our study, Dieckmann and Plank (2011) find evidence of a private-to-public risk transfer for countries whose governments have intervened in the financial system. By employing panel regressions, the authors analyze the determinants of changes in sovereign CDS spreads, and find that both domestic and international financial systems play an important role in explaining the dynamics of CDS spreads. They also argue that countries in the European Monetary Union (EMU) are more sensitive to the health of the financial system than non-emu countries. Fontana and Scheicher (2010) identify the main determinants of bond and CDS spreads. They include in their set of explanatory factors proxies for market liquidity and global risk appetite, and these are found to be significant. Furthermore, they employ a lead-lag analysis for bond and CDS markets and find that for France, Germany, the Netherlands, Austria, and Belgium the cash market dominates, while 5

Chapter 1: Credit Spread Interdependencies of European states and banks for Greece, Italy, Ireland, Spain, and Portugal the CDS market is more important in terms of price discovery. Hull et al. (2004) and Norden and Weber (2004) analyze the impact of unique events on CDS markets, such as credit rating announcements. Both studies find that markets anticipate both news and reviews of downgrades, and that credit rating announcements contain important information and have a significant effect, especially on the CDS market. Furthermore, there are studies that solely investigate the sovereign bond market. Using a GARCH-in-mean model, Dötz and Fischer (2010) analyze the EMU sovereign bond spreads during the financial crisis and find that the implied probability of default reached unprecedented values and the increased expected loss component made some sovereign bonds lose their status as a safe haven investment. Gerlach et al. (2010) analyze the determinants of Eurozone sovereign bond spreads. They show that the size of the banking sector has an important explanatory value for changes in bond spreads, suggesting that markets perceive countries with a large stake in this sector at higher risk of stepping up and rescuing the banks. Employing a dynamic panel, Attinasi et al. (2009) highlight the main factors that explain the widened sovereign bond spreads in some Eurozone countries for the period that covers the core part of the financial crisis in Europe. Within the second strand of literature, Ejsing and Lemke (2011) investigate the co-movement of CDS spreads of Eurozone countries and banks with a common risk factor, i.e. the itraxx CDS index of non-financial corporations. The authors find that the government bailout and guarantee programs for the financial sector induced a drop in the credit spreads for banks but a jump in governments CDS spreads. Furthermore, the sovereign CDS series became more sensitive to the common risk factor, while the banks CDS spreads became less so. Besides providing a model for the interrelation of bank and government credit risk, Acharya et al. (2011) outline the same mechanism empirically, showing a widening of the sovereign and a narrowing of the bank CDS spreads. Focusing on the financial crisis, Demirgüç-Kunt and Huizinga (2010) find that bank CDS spreads are significantly affected by the deterioration of public finance conditions. A high sovereign debt burden impairs the ability to provide support to the financial sector and too-big-to-fail banks might thus become too-big-to-be-saved. 6

Chapter 1: Credit Spread Interdependencies of European states and banks 1.3 Hypotheses, data, and econometric methodology 1.3.1 Hypotheses In this subsection we develop the hypotheses to be tested in our study. Firstly we describe the main transmission channels that emerge when either a (systemic) banking crisis develops or sovereign distress appears. Based on Acharya et al. (2011), Gray (2009) and IMF (2010), we present both directions of the contagion mechanism. If a financial institution faces funding and/or liquidity issues, this can trigger a sharp rise in its default risk and may have specific contagion effects: (I) the bank cannot pay its obligations to another financial counterparty which in turn can set off funding/liquidity difficulties for the latter and increases its perceived default risk; (II) the state might intervene in order to prevent bank bankruptcies. This private-to-public risk transfer augments the probability of default for the state and lowers the default risk of the financial institution. If (I) occurs, difficulties within the entire financial system (e.g. systemic banking crisis) might arise and translate into a contraction of the economy, which would also weaken public finances (e.g. a decrease in the present value of taxes) and, again, the sovereign default risk would increase. In the case of a country s distress, in the first wave, the contagion to other entities can be triggered via three direct channels (Chapter 1, IMF (2010)): (i) from the affected state to other countries that are highly interconnected through bilateral trade or share similar problems (e.g. public deficit, funding needs, etc.); (ii) from the distressed country to domestic banks as the market value of government bonds held by these banks decreases, and government support loses credibility; (iii) from the impaired state to foreign banks that hold government (or bank) bonds (or other assets) from the affected country. Before the recent government interventions, we argue that financial sector issues had a systemic component, leading to contagion mechanism (I). Thus, the rising default risk of banks had an indirect effect on governments credit risk. Additionally, state interventions in response to financial sector problems were possibly expected by market participants. Thus, the perceived sovereign default risk increased but was considered of limited importance in terms of having any visible impact on banks default risk. 7

Chapter 1: Credit Spread Interdependencies of European states and banks Hypothesis 1. Prior to state interventions, changes in the default risk of banks affect the default risk of European governments, but not viceversa. After government interventions, states not only bear an asset exposure to the banking sector but their balance sheets contain contingent liabilities (e.g. government guarantees) as well. Thus, the sensitivity of government default risk to the banking sector risk is expected to increase. Furthermore, through the credibility of government contingent liabilities, changes in government default risk have a direct impact on the perceived risk of financial institutions. Hypothesis 2 (a). In the period after a government intervention, changes in the default risk of banks affect the sovereign default risk more strongly than before. Hypothesis 2 (b). After bailout programs have been implemented, an increase/decrease in sovereign default risk causes a change in the default risk of the domestic banks in the same direction. Some banks received direct capital injections from their governments. If the capital injections were sufficient, we would expect the dependency on future bailouts to be the same as for the rest of the financial sector. On the other hand, in case of a partial recapitalization or any other insufficient intervention, the bank in question should be highly sensitive to the health and credibility of the host government. The following hypothesis links the sensitivity of banks default risk to the probability of future government support. Hypothesis 3. The bank s sensitivity to the sovereign default risk increases with the bank s reliance on future government aid. Our last hypothesis compares the outcomes of bailout programs in different countries. The magnitude of different support measures provided by each country was heterogeneous among the analyzed Eurozone countries. This was induced by, at least, three factors: (i) the economic health of the country, (ii) the size of its financial sector relative to the total economy and (iii) the exposure of the banking sector to the systemic crisis. Hypothesis 4. Heterogeneity of bailout programs across European countries translates into asymmetric interdependence between sovereign and banks default risk. The model introduced by Acharya et al. (2011) describes in detail this feedback mechanism, i.e. how financial sector and sovereign default risk are linked. The 8

Chapter 1: Credit Spread Interdependencies of European states and banks authors present a three-period model, in which a financial and corporate sector jointly produce aggregate output. There exists a potential underinvestment problem. Bank bailouts are used to help resolve this problem in the financial sector. The framework predicts that bank bailouts increase sovereign credit risk. The latter affects the financial sector as the value of guarantees and bond holdings decreases. This linkage implies a post-bailout increase in the co-movement of government and financial sector default risk. 1.3.2 Bailout specific characteristics In order to compare the selected countries, we relate our analysis to the specific bailout schemes provided in each country. Hence, we look at the magnitude of the different support measures utilized by each country, while additionally considering the particular aid offered to each bank. Following Stolz and Wedow (2010), we categorize the general set of measures, emphasizing the differences and similarities across countries. Even though there are differences in the number and types of institutions involved in banking crisis management, there is less variation across the countries in terms of the types of support measures that were applied. The financial aid programs can be classified into four broad categories: capital injections, guarantees for bank liabilities, asset support programs, and deposit insurance (see Table 1.1). Table 1.1: Government Support Measures for Financial Institutions (October 2008 - May 2010) Country Capital injection Liability guarantees Asset support Total commitment Deposit insurance Guaranteed Other Within Outside issuance of guarantees, Within Outside as % of Schemes Schemes bonds loans Schemes Schemes 2008 GDP in EUR France 8.3 (21) 3 134.2 (320) 0 - (-) - 18% 70,000 Germany 29.4 (40) 24.8 110.8 (400) 75 17 (40) 39.3 25% Unlimited Ireland 12.3 (10) 7 72.5 (485) 0 8 (90) - 319% Unlimited Italy 4.1 (12) - - (-) 0 - (50) - 4% 103,291 Netherlands 10.2 (20) 16.8 54.2 (200) 50 - (-) 21.4 52% 100,000 Portugal - (4) - 5.4 (16) 0 - (-) - 12% 100,000 Spain 11 (99) 1.3 56.4 (100) 9 19.3 (50) 2.5 24% 100,000 Note: All amounts are in billions of e, except for the last two columns. Figures in brackets denote total committed funds and figures outside brackets are the utilized amounts up to May 2010. Within schemes refers to a collective bailout program that can be accessed by any bank that fulfills the requirements for that particular aid scheme. Outside schemes refers to individually tailored aid measures (ad hoc schemes). Source: Stolz and Wedow (2010) Based on the ratio of total commitment to GDP, the selected countries can be ranked (from high to low): Ireland, the Netherlands, Germany, Spain, France, Portugal, and Italy. Furthermore, the set of countries can be clustered into three groups: Ireland (high commitment - above 75% of GDP); the Netherlands, Germany, Spain, and France (medium commitment - 20% - 75% of GDP); Portugal and Italy (low commitment - below 20% of GDP). 9

Chapter 1: Credit Spread Interdependencies of European states and banks 1.3.3 Data and sub-sample selection We use daily CDS spreads collected from Datastream 4 for seven European countries together with two banks from each country, a total of 21 institutions: France (FR), BNP Paribas (BNP), Société Générale (SG), Germany (DE), Commerzbank (COM), Deutsche Bank (DB), Italy (IT), Intesa Sanpaolo (ISP), Unicredito (UCR), Ireland (IR), Allied Irish Banks (AIB), Bank of Ireland (BOI), the Netherlands (NL), ABN Amro Bank (ABN), ING Group (ING), Portugal (PT), Banco Comercial Portugês (BCP), Banco Espírito Santo (BES), and Spain (SP), Banco Santander (BS), Banco Bilbao Vizcaya Argentaria (BBVA). The selection of bank and sovereign CDS series was restricted by data availability. In order to maintain a homogeneous framework, i.e. the same number of banks from each country, while achieving the longest time frame possible, we were able to use only two bank CDS series for each country. All of the selected banks are important financial institutions, most (8 out of 14) belonging to the itraxx Europe index. In terms of CDS spreads, we decided to use contracts on senior unsecured debt with 5 years maturity, as they are the most liquid ones. Briefly, a CDS is a bilateral agreement that transfers the credit risk of a reference entity, which can be a corporation, a sovereign, an index, or a basket of assets that bears credit risk, from the protection buyer to the protection seller. The former party pays a periodic fee to the latter party (the credit-risk taker), and in return is compensated with a payoff in the case of default (or a similar credit event) of the underlying entity. 5 The CDS spread represents the insurance premium and is paid quarterly until either the contract ends or a credit event (e.g. default) occurs. CDS markets are commonly used as a proxy for credit risk. Our sample covers the time span from 1 June 2007 to 31 May 2010 and includes 772 observations of daily data for each of the selected series. 6 Prior to performing the econometric analysis, we log-transform the CDS levels, as suggested by Forte and Pena (2009). Further justification for this step is provided by the relatively low sovereign CDS spreads early in the sample period compared to later on. Our aim is to analyze the linkages between bank and sovereign CDS series in a two sub-period setup: (i) before and (ii) during and after bank aid schemes were 4 We downloaded CDS data from Datastream, which is provided by Credit Market Analysis (CMA). 5 In the case of cash settlement only, the difference between the par value of the bond (notional amount of the loan) and its recovery value when the credit event occurs is paid in cash by the protection seller. In the case of physical settlement, the par value is paid in exchange for the physical underlying bond. 6 In the case of Ireland, the sample starts on 4 October 2007 because of inconsistencies with the data obtained from Datastream. 10

Chapter 1: Credit Spread Interdependencies of European states and banks implemented. In order to capture other structural breaks, we follow BIS (2009) and divide the entire time span into six stages. 7 We group the first two stages (i.e. Stage 1+2) to form the sub-period before government interventions took place and the last three stages (i.e. Stage 4+5+6) to constitute the sub-period during and after the implementation of bank aid schemes. When issues concerning structural breaks appear in our stability analysis (see Section 1.3.4 and 1.A.1), we analyze stages in combinations (i.e. Stage 4+5, Stage 5+6) or individually. Stage 3 is excluded from our analysis. It is regarded as a period of structural market adjustments, in which the dependencies between the analyzed CDS series shift. BIS (2009) defines the third stage as lasting from mid-september until late October 2008. Thus, it commences with the bankruptcy of Lehman Brothers, which can be seen as the peak event of the financial crisis. After a period of financial market turmoil, the first coordinated policy measures stabilize investor s confidence at the end of the third stage. 8 Because of the accumulation of structural breaks during this stage, and due to the fact that it lasts for only 30 trading days, econometric analysis does not yield meaningful results. The following outlines the remaining five stages included in our analysis. The first stage runs from June 2007 to mid-march 2008 and contains 203 observations. This period is characterized by financial stress, triggered by fears of losses due to US subprime mortgage loans and spillovers to European banks (e.g. IKB Deutsche Industriebank, BNP Paribas). The second stage begins in March 2008 with the liquidity shortage of Bear Stearns. This time span consists of 126 observations and ends in mid-september 2008 with the collapse of Lehman Brothers. The fourth stage is defined as lasting from late October 2008 to mid-march 2009 and contains 98 observations. This period is marked by concerns about a deepening of the global recession. By issuing guidelines 9 for European states, the European Commission gives the green light for bank bailout programs. Stage 5 starts in mid- March 2009, when the first signs of recovery appear. Announcements by central banks concerning balance sheet expansions, and the range and the amount of assets to be purchased, lead to significant relief among the financial markets. The fifth stage ends on 30 November 2009, right before the inception of the sovereign debt crisis in Europe. This stage includes 143 observations. Stage 6, the last one in 7 BIS (2009) covers only our first five stages, from 1 June 2007 to 15 March 2009, when Stage 5 starts. For the time span that was not included in the latter study, we define a sixth stage. The last stage is selected to start based on developments in the sovereign CDS market at the end of 2009. 8 UK authorities intervened in financial markets and major central banks tried to control the situation with coordinated actions. 9 IP/08/1495 11

Chapter 1: Credit Spread Interdependencies of European states and banks our sample, begins in December 2009 and ends on 31 May 2010. It consists of 172 observations. This period is marked by concerns about European sovereign debt. For instance, fears arose that Greece s debt crisis would spread to Portugal, Spain, Italy, and Ireland. 10 On 9 May 2010, European governments set up a rescue fund for aiding Eurozone countries in trouble. 1.3.4 Econometric methodology In order to analyze the dynamics of the short- and long-run interdependencies between the selected CDS series, this study employs a bivariate vector error correction (VEC) 11 and bivariate vector autoregressive (VAR) framework. Besides interpreting the cointegration relations, we additionally conduct tests on Granger-causality and consider impulse responses in order to describe the entire dynamics between the CDS spreads. We conduct our analysis by considering two main sub-periods: before and during/after the government bailouts. Results from the Granger-causality and impulse response analyses are reported for these two periods. Only the study of the longrun relations, i.e. using the VEC framework, makes use of further sub-samples, as required. 12 Impulse responses are obtained using the VEC framework, if available for the two main periods. If the tests do not clearly indicate that there is a long-run relation, we obtain the impulse responses from a VAR with the variables modeled in log-levels. Thus we do not cancel out the dynamic interactions in the levels, as opposed to modeling the variables in first differences, and leave the dynamics of the series unrestricted, i.e. we follow an agnostic approach. The Granger-causality tests used in this chapter are Wald tests on lag-augmented VARs, as proposed by Dolado and Lütkepohl (1996). This test is chosen as it guarantees the validity of the asymptotic distribution of the test statistic even when there is uncertainty about the cointegration properties and stationarity of the variables. For a global view on the interrelations of the series we employ generalized impulse responses (GIR), as proposed by Pesaran and Shin (1998). Routinely, the analysis of impulse responses is carried out via the application of the Cholesky decomposition. However, to do so the researcher has to specify some causal ordering of the variables. 10 On 6 May 2010, Moody s emphasized a possible contagion for banks. This coincided with a major US stock market crash and both events led to a plunge of stock markets around the world. When we exclude events related to the intensifying Greek debt crisis, i.e. when we end our sample period on 5 May, our econometric analysis yields the same conclusion. 11 During tranquil times we believe that the CDS series of the financial and government sectors are stationary. However, during times of market turmoil we argue that both are impacted by the same stochastic trend, because they are linked by the channels described in Subsection 1.3.1. 12 See 1.A.1 for further information. 12

Chapter 1: Credit Spread Interdependencies of European states and banks In our case, a theory defining such ordering is hard to justify, especially in the context of daily data. As a result, we decided to use GIR because no ordering is necessary and contemporaneous relations are allowed for. One can regard GIR as the effects of a shock in the structural error of the variable that is ordered first in the system of orthogonalized impulse responses. To model the uncertainty around our point estimates of impulse responses, we apply the recursive-design wild bootstrap, as described in Gonçalves and Kilian (2004). This bootstrap technique delivers valid confidence bands in the case of conditional heteroskedasticity. We simulate the 95% confidence intervals using 2000 replications. In our bivariate setup, i.e. with a sovereign CDS spread (in short Sov ) and a selected domestic bank CDS spread (in short Bk ), the GIR function can be written as follows: Sov(n) = σ 1/2 (Sov,Sov) Sov(n) Φ nσ u 1, 0 ψsov ψ Bk Bk (n) = σ 1/2 (Bk,Bk) Bk(n) Φ nσ u 0, (1.1) 1 ψsov ψ Bk where σ (j,k) is the variance related to the error of variable j, k (j, k {Sov, Bk}) and n denotes the period after the impulse occurred. Φ n represents the matrix of vector moving average coefficients at lag n, which can be calculated in a recursive way from the VAR coefficient matrices. It is worth emphasizing that, as we deal with possibly cointegrated VAR models, the effects of shocks may not die out asymptotically (Lütkepohl, 2007, pp. 18-23, 263). For example, ψ Sov Bk (n) denotes the response of the sovereign log CDS to a shock in Bk, n periods ago. The interpretation of the impulse responses follows the usual reading for semi-elasticities. For instance, taking into account that Φ 0 = I K, an impulse in variable j in period 0 means a unit increase in the structural error that leads to an increase in the respective CDS series by σ 1/2 (j,j) %. In order to facilitate a comparison of the results across banks and countries, we standardize each series of impulse responses, i.e. the responses caused by the same shock are divided by the standard deviation of the impulse variable; in the example above, our responses would be divided by σ 1/2 (j,j). This means that the initial response of the j-th variable to its own shock is equal to 1 or 100% of the initial shock of size of one standard deviation. Responses can, thus, be interpreted as percentages of the initial shock in the impulse variable. In the following, the VEC and VAR model setups are discussed. A VEC model 13

Chapter 1: Credit Spread Interdependencies of European states and banks (VECM) with p 1 lags can be written as follows: 13 cds Sov,t cds Bk,t = α Sov α Bk (β Sov cds Sov,t 1 + β Bk cds Bk,t 1 + β 0 ) + p 1 γ SovSov,i i=1 γ BkSov,i γ SovBk,i γ BkBk,i cds Sov,t i cds Bk,t i + u t, (1.2) where cds j,t with j {Sov, Bk} refers to log CDS j,t, i.e. the logarithmized CDS series of the country or bank. cds j,t denotes the difference between cds j,t and cds j,t 1. β 0 is a (restricted) constant, and u t is assumed to be wn(0, Σ u ) 14. The γ- coefficients portray the short-run dynamics. In contrast, the β-coefficients describe the long-run relationship between banks and sovereign log-cds spreads. β Sov is normalized (i.e. β Sov = 1) and only β Bk is estimated. The loading coefficients, α, measure the speed of adjustment with which a particular CDS adjusts to the long-run relationship. 15 The bivariate VAR setup with p-lags can be written as follows: cds Sov,t cds Bk,t p = ν + α SovSov,i i=1 α BkSov,i α SovBk,i α BkBk,i cds Sov,t i cds Bk,t i + u t, (1.3) where ν is a vector of intercepts and the α s refer to the respective VAR coefficients. 16 1.4 Results This section presents the results for long-run and short-run relationships and, in addition, considers the GIR. First, the cross-country analysis is presented and then we report specific results for three of the countries. Table 1.2 shows the results of the Granger-causality tests for all countries, Table 1.4 outlines the results from our cointegration analysis and Table 1.5 summarizes the GIR for all countries. 13 We use the notion of p 1 lags, to reinforce of the fact that a VECM(p 1) has a VAR(p) representation. 14 wn stands for white noise and refers to a discrete time stochastic process of serially uncorrelated random variables with the abovementioned first two moments. 15 For further details on the interpretation of the long-run relations in a VEC framework, please see 1.A.1. 16 The Granger-causality test (e.g. the bank does not Granger-cause the government CDS series if and only if the hypothesis H 0 : α SovBk,i = 0 for i = 0,..., p cannot be rejected) in this chapter is carried out on a VAR with p + 1 lags. 14

Chapter 1: Credit Spread Interdependencies of European states and banks Table 1.2: Results of Granger-Causality Tests for all Countries. Country Period Independent Dependent p-value Independent Dependent p-value France Before BNP FR 0.948 SG FR 0.662 FR BNP 0.014 FR SG 0.059 After BNP FR 0.089 SG FR 0.096 FR BNP 0.000 FR SG 0.002 Germany Before COM DE 0.005 DB DE 0.152 DE COM 0.711 DE DB 0.772 After COM DE 0.008 DB DE 0.003 DE COM 0.009 DE DB 0.004 Ireland Before AIB IR 0.499 BOI IR 0.002 IR AIB 0.333 IR BOI 0.451 After AIB IR 0.174 BOI IR 0.216 IR AIB 0.000 IR BOI 0.000 Italy Before ISP IT 0.000 UCR IT 0.002 IT ISP 0.156 IT UCR 0.536 After ISP IT 0.392 UCR IT 0.348 IT ISP 0.008 IT UCR 0.002 Netherlands Before ABN NL 0.062 ING NL 0.012 NL ABN 0.705 NL ING 0.160 After ABN NL 0.003 ING NL 0.040 NL ABN 0.059 NL ING 0.033 Portugal Before BCP PT 0.001 BES PT 0.000 PT BCP 0.909 PT BES 0.846 After BCP PT 0.871 BES PT 0.871 PT BCP 0.000 PT BES 0.000 Spain Before BBVA SP 0.001 BS SP 0.000 SP BBVA 0.024 SP BS 0.009 After BBVA SP 0.023 BS SP 0.020 SP BBVA 0.000 SP BS 0.000 Note: This table presents the Granger-causality tests for the entire period before government interventions and for the entire period during and afterwards. Before stands for Stage 1+2 and After denotes Stage 4+5+6. We report the p-values of the tests. The significant results are emphasized in bold. The results show whether the independent variable Granger-causes the dependent variable. 1.4.1 Cross-country analysis The results of the impulse response analysis underline the change in the interdependence of European sovereign CDS spreads and bank CDS spreads over the sample period. As we analyze the levels of the CDS spreads, our responses in the long run (after 22 days) report whether a long-term change in the respective CDS series occurs due to a shock in either the sovereign or the financial sector. Table 1.3 shows the percentage of long-run responses that are reported to be significantly/insignificantly different from zero after 22 days. Table 1.3: Percentage of Significant/Insignificant Responses in the Long Run (after 22 days) Bank Country Country Bank Before During/After Before During/After Significant 100% 21.43% 14.29% 100% Insignificant 0% 78.57% 85.71% 0% Note: Significant/Insignificant refers to evaluating a 95% confidence interval estimated using a recursive-design wild bootstrap with 2000 replications. The left side of the table concerns the country responses to a banking sector CDS shock. The right side refers to banks responses to a sovereign CDS shock. Before concerns the period preceding banking sector bailouts and During/After the period during and after government interventions. 15

Chapter 1: Credit Spread Interdependencies of European states and banks Table 1.4: Results of Cointegration Analysis for all Countries. Country Period Sov - Bk 1 α Sov α Bk β Sov β Bk Constant France Stage 1 + 2 FR - BNP -0.085 0.024 1.000-1.059 2.031 [-3.273] [ 2.050] - [-6.997] [ 3.693] FR - SG -0.124 0.022 1.000-0.892 1.584 [-3.991] [ 1.864] - [-8.934] [ 4.136] Stage 4 + 5 + 6 FR - BNP 0.018 0.018 1.000-2.795 8.237 [ 3.582] [ 3.154] - [-5.636] [ 3.889] FR - SG 0.017 0.015 1.000-3.821 13.769 [ 3.712] [ 3.136] - [-5.614] [ 4.425] Germany Stage 1 + 2 DE - COM -0.108-0.009 1.000-0.719 1.235 [-3.943] [-0.583] - [-5.775] [ 2.458] DE - DB -0.122 0.009 1.000-0.930 2.087 [-4.046] [ 0.561] - [-7.866] [ 4.428] Stage 5 DE - COM -0.045 0.004 1.000-1.007 1.330 [-2.211] [ 0.233] - [-1.913] [ 0.541] Stages 4 + 5 + 6 DE - DB 0.015 0.011 1.000-3.432 12.382 [ 3.442] [ 3.068] - [-5.082] [ 3.944] Ireland Stage 2 IR - AIB -0.278 0.008 1.000-0.567-0.520 [-3.826] [ 0.171] - [-5.432] [-1.032] IR - BOI -0.475-0.043 1.000-0.581-0.349 [-5.170] [-0.655] - [-10.122] [-1.212] Stage 4 + 5 + 6 IR - AIB 0.014 0.060 1.000-0.724-1.116 [ 1.012] [ 4.582] - [-6.905] [-1.903] IR - BOI -0.002 0.096 1.000-0.694-1.292 [-0.086] [ 5.414] - [-10.794] [-3.584] Italy Stage 1 + 2 IT- ISP -0.012 0.020 1.000-1.404 2.003 [-2.282] [ 2.078] - [-6.927] [ 2.706] IT - UCR -0.010 0.014 1.000-1.502 2.647 [-2.110] [ 1.767] - [-5.845] [ 2.658] Stage 5 IT - UCR 0.021 0.097 1.000-1.280 1.462 [ 0.761] [ 3.318] - [-9.331] [ 2.247] Stage 4 + 5 + 6 IT - ISP 0.003 0.066 1.000-0.864-0.922 [ 0.162] [ 3.167] - [-9.881] [-2.393] Netherlands Stage 1 + 2 NL - ABN -0.097 0.002 1.000-0.829 1.416 [-3.865] [ 0.146] - [-8.708] [ 3.734] NL - ING -0.152-0.009 1.000-0.741 1.013 [-4.763] [-0.410] [-13.565] [ 4.787] Stage 6 NL - ABN -0.017 0.038 1.000-1.596 4.158 [-0.944] [ 2.929] - [-5.938] [ 3.243] Stage 4 + 5 NL - ING 0.007 0.042 1.000-1.572 3.125 [ 0.427] [ 3.353] - [-7.475] [ 3.220] Portugal Stage 2 PT - BCP -0.031 0.128 1.000-0.986 0.715 [-1.030] [ 2.313] - [-8.592] [ 1.443] PT - BES -0.151 0.072 1.000-0.789 0.101 [-2.916] [ 0.682] - [-15.128] [ 0.420] Stage 4 + 5 + 6 PT - BCP 0.021 0.037 1.000-0.793-0.701 [ 1.808] [ 3.687] [-4.811] [-0.892] PT - BES - - - - - Spain Stage 1 + 2 SP - BBVA -0.019 0.023 1.000-1.631 3.658 [-1.693] [ 2.975] - [-7.714] [ 4.404] SP - BS -0.022 0.023 1.000-1.619 3.632 [-1.931] [ 2.871] - [-7.873] [ 4.488] Stage 4 + 5 + 6 SP - BBVA 0.032 0.061 1.000-0.985-0.009 [ 1.927] [ 3.756] - [-5.796] [-0.012] SP - BS 0.043 0.072 1.000-1.106 0.527 [ 2.555] [ 4.258] - [-7.215] [ 0.743] Note: This table presents the cointegration relationships that passed the stability test. Sub-periods are only included if the longer period did not pass the stability test (see Section 1.3.4). Coefficients are labeled in reference to equation 1.2. β-coefficients describe the long-run relationship between banks and sovereign log-cds spreads. The loading coefficients α measure the speed of adjustment with which a particular CDS adjusts to the long-run relationship. When α Sov is significant and has the opposite sign to β Sov it means that the sovereign adjusts back to the long-run equilibrium defined by β y t = 0, whenever β y t 0. Whenever one of the α-coefficients is not significant, it means that the respective variable can be argued to provide the stochastic trend that determines the long-run relation and it is not adjusting at all to the long-run equilibrium. Whenever an α-coefficient is significant but with the same sign as the respective β parameter, the variable moves the entire equilibrium (see 1.A.1). t-statistics are reported in square brackets. 16

Chapter 1: Credit Spread Interdependencies of European states and banks Table 1.5: Generalized Impulse Responses Impulse Response Before Gvt. Interventions 1 Remark During/After Gvt. Interventions 2 Remark Days Days 0 1 5 22 0 1 5 22 FR FR FR 1.000 0.657 0.579 0.328 1.000 1.203 1.186 0.923 BNP 0.046 n 0.120 0.150 0.228 0.565 0.755 0.731 0.483 BNP BNP 1.000 1.006 0.942 0.835 1.000 1.052 0.891 0.290 n FR 0.230 n 0.204 n 0.418 0.764 0.452 0.584 0.416-0.227 n FR FR 1.000 0.638 0.495 0.217 1.000 1.201 1.114 0.790 SG 0.030 n 0.080 n 0.125 n 0.192 n 0.499 0.691 0.642 0.348 SG SG 1.000 1.121 1.083 1.004 1.000 1.041 0.843 0.206 n FR 0.202 n 0.246 n 0.502 0.840 0.520 0.626 0.383-0.389 n DE DE DE 1.000 0.780 0.474 0.157 1.000 1.132 1.072 0.587 VAR COM 0.088 0.125 0.101 n 0.040 n 0.425 0.592 0.627 0.550 VAR COM COM 1.000 1.091 1.088 1.171 1.000 1.060 1.004 0.580 VAR DE 0.285 n 0.356 0.285 n 0.675 0.435 0.608 0.441-0.254 n VAR DE DE 1.000 0.778 0.461 0.201 n 1.000 1.140 1.129 0.889 DB 0.071 0.103 0.125 n 0.146 n 0.433 0.615 0.611 0.412 DB DB 1.000 1.092 1.117 1.094 1.000 1.156 1.034 0.428 n DE 0.267 n 0.453 0.450 0.898 0.569 0.766 0.603-0.127 n IR IR IR 1.000 0.539 0.526 0.397 VAR 1.000 1.266 1.123 1.270 AIB 0.122 n 0.184 n 0.181 n 0.195 n VAR 0.251 0.512 0.769 1.276 AIB AIB 1.000 1.168 1.172 0.755 VAR 1.000 0.953 1.063 0.676 IR 0.266 n 0.263 n 0.331 0.524 VAR 0.291 0.385 0.221 n 0.282 n IR IR 1.000 0.529 0.500 0.397 VAR 1.000 1.268 1.116 1.250 BOI 0.115 n 0.194 0.211 n 0.222 n VAR 0.212 0.508 0.677 1.410 BOI BOI 1.000 1.088 1.142 0.803 VAR 1.000 0.831 0.807 0.459 n IR 0.216 n 0.400 0.365 0.431 VAR 0.220 0.222 n 0.134 n 0.259 n IT IT IT 1.000 1.031 0.981 0.966 1.000 1.275 1.378 1.379 ISP 0.498 0.350 n 0.519 n 0.619 n 0.760 1.021 1.226 1.477 ISP ISP 1.000 1.074 1.122 0.729 1.000 1.179 1.156 0.960 IT 0.152 0.316 0.359 0.482 0.570 0.708 0.751 0.752 IT IT 1.000 1.043 0.923 0.921 1.000 1.259 1.262 0.851 VAR UCR 0.537 0.471 n 0.542 n 0.573 n 0.696 0.892 0.936 0.746 VAR UCR UCR 1.000 1.064 1.125 0.785 1.000 1.083 0.992 0.539 VAR IT 0.197 0.332 0.352 0.475 0.598 0.712 0.632 0.205 n VAR NL NL NL 1.000 0.658 0.469 0.204 n 1.000 1.143 1.095 0.744 VAR ABN 0.047 n 0.093 n 0.094 n 0.073 n 0.347 0.468 0.473 0.364 VAR ABN ABN 1.000 1.003 1.132 1.173 1.000 1.111 1.084 0.836 VAR NL 0.104 0.095 0.328 0.730 0.408 0.594 0.506 0.016 n VAR NL NL 1.000 0.680 0.434 0.160 n 1.000 1.152 1.165 1.012 VAR ING 0.109 n 0.171 0.184 n 0.136 n 0.438 0.585 0.623 0.587 VAR ING ING 1.000 0.962 1.075 1.135 1.000 1.123 1.011 0.539 VAR NL 0.233 n 0.135 n 0.400 0.759 0.606 0.785 0.723 0.368 n VAR PT PT PT 1.000 0.982 0.949 0.806 VAR 1.000 1.264 0.990 1.170 BCP 0.342 0.387 0.406 0.424 VAR 0.535 0.785 0.809 1.056 BCP BCP 1.000 1.104 1.022 0.713 VAR 1.000 1.151 1.105 1.002 PT 0.227 0.358 0.396 0.450 VAR 0.724 0.897 0.675 0.653 PT PT 1.000 0.980 0.941 0.791 VAR 1.000 1.259 1.306 1.079 VAR BES 0.295 0.325 0.353 0.402 n VAR 0.542 0.804 0.941 1.000 VAR BES BES 1.000 1.141 1.066 0.750 VAR 1.000 1.250 1.298 1.098 VAR PT 0.207 0.371 0.421 0.483 VAR 0.794 0.975 0.954 0.599 n VAR SP SP SP 1.000 0.554 0.527 0.482 1.000 1.202 0.953 1.012 BBVA 0.061 n 0.128 n -0.067 n 0.172 n 0.648 0.874 0.682 0.806 BBVA BBVA 1.000 1.083 1.018 0.595 1.000 1.172 0.804 0.586 SP 0.133 n 0.175 n 0.605 0.511 0.651 0.812 0.537 0.398 SP SP 1.000 0.559 0.552 0.486 1.000 1.188 0.897 0.950 BS 0.069 n 0.146 n -0.053 n 0.168 n 0.663 0.893 0.628 0.739 BS BS 1.000 1.085 0.999 0.573 1.000 1.155 0.690 0.405 SP 0.142 n 0.172 n 0.648 0.511 0.652 0.808 0.418 0.226 n Avg. SOV SOV 1.000 0.743 0.629 0.465 1.000 1.210 1.127 0.994 BK 0.174 0.206 0.205 0.256 0.501 0.714 0.741 0.804 BK BK 1.000 1.077 1.079 0.865 1.000 1.094 0.985 0.615 SOV 0.205 0.277 0.419 0.609 0.535 0.677 0.528 0.197 Note: Each impulse variable has an effect on itself and the second variable of the bivariate system. A unit shock in the structural error leads to a one standard deviation (in %) increase in the level of the impulse variable. This effect is normalized to 1. The GIR of the second response variable represents the percentage change in the level, given the normalized impulse. n denotes insignificant effects, by considering bootstrapped 95% confidence intervals with 2000 replications. 1 denotes Stage 1+2 and 2 denotes Stage 4+5+6. We report contemporaneous responses (Days = 0) and effects after 1 day, 5 days (after one week), and 22 days (after one month). VAR means that we use a VAR in levels to obtain the GIR. This is done when tests and/or cointegration relation checks do not indicate an equilibrium relation for the whole of Stage 1+2 or Stage 4+5+6. In the Avg. section, we provide the mean impulse responses to a shock in sovereign CDS spreads (SOV) and to a shock in bank CDS spreads (BK). Comparing the periods before and after government interventions, one can observe the pronounced effects of the risk transfer mechanism. The ratio of significant bank responses to a sovereign shock increases from 14.29% before to 100% after the interventions. In contrast, the percentage of significant country responses to a banking sector shock decreases from 100% before to 21.43% after. The banks for which 17

Chapter 1: Credit Spread Interdependencies of European states and banks we do still see significant responses after the bailouts are the Portuguese banks and one of the Italian banks (Intesa Sanpaolo). In the period before the bailouts, there is a stark contrast between the result that all banks are found to impact their respective sovereign CDS series and only a very small fraction of countries affect bank CDS spreads. We argue that the roots of this finding are in the systemic component of the crisis, which originated from financial institutions and spilled over onto the sovereign CDS market. In the period after the bailouts, the picture changes completely: the effects of sovereign shocks on bank CDS spreads become permanent, while banking sector shocks are less important than before. As emphasized in other recent papers, these findings reflect the private-to-public risk transfer. Figure 1.1: Effects of a Banking Sector Shock on Government Spreads: Before Government Interventions 0.2.4.6.8 FR (BNP) DE (COM) IR (BOI) IT (UCR) NL (ABN) PT (BCP) SP (BS) Average 0 5 10 15 20 Day Note: Sources of the banking shock are written in parentheses. Shocks to bank spreads within the same country have very similar impacts on the sovereign spread in the period before government interventions. Only one of the two bank responses per country are depicted as the results are similar. The Average line represents the mean of the sovereign responses to shocks in the seven bank CDS spreads. Figure 1.1 depicts the state responses to banking sector shocks. Considering the long-run effects (after 22 days) depicted in this graph, which are all estimated to be significant, the countries can be separated into two groups: INNER composed of FR, DE and NL (with responses above the Average line) and OUTER composed of IR, IT, SP and PT (with responses below the Average line). The results for the INNER group can be argued by a weak interest (i.e. low liquidity of the CDS contracts) in insuring against a country default in the period before Lehman Brothers collapse. This could have led first to market inefficiency and then to a strong adjustment effect as the volume increased. Furthermore, the size of the INNER banks exposures to the subprime-linked securities was considered much bigger than that of the OUTER 18

Chapter 1: Credit Spread Interdependencies of European states and banks banks. On the other hand, in this period, the OUTER countries were already at levels (of sovereign CDS spreads) closely linked to their domestic banks CDS spreads, i.e. public imbalances and high debt burdens were priced in for the latter group, thus these spreads adjusted less after the bailouts. Concentrating on the point estimates of the responses at day 1, i.e. Figure 1.2 (a) and (b), two important results can be emphasized. Firstly, one can see how the bank bailouts affected the risk transfer mechanism and secondly that the same INNER and OUTER groups can be distinguished in the short run as well. In terms of the change in the risk transfer mechanism, Figure 1.2 (a) reveals that the sovereign CDS series are more sensitive to banking sector shocks than before the bailouts, while the sensitivity of the banks to their own shocks remain of a similar magnitude. Only the responses of the Irish banks AIB and BOI to state shocks seem to stay at approximately the same level as before the bailouts, while their impacts on themselves decrease. Thus, the risk transfer from banks to governments seems to be most evident in Ireland. In the case of a country shock (Figure 1.2 (b)), we find an increase in sensitivity in both dimensions. Countries as well as banks suffer more from a government shock after the bailouts. In terms of the second point that can be made about the short run, in the period during/after bank bailouts, the responses one day after each shock, almost all of which are significantly different from zero, can be clustered into the INNER and OUTER groups, as before. Figure 1.2: Responses on Day 1 after the Shock Bank Response (Impulse Variable).8.9 1 1.1 1.2 1.3 ABN AIB SG BES BCP BS BOIDB ABN COM BBVAISP UCR BNP ING BNP BOI AIB BBVA ISP DB BS BCP ING COM UCR SG INNER Before OUTER Before BES INNER After OUTER After State Response (Impulse Variable).6.8 1 1.2 1.4 DB COM ABN ING SG BNP AIB BBVA BS BOI BOI BCP UCR ISP AIB SG BES BBVA ING BNP ABN DB BS COM ISP UCR BES BCP INNER Before OUTER Before INNER After OUTER After 0.2.4.6.8 1 State Response 0.2.4.6.8 1 Bank Response (a) Bank Shock (b) Country Shock Note: Responses of both variables of the bivariate systems are plotted (i.e. bank response (y-axis) vs. country response (x-axis) and country response (y-axis) vs. bank response (x-axis)). For example, ABN is located at (1,.1), indicating that a shock (on day 0, before government interventions) in the CDS series of ABN, leading to a 1% increase in the ABN spread, affects the Dutch CDS spread by 0.1% on day 1. As noted above, the importance of a sovereign shock augments dramatically in the post-intervention era. Figure 1.3 depicts the entire impulse response series of the selected banks to a shock in the government sector. Sorting banks by the effects they experience in the long run, which are shown to be significant in all cases, we 19

Chapter 1: Credit Spread Interdependencies of European states and banks Figure 1.3: Effects of a Sovereign Shock on Bank Spreads: After Government Interventions. 0.5 1 1.5 BNP COM AIB UCR ABN SG DB BOI ISP ING BCP BES BBVA BS Average 0 5 10 15 20 Day Note: The Average line represents the mean of the bank responses to shocks in the seven sovereign CDS spreads. obtain the following ranking (from lowest effect to highest): Société Générale (SG), ABN Amro Bank (ABN), Deutsche Bank (DB), BNP Paribas (BNP), Commerzbank (COM), ING Group (ING), Banco Santander (BS), Unicredito (UCR), Banco Bilbao Vizcaya Argentaria (BBVA), Banco Comercial Português (BCP), Banco Espírito Santo (BES), Allied Irish Banks (AIB), Bank of Ireland (BOI), Intesa Sanpaolo (ISP). The long-run responses of the banks from the same country are generally clustered. The only exception are the Italian banks, with ISP being more sensitive to sovereign shocks than UCR (148% compared to 75%). While SG is affected by only 35% of the initial shock, the strongest three impacts range from 128% to 148%. ISP and the Irish banks respond most strongly to sovereign shocks. They are followed by the Portuguese and then the Spanish banks, with the Italian UCR coming between BBVA and BS. At the bottom of the ranking are the Dutch, German and French banks. 1.4.2 Specific country analysis In this subsection, we present the results for three of the countries: Germany, Ireland and Italy. These were selected for their differing total commitment to the financial sector (offered in their bailouts) relative to their 2008 GDP. Ireland is the country with the highest commitment and Italy that with the lowest, while Germany can be argued to lie in the middle of these two. 20

Chapter 1: Credit Spread Interdependencies of European states and banks Germany In the case of Germany, we analyze, using a bivariate setup, the German (DE) sovereign CDS spread in relation to the CDS spreads of Commerzbank (COM) and Deutsche Bank (DB), respectively. The results for the tests of Granger-causality are depicted in Table 1.2, the cointegration relations in Table 1.4, and the impulse responses in Table 1.5. 17 Cointegration and Granger-causality analysis For the entire period before the government interventions (i.e. Stage 1+2), we find evidence of a stable long-run equilibrium relationship between the German CDS spread and both bank CDS series. The hypothesis that both estimated β-coefficients for the banks are equal to 1 cannot be rejected using a standard t-test. The error correction equation, e.g. for the relation with DB, can be written as follows: cds DE,t = 0.930 (0.118) cds DB,t 2.087 (0.471) ec t, 18 where ec t refers to the value of the long-run relation at time t and standard errors are provided in parentheses. As the variables are measured in logs, the β-coefficients may be interpreted as elasticities, yielding a bank-sovereign CDS equation. This relation implies, neglecting the rest of the estimated dynamics in the model, that a 1% increase in the CDS spread of DB leads to a 1% increase in the CDS spread of DE. For COM the same interpretation applies. The α-coefficients in the relations of DB and COM with DE suggest that the bank spreads do not adjust to any deviations from the long-run equilibrium, while the German CDS spread adjusts at a rate of ˆα DE = 0.122 and ˆα DE = 0.108 to changes in the DB and COM spreads respectively. A formal test confirms this result as cds DB,t and cds COM,t are found to be weakly exogenous, which leads to the argument that DB and COM provide the stochastic trend in the cointegration relations. Tests for Granger-causality indicate that only COM Granger-causes DE at the 1% significance level in the period before state interventions took place. After the bank aid schemes are in place, the long-run relations change. First of all, we do not find a stable long-run relation for DE-COM for the entire postintervention period, but only in Stage 5. We find equal values for the β-coefficients as in the pre-intervention results, implying the same elasticities as mentioned above. However, the constant changes from 1.24 (before) to insignificant (after), yielding 17 Test results and the graph of the German sovereign CDS together with the German banks CDS time series are presented in 1.B.2. 18 The cointegration graph is provided in Figure 1.B.8. 21

Chapter 1: Credit Spread Interdependencies of European states and banks the interpretation that the gap between the two CDS series vanishes. In contrast, we find a cointegration relation for DE and DB for the entire post-intervention period. The relation between COM and DE in Stage 5 yields the conclusion that COM is weakly exogenous and DE adjusts at a rate of ˆα DE = 0.045, which is close to the α-value from the period before the interventions took place. In the second cointegration relation, which considers all three stages after the bailouts together, we find that the equilibrium for DE moves in the direction of its development (as DE s α- and β-coefficients are both positive). Furthermore, Granger-causality tests for the period during and after state interventions indicate that all variables Granger-cause each other at the 1% level. Impulse response analysis Figure 1.4: Generalized Impulse Responses for Germany: (Solid) Before, (Dotted) During & After Government Interventions 1.4 DE -> DE 1.2 COM -> DE 1.6 DE -> DE 1.6 DB -> DE 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.8 0.4 0.0-0.4 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1.2 0.8 0.4 0.0-0.4-0.8-0.2 0 2 4 6 8 10 12 14 16 18 20 22-0.8 0 2 4 6 8 10 12 14 16 18 20 22-0.2 0 2 4 6 8 10 12 14 16 18 20 22-1.2 0 2 4 6 8 10 12 14 16 18 20 22 1.0 DE -> COM 1.8 COM -> COM 1.0 DE -> DB 1.6 DB -> DB 0.8 0.6 1.6 1.4 1.2 0.8 0.6 1.4 1.2 1.0 0.4 0.2 1.0 0.8 0.4 0.8 0.6 0.0-0.2 0.6 0.4 0.2 0.2 0.0 0.4 0.2 0.0-0.4 0 2 4 6 8 10 12 14 16 18 20 22 0.0 0 2 4 6 8 10 12 14 16 18 20 22-0.2 0 2 4 6 8 10 12 14 16 18 20 22-0.2 0 2 4 6 8 10 12 14 16 18 20 22 Note: Solid lines: responses before government interventions (bold) and the 95% bootstrapped confidence interval (thin). Dotted lines: responses during and after government interventions (bold) and the 95% bootstrapped confidence interval (thin). X-axis: number of days (after the shock). Y-axis: impact relative to a one standard deviation shock in the impulse variable. [Left Panel] Upper-Left: DE (impulse variable) - DE (response variable). Lower-Left: DE (impulse var.) - COM (response var.). Upper-Right: COM (impulse var.) - DE (response var.). Lower-Right: COM (impulse var.) - COM (response var.). [Right Panel] Upper-Left: DE (impulse var.) - DE (response var.). Lower-Left: DE (impulse var.) - DB (response var.). Upper-Right: DB (impulse var.) - DE (response var.). Lower-Right: DB (impulse var.) - DB (response var.). The results of the impulse response analysis are depicted in Figure 1.4. The analysis of the period before government interventions refers to the VECM setup; only in the period after interventions do we use a VAR framework to examine the relationship between DE and COM. In all graphs, the three solid lines represent the impulse responses before the interventions, with the light ones indicating the 95% 22

Chapter 1: Credit Spread Interdependencies of European states and banks bootstrapped confidence interval. The bold dotted line describes the responses during and after the rescue schemes had been implemented and the light dotted lines the bootstrapped confidence bands. Firstly, we observe that the pattern in the left panel strongly resembles the pattern in the right panel. In the upper-right corner of each panel, the effects of a shock in the bank CDS spread on the German CDS are plotted. Before the interventions (solid line), a banking sector shock permanently affects the government CDS series, while in the period afterwards (dotted) there is only a temporary effect. In the case of a government shock spilling over onto the banking sector, we notice that DB (right panel) and COM (left panel) are only affected in the very short-run (t 3) before the interventions. In the period after the bank bailouts, we find that both series react permanently to a shock stemming from the sovereign. Additionally, the graphs show that the effects of a banking sector shock on itself are stronger in the pre-interventions period, as they are estimated to have a permanent effect. The responses after the state interventions suggest a decrease in the impact of the latter for both banks. The shocks from the government CDS spread on itself have a stronger impact in both bivariate setups (i.e. in the analyses based on each of the two banks) after the interventions. Discussion From October 2008 until the end of May 2010, Germany provided total support to the local financial sector of e 619.1 Bn, or 25% of total 2008 GDP. From a total committed amount of EUR 64.8bn for capital injections, e 54.5 Bn were demanded by German banks up to the end of May 2010. Germany pledged EUR 475bn in the form of liability guarantees, of which local banks utilized e 185.8 Bn up to the end of our time frame. SoFFin 19 securities. 20 granted COM an individual guarantee for issuing e 15 Bn of debt Furthermore, SoFFin provided EUR 8.2bn in the form of a silent equity holding ( silent participation ) and COM s recapitalization by the government amounted to e 10 Bn. 21 On the other hand, DB, the biggest German bank, resisted state capital injections. Given the complete recapitalization of COM we would expect a lower reliance on government guarantees, but we find no significant differences in the dynamics of the two bank CDS series in relation to the German 19 The German Special Fund for Financial Market Stabilization (SoFFin) is in charge of managing the German financial support programs. 20 https://www.commerzbank.de/en/hauptnavigation/aktionaere/service/archive/ ir-nachrichten_1/2008_5/ir_nachrichten_detail_08_2203.html 21 These capital injections were announced to the public on 3 November 2009. 23

Chapter 1: Credit Spread Interdependencies of European states and banks sovereign CDS spread. Furthermore, our results suggest that investors anticipated the direct support for COM, as the Granger-causality tests support the idea that the CDS spreads of COM contain important information for determining the German spreads. A shock to the sovereign spread has a permanent effect on the CDS spread of COM. Thus, before the interventions, we have evidence that the dynamics of the two series differ, suggesting that the link between the CDS series of COM and DE is more sensitive than the link between DB and DE. COM is known to have had severe difficulties during the last crisis, which led SoFFin to provide extra support to this bank. The results of our empirical analysis underline that the dynamics of the two banks do not substantially differ in the postintervention period. Assuming that this similarity is a consequence of the extra support provided, we conclude that the German rescue schemes were successful in transferring the default risk. Thus, the extra funding for COM was necessary in order to induce a credible perception that the tail risk of the latter had been absorbed by the state. We find that shocks to both banks have a weaker effect on their own spreads after the bailout schemes had been implemented. However, the result is stronger for DB. The cost of this positive aspect is a higher sensitivity of both banks to developments in the government CDS spreads. Notably, the German spread is not influenced in the long term by banking sector shocks after the bailout measures have been provided. Altogether, the results highlight that the contagion emerged from the banking sector and spilled over onto German sovereign CDS spreads in the period before the rescue schemes had been implemented. Thus, we find evidence in favor of H1. The dependence in the other direction is weaker or only exists in the very short run. Afterwards, developments in the perceived default risk of all series are strongly interwoven, as suggested by the cointegration analysis and the results of the Grangercausality tests. Furthermore, the impulse responses highlight a stronger interdependency between all series, while an unexpected change in the bank CDS series has only a temporary effect on the sovereign CDS spread (H2a, H2b). Moreover, we find no strong differences in the dynamics of COM and DB in relation to changes in the German CDS spreads (H3). Our results suggest that the extra support for COM credibly transferred the default risk on to the government s balance sheet. Ireland Within the set of analyzed countries, the results for Ireland reveal most clearly the impact of government interventions. As the dynamics for both setups, i.e. Ireland (IR) - Allied Irish Banks (AIB) and Ireland (IR) - Bank of Ireland (BOI), resem- 24

Chapter 1: Credit Spread Interdependencies of European states and banks ble each other strongly we report only one of them. Tests of Granger-causality are depicted in Table 1.2, cointegration relations in Table 1.4, and impulse responses in Table 1.5 in the Appendix. 22 Cointegration and Granger-causality analysis The cointegration analysis uncovers a long-run relation in Stage 2, in which ˆβ AIB = 0.567. Interpreting the cointegration coefficients for the period before the interventions, a 1% increase in bank CDS spreads translates into an approximate 0.57% gain in the Irish spread. The gap (the constant from the cointegration equation) between the two CDS series is insignificant. Furthermore, in the period before government interventions there is evidence that the stochastic trend originates from the banking sector and affects the sovereign CDS series. The estimated α-coefficient for AIB is not significantly different from zero and the hypothesis of weak exogeneity for the banking sector series cannot be rejected. Thus, we conclude that the series of AIB influences IR in the long run. In the short run, Granger-causality is not significant in either direction. During and after the interventions the dynamics change and emphasize a different role of the Irish CDS spread, which we argue occurs because of the government interventions. The error correction equation can be written as cds IR,t = 0.724 (0.105) cds AIB,t + 1.116 (0.587) ec t. 23 Comparing elasticities, we now find an increase in ˆβ AIB to 0.724, implying that a 1% increase in the Irish spread augments the bank spread by 1.38%. 24 between the two series is enlarged and is significantly different from zero. The gap The estimated α-coefficients suggest that during and after the interventions the Irish spread provides the stochastic trend, as the weak exogeneity of this series cannot be rejected. Only the bank CDS spread adjusts to deviations from the long-run equilibrium, at a rate of ˆα AIB = 0.06. The prominent role of the Irish CDS series is also emphasized in the short-run dynamics, where we find that the CDS spread of IR Granger-causes the CDS spread of AIB but not vice versa during this period. Impulse Response Analysis The GIR depicted in Figure 1.5 underline the shift in the dependence between the two CDS series. Firstly, the graph in the upper right corner indicates that a shock 22 Preliminary test results and the graph of the respective time series are presented in 1.B.3. 23 The cointegration graph is provided in Figure 1.B.9. 24 This number is obtained by normalizing the coefficients by the estimated β-coefficient of AIB. 25

Chapter 1: Credit Spread Interdependencies of European states and banks from the banking sector permanently influences the government CDS spread before the interventions but only does so temporarily (t 2) afterwards. The opposite pattern is found for a government sector shock. In the pre-intervention period, the graph in the lower left corner highlights that the latter shock does not significantly influence the CDS spread of AIB, while there is a permanent impact in the period during and after implementation of the rescue schemes. Moreover, the remaining two graphs (upper left and lower right corners) suggest that there has been a change in the sensitivities to shocks from the same sector. A banking shock has a permanent effect on itself before the interventions but a much lower one afterwards. For the Irish spread, the GIR results show an opposing development. Whilst both deviations are permanent, that after interventions is far stronger. Figure 1.5: Generalized Impulse Responses for Ireland: (Solid) Before, (Dotted) During & After Government Interventions 2.4 IR -> IR 1.2 AIB -> IR 2.0 0.8 1.6 0.4 1.2 0.0 0.8 0.4-0.4 0.0 0 2 4 6 8 10 12 14 16 18 20 22-0.8 0 2 4 6 8 10 12 14 16 18 20 22 2.0 IR -> AIB 1.6 AIB -> AIB 1.6 1.2 1.2 0.8 0.8 0.4 0.4 0.0 0.0-0.4 0 2 4 6 8 10 12 14 16 18 20 22-0.4 0 2 4 6 8 10 12 14 16 18 20 22 Note: Upper-Left: IR (impulse variable) - IR (response variable). Lower-Left: IR (impulse var.) - AIB (response var.). Upper-Right: AIB (impulse var.) - IR (response var.). Lower-Right: AIB (impulse var.) - AIB (response var.). Solid lines: responses before government interventions (bold) and the 95% bootstrapped confidence interval (thin). Dotted lines: responses after government interventions (bold) and the 95% bootstrapped confidence interval (thin). X-axis: number of days (after the shock). Y-axis: impact relative to a one standard deviation shock in the impulse variable. Generalized impulse responses for BOI behave similarly to those for AIB. Discussion Not surprisingly, the study of the Irish risk transfer mechanism depicts the clearest change in dynamics, as Ireland is, by far, the country that made the greatest total commitment to the financial sector relative to its GDP. Remarkably, this amounted to 319% of 2008 GDP, or in monetary terms, e 592 Bn. Up to the end of May 2010, e 99.8 Bn were required in total by the Irish banks. This amount includes e 19.3 Bn that were used as capital injections (Table 1.1). Both banks in our study were 26

Chapter 1: Credit Spread Interdependencies of European states and banks recapitalized by the Irish government on 21 December 2008 and approved by the European Commission on 26 March 2009 (BOI) and 12 May 2009 (AIB). 25 Under this scheme, AIB and BOI were each provided with e 3.5 Bn. The similar public aid structures for the two banks lead to homogeneous findings, which supports our H3. The impact of a banking sector shock on itself decreases substantially after the measures have been provided. Furthermore, there is a significant impact on the government spreads but only in the short run. The flip side of the coin is the strong influence of government sector shocks on the banks after the rescue schemes had been put in place, which amplified the serious issues in the Irish financial sector as sovereign debt problems emerged. Combining the results from the two analyses, we find strong evidence in favor of H1, H2a, and H2b. Pre-bailout, the data show that the channel through which risk is spread into the market originates from the banking sector rather than the government. After the government interventions, the risk transfer mechanism puts more weight on the developments of the government CDS spread. As the government takes over the tail risk from the banks, the development of the Irish CDS series begins to play an increasingly important role. Only in the very short run do changes in banks CDS spreads influence the government series during and after the state intervention. The effects of banking sector shocks on itself have weakened postbailout, similar to the German case. Italy The main cointegration relations between Italy and the selected domestic banks (Intesa Sanpaolo (ISP) and Unicredito (UCR)) are presented in Table 1.4. Table 1.2 presents the findings from the Granger-causality tests and Table 1.5 the GIR. 26 Cointegration and Granger-causality analysis In the period before government support was provided to the Italian banking industry (i.e. Stage 1+2), we find that the banks and sovereign CDS series are tied together in a long-run equilibrium. Interpreting the β-coefficients, neglecting the remaining dynamics of the system, we argue that in the long-run a 1% increase in ISP s (UCR s) CDS spread leads to a 1.4% (1.5%) increase in the CDS series of Italy. The gaps (i.e. the constants in the cointegration relations) between the two CDS series are estimated to be significantly different from zero in both setups. The speed 25 IP/09/744 and IP/09/483. 26 Preliminary test results and the graph of the respective time series are presented in 1.B.4. 27

Chapter 1: Credit Spread Interdependencies of European states and banks of adjustment, reflected by the estimated α-coefficients, is faster for the banks CDS spreads, i.e. ˆα IT = 0.012 < 0.020 = ˆα ISP and ˆα IT = 0.010 < 0.014 = ˆα UCR. Regarding the short-run dynamics, the results reveal that Italy is Granger-caused by the developments in ISP s and UCR s CDS spreads in Stage 1+2, consistent with our assumption that the information from the financial sector was systemically important then. During and after the implementation of the Italian bank bailout program the dynamics between the sovereign and banks CDS spreads change. Firstly, UCR is found to be in a stable long-run equilibrium with the Italian government CDS series only during Stage 5. In this setup, the estimated β-coefficients imply that a 1% increase in the government spread induces an upward adjustment of UCR s CDS of 0.78%. The error correction mechanism of IT-ISP for the entire post-intervention period is cds IT,t = 0.864 (0.087) cds ISP,t + 0.922 (0.385) ec t. 27 A marginal change in the Italian CDS series by 1% leads to an adjustment in cds ISP by 1.16%. The elasticities of the two banks cannot be compared as they refer to different stages in our sample period. The constant is significantly different from zero in both setups. In the period after government interventions, the loading coefficients indicate that Italy provides the stochastic trend, as the CDS series of the latter is tested to be weakly exogenous. This result implies that, although the Italian CDS spread does not adjust to deviations from the long-run equilibrium, the banks CDS spreads react to these changes. In contrast to the results for the pre-intervention period, after government interventions the Italian CDS spreads Granger-cause both bank CDS spreads but not vice versa. Impulse response analysis The graph in the upper right corner of each panel of Figure 1.6 depicts the effect of a banking shock on the sovereign CDS series. The solid line emphasizes that, pre-intervention, risk permanently spread to the government CDS series. After the interventions, a shock originating from ISP (left panel) is found to lead to a permanent shift in the government CDS spread, while a shock from UCR (right panel) shifts the Italian CDS series by a greater amount but only temporarily (t 12). These findings support our H2a and H3. In contrast, in the period before inter- 27 The cointegration graph is provided in Figure 1.B.10. 28

Chapter 1: Credit Spread Interdependencies of European states and banks Figure 1.6: Generalized Impulse Responses for Italy: (Solid) Before, (Dotted) During & After Government Interventions 2.0 IT -> IT 1.4 ISP -> IT 1.8 IT -> IT 1.2 UCR -> IT 1.8 1.2 1.6 1.0 1.6 1.0 1.4 0.8 1.4 0.8 1.2 0.6 1.2 1.0 0.4 1.0 0.6 0.8 0.2 0.8 0.4 0.6 0.0 0.6 0.2 0.4-0.2 0.4 0 2 4 6 8 10 12 14 16 18 20 22 0.0 0 2 4 6 8 10 12 14 16 18 20 22 0.2 0 2 4 6 8 10 12 14 16 18 20 22-0.4 0 2 4 6 8 10 12 14 16 18 20 22 2.4 IT -> ISP 1.6 ISP -> ISP 1.4 IT -> UCR 1.6 UCR -> UCR 2.0 1.4 1.2 1.4 1.6 1.2 1.0 1.2 1.2 1.0 0.8 1.0 0.8 0.6 0.8 0.8 0.6 0.4 0.6 0.4 0.4 0.2 0.4 0.0 0.2 0.0 0.2-0.4 0 2 4 6 8 10 12 14 16 18 20 22 0.0 0 2 4 6 8 10 12 14 16 18 20 22-0.2 0 2 4 6 8 10 12 14 16 18 20 22 0.0 0 2 4 6 8 10 12 14 16 18 20 22 Note: [Left Panel] Upper-Left: IT (impulse variable) - IT (response variable). Lower-Left: IT (impulse var.) - ISP (response var.). Upper-Right: ISP (impulse var.) - IT (response var.). Lower-Right: ISP (impulse var.) - ISP (response var.). [Right Panel] Upper-Left: IT (impulse var.) - IT (response var.). Lower-Left: IT (impulse var.) - UCR (response var.). Upper-Right: UCR (impulse var.) - IT (response var.). Lower-Right: UCR (impulse var.) - UCR (response var.). Solid lines: responses before government interventions (bold) and the 95% bootstrapped confidence interval (thin). Dotted lines: responses after government interventions (bold) and the 95% bootstrapped confidence interval (thin). X-axis: number of days (after the shock). Y-axis: impact relative to a one standard deviation shock in the impulse variable. ventions (solid lines), the effects of a shock in the government sector (the lower-left graph in each panel) are significant in the short run for both banks. During/after the interventions (dotted lines), the impact is stronger and permanent, in line with our H2b. The pattern of bank shocks on their own series is very similar in the two periods (the lower-right corner in each panel). A government shock has a stronger effect on itself in the period after interventions, in both setups. Discussion Italy has one of the highest debt burdens of all the European Union countries. 28 This fact led the Italian government to pledge a total of e 62 Bn in its bailout package, representing slightly more than 4% of 2008 GDP. This ratio is the lowest among all the countries analyzed in this chapter. Actual capital injections accounted for e 4.1 Bn out of a committed amount of e 12 Bn. Italy also promised to support its domestic banks with an asset purchase scheme worth e 50 Bn, which had not been utilized by the end of our time frame. Compared with the other countries analyzed, the Italian government offered no liability guarantees in its support measures for 28 Italy s public debt was estimated to be around 105% of GDP in 2008. 29

Chapter 1: Credit Spread Interdependencies of European states and banks financial institutions. Notably, this instrument was highly utilized elsewhere in our sample of countries. On 20 March 2009, ISP started a procedure to obtain e 4 bn in public aid for recapitalization. 29 On the other hand, UCR, which is the biggest Italian bank, did not request any capital from Italy. The increased possibility of government aid being given to ISP in the future is reflected in our GIR analysis: the CDS series of ISP became more sensitive to unexpected changes in the Italian spread than the CDS series of UCR. This result and the cointegration relation between IT and ISP (in Stage 4+5+6) provide evidence in support of our third hypothesis (H3). Since ISP did not make use of any public support, the tail risk of the bank was not completely transferred to the Italian government. A shock to the bank has an even stronger effect on the bank itself post-bailout. The increased impact on the government CDS of a shock to the bank underpins the idea that investors believe that any difficulties faced by ISP will feed back to the government sector. In the case of UCR, we detect a similar pattern to that seen in other countries: the effect of a banking sector shock on the banking sector decreases slightly. Before Lehman Brothers default, the systemic banking crisis spilled over into the sovereign market, which is supported by the Granger-causality analysis results, and by the permanent effect of a banking sector shock shown by the GIR analysis. However, movements in IT s CDS spread have an effect on the bank spreads as well, which partly contradicts our H1. After the state interventions, this relation becomes more pronounced, with IT now Granger-causing both banks, providing the stochastic trend in the cointegration relations, and government shocks causing strong deviations in the banks CDS series. Nonetheless, the banks still influence the government CDS series, albeit only temporarily in UCR s case. Bailout schemes seem not to limit the effects of banking sector shocks on itself, as the intensity of those effects is almost the same as in the period before government interventions. Thus, Italy s banks still maintain the tail risk that was transferred to the government s balance sheet in other countries. This can be related to the small commitment the Italian government made to the financial sector relative to other countries governments. The lack of liability guarantees as part of the bailout mechanism, and the low usage of the bailout funds offered, might have further contributed to the differences in the outcome for Italy. Moreover, the credibility of the support package is in question, as 29 http://www.group.intesasanpaolo.com/scriptisir0/si09/contentdata/view/ content-ref?id=cnt-04-000000003f8d4 According to this document, on 29 September 2009 ISP decided that it would no longer participate in the Italian aid program for the banking sector, the so-called Tremonti Bonds program, but would issue debt to private investors. 30

Chapter 1: Credit Spread Interdependencies of European states and banks Italy had a high debt burden even before the financial crisis. This is also reflected in the cost of insuring the Italian government bonds and the impact of Italian CDS spread changes on the creditworthiness of Italian banks. Lastly, as was found in other countries, the sovereign spreads are more sensitive to sovereign shocks after the bank support schemes have been put in place. 1.5 Conclusion The recent financial crisis led governments to design aid programs for their financial institutions. The magnitude and dimensions of these programs were unique in European history. A series of bank failures would have threatened the whole economy since the financial system incorporates a systemic component. Hence, governments, along with central banks, took crucial steps to attempt to rescue the financial system. By arguing that the government bailout programs marked an important event for investors, we derive hypotheses about how the relations between the government and financial sectors would be expected to change as a result. First, we hypothesize that the increase in default risk prior to the interventions originated mainly from the financial sector. After the bailout programs had been set up by the European governments, we argue that the sensitivity of the sovereign default risk to financial sector shocks would have increased due to the private-to-public risk transfer. Moreover, the default risk of the banking sector is asserted to be strongly influenced by the government sector. Market stakeholders expectations about a bank s future participation in the rescue schemes should affect its CDS sensitivity to changes in sovereign credit risk. Finally, we argue that country-specific bailout characteristics are important determinants of the changes in these linkages. As stated in our first hypothesis, before the government interventions, sovereign credit risk is strongly affected by movements in bank CDS spreads, while changes in the sovereign CDS spreads have a weak impact on both the bank and sovereign CDS markets. Our findings support this in the case of FR, DE, IR, NL and SP but not in the case of IT and PT. Portugal s and Italy s default risk seem to have played an important role in the development of their local banks default risk even before the Lehman Brothers event. For the second set of hypotheses (H2a, H2b), we can conclude homogeneously that, during and after the government interventions, changes in the sovereign CDS spreads contribute permanently to the financial sector CDS spreads. On the other hand, changes in banks default risk are found to affect the sovereign CDS spreads only transitorily. Relative to the period before the bailouts, changes in banks default 31

Chapter 1: Credit Spread Interdependencies of European states and banks risk have a stronger impact in the short run (i.e. on days 0 and 1) in all countries, while for most countries the influence becomes insignificant in the long run (i.e. after 22 days); exceptions are IT, SP and PT. Countries offering similar state aid to both analyzed banks (i.e. FR, IR, SP, and PT) show an equal bank CDS sensitivity to the changes in sovereign credit risk. Banks in Germany (DB and COM) and Italy (ISP and UCR) were differently involved in the rescue schemes, but we only find heterogeneous linkages between the Italian banks and the sovereign CDS spreads. Our results suggest that the extra aid provided to COM has been successful in absorbing the default risk, while the high probability of future government aid being needed by ISP strongly links the default risk of the latter to the development of the Italian CDS spread and amplifies its sensitivity to shocks in both the banking and the sovereign sector. Furthermore, in the case of Ireland, our results indicate that the bailout schemes led to the desired result, in the sense that the default risk has clearly been transferred from the financial sector to the government. Lastly, the cross-country analysis reveals heterogeneity in the impact of the bank support programs. On the one hand, the effects of a sovereign shock on banks from the same country are closely linked; on the other hand, the effects of a sovereign shock on banks across countries can be clustered in to two groups: INNER (FR, DE, NL) and OUTER (IR, IT, PT, SP). With regards to policy implications, it is vital to note that the effectiveness of bank bailouts strongly depends on the economic health of the host country and, thus, the credibility of the rescue scheme. To weaken this link, regulators should provide incentives for banks to hold diversified government bond portfolios, in line with portfolio management theory. Sovereign bonds are often zero risk-weighted under Basel regulations, which sets the wrong incentive. It would be optimal if the diversified portfolio of sovereign bonds was not highly correlated with the government guarantees. Concerning international cooperation, BIS (2011) suggests that banks with branches or subsidiaries in several countries should be closely monitored by their domestic regulators, and closer cooperation between the countries concerned should benefit euro-wide financial stability. In addition, our study highlights, in line with previous research, elevated financing costs for countries with contingent liabilities in the financial sector and a higher volatility in sovereign yield spreads. Thus, in assessing the total cost of bank bailouts, governments need to include higher interest payments due to augmented spreads. Moreover, our results indicate that, even before the bank bailouts, there was an increased financing cost for governments, implying that investors anticipated future bailouts. Regulators could internalize this 32

Chapter 1: Credit Spread Interdependencies of European states and banks negative externality by setting up a systemic capital surcharge or by levying a tax, as suggested in Acharya et al. (2011). With respect to future research, by applying the same methodology in the analysis of credit risk interdependence between European states, researchers could shed light on the dynamics of the public-to-public risk transfer mechanism in the Eurozone. Drawing a comparison between the private-to-public and public-to-public transfer mechanisms, policy makers could gain important insights into how INNER sovereign CDSs are affected by the risk transfer from the OUTER group. Hence, Chapter 2 intends to generalize the methodology presented in Chapter 1. Since these relationships change over time, the second chapter tries to bridge this gap by analyzing the default risk of sovereigns and banks in an dynamic framework and by emphasizing how public-to-private and public-to-public risk transfers interact in the Eurozone. Bibliography Acharya, V., I. Drechsler, and P. Schnabl (2011). A Pyrrhic victory? Bank bailouts and sovereign credit risk. NBER Working Paper Series No. 17136. Attinasi, M. G., C. D. Checherita, and C. Nickel (2009). What explains the surge in euro area sovereign spreads during the financial crisis of 2007-09? ECB Working Paper No. 1131. Berndt, A. and I. Obreja (2010). Decomposing European CDS returns. Review of Finance 14, 189 233. BIS (2008, June). Quarterly Review. Basel: Bank for International Settlements. BIS (2009, June). 79th Annual Report. Basel: Bank for International Settlements. BIS (2011). The impact of sovereign credit risk on bank funding conditions. Basel: Bank for International Settlements. Collin-Dufresne, P., R. Goldstein, and J. Martin (2001). The determinants of credit spread changes. Journal of Finance 56, 2177 2207. Demirgüç-Kunt, A. and H. Huizinga (2010). Are banks too big to fail or too big to save? International evidence from equity prices and CDS spreads. CEPR Discussion Papers No. 7903. Dieckmann, S. and T. Plank (2011). Default risk of advanced economies: An empirical analysis of credit default swaps during the financial crisis. Review of Finance 0, 1 32. Dolado, J. and H. Lütkepohl (1996). Making Wald tests work for cointegrated VAR systems. Econometric Reviews 15, 396 386. 33

Chapter 1: Credit Spread Interdependencies of European states and banks Dötz, N. and C. Fischer (2010). What can EMU countries sovereign bond spreads tell us about market perceptions of default probabilities during the recent financial crises? Deutsche Bundesbank Discussion Paper No. 11. Ejsing, J. and W. Lemke (2011). The Janus-headed salvation: Sovereign and bank credit risk premia during 2008-2009. Economics Letters 110, 28 31. Fontana, A. and M. Scheicher (2010). An analysis of euro area sovereign CDS and their relation with government bonds. ECB Working Paper No. 1271. Forte, S. and J. I. Pena (2009). Credit spreads: An empirical analysis on the informational content of stocks, bonds, and CDS. Journal of Banking and Finance 33, 2013 2025. Gerlach, S., A. Schulz, and G. Wolff (2010). Banking and sovereign risk in the euro area. Deutsche Bundesbank Discussion Paper No. 09. Gonçalves, S. and L. Kilian (2004). Bootstrapping autoregressions with conditional heteroskedasticity of unknown form. Journal of Econometrics 123, 89 120. Gray, D. F. (2009). Modeling financial crises and sovereign risks. Annual Review of Financial Economics 1, 117 144. Gray, D. F., R. C. Merton, and Z. Bodie (2008). New framework for measuring and managing macrofinancial risk and financial stability. NBER Working Papers No. 13607. Hansen, H. and S. Johansen (1999). Some tests for parameter constancy in cointegrated VAR-models. Econometrics Journal 2, 306 333. Hansen, P. R. and S. Johansen (1998). Workbook on Cointegration. Oxford: Oxford University Press. Hull, J., M. Predescu, and A. White (2004). The relationship between credit default swap spreads, bond yields, and credit rating announcements. Journal of Banking and Finance 28, 2789 2811. IMF (2010). Global Financial Stability Report - Sovereigns, Funding, and Systemic Liquidity. Washington D.C. Lütkepohl, H. (2007). New Introduction to Multiple Time Series Analysis (2nd ed.). New York: Springer-Verlag. Norden, L. and M. Weber (2004). Informational efficiency of credit default swap and stock markets: The impact of credit rating announcements. Journal of Banking and Finance 28, 2813 2843. Pesaran, H. H. and Y. Shin (1998). Generalized impulse response analysis in linear multivariate models. Economics Letters 58, 17 29. 34

Chapter 1: Credit Spread Interdependencies of European states and banks Schweikhard, F. and Z. Tsesmelidakis (2009). The impact of government interventions on CDS and equity markets. Working Paper, SSRN. Stolz, S. M. and M. Wedow (2010). Extraordinary measures in extraordinary times - Public measures in support of the financial sector in the EU and the United States. Deutsche Bundesbank Discussion Paper No. 13, Series 1: Economic Studies. 35

Chapter 1: Credit Spread Interdependencies of European states and banks Appendix 1.A Further issues on methodology 1.A.1 VEC-analysis - Selection of sub-stages The selection of sub-stages for the study of the long-run relations is carried out using the following steps: if the tests (see below) do not provide evidence of cointegration relations for a certain stage, we consider its sub-periods. Also, if the stability of a cointegration space is rejected we consider a finer grid for the time periods. To investigate this, we consider recursively estimated eigenvalues as proposed by Hansen and Johansen (1999). Cointegration results are only reported for the stages that pass the stability test using the 1% critical value as a decision boundary. If there is no evidence of a (stable) cointegration relation on the finer grid either, we report none for the entire stage (i.e. before or during/after government interventions). 1.A.2 Pre-analysis of the data, model specification, and estimation First, we apply the standard unit root (stationarity) testing procedures, i.e. the Augmented-Dickey-Fuller (ADF), Phillips-Perron (PP), and Kwiatkowski-Phillips- Schmidt-Shin (KPSS) tests, to the respective time series in each sub-sample. 30 All of the latter include an intercept because we disregard the possibility of a zero mean or trend stationary process. The latter process is not considered as it is economically unreasonable to assume that CDS series rise perpetually. We do not analyze systems of CDS series in a VECM if there is evidence that one or both series are stationary as in this case they cannot share a joint stochastic trend. For detecting a common stochastic trend, this study considers, both the Engle-Granger ADF test and Johansen s trace and maximum eigenvalue tests. The latter tests focus only on the setup with a restricted constant. As argued before, any deterministic trend in the variables or cointegration relation would be economically unjustified. When a common stochastic trend is detected by one of the previous tests and stability of the cointegration space is not rejected, we model the series in a VECM framework. If not, we proceed as described above. In finalizing our exact specifications of the models, we determine the optimal lag order p by, first, minimizing one of the common information criteria 31 and, second, taking care of the remaining serial correlation 30 Results are available upon request from the authors. 31 Akaike information criterion, Hannan Quinn criterion, Schwarz criterion, and final prediction error 36

Chapter 1: Credit Spread Interdependencies of European states and banks in the residuals. 32 The VECM is estimated by Johansen s maximum likelihood procedure and the VAR model via ordinary least squares. 1.A.3 Interpretation of long-run relations in a VECM The loading coefficients, α, measure the speed of adjustment with which a particular CDS adjusts to the long-run relationship. The adjustment forces start acting whenever the long-run relation (defined by β y t 1 = 0, where y t 1 = (cds Sov,t 1, cds Bk,t 1 ) ) is out of equilibrium, i.e. if β y t 1 0. If α Sov is significant and has the opposite sign to β Sov (i.e. in our setup α Sov < 0) it means that the sovereign is driven by the error correction mechanism or, put differently, that it adjusts back to the longrun equilibrium defined by β y t 1 = 0, whenever β y t 1 0. Equivalently, when α Bk is significant and has the opposite sign to β Bk, it shows the speed of adjustment of the bank to the equilibrium. When both α-coefficients are significant and have the opposite signs to their respective β-coefficients, the variables are said to be in a real cointegration relationship; both series are taking part in the error correction mechanism. Whenever one of the α-coefficients is not significant, it means that the respective variable can be argued to provide the stochastic trend that determines the long-run relation. This can be formally tested using a likelihood ratio test through a zero restriction on this parameter. If the restriction cannot be rejected, the variable of the respective α-coefficient is called weakly exogenous. Furthermore, it is not adjusting at all if the variables are not in long-run equilibrium, i.e. when β y t 1 0. Whenever an α-coefficient is significant but with the same sign as the respective β-parameter, the variable is said not to be part of the error correction mechanism as the forces in the model do not attract both series back to the equilibrium. Series in this setup can only define a long-run relation if the variable that is in a formal error correction relation adjusts faster to the new equilibrium than the other variable. One can think of this phenomenon as the variable that is not part of the error correction mechanism moving the entire equilibrium (i.e. when the variable increases in value, a long-run equilibrium will be established with both series at a higher value). In the literature, the term overshooting is used to describe this occurrence. 33 32 When applicable, we also look at the plots of the cointegration relations in order to check whether these can be argued to be stable. The plot is expected to a show a time series that fluctuates nicely around some mean. 33 For a discussion of a model with overshooting, please refer to Hansen and Johansen (1998). 37

Chapter 1: Credit Spread Interdependencies of European states and banks Appendix 1.B Specific country analysis 1.B.1 France Table 1.B.1: France: Bivariate Cointegration Tests Period Variables Lags Trace Statistic Max Eigenvalue Engle-Granger Test r = 0 r = 1 r = 0 r = 1 Stage 1 FR - BNP 0 0.021 0.212 0.031 0.212-2.406 FR - SG 0 0.006 0.119 0.012 0.119-4.446 Stage 2 FR - BNP * FR - SG 1 0.038 0.332 0.040 0.332-5.701 Stage 1 + 2 FR - BNP 1 0.017 0.109 0.045 0.109-3.102 FR - SG 1 0.005 0.147 0.010 0.147-4.455 Stage 4 FR - BNP 6 0.119 0.130 0.296 0.130-1.507 FR - SG 5 0.764 0.779 0.706 0.779-1.663 Stage 5 FR - BNP 2 0.321 0.290 0.477 0.290-2.260 FR - SG 8 0.062 0.124 0.158 0.124-3.101 Stage 6 FR - BNP 1 0.611 0.583 0.631 0.583-2.033 FR - SG 1 0.507 0.504 0.554 0.504-1.573 Stage 4 + 5 FR - BNP 1 0.282 0.735 0.192 0.735-1.163 FR - SG 1 0.295 0.944 0.142 0.944-2.458 Stage 5 + 6 FR - BNP 1 0.211 0.447 0.216 0.447-2.535 FR - SG 1 0.105 0.297 0.138 0.297-2.053 Stage 4 + 5 + 6 FR - BNP 1 0.057 0.313 0.067 0.313-2.230 FR - SG 1 0.072 0.514 0.054 0.514-2.250 Note: Trace and Max Eigenvalue are the Johansen test statistics (with a restricted constant). p-values are reported. The respective null hypothesis is denoted by r = {0, 1}, where e.g. r = 1 denotes one cointegration relation. * signifies that at least one of the series is stationary. For the Engle-Granger test the ADF test statistic is reported; critical values at 5% and 10% are -3.37 and -3.07 respectively. Figure 1.B.1: France: CDS Level Series 240 Stage 1 Stage 2 Stage 4 Stage 5 Stage 6 200 160 FRANCE BNP PARIBAS SOCIETE GENERALE 120 80 40 0 2007-06 2007-09 2007-12 2008-03 2008-06 2008-09 2008-12 2009-03 2009-06 2009-09 2009-12 2010-03 38

Chapter 1: Credit Spread Interdependencies of European states and banks 1.B.2 Germany Table 1.B.2: Germany: Bivariate Cointegration Tests Period Variables Lags Trace Statistic Max Eigenvalue Engle-Granger Test r = 0 r = 1 r = 0 r = 1 Stage 1 DE - COM 0 0.044 0.171 0.086 0.171-3.696 DE - DB 3 0.113 0.177 0.226 0.177-4.024 Stage 2 DE - COM * DE - DB * Stage 1 + 2 DE - COM 3 0.014 0.062 0.057 0.062-4.441 DE - DB 3 0.005 0.048 0.027 0.048-5.273 Stage 4 DE - COM 1 0.413 0.663 0.350 0.663-1.012 DE - DB 1 0.064 0.331 0.071 0.331-1.596 Stage 5 DE - COM 1 0.164 0.496 0.146 0.496-2.983 DE - DB 7 0.0471 0.117 0.124 0.117-1.778 Stage 6 DE - COM 1 0.688 0.529 0.763 0.529-1.368 DE - DB 1 0.724 0.682 0.711 0.682-0.900 Stage 4 + 5 DE - COM 1 0.0421 0.2814 0.052 0.2814-1.485 DE - DB * Stage 5 + 6 DE - COM * DE - DB * Stage 4 + 5 +6 DE - COM 1 0.0063 0.1166 0.0145 0.1166-1.774 DE - DB 1 0.0692 0.2769 0.0919 0.2769-2.088 Note: Trace and Max Eigenvalue are the Johansen test statistics (with a restricted constant). p-values are reported. The respective null hypothesis is denoted by r = {0, 1}, where e.g. r = 1 denotes one cointegration relation. * signifies that at least one of the series is stationary. For the Engle-Granger test the ADF test statistic is reported; critical values at 5% and 10% are -3.37 and -3.07 respectively. Figure 1.B.2: Germany: CDS Level Series 240 200 160 Stage 1 Stage 2 Stage 4 Stage 5 Stage 6 GERMANY COMMERZBANK DEUTSCHE BANK 120 80 40 0 2007-06 2007-09 2007-12 2008-03 2008-06 2008-09 2008-12 2009-03 2009-06 2009-09 2009-12 2010-03 39

Chapter 1: Credit Spread Interdependencies of European states and banks 1.B.3 Ireland Table 1.B.3: Ireland: Bivariate Cointegration Tests Period Variables Lags Trace Statistic Max Eigenvalue Engle-Granger Test r = 0 r = 1 r = 0 r = 1 Stage 1 IR - AIB 2 0.429 0.620 0.389 0.620-1.361 IR - BOI 2 0.390 0.601 0.354 0.601-1.325 Stage 2 IR - AIB 1 0.232 0.999 0.080 0.999-2.577 IR - BOI 1 0.010 0.997 0.002 0.997-3.376 Stage 1 + 2 IR - AIB 2 0.323 0.354 0.421 0.354-2.099 IR - BOI 2 0.436 0.306 0.628 0.306-2.155 Stage 4 IR - AIB 0 0.016 0.233 0.021 0.233-1.806 IR - BOI 1 0.260 0.330 0.349 0.330-1.981 Stage 5 IR - AIB 1 0.227 0.183 0.445 0.183-1.630 IR - BOI 1 0.269 0.151 0.579 0.151-2.149 Stage 6 IR - AIB 4 0.049 0.679 0.024 0.679-1.918 IR - BOI 4 0.177 0.786 0.098 0.786-2.900 Stage 4 + 5 IR - AIB 1 0.005 0.129 0.011 0.129-1.948 IR - BOI 1 0.027 0.393 0.023 0.393-1.892 Stage 5 + 6 IR - AIB 9 0.003 0.122 0.005 0.122-3.080 IR - BOI 9 0.001 0.117 0.002 0.117-3.202 Stage 4 + 5 + 6 IR - AIB 9 0.001 0.057 0.006 0.057-2.446 IR - BOI 9 0.000 0.164 0.000 0.164-3.055 Note: Trace and Max Eigenvalue are the Johansen test statistics (with a restricted constant). p-values are reported. The respective null hypothesis is denoted by r = {0, 1}, where e.g. r = 1 denotes one cointegration relation. * signifies that at least one of the series is stationary. For the Engle-Granger test the ADF test statistic is reported; critical values at 5% and 10% are -3.37 and -3.07 respectively. Figure 1.B.3: Ireland: CDS Level Series 700 600 500 Stage 1 Stage 2 Stage 4 Stage 5 Stage 6 IRELAND BANK OF IRELAND ALLIED IRISH BANKS 400 300 200 100 0 2007-06 2007-09 2007-12 2008-03 2008-06 2008-09 2008-12 2009-03 2009-06 2009-09 2009-12 2010-03 40

Chapter 1: Credit Spread Interdependencies of European states and banks 1.B.4 Italy Table 1.B.4: Italy: Bivariate Cointegration Tests Period Variables Lags Trace Statistic Max Eigenvalue Engle-Granger Test r = 0 r = 1 r = 0 r = 1 Stage 1 IT - ISP 3 0.107 0.130 0.267 0.130-1.948 IT - UCR 3 0.140 0.180 0.278 0.180-1.538 Stage 2 IT - ISP 1 0.089 0.919 0.032 0.919-2.574 IT - UCR 1 0.195 0.936 0.083 0.936-1.797 Stage 1 + 2 IT - ISP 4 0.052 0.131 0.125 0.131-2.313 IT - UCR 3 0.083 0.108 0.236 0.108-1.883 Stage 4 IT - ISP 1 0.761 0.561 0.829 0.561-1.931 IT - UCR 1 0.946 0.898 0.910 0.898-1.696 Stage 5 IT - ISP 2 0.091 0.125 0.231 0.125-2.334 IT - UCR 2 0.044 0.143 0.098 0.143-2.140 Stage 6 IT - ISP 4 0.248 0.389 0.293 0.389-3.125 IT - UCR 1 0.821 0.530 0.908 0.530-1.762 Stage 4 + 5 IT - ISP 3 0.158 0.803 0.082 0.803-2.181 IT - UCR 1 0.590 0.584 0.605 0.584-1.554 Stage 5 + 6 IT - ISP 4 0.042 0.768 0.017 0.768-2.846 IT - UCR * Stage 4 + 5 + 6 IT - ISP 1 0.059 0.514 0.042 0.514-3.450 IT - UCR 1 0.284 0.256 0.453 0.256-1.893 Note: Trace and Max Eigenvalue are the Johansen test statistics (with a restricted constant). p-values are reported. The respective null hypothesis is denoted by r = {0, 1}, where e.g. r = 1 denotes one cointegration relation. * signifies that at least one of the series is stationary. For the Engle-Granger test the ADF test statistic is reported; critical values at 5% and 10% are -3.37 and -3.07 respectively. Figure 1.B.4: Italy: CDS Level Series 300 250 200 Stage 1 Stage 2 Stage 4 Stage 5 Stage 6 INTESA SANPAOLO ITALY UNICREDITO 150 100 50 0 2007-06 2007-09 2007-12 2008-03 2008-06 2008-09 2008-12 2009-03 2009-06 2009-09 2009-12 2010-03 41

Chapter 1: Credit Spread Interdependencies of European states and banks 1.B.5 The Netherlands Table 1.B.5: The Netherlands: Bivariate Cointegration Tests Period Variables Lags Trace Statistic Max Eigenvalue Engle-Granger Test r = 0 r = 1 r = 0 r = 1 Stage 1 NL - ABN 0 0.029 0.099 0.085 0.099-3.646 NL- ING 0 0.007 0.155 0.014 0.155-4.389 Stage 2 NL - ABN * NL- ING * Stage 1 + 2 NL - ABN 2 0.005 0.059 0.021 0.059-3.422 NL- ING 2 0.002 0.145 0.004 0.145-3.918 Stage 4 NL - ABN 5 0.151 0.474 0.139 0.474-2.419 NL- ING 0 0.932 0.761 0.940 0.761-1.385 Stage 5 NL - ABN 1 0.106 0.085 0.349 0.085-2.801 NL- ING 1 0.095 0.119 0.252 0.119-2.662 Stage 6 NL - ABN 6 0.082 0.617 0.051 0.617-3.350 NL- ING 7 0.862 0.862 0.794 0.862-3.053 Stage 4 + 5 NL - ABN 1 0.132 0.536 0.104 0.536-1.622 NL- ING 8 0.220 0.890 0.107 0.890-2.243 Stage 5 + 6 NL - ABN * NL- ING * Stage 4 + 5 + 6 NL - ABN 1 0.624 0.848 0.487 0.848-1.422 NL- ING 1 0.522 0.750 0.427 0.750-2.372 Note: Trace and Max Eigenvalue are the Johansen test statistics (with a restricted constant). p-values are reported. The respective null hypothesis is denoted by r = {0, 1}, where e.g. r = 1 denotes one cointegration relation. * signifies that at least one of the series is stationary. For the Engle-Granger test the ADF test statistic is reported; critical values at 5% and 10% are -3.37 and -3.07 respectively. Figure 1.B.5: The Netherlands: CDS Level Series 240 Stage 1 Stage 2 Stage 4 Stage 5 Stage 6 200 160 NETHERLANDS ABN AMRO ING 120 80 40 0 2007-06 2007-09 2007-12 2008-03 2008-06 2008-09 2008-12 2009-03 2009-06 2009-09 2009-12 2010-03 42

Chapter 1: Credit Spread Interdependencies of European states and banks 1.B.6 Portugal Table 1.B.6: Portugal: Bivariate Cointegration Tests Period Variables Lags Trace Statistic Max Eigenvalue Engle-Granger Test r = 0 r = 1 r = 0 r = 1 Stage 1 PT - BCP 1 0.272 0.420 0.307 0.420-1.997 PT - BES 3 0.280 0.464 0.293 0.464-1.986 Stage 2 PT - BCP 1 0.103 0.599 0.069 0.599-3.570 PT - BES 2 0.028 0.688 0.013 0.688-3.374 Stage 1 + 2 PT - BCP 0 0.038 0.078 0.135 0.078-2.647 PT - BES 0 0.038 0.093 0.119 0.093-2.349 Stage 4 PT - BCP 6 0.291 0.717 0.206 0.717-0.711 PT - BES 6 0.257 0.874 0.135 0.874-1.036 Stage 5 PT - BCP 1 0.302 0.182 0.584 0.182-2.256 PT - BES * Stage 6 PT - BCP 1 0.057 0.596 0.034 0.596-1.573 PT - BES 1 0.188 0.546 0.157 0.546-1.711 Stage 4 + 5 PT - BCP 1 0.344 0.411 0.408 0.411-2.074 PT - BES 1 0.318 0.643 0.258 0.643-0.837 Stage 5 + 6 PT - BCP 1 0.054 0.652 0.029 0.652-1.458 PT - BES 1 0.349 0.659 0.283 0.659-1.724 Stage 4 + 5 + 6 PT - BCP 1 0.049 0.472 0.037 0.472-2.104 PT - BES 1 0.378 0.571 0.355 0.571-1.769 Note: Trace and Max Eigenvalue are the Johansen test statistics (with a restricted constant). p-values are reported. The respective null hypothesis is denoted by r = {0, 1}, where e.g. r = 1 denotes one cointegration relation. * signifies that at least one of the series is stationary. For the Engle-Granger test the ADF test statistic is reported; critical values at 5% and 10% are -3.37 and -3.07 respectively. Figure 1.B.6: Portugal: CDS Level Series 700 600 500 400 Stage 1 Stage 2 Stage 4 Stage 5 Stage 6 PT BANCO COM. PORT. BANCO ESP.SANTO 300 200 100 0 2007-06 2007-09 2007-12 2008-03 2008-06 2008-09 2008-12 2009-03 2009-06 2009-09 2009-12 2010-03 43

Chapter 1: Credit Spread Interdependencies of European states and banks 1.B.7 Spain Table 1.B.7: Spain: Bivariate Cointegration Tests Period Variables Lags Trace Statistic Max Eigenvalue Engle-Granger Test r = 0 r = 1 r = 0 r = 1 Stage 1 SP - BBVA 1 0.130 0.148 0.296 0.148-2.712 SP - BS 1 0.086 0.146 0.196 0.146-2.860 Stage 2 SP - BBVA 1 0.017 0.468 0.011 0.468-6.240 SP - BS 2 0.020 0.578 0.011 0.578-6.905 Stage 1 + 2 SP - BBVA 1 0.013 0.102 0.036 0.102-3.851 SP - BS 1 0.006 0.090 0.018 0.090-3.420 Stage 4 SP - BBVA 1 0.503 0.569 0.506 0.569-1.395 SP - BS 2 0.026 0.136 0.058 0.136-2.000 Stage 5 SP - BBVA 1 0.507 0.407 0.628 0.407-1.828 SP - BS 1 0.545 0.441 0.651 0.441-2.348 Stage 6 SP - BBVA 4 0.778 0.535 0.862 0.535-2.008 SP - BS 4 0.740 0.561 0.804 0.561-2.108 Stage 4 + 5 SP - BBVA 1 0.300 0.416 0.345 0.416-1.589 SP - BS 2 0.080 0.243 0.121 0.243-1.987 Stage 5 + 6 SP - BBVA 1 0.606 0.563 0.640 0.563-2.088 SP - BS 4 0.487 0.927 0.299 0.927-2.012 Stage 4 + 5 + 6 SP - BBVA 11 0.078 0.459 0.065 0.459-2.427 SP - BS 1 0.066 0.184 0.124 0.184-2.619 Note: Trace and Max Eigenvalue are the Johansen test statistics (with a restricted constant). p-values are reported. The respective null hypothesis is denoted by r = {0, 1}, where e.g. r = 1 denotes one cointegration relation. * signifies that at least one of the series is stationary. For the Engle-Granger test the ADF test statistic is reported; critical values at 5% and 10% are -3.37 and -3.07 respectively. Figure 1.B.7: Spain: CDS Level Series 280 240 200 Stage 1 Stage 2 Stage 4 Stage 5 Stage 6 BBVA BANCO SANTANDER SPAIN 160 120 80 40 0 2007-06 2007-09 2007-11 2008-02 2008-06 2008-09 2008-12 2009-03 2009-06 2009-08 2009-11 2010-02 2010-05 44

Chapter 1: Credit Spread Interdependencies of European states and banks 1.B.8 Cointegration graphs Figure 1.B.8: Cointegration Graph of Germany and Commerzbank (Before Government Interventions) 2.0 1.5 1.0 0.5 0.0-0.5-1.0-1.5 2007-07 2007-10 2008-01 2008-04 2008-07 Figure 1.B.9: Cointegration Graph of Ireland and Allied Irish Banks (During and After Government Interventions).8.6.4.2.0 -.2 -.4 -.6 2008-12 2009-03 2009-06 2009-08 2009-11 2010-02 2010-05 Figure 1.B.10: Cointegration Graph of Italy and Intesa Sanpaolo (During and After Government Interventions).5.4.3.2.1.0 -.1 -.2 -.3 -.4 2008-12 2009-03 2009-06 2009-08 2009-11 2010-02 2010-05 45

Chapter 1: A Contagion Index for the Euro Area 46

Chapter 2 A Contagion Index for the Euro Area

Chapter 2: A Contagion Index for the Euro Area 2.1 Introduction The recent financial crisis, that developed from a global banking turmoil to a European sovereign debt crisis, is one of the most challenging episodes for policy makers both of governments and central banks since the introduction of the euro. 1 After the collapse of Lehman Brothers in autumn 2008, the fear of contagion is one of the most prominent issues on the agenda both for financial research and policy making. Clearly, the fear of contagion has and still does put pressure on policy makers and influences policy decisions in particular within the Eurozone. Being able to gauge the potential risk of contagion is therefore of paramount interest for policy makers and agents in financial markets. In the existing empirical and theoretical literature there is a broad range of definitions for contagion, see e.g. Forbes (2012). By the same token, a variety of approaches and methods on how to measure contagion has been proposed. Dornbusch et al. (2000) or Forbes and Rigobon (2002), among others, describe contagion as a significant increase in cross-market interdependencies after a large shock hits one country or a group of countries. Contagion viewed from that perspective is hence determined by the portion of interdependency that exceeds any fundamental relationship among countries and that is not attributable to the magnitude of common shocks. More generally, contagion can also be associated with a negative externality triggered by institution(s) or market participant(s) in distress that might affect other players. Constâncio (2012) extends the definition of contagion in two directions: the existence of an initial trigger-event and the abnormal speed, strength or scope that accompanies financial instability. More recently, contagion is sometimes explained as a propagation of shocks that are related to a perceived non-zero probability of a possible albeit unlikely break-up of the Eurozone. For the purpose of this chapter we borrow as benchmark the approach put forward by Allen and Gale (2000) who explain contagion as a consequence of spillover effects. In their example, a banking crisis in one region may spill over to other regions. Contagion in their view is hence the phenomenon of extreme amplification of spillover effects. Spillover effects are therefore a necessary - but not sufficient - condition for contagion. But when are spillovers extreme and when would they trigger contagion and how can they be distinguished from those that occur within normal i.e. non-dangerous magnitudes? In this paper we present a method and an index that can answer these questions in quasi real time. We propose an analytical and empirical framework for measuring spillover effects and we illustrate our method 1 This chapter is a partial rewrite of the CFS Working Paper No. 2012/13 and ECB Working Paper No. 2013/1558 The dynamics of spillover effects during the European sovereign debt turmoil, joint work with Andreas Beyer (ECB). 48

Chapter 2: A Contagion Index for the Euro Area by providing an empirical application to the inter-linkages between sovereign credit markets and systemically relevant banks. By analysing daily data of CDS spreads we quantify those spillover effects based on a 80-days rolling regression window. Our measure internalises interdependencies of the variables in our system. We aggregate this information into a Contagion Index. This index has four main excessive spillover components: average potential spillover i) amongst sovereigns, ii) amongst banks, iii) from sovereigns to banks and iv) vice-versa. There are several mechanisms that could explain the transmission of spillover effects within these four channels. As regards spillover amongst Eurozone sovereign bonds they are at least indirectly linked by the joint monetary policy transmission mechanism, the Eurosystem s collateral framework and by a shared default risk of Eurozone member countries via the European Financial Stability Facility (EFSF hereafter) and future European Stability Mechanism (ESM). 2 Spillover effects between (domestic) sovereign creditworthiness and (domestic) banks are induced by a feedback mechanism that intensified during the financial crisis. The dynamics of such a sovereign-and-banks feedback loop are driven by systemic financial externalities that have a negative impact on the real economy and consequently on public finances, see e.g. Acharya et al. (2011), Alter and Schüler (2012), Bicu and Candelon (2012), De Bruyckere et al. (2012), Merler and Pisani-Ferry (2012) or Gross and Kok (2012). Sovereign debt amplification feeds back into the financial sector by affecting balance sheets of financial institutions and thereby having a negative impact on domestic banks ratings that pushes up their funding costs, see e.g. BIS (2011). With a domestic financial sector in distress government guarantees for the financial sector lose credibility when sovereign creditworthiness deteriorates as well and thereby yielding further amplification of spillovers. If government liabilities increase, this causes a higher debt burden and hence increased pressure for sovereigns. Finally, there are several channels that transmit contagion risks within the banking sector alone, such as common credit exposures, interbank lending or trade of derivatives. Apart from the fundamental-based contagion channels, portfolio rebalancing theory and information asymmetries among market participants might induce spillover effects as well. 2 The EFSF was created on 9 May 2010 as a temporary facility and will be merged with the European Stability Mechanism (ESM hereafter). The ESM was set up on 24 June 2011 as a permanent crisis mechanism. The share of the countries guaranteeing the EFSF s debt is in proportion to each country s capital share in the European Central Bank (ECB) adjusted to exclude countries with EU/IMF supported programs. 49

Chapter 2: A Contagion Index for the Euro Area Our empirical framework is based on a medium-size vector autoregressive model with exogenous variables (VARX). These exogenous variables account for common global and regional trends that allow us to identify and to measure the systemic contribution of sovereigns and banks. We fit the model recursively based on daily log-returns of sovereign and bank CDS series over the period October 2009 until July 2012. The use of CDS data was partly motivated by recent studies which show that past CDS spreads improve the forecast quality of bond yield spreads, see e.g., Palladini and Portes (2011) or Fontana and Scheicher (2010) who provide a detailed discussion on the relationship between euro area sovereign CDSs and government bond yields. We derive generalized impulse response functions (GIRF) as functions of residuals together with the interdependence coefficients. The GIRFs serve as input for inference and detection of spillovers in the euro area. Based on recent work by Diebold and Yilmaz (2011), we extend their methodology that accounts for spillover and contagion in several directions. Instead of using the forecast error variance decomposition, we use the framework of generalized impulse responses. In this setup, we analyse the normalized potential spillover effects of an unexpected shock in each variable on others. We determine an optimal rolling window size for our VARX model (80 days). The optimal size is characterized by a trade-off between robustness and reliability of estimated coefficients on the one hand (the longer the sample the better the quality) and gaining information about a build-up of spillover effects over time on the other hand (by aiming for many windows of shorter samples). Our main results reflect increasing spillover measures and therefore a high level of potential contagion before key financial market events or policy interventions during the sovereign debt crisis. While the contagion index amongst banks remains stable during the analysed period, both the contagion index of sovereigns and the overall contagion index (for both banks and sovereigns) trend upward. The individual net contribution of the IMF/EU program countries is highly elevated during the periods that precedes their respective bailout, but declines considerably afterwards. Spillover effects from banks to sovereigns and vice-versa trend upward in periods of stress, reflecting the evidence of a tightening nexus between banks and sovereigns in the Eurozone. The remainder of this chapter is organized as follows. In Section 2.2 we discuss studies related to our research. Section 2.3 presents the data and the methodology utilized. Section 2.4 presents our results, Section 2.5 provides some empirical robustness checks, and Section 2.6 concludes. 50

Chapter 2: A Contagion Index for the Euro Area 2.2 Related Literature The main strand of literature related to this chapter focuses on contagion in financial markets. As defined by Forbes and Rigobon (2002), contagion refers to a significant increase in cross-market correlation compared to the one measured during tranquil periods. They find that the estimated correlation increases during stress times but tends to be biased upwards. If tests are not adjusted for heteroskedasticity bias they result in misleading evidence of contagion. They conclude that a stable and elevated co-movement during both tranquil and stress times should be referred to as interdependence. Allen and Gale (2000) provide an analysis of contagion caused by linkages between banks. When one region suffers a banking crisis, banks from other regions that hold claims against the affected region devalue these assets and their capital is eroded. Spillover effects from the affected region can trigger an infection of other adjacent regions. The extreme amplification of spillover effects is referred to as financial contagion. This mechanism could also be explained by self-fulfilling expectations: if shocks from a region serve as signals that improve the prediction of shocks in another region then a crisis in the former creates the expectation of a crisis in the latter. In this chapter, we propose a new methodology that complements contagion methodologies developed by Caceres et al. (2010), Caporin et al. (2012), Claeys and Vašíček (2012), De Santis (2012), Donati (2011) and Zhang et al. (2011). Dungey et al. (2004) provide an exhaustive review of the empirical methods that deal with financial contagion. Analysing bond spreads of the euro area countries, De Santis (2012) finds that global, country-specific and contagion risks are the main factors that drive sovereign credit spreads. Based on a multivariate model with time-varying correlations and volatilities, Zhang et al. (2011) use CDS spreads to infer joint and conditional probabilities of default of the euro area countries. Furthermore, Caceres et al. (2010) use the methodology developed by Segoviano (2006) and estimate the spillover coefficients for each country in the euro area. Their findings suggest that the gravity center of contagion source shifted from countries that were at the beginning more affected by the financial crisis (i.e. Ireland, Netherlands, and Austria) to those euro area countries with weak long-term sustainability and high short-term refinancing risk (i.e. Greece, Portugal and Spain). Caporin et al. (2012) study sovereign risk contagion within the euro area countries. They find that contagion in Europe remained subdued in the period they analyze. They conclude that the common shift observed in CDS spreads is the outcome of the usual interdependence and that the strength in propagation mechanisms has not changed during the re- 51

Chapter 2: A Contagion Index for the Euro Area cent crisis. Similar to Favero and Giavazzi (2002), our model is embedded into a vector autoregressive framework that is able to capture interdependencies between variables in the system, taking into account their lagged dynamics. Bekaert et al. (2005) analyze contagion across international equity markets. They use a two-factor asset pricing model and provide evidence for global and regional market integration. Furthermore, they decompose sources of volatility into global, regional and local and measure their weights. A critical issue that has to be solved before pursuing any econometric inference is how to account for common shocks and to obtain idiosyncratic residuals. Our model is inspired by the Arbitrage Pricing Theory (APT), where asset returns are determined by a set of common factors and several characteristics related to idiosyncratic (non-diversifiable) risk. The second strand of literature associated with this chapter is related to common factors in asset returns. Berndt and Obreja (2010) study the determinants of European corporate CDS returns and identify as one of the main common factors the super-senior tranche of the itraxx Europe index, referred to as the economic catastrophe risk. Longstaff et al. (2011) analyze the determinants of sovereign credit risk and divide them into local economic variables, global financial market variables, global risk premium, and net investment flows into global funds. They find evidence that sovereign credit risk is driven mainly by global financial market variables or a global risk premium and to a lesser extent by local macroeconomic variables. Similar, by analyzing sovereign CDS spreads in the US and Europe, Ang and Longstaff (2011) show that systemic sovereign risk is more related to financial markets than to country-specific macro-characteristics. Beirne and Fratzscher (2012) find evidence for wake-up call contagion, suggesting that global financial markets are more influenced by economic fundamentals during periods of stress than in tranquil times. In contrast, regional contagion is less able to explain sovereign risks. Ejsing and Lemke (2011) investigate the co-movements of CDS spreads of euro area countries and banks with a common risk factor and find that sovereign CDS series became more sensitive to the common risk factor than banks CDS spreads. These findings motivate our choice for using several global and regional common factors, in order to filter the CDS returns. Kalbaska and Gatkowski (2012) study contagion among several European sovereigns using CDS data. They employ a correlation analysis and find that countries under stress (such as Greece, Ireland, Portugal, Spain and Italy) tend to trigger very little or no contagion among the core countries during their analyzed period. Our results show that the potential spillovers from Spain and Italy, especially during the devel- 52

Chapter 2: A Contagion Index for the Euro Area opments until July 2012, might be a game-changer from this perspective. We find that after the establishment of the EFSF in 2010 core countries are highly sensitive to shocks from periphery countries. Diebold and Yilmaz (2009, 2011, 2012) introduce and develop a framework based on forecast error variance decomposition for vector autoregressive (VAR) models. They implement their framework to equity markets and across different asset classes, building both on total and on directional volatility spillover measures. Among other results, they find that equity markets had an important contribution in transmitting spillovers to international markets and other asset classes. Claeys and Vašíček (2012) use a similar econometric framework as Diebold and Yilmaz (2011) and apply it to EU sovereign bond spreads relative to the German Bund. Their results show that spillover among sovereign yields increased considerably since 2007 but its importance is different across countries. They find that spillover effects dominate the domestic fundamental factors for EMU countries. Finally, Alter and Schüler (2012) find evidence for contagion from the financial sector to sovereign CDS before public rescue programs were launched, whereas sovereign CDS spreads do spill over to bank CDS series thereafter. 2.3 Econometric Methodology and Data Description In order to capture potential spillovers that could trigger financial contagion across the euro area, we apply an econometric framework based on daily sovereign and bank CDS spreads, see Appendix 2.A for details about the data. In addition we use a number of exogenous control variables. The CDS data series considered refer to senior five year spreads denominated in USD (for sovereigns) and in EUR (for banks). Our sample starts in October 2009 and ends on 3 July 2012. 3 Tests for unit roots suggest that the series are difference-stationary. Table 2.A.2 summarizes the main statistical characteristics of the data in log-levels and in first differences. In order to obtain time-varying parameters we decide to use a rolling-window estimation approach similar to that by Diebold and Yilmaz (2011). Since in our framework the rolling window size is 80 days, the first estimation point refers to end of January 2010. 3 The starting point was influenced by the availability of exogenous variables (i.e. itraxx SovX Western Europe index). This period also coincides with the first signs of sovereign debt problems related to Greece. 53

Chapter 2: A Contagion Index for the Euro Area 2.3.1 Vector autoregressive model with exogenous variables (VARX) We write a vector autoregressive model amended by several exogenous variables as: y 1,t α. = 1,0 γ p. + 11,i... γ 1n,i y 1,t 1...... i=1 y n,t α n,0 γ n1,i... γ nn,i y n,t 1 β q 11,j... β 1k,j Exo 1,t j u 1,t +...... +., u t iid(0, Σ u ) j=0 β n1,j... β nk,j Exo k,t j u n,t (2.1) In our case, we estimate a VARX model with two lags (p = 2) for the endogenous variables and contemporaneous exogenous variables (q = 0). 4 The vector of endogenous (y) variables consists of first log-differences of daily CDS spreads from eleven euro area countries: Austria (AT), Belgium (BE), Finland (FI), France (FR), Germany (DE), Greece (GR), Ireland (IE), Italy (IT), the Netherlands (NL), Portugal (PT) and Spain (ES). Together with the sovereign CDS spreads we use in each of the above mentioned countries an aggregated index for the domestic banks. 5 As a vector of exogenous variables (i.e. Exo t ) we utilise several control factors in first differences: the itraxx WE SovX index (as the main common factor of the Eurozone sovereign CDS spreads), the itraxx Senior Financials Europe index (as the main common factor of the European bank CDS spreads), the itraxx Europe index (that refers to 125 European investment grade companies across all sectors, including financials, that incorporates the overall credit performance of the Eurozone s real economy), the itraxx Crossover (that refers to 50 European companies with high yields/sub-investment grade, that refers to lower quality credit instrument for the real economy), the spread between 3 month Euribor and EONIA (a common measure of the interbank risk premium), the EuroStoxx 50 index (the representative European stock index), the US and the UK sovereign CDS series and the VIX index (that is based on S&P 500 option prices and it is regarded as a common measure 4 We choose two lags based on several constraints: should be consistent across variables and across time and more lags translates into a larger estimation window size. 5 With the exception of Finland and Ireland. For these two countries CDS data for banks is not available over a meaningful sample length. Bank variables together with exogenous variables are described in Table 2.A.1 in Appendix 2.A. Bank country-specific indices are weighted by assets of the component banks. 54

Chapter 2: A Contagion Index for the Euro Area of investors risk aversion). 6 As discussed in the previous section, by including the exogenous variables, we attempt to account for common/systematic factors, both regional and global, that affect at the same time all sovereign and bank CDS spreads. After accounting for all explanatory variables (the lagged endogenous variables and the exogenous control variables), the remaining residuals u from eq (2.1) represent the isolated idiosyncratic part. The explicit model with bank and sovereign variables is presented in Appendix 2.B. 7 2.3.2 Generalized impulse response functions (GIRF) Impulse response analysis provides a dynamic perspective of the interactions between the endogenous variables of the VARX process. It takes into account both the variance-covariance matrix if the residuals and the estimated Îş-coefficients from the VARX model in eq. (2.1). 8 Using the framework proposed by Koop et al. (1996) and Pesaran and Shin (1998), we specify the generalized impulse responses function (GIRF). 9 The generalized impulse response function can be written as: 1 ψ y 1 y 1 (n). = 1 0 σ 2 y 1,y 1 φ n Σ u ψy yn 1 (n) } {{ } }{{} }{{}. Normalization MA-coefficients VAR-covariance 0 } {{ } matrix matrix of residuals Selection vector (2.2) where φ n represents the matrix of moving average coefficients at lag n, which can be calculated in a recursive way from the VARX coefficient matrices (see Appendix 2.B); 6 The spread between 3m Euribor and 3m Eonia swap is the efunding equivalent of the spread between 3m LIBOR and 3m USD OIS, for the USD funding. Eonia swap (the variable used in our analysis) is an overnight index swap (OIS) on Eonia, which is a weighted average of all overnight unsecured lending interbank transactions, executed by a panel of banks. The Bloomberg ticker of this instrument is EUSWEC CMPN Curncy. Since our focus is centered on euro area banks and sovereigns this market indicator should better reflect interbank risk premium (see e.g. De Socio (2011)). 7 As a robustness check, we have also estimated our analysis in a two-step setup: first regressing the CDS returns on the common factors and control variables and second estimating a simple VAR model between the residuals from the first step. There are no significant differences in our results. 8 In the context of financial markets, it is difficult to assume a certain identification structure (like in the case of the monetary policy) and to use either Cholesky decomposition or the non-factorized impulse responses. 9 Following Lütkepohl (2007), we present in Appendix 2.B the steps towards a moving average (MA) representation of the VAR model. 55

Chapter 2: A Contagion Index for the Euro Area Σ u denotes the variance-covariance matrix of the residuals; σ 1 2 y 1,y 1 is the standard deviation related to the error of shock variable. The selection vector chooses the first variable as the impulse variable. The interpretation of the impulse responses is analogue to the interpretation of semi-elasticities. For instance, an impulse or a shock in variable ES (in period t = 0) means a unit increase in the structural error that leads to an increase of the respective CDS series by one standard deviation in percentage. The quantitative measure of potential spillover effects is computed as the average cumulated response of a variable in the following week, as percentage of the initial shock to the impulse variable (i.e. we normalize by the standard deviation of the impulse variable at day t = 0). 10 The average cumulated response of variable y 2 to a shock in the impulse variable y 1 is computed as the mean of the cumulated responses at day t = 0, day t = 1 and day t = 5: IR y1 y 2 = ψy 2 y 1 (0) + 1 h=0 ψ y 2 y 1 (h) + 5 h=0 ψ y 2 y 1 (h) 3 (2.3) The weighted averaging of the responses from these three days (over the following week) incorporates the feedback effects of the two lags and reflects temporary or persistent long-run effects of a potential shock in the impulse variable. 2.3.3 The spillover matrix Similar as in the framework described by Diebold and Yilmaz (2011) for the forecast error variance decomposition, we derive the impulse responses (IRs) from each variable to all other variables in the system and define the spillover matrix (see Figure 2.1). Notice that substituting the forecast error variance decomposition with the impulse responses from the GIRF framework would not change the basic economic implications of the results. In other words, we construct a matrix of potential spillover effects from each variable in the system (i.e. each variable is ordered first). These possible spillover effects answer the question How would variable y 2 (column variable) evolve in the following week if variable y 1 increases by one standard deviation? On each line of this matrix we write the responses of the other variables from a shock in the variable on the main diagonal (values on the main diagonal are set to zero). 11 10 By using this normalization, changes in volatility have no impact on our potential contagion measures and we can compare our results across variables and across time. 11 We will not take into account the main diagonal values in computing the average potential spillover (i.e. the Contagion Index and its components). 56

Chapter 2: A Contagion Index for the Euro Area Table 2.1: The Spillover Matrix Response Shock y 1 y 2... y n To Others y 1 IR y1 y2... IR Nj=1 y1 yn IR y1 yj, j 1 y 2 IR y2 y1... IR Nj=1 y2 yn IR y2 yj, j 2........ y n IR yn y 1 IR yn y 2... Nj=1 IR yn y j, j n From Others Nj=2 IR yj y 1 Nj=1 IR yj y 2... N 1 j=1 IR yj y n CI = 100 N(N 1) Ni=1 Nj=1 IR yi Note: Row variables are the origin of the unexpected shock. Column variables are the respondents or spillover receivers. CI represents the contagion index, calculated as the average response in the spillover matrix. The potential spillover effects are aggregated on each line and column and represent the total OUT and the total IN as potential contributions to contagion from and to each variable. Furthermore, based on the spillover matrix, we define several measures that allow for inference of the systemic contribution of each variable or the total spillover in the system. Let us first define the individual OUT spillover effects as the average sum of the impulse responses to others: N SE OUT,yi = IR yi y j. (2.4) j=1, j i Second we define the individual spillover IN effects as the average sum of the impulse responses from others: N SE IN, yi = IR yj y i. (2.5) j=1, j i Similar to net exports from the international trade, we define the bilateral net spillover effect as the difference between the impulse responses sent and received from/to another variable: SE NET, yi y j = IR yi y j IR yj y i. (2.6) The net measure in eq (2.6) enables us to distinguish between pure covariance spillovers and feedback effects. The net spillover effects represent the amplification 57

Chapter 2: A Contagion Index for the Euro Area contribution of the first two lags of the impulse variable to the response variable. In this way, we are able to capture the sequential feature associated with systemic events (see for example De Bandt et al. (2009)). Furthermore, this is also in line with the concept of systemic risk defined as the negative externality that one (financial) institution poses to the rest of the (financial) system. The net spillover effects help us to construct our new measure of systemic contribution, as defined below in eq (2.11). Bilateral net spillover effects for a pair of sovereigns can either be negative or positive and have the property that SE NET, yi y j + SE NET, yj y i = 0. Using SE NET, yi y j for each variable, we can set up a net spillover matrix that has the property of being anti-symmetric. This matrix shows the net potential spillover from y i y j and vice-versa. The total bilateral net spillover effects for variable y i is the sum of its bilateral net effects: N ( ) N T SE NET, yi = IRyi y j IR yj y i = SE NET, yi y j. (2.7) j=1, j i j=1, j i The sum of all T SE NET, yi in the system is equal to zero. In order to get the systemic contribution of each variable, we define the total net positive (TNP) spillover of the system. TNP spillover is the sum across all variables of their total net spillover effects (eq (2.7)) if T SE NET, yi is positive: N T NP Spillover = T SE NET, yi. (2.8) i=1; T SE NET, yi >0 We define further individual Total Flow as the sum of the spillovers sent and received by a certain variable y i : N N ( ) T F yi = IRyi y j + IR yj y i. (2.9) j=1 j i Total Flow of the entire system (TFS) is just the sum of all individual total flows: N T F S = T F yi. (2.10) i=1 Now we can introduce the systemic contribution of each variable y i in our system as the weighted sum between the ratio of the individual total net contagion effects and 58

Chapter 2: A Contagion Index for the Euro Area the total net positive spillover of the system, on one hand, and the ratio between the individual total flow and system s total flow, on the other hand: SC yi = α ( T SENET, yi T NP Spillover ) ( ) T Fyi + (1 α). (2.11) T F S Where α is the tuning parameter and takes values between 0 and 1. We can think of the systemic contribution in two ways: i) the share of the total excess spillovers, and ii) the share of the total system spillovers that are mediated by a certain variable. 2.3.4 Contagion indices Next, we introduce the contagion index of the system (here for sovereigns and banks) as: 100 N N CI = IR yi y N(N 1) j. (2.12) i=1 j i If we restrict the cumulative impulse responses in the interval [0, 1], our index will be bound between 0 and 100. 12 It shows the average potential spillover effects in our system, based on the previous 80-days interdependencies. When we relate to the total Contagion Index, we use the term Contagion Index of sovereigns and banks (i.e. CI sovs and banks). This index can be further decomposed into four main averaged components: CI-sovs (for the spillover among sovereigns), CI-banks (for the spillover among banks), CI from banks to sovereigns (for the spillover from banks to sovereigns) and CI from sovereigns to banks (for the spillover from sovereigns to banks). Let M be the number of sovereigns and P the number of banks (where M + P = N, the total number of endogenous variables), and sovereigns ordered first, then: CI sovs = CI bks = 100 M(M 1) 100 P (P 1) CI sovs bks = 100 M P CI bks sovs = 100 P M M M IR yi y j (2.13) i=1 j i N N IR yi y j (2.14) i=m+1 j i M N IR yi y j (2.15) i=1 j=m+1 N M IR yi y j (2.16) i=m+1 j=1 12 We relax this condition below in Section 2.5.3 and discuss some implications. Results remain qualitatively very similar. 59

Chapter 2: A Contagion Index for the Euro Area Finally, CI of sovereigns and banks can be re-written as the weighted average of its four components (see eq (2.21) in Appendix 2.C). 2.4 Results This section presents our main empirical results along two dimensions: dealing with simultaneity i.e. interaction between sectors and their entities; and addressing dynamics of time-varying parameters of the underlying rolling window models. First we show the spillover index in action by looking for example at the effects from Spanish sovereign CDS to all other variables in the system at two single points in time, i.e. focusing on a single sample window as a snapshot. Next we extend the static dimension to a dynamic analysis. We present empirical results for the contagion index for each point in time over the entire sample. Moreover we discuss systemic contributions of individual sovereign CDS to the total contagion index and we demonstrate how the indicators are evolving before and after key market and policy events. Finally we suggest a method to identify and determine thresholds for excessive spillovers i.e. the threshold beyond which we identify acute risks of contagion. 2.4.1 A static perspective We start our empirical analysis with the framework introduced in the previous section, by estimating spillover effects for individual points in time. An illustrative example: The case of Spanish sovereign CDS Focusing on Spanish sovereign CDS as impulse variable we present the results of isolated sample windows. The responses of other variables are compared over two static periods: at 13 January 2012 (based on the estimation period end of July 2011 - January 2012 i.e. 2011H2) and 15 June 2012 (based on the estimation period January 2012 until beginning of June 2012 i.e. 2011H1). The quantitative measure of a potential spillover effect is the cumulated response of a variable as percentage of the shock to the impulse variable. Two aspects are analysed: the impact of a shock in Spanish sovereign CDS on other sovereign CDS spreads; and the impact on CDS of bank groups in various countries. 60

Chapter 2: A Contagion Index for the Euro Area Figure 2.1 shows the potential cumulative impact on sovereign CDS spreads in response to a shock in Spanish CDS. The magnitude of spillover effects to Italian sovereign CDS decreased in the first half of 2012, from 83% to 68%. An unexpected shock of 100 bps to Spanish sovereign CDS would, therefore, translate into a 68 bps increase in Italian sovereign CDS over the following week (compared to nearly 83 bps in 2011H2). The potential spillover to other sovereign CDS has, however, increased dramatically during 2012H1. The biggest relative increase from 2011 to 2012 is the spillover to German CDS, which has grown by factor 22, from 2% to 44%. In absolute terms, the potential spillover is the highest in the case of French CDS (85%, up from 26%) and Austrian CDS (76%, up from 30%). Similar in the case of Italy, we notice that spillovers to Ireland and Greece have decreased. We therefore conclude that the potential impact on Non-Core countries decreased (with the exception of Portugal) at the expense of a higher potential impact on Core countries. Figure fig:2.2 shows the expected cumulated impact of a shock in other countries CDS to Spanish sovereign CDS, again for both periods. As can be seen, the reverse spillover effects to Spanish sovereign CDS are different, in most cases (sometimes even qualitatively when comparing over the two periods, see e.g. Portugal). In other words, these results translate into a positive net potential spillover from Spanish sovereign CDS to the other sovereign CDS spreads, showing the increased systemic relevance of the Spanish CDS spread in 2012H1. The potential spillover effects from Italian to Spanish CDS did not change and remained at around 67% in both periods. Hence, the results in Figure 2.2 can be interpreted as a successful robustness check for the validity of the economic interpretations of the estimated spillover measures. The potential impact of a shock in Irish, Greek or Portuguese sovereign CDS decreased in 2012H1 compared to 2011H2. 13 Turning to the potential spillover effects from Spanish sovereign CDS to bank CDSs, the development since 2011 is even more dramatic as can be seen in Figure 2.3. Here we split into two categories of Spanish banks by distinguishing the two large and complex banking groups from the others. 14 Apart from the Spanish banks, the impact of a shock to Spanish sovereign CDS is largest for Italian banks, which increased from 14% in 2011 to 48% over the second period. The impact on German 13 Although we consider Greece in our analysis, results for GR should be interpreted with caution since the CDS spreads reached implausible traded quotes and the Private Sector Involvement (PSI) program distorted these asset prices during 2012H1. 14 Group 1 (ES_bks_G1 ) consists of Banco Santander and BBVA, and the banks in Group 2 (ES_bks_G2 ) are Banco Pastor, Banco Popolar Espanol, Caja de Ahorros, and Banco Sabadell. See Appendix 2.A for a complete list of the country-specific bank CDS groups used. 61

Chapter 2: A Contagion Index for the Euro Area Figure 2.1: Potential impact of a Spanish sovereign CDS shock on other sovereign CDS spreads Figure 2.2: Potential impact on Spanish sovereign CDS from a shock in the other sovereign CDS spreads Note: The results can be read as follows: (left-panel) for example a 100 bps unexpected shock in the Spanish CDS would increase the French CDS by almost 30 bps (in the first period) and 85bps (in the second one); (right-panel) for example a 100 bps unexpected shock in the French CDS would increase the Spanish CDS by almost 20 bps (in the first period) and 40 bps (in the second one). Impact refers to the average cumulated impulse responses in the following week. bank CDS has increased by more than factor six, from 5% up to 34%. In the recent debt crisis a fundamental problem is the feedback loop between domestic banks and their sovereign. Our analysis shows strong evidence this mechanism. The potential spillover effects from a shock in the Spanish sovereign CDS to Spanish G1 banks have increased dramatically: 51% in 2012H1 compared to 17% in the 2011H2. Similarly, but slightly less, the impact of a shock to Spanish G2 banks has increased to 26%, compared to 11% in 2011. With regard to the robustness check, the same applies as with the effects of sovereigns on Spanish CDS. Results in Figure fig:2.4 show that the potential effects from individual bank CDSs on Spanish sovereign CDS are much less pronounced than vice versa, but they nevertheless increased as well in 2012H1 from close to zero (in 2011H2), in nearly all cases. A snapshot of spillover matrices- the use of heat-maps Table 2.2 and Table 2.3 present the entire picture on 21 June 2012, for all variables in the system. 15 In Table 2.2 shocks feed from row variables to column variables. 15 In order to be consistent across all countries, Spanish banks are merged in a single group. A similar snapshot is available in Appendix 2.D (Table 2.D.1 and Table 2.D.2) at the end of July 2011. A detailed description of the inference based on the two types of matrices and a comparison between the two periods is provided in Section 2.4.4. 62

Chapter 2: A Contagion Index for the Euro Area Figure 2.3: Potential impact of a shock in Spanish sovereign CDS on bank CDSs Figure 2.4: Potential impact of a shock in bank CDSs on Spanish sovereign CDS Note: Potential impact refers to the average cumulated impulse responses in the following week. Each row shows the spillover effects of an impulse to the variable in the first column. The responding variables are highlighted on the top row. In the last column (Sum OUT) we aggregate the total potential spillover sent (SE OUT,yi ), see eq (2.4) by each row variable and on the bottom row (Sum IN) we aggregate the total spillover received (SE IN, yi ), see eq (2.5) by each column variable. The four quadrants represent potential spillover effects: among sovereigns (top-left), among banks (bottom-right), from sovereigns to banks (top-right) and from banks to sovereigns (bottom-left). Greece and Greek banks have almost no impact on the rest of the variables, while they receive substantial spillover. Table 2.3 presents the net spillover effects for each pair of variables i.e. the difference between the spillovers sent and received by the row variable to the column variable. Looking at the net spillover matrix on 21 June 2012, Spain ranks first, based on the total net spillover T SE NET, yi, see eq (2.7), (the sum of net spillover effects to all variables in the Sum NET column). Among banking groups, German banks (DE_bks, ranked second) have an important influence on the rest of the system, with a net spillover of 4.34. Although French banks (FR_bks) have a negative total net spillover and therefore being net receivers of potential spillovers, they intermediate the largest potential spillover flow (the sum of SE OUT, yi and SE IN, yi in Table 2.2), corresponding to eq (2.4) and (2.5). 63

Table 2.2: The spillover matrix of EA sovereigns and banks (on 21 June 2012) Note: Variables in the first column are the impulse origin. Variables on the top row are the respondents to the shock. Values in the matrix represent the average cumulated spillover effect over the first 5 days. The intensity of a shock on a respondent is marked by different levels of colour (white means no impact and intense red means very strong impact). The cumulative impact is bound between 0 and 1. A value of 0.5 means that the response variable would be impacted in the same direction with an intensity of 50% the initial unexpected shock in the impulse variable. If the initial shock has a magnitude of 10 bps then the response variable is expected to increase by 5 bps in the following week. In the last column we have the aggregated impact sent (Sum OUT) by each row variable and on the bottom row the aggregated spillover received (Sum IN) by each column variable. The bottom-right cell (in bold) shows total spillover in the system (by dividing this value to the total number of non-diagonal cells i.e. 20x19 we obtain the contagion index of EA sovereigns and banks, as introduced in eq (2.12)). The results for GR and GR_bks should be interpreted with caution since the CDS spreads reached implausible traded quotes during this period.

Table 2.3: Net Spillover matrix of EA sovereigns and banks (on 21 June 2012) Note: If the value in the cell is negative (blue horizontal bar) it means that the row variable is the net receiver and the column variable is the net sender. If the value is positive (red horizontal bar) the column variable is net receiver and the row variable is net sender. The last column shows the sum of net spillover effects of the row variable. In case the NET sum spillover is positive (bold values) then the variable is a net sender of the system.

Chapter 2: A Contagion Index for the Euro Area 2.4.2 The dynamics of potential spillover effects In this sub-section we extend the snapshot perspective from Section 4.1 to a dynamic analysis. We analyse the responses from a shock in Spanish sovereign CDS based on a 80-day rolling-window. First, we start with a model that consists only of sovereign CDS changes. Second, we estimate a model with both sovereigns and banks, similar to eq (2.17) presented in Appendix 2.B. Time-varying impact on euro area sovereigns - the case of Spain Using a 80-day rolling window, we estimate the VARX coefficients and the residuals recursively. We further obtain the dynamics of the cumulated impact on euro area sovereigns. In Figure 2.5 we present our results of the impulse response analysis from a shock in ES sovereign CDS. We aggregate the impact on three different groups: Non-core (GR, IE, IT, and PT), EA (euro area) (AT, BE, FI, FR, DE, GR, IE, IT, NL and PT) and Core countries (AT, BE, FI, FR, DE, and NL). Each group index is a GDP weighted average of the individual responses. Static analysis has already signalled an increase in the interdependence between Spain and Core countries and an untightening the relationships within the Non-core countries in 2012H1. This trend reverses at the end of June 2012, after the G20 meeting and EU summit. There is clear evidence that the Non-core countries are more sensitive to a shock in the Spanish CDS than Core countries. An interesting result of our analysis is that during times of distress the gap between the two groups narrows while during tranquil episodes the gap widens. The amplification of potential contagion can be seen as a result of increased interdependences between sovereign CDS spreads. Time-varying impact on European banks The average time-varying potential spillover to European banks is depicted in Figure 2.6. There we show the differences between the effects from a shock in Spanish sovereign CDS and from a shock in German sovereign CDS. 16 During the entire data sample the mean impact from DE is slightly below the mean impact from ES (15.6% compared with 16.7%). The average potential spillover effect on banks is the mean of a shock from the 16 We merge Spanish banks (ES_bks_G1 and ES_bks_G2 ) in this analysis in order not to have biased results towards Spanish banks i.e. to have a uniform framework across all countries. 66

Chapter 2: A Contagion Index for the Euro Area Figure 2.5: The dynamics of the cumulated potential impact on CDS spreads of Non-core countries group (red), EA (euro area) (black) and Core countries group (green) from a shock in the Spanish sovereign CDS Note: Core refers to the average impact on AT, BE, FI, FR, DE, and NL weighted by GDP; EA refers to the average impact on the entire sample of Eurozone countries: AT, BE, FI, FR, GR, DE, IE, IT, NL, and PT weighted by GDP; Non-core refers to the average impact on GR, IE, IT and PT weighted by GDP. respective country (here e.g. ES and DE) at the end of each rolling window. 17 As can be seen in Figure 2.6, at the beginning of April 2012, the average impact from a shock in Spanish sovereign CDS exceeds the mean impact (over the entire period) and exceeds the previous peak that was reached at the end of November 2011. By mid-may 2012 the average potential spillover effects from a Spanish shock reaches the level of 65%. In other words, the entire European banking system reacted strongly to the Spanish sovereign debt crisis during the April-June 2012 period. After the G20 and EU summits, the potential contagion pressure to the European banking system mitigates. This analysis highlights the advantage of monitoring the time-varying potential impact from each variable of the system. 17 This can be refined with weights from the BIS foreign claims exposures as in eq (2.27) of Appendix 2.C. 67

Chapter 2: A Contagion Index for the Euro Area Figure 2.6: Average cumulated impact on European banks from a shock in the Spanish sovereign CDS ( AvgESbks, red) and from a shock in the German government CDS ( AvgDEbks, green) Note: AvgESbks and AvgDEbks refer to the average potential impact on European banks from a shock in the Spanish sovereign CDS, and German sovereign CDS respectively; MeanImpactES and MeanImpactDE are the mean impact over the entire sample from a shock in Spanish sovereign CDS, and German sovereign CDS respectively. 2.4.3 The euro area Contagion Index The euro area Contagion Index of sovereigns In this sub-section we analyse the dynamics of the Contagion Index for all sovereigns (CI-sovs) as introduced in eq (2.13) and shown in Figure 2.7. We highlight several important events in the Eurozone that preceded changes in the CI-sovs. 18 We also present the sovereign CDS series in levels from all analysed countries (right axis, with the exception of the Greek sovereign CDS). During the analysed period, CI-sovs takes values between a minimum value of 15.34 (on 28 October 2010) and a maximum level of 43.33 (on 09 June 2010). As can be seen in Figure 2.7, several news/events (e.g. policy related actions) had a decreasing impact on the index. This aspect will be developed in detail in sub-section 4.6. During the period related to the Spanish banking/sovereign debt crisis the sovereign contagion index reached a peak on 22 June 2012 (42.36) very close to the 2010 peak. 18 The description of selected events and the exact dates are presented in Table 2.A.4 (in Appendix 2.A). 68

Chapter 2: A Contagion Index for the Euro Area After the G20 and EU summit, the index drops to around 34 (on 3 July 2012). Figure 2.7: Sovereign CDS series (right axis; in basis points) and the EA Contagion Index (only for sovereigns; left axis; the purple-grey area) Note: CI-sovs is the Contagion Index of sovereigns, as introduced in eq (2.13). It takes values between 0 and 100. It is calculated as the average potential spillover effect from each sovereign to the others. The list of events marked by vertical lines is presented in Appendix 2.A, Table 2.A.4. The euro area Contagion Index of sovereigns and banks In this sub-section, we focus on the results from our joint analysis of banks and sovereigns. To exemplify our results we provide the contagion matrices (both in absolute and in net terms) for some particular dates. As previously mentioned, in this analysis, the two Spanish banking groups (ES_bks_G1 and ES_bks_G2 ) are merged into a single group (ES_bks) in order to be consistent across all countries. 19 In the sample period under scrutiny (Figure 2.8), the Contagion Index for banks (CI-banks) takes values between a minimum level of 18.4 (reached on 16/02/2012, 19 Similar, the new single group of Spanish banks (ES_bks) is weighted by banks total assets. See Table 2.A.2. 69

Chapter 2: A Contagion Index for the Euro Area between the two LTROs) and a maximum level of 50.2 (on 3 Nov. 2010 around time when Ireland has seek a bailout). At the beginning and towards the end of our sample, CI-banks and CI-sovs are characterized by a tighter co-movement. During most of that period, the average potential spillovers among banks exceed those between sovereigns. This characteristic is reversed in the first half of 2010 and in 2012. The spillover index for the entire system (both banks and sovereigns) has a slight upward trend. We conclude in the following section that this provides evidence for an increasing interconnectedness between banks and sovereigns, i.e. a tightening of the nexus between these two sectors. Figure 2.8: EA Contagion Indices: only sovereigns (CI-sovs; black), only banks (CI-banks; red) and the entire system (the average potential spillover effect from the Contagion matrix; CI banks and sovs; green) Note: CI banks and sovs, as introduced in eq (2.12), is not the average of CI-banks and CI-sovs. It summarizes the information from all four sub-components i.e. the entire system of banks and sovereigns, including the potential spillover effects from banks to sovereigns and vice-versa. The feedback loop between sovereigns and banks We now turn to the indices related to spillover effects on banks from a shock in sovereign CDSs and vice-versa, see Figure 2.9 and eqs (2.15) and (2.16). These two indices capture the average interdependence between the sovereign and the banking sector. After the collapse of Lehman Brothers in 2008, governments in many countries have contributed to bailing out financial institutions. This has implied at 70

Chapter 2: A Contagion Index for the Euro Area least a partial credit risk transfer from banks to sovereigns. Over the last two years, both indices increased more than twice their initial values in February 2010. At the beginning of the sample, the contagion index from banks to sovereigns takes a value of around eight. It reaches the peak level of 37, after the publication of the stress test results for the European banking industry. This period reflects also a widening of the gap between the two indices. On the other side, the contagion index from sovereigns to banks takes a value of around five at the beginning, and peaks during the Spanish sovereign debt crisis in June 2012, at a value of 26.9, more than five times higher than at the beginning of the sample. Figure 2.9: Average potential spillover from banks to sovereigns (red) and from sovereigns to banks (black) Note: CI banks to sovs refers to the average spillover effects sent by banks to sovereigns as introduced in eq (2.16). CI sovs to banks refers to the average spillover effects sent by sovereigns to banks as introduced in eq (2.15). 2.4.4 The spillover and net spillover matrices In this sub-section, we present both spillover and net spillover matrices of sovereigns and banks together with several measures of systemic relevance of our variables in the system derived from these matrices. For illustration purposes, we present two 71

Chapter 2: A Contagion Index for the Euro Area snapshots: first on 18 July 2011 (after bank stress tests results are published) and second on 21 June 2012 (after the G20 summit). At each point in time, both spillover matrices are based as before on an information set of past 80 days. Table 2.D.1 and Table 2.D.2 (in Appendix 2.A) show the spillover and the net spillover matrices on 18 July 2011. The four quadrants reflect the flow of different components of the index: interactions between sovereigns (top-left), spillover effects from sovereigns to banks (top-right), interactions between banks (bottom-right) and spillover effects from banks to sovereigns. The overall picture shows that stress in the banking sector impacts severely on euro area sovereigns. The information related to the sent and received spillover effects together with the total flow is summarized in Table 4. As discussed above, Tables 2.2 and 2.3 present the contagion and the net spillover matrices on 21 June 2012. Compared with the two matrices from July 2011, this period is characterised by an overall elevated spillover level in all four quadrants. Both sovereigns and banks strongly impact on each other. Focusing on the net spillover matrix, we can identify the main drivers of potential contagion in our system. This relates to the ranking of variables as presented in Table 2.4 and Table 2.5. Table 2.4: Ranking of NET senders and receivers of spillover effects on the 18 July 2011 Variable Sum OUT (1) Sum IN (2) Sum NET (1)-(2) SC α=0 Rank (i) Total FLOW (1)+(2) SC α=1 Rank (ii) SC α=0.75 Rank (iii) SC α=0.5 Rank (iv) SC α=0.25 DE_bks 10,30 5,55 4,75 1 15,85 2 13,08 1 10,30 1 7,53 1 IT_bks 8,12 4,83 3,29 2 12,95 7 10,54 5 8,12 3 5,71 2 AT_bks 5,79 2,71 3,09 3 8,50 16 7,15 13 5,79 8 4,44 4 AT 8,95 7,45 1,51 4 16,40 1 12,68 2 8,95 2 5,23 3 BE_bks 5,16 4,15 1,01 5 9,32 14 7,24 11 5,16 9 3,08 7 NL_bks 4,40 3,50 0,90 6 7,90 17 6,15 16 4,40 15 2,65 10 PT_bks 8,02 7,19 0,83 7 15,21 3 11,62 3 8,02 4 4,43 5 ES_bks 7,32 6,91 0,41 8 14,22 4 10,77 4 7,32 5 3,86 6 PT 3,70 3,47 0,23 9 7,17 18 5,43 17 3,70 17 1,96 14 DE 5,01 4,91 0,10 10 9,92 11 7,46 10 5,01 11 2,55 11 BE 4,64 5,01-0,38 11 9,65 13 7,14 14 4,64 13 2,13 12 NL 4,60 5,21-0,61 12 9,81 12 7,20 12 4,60 14 1,99 13 FR 6,71 7,40-0,69 13 14,11 5 10,41 6 6,71 6 3,01 8 FR_bks 6,15 6,89-0,74 14 13,04 6 9,59 7 6,15 7 2,71 9 FI 1,53 2,44-0,91 15 3,97 19 2,75 19 1,53 19 0,31 18 IE 4,68 5,63-0,95 16 10,30 10 7,49 9 4,68 12 1,86 15 GR_bks 0,82 2,82-2,01 17 3,64 20 2,23 20 0,82 20-0,60 19 ES 5,04 7,37-2,33 18 12,41 8 8,72 8 5,04 10 1,35 16 IT 3,73 6,67-2,94 19 10,39 9 7,06 15 3,73 16 0,40 17 GR 2,00 6,58-4,58 20 8,57 15 5,29 18 2,00 18-1,29 20 NET SENDERS NET RECEIVERS Note: Variables are ordered from the highest to lowest net spillover effect in the system (in column Rank (i)). Rank (i) refers to SC α=0. Rank (ii) refers to SC α=1. Rank (iii) refers to SC α=0.75. Rank (iv) refers to SC α=0.5. Rank (v) refers to SC α=0.25. Rank (v) Tables 2.4 and 2.5 rank our variables according to the net spillover contribution 72

Chapter 2: A Contagion Index for the Euro Area Table 2.5: Ranking of NET senders and receivers of spillover effects on the 21 June 2012 Variable Sum OUT (1) Sum IN (2) Sum NET (1)-(2) SC α=0 Rank(i) Total FLOW (1)+(2) Rank(ii) SC α=0.75 Rank(iii) SC α=0.5 Rank(iv) SC α=0.25 Rank(v) SC α=1 ES 8,50 3,87 4,63 1 12,38 11 10,44 8 8,50 6 6,57 3 DE_bks 9,83 5,50 4,34 2 15,33 5 12,58 4 9,83 2 7,08 1 IT 10,10 6,65 3,45 3 16,75 2 13,42 1 10,10 1 6,78 2 BE 9,52 6,97 2,55 4 16,49 3 13,00 2 9,52 3 6,04 4 AT 8,68 6,52 2,16 5 15,20 6 11,94 6 8,68 4 5,42 5 IE 7,75 6,00 1,75 6 13,75 7 10,75 7 7,75 8 4,75 7 IT_bks 8,62 6,95 1,67 7 15,57 4 12,10 5 8,62 5 5,14 6 NL_bks 6,43 5,38 1,05 8 11,81 12 9,12 10 6,43 10 3,74 8 BE_bks 2,66 1,87 0,79 9 4,53 19 3,59 19 2,66 18 1,73 16 PT_bks 5,76 5,27 0,49 10 11,03 13 8,39 13 5,76 11 3,13 11 FI 6,52 6,53-0,01 11 13,04 9 9,78 9 6,52 9 3,25 9 ES_bks 5,01 5,06-0,05 12 10,07 16 7,54 15 5,01 14 2,48 13 DE 5,18 5,28-0,10 13 10,46 15 7,82 14 5,18 13 2,54 12 AT_bks 4,16 4,40-0,24 14 8,55 18 6,36 17 4,16 16 1,96 15 FR 5,57 7,08-1,52 15 12,65 10 9,11 11 5,57 12 2,02 14 FR_bks 8,05 9,72-1,68 16 17,77 1 12,91 3 8,05 7 3,18 10 GR 0,13 3,23-3,09 17 3,36 20 1,75 20 0,13 20-1,48 19 NL 3,43 7,41-3,99 18 10,84 14 7,13 16 3,43 17-0,28 17 PT 4,20 8,99-4,79 19 13,19 8 8,69 12 4,20 15-0,30 18 GR_bks 0,59 8,01-7,42 20 8,60 17 4,60 18 0,59 19-3,41 20 NET SENDERS NET RECEIVERS Note: Variables are ordered from the highest to lowest net spillover effect in the system (in column Rank (i)). Rank (i) refers to SC α=0. Rank (ii) refers to SC α=1. Rank (iii) refers to SC α=0.75. Rank (iv) refers to SC α=0.5. Rank (v) refers to SC α=0.25. (Rank (i)) to the system in July 2011 and at the end of June 2012. 20 The ranking of net senders for the first period that ends on 18 July 2011 (i.e. after the publication of the results from the EBA bank stress-testing exercise) is clearly dominated by banking groups. German, Italian and Austrian banks are the biggest net senders of spillover effects. Biggest net spillover receivers (at the bottom of the table) are sovereign CDS of Spain, Italy and Greece. The period (ending on 21 June 2012 after the G20 summit) is qualitatively remarkably different. Sorting by the net spillover effects, the top five is dominated by sovereign CDS spreads: Spain, Italy, Belgium, and Austria. German, Italian and Dutch banks remain in the first 10 most important net spillover senders, but on lower positions than in the first period. At the bottom part, Greece, French and Greek banks seem to be the most vulnerable to potential contagion in both periods. This is also consistent with the peak in our Contagion Index around that period. Moreover, Italy, Spain and Ireland that are highly receptive to spillover effects in the first period, become top net senders in the second period. French and German banks seem to be among of the important nodes by total flow in both periods, reflecting their systemic relevance in the euro area sovereign-banking system. 20 As a robustness check to rank (i), we provide also SCs for different weights (α s) as suggested in eq (2.11). In the first period (18 July 2011), rankings are similar across different weights between net and total spillover share. In the second period (21 June 2012), the differences between Rank (i) and Rank (ii) are stronger. 73

Chapter 2: A Contagion Index for the Euro Area 2.4.5 The systemic contribution of sovereigns Next we focus more closely on the total net positive (TNP) spillover, as defined in eq (2.8), which captures the sum of net positive spillovers from all banks and sovereigns. In Figure 2.10 we plot the time-varying systemic contributions (i.e. where the weight (α) on individual net spillover in the TNP spillover, in eq (2.11) equals one) of the IMF/EU program countries (Greece, Ireland, and Portugal; dotted lines; left-hand scale) together with other countries being currently under stress, namely Spain and Italy (grey and red lines; left-hand scale). As introduced in eq (2.11), the systemic contribution (SC) of each variable y i from our system is the ratio between the individual total net potential spillovers to each other variables and TNP spillover of the system. The SC of Greece is most of the time in negative territory, meaning that it receives net potential spillover from the others. The SC of Ireland decreases after the implementation of EFSF. Furthermore, the SC of Portugal becomes negative after the implementation of LTRO I. The SCs of Italy, Spain and Ireland fluctuate between -0.2 and 0.25. From summer 2011 onwards, their weights have a clear upward trend. Since March 2012, Italy and Spain have a positive and significant SC. The main observation is that after countries receive aid from EU/IMF the overall systemic risk significantly decreases. This can be interpreted as a partial transfer of (tail-) risk from the program countries to the EFSF after the latter was established. Finally, the evolution of the TNP spillover follows a similar pattern compared with the contagion indices described in previous sections. To sum up, this analysis highlights in Figure 2.10 time-varying systemic contributions of several euro area countries from our system of banks and sovereigns together with the impact of some relevant events presented in Table 2.A.4. 2.4.6 The impact of different economic/policy events on the contagion index An important qualitative robustness check for any empirical approach is in-sample consistency (or fit of the data ) with historical events. Here, we analyze both qualitatively and quantitatively the short-term impact of different events on our proposed contagion indices. Together with the cumulated returns of components of the contagion index, the events are summarized in Table 2.A.4 and depicted in Figure 2.11. Several events had a positive effect on all four components: the establishment of the EFSF (Event 2), the announcement of the second CBPP (Event 6) and the 25bps rate-cut by the ECB (Event 7; with the exception of the CI sovereigns that 74

Chapter 2: A Contagion Index for the Euro Area Figure 2.10: Systemic contributions of GIIPS countries (left axis) and the Total Net Positive (TNP) Spillover (right axis) Note: TNP Spillover (right axis) is the Total Positive Net Spillover in our system of banks and sovereigns (normalized by the Contagion Index, in this figure). Time-varying systemic contributions of each sovereign are smoothed with the HP filter (smoothing parameter = 5000). SC are considered with α = 1 in eq (2.11). do not have a negative return over both +10-days interval and ±10-days interval). The nationalization of BANKIA (Event 10) is the event that is related to the most adverse impact on all contagion components. There are two events that suggest evidence for a clear risk transfer from banks to sovereigns: when EU offers support to Greece (Event 1) and after Ireland seeks financial support (Event 3). We find that there are also three events in which we observe afterwards lower potential contagion among sovereigns and likewise from sovereigns to banks. However, at the same time this analysis shows an increase of the interdependence among banks themselves: LTRO II (Event 9) and Event 4, when Portugal requests activation of the aid mechanism. 2.4.7 Critical spillover thresholds for contagion To provide a stylized example suppose financial variable X is identified as a net spillover sending variable. Assume further that from an observed empirical distri- 75

Chapter 2: A Contagion Index for the Euro Area Figure 2.11: Impact on Contagion Index components at some specific news/policy events Note: Each window refers to 10 days before and after the event. A list of the complete description of events and the cumulative returns are presented in Table 2.A.4 (in the Appendix 2.A). 76

Chapter 2: A Contagion Index for the Euro Area bution it is known how often that variable has increased at least n basis points over a given time unit. Finally assume, that the potential contagion risk from X to Y is a function of the magnitude with which Y reacts to a shock induced by X. Then there exists a threshold beyond which reactions in responses of Y are considered to be excessive and hence trigger contagion. In Table 2.6 we show how to apply this idea to our model. We first derive the empirical distribution of daily changes in CDS from a sample of more than 700 observations and from there we take the critical magnitudes of spillover thresholds from characteristic percentiles. This is presented in the left panel of Table 2.6 where for illustrative purposes we restrict ourselves to four shock-inducing variables: sovereign CDS and bank CDS (both from ES and IT). Obtaining a threshold spillover for contagion follows along a two-step algorithm. First, one has to choose a tail probability (from the left panel in Table 2.6) according to a subjective risk aversion. Second, one has to pick a subjectively tolerable increase of basis points for a shock-response variable. Table 2.6 accounts for levels from 15 to 50 basis points (right hand panel). Consider, as example, first a 0.1% subjective tail risk probability for a Spanish government CDS (the probability of a day-to-day increase of more than 54 basis points). Second, assume that a tolerable magnitude for a (here day-to-day) increase in any response variable as a response to a shock in a Spanish sovereign CDS is 20 basis points. The critical threshold level would then be a 37% spillover effect in eq (2.4) from Spanish sovereign CDS to any chosen variable. For a less risk averse player who chooses a subjective tail probability of 5% and who picks as well 20 basis points as tolerable response, the subjective threshold of contagion is higher, i.e. 87%. These are two extreme examples. However, the snapshot taken in June 2012 (see Figure 2.1) shows that even an extreme non-risk-averse player would perceive the spillover effect from Spanish to French sovereign CDS (bigger than 90%) as risk of contagion. Risk-averse players who fear contagion at much lower spillover levels would conclude to observe strong evidence for contagion in June 2012 as the threshold of 37% is passed for almost all variables. 21 21 In a more sophisticated way we will simulate critical values based on Monte Carlo techniques. We leave this for future research. 77

Chapter 2: A Contagion Index for the Euro Area Table 2.6: Critical spillover levels for contagion of an unexpected shock in the impulse variable: A. Spanish (ES) sovereign CDS; B. Italian (IT) sovereign CDS; C. Spanish banks (ES_bks) CDS; and D. Italian banks (IT_bks) CDS Note: Historical probabilities of events refer to our analyzed period: October 2009 - July 2012, 717 observations in total. We do not report any spillover thresholds of the response variable above 200%. 2.5 Robustness and motivation of setup parameters To assess the sensitivity of choices and assumptions with respect to the specification of our model we apply several robustness checks. We discuss the potentially timevarying distributions of residuals from the estimated VARX system and some model constraints. The choice of the window size is presented in the Appendix 2.E. 2.5.1 Differences in distributions of residuals Furthermore, we show the results for the residuals distributions over time. In order to check whether these distributions change, we employ the two-sample Kolmogorov- 78

Chapter 2: A Contagion Index for the Euro Area Figure 2.12: Rejection of the Null hypothesis of the Kolmogorov-Smirnov (KS) test Note: The test compares the sample of the VAR residuals at time t with the sample of the residuals from the VAR estimated 80days before. Values of 1(blue bars) refer to the rejection of the null hypothesis (i.e. same distribution for the two samples) at 1% confidence level. Smirnov (KS test) 22 test to compare whether the distribution at any time = t is different from the distribution 80 days before. Figure 2.12 presents the results and persistence of the test rejection in the analyzed sample. The first test refers to the observation in June 2010 that is compared with our first distribution at the end of January 2010. There are at least three different regimes in our sample. In order to get a more detailed picture about the time-varying distributions we present in Figure 2.13 the second, third and fourth moment of the empirical distribution of the residuals. These results motivate our choice of a VAR with time-varying parameters, since there is clear evidence of structural breaks. 2.5.2 Relaxing restrictions imposed on impulse responses In the analysis above, when estimating the Contagion Index and its components we restricted the IRs to take values in the [0,1] interval. We relax the restriction imposed on the impulse response functions and Figure 2.14 shows that results do not change dramatically. In particular, in stress periods the differences are very small, while in calm periods the [0,1] restriction yields a higher contagion index. 22 KS test compares the distributions of two data samples. The null hypothesis is that both samples are from the same continuous distribution. The alternative hypothesis is that they are from different continuous distributions. If the result is 1 the test rejects the null hypothesis at the 1% significance level; and if is 0 the null hypothesis cannot be rejected. 79

Chapter 2: A Contagion Index for the Euro Area Figure 2.13: Moments of the sample distributions of residuals from the VAR model Note: Variance and kurtosis (Left-axis) and skewness (Right-axis). Figure 2.14: The Contagion Index with restricted and unrestricted IRs Note: The restriction imposed on the cumulative impulse responses is to be bounded by the [0,1] interval. 80

Chapter 2: A Contagion Index for the Euro Area 2.6 Conclusion and Outlook During the recent sovereign debt crisis a prominent theme discussed by academics, policy makers and market participants is that of contagion. There is an urgent need for tools and instruments to provide reliable information - in particular for policy makers - to take effective and efficient policy measures. New tools for the measurement of contagion and spillover effects will have the potential for playing an important role in monitoring and identifying systemic risks. In this chapter we present an empirical framework that is able to quantify spillover effects. Based on standard VAR techniques we use generalized impulse response functions to calculate spillover indices. Following the definition of contagion by (Allen and Gale, 2000) who interpret it as a consequence of excess spillover, we propose a method to construct contagion indices based on measures for aggregated spillover effects. We define spillover as the transmission of an unexpected but identified shock from one variable to receiving or responding variables in the system. Aggregation of spillover effects at each point in time yields a contagion index. We apply our method to investigate interactions between banks and sovereigns and use their CDS spreads as market-based asset prices from a typically liquid market. The contagion index proposed in this chapter can be disentangled into four components which signal excess spillover i) amongst sovereigns, ii) amongst banks, iii) from sovereigns to banks, iv) vice-versa. By using a rolling-window estimation technique we are able to capture changes of interdependencies over time, in quasi-real time, which allows us to gauge the effectiveness of policy interventions. Our measure can be used in a static or dynamic context, by showing the state of potential contagion at a certain point in time or a time dependent contagion index. Presenting interdependent spillover magnitudes in a system e.g. by attaching different intensities of colour corresponding to the magnitude of a particular spillover effect generates a so called heat map. By looking at consecutive points in time those heat maps change colour and illustrate the build-up or diminishing of potential contagion. Features of this toolbox allow us to identify systemically relevant entities (i.e. country specific banking sectors and sovereigns) from the proposed set of sovereigns and banks in our system. In this chapter we have proposed a simple method to compute thresholds for excessive spillovers, based on empirical distributions of CDS changes in combination with subjective preferences. Our results show clear growing interdependencies between banks and sovereigns, that represents a potential source of systemic risk. Euro area sovereign creditworthiness 81

Chapter 2: A Contagion Index for the Euro Area carries a growing weight in the overall financial market picture, with a sub-set of sovereigns that can potentially produce negative externalities to the financial system. We find that several previous policy interventions had a mitigating impact on spillover risks. In our application we find that a shock in Spanish sovereign CDS reveals an elevated impact on both euro area sovereigns and banks during the first half of 2012, compared to 2011. Moreover, spillover effects from a shock to Spanish sovereign CDS to Eurozone core countries and to non-core countries become more similar in magnitude during 2012. We also found strong evidence that the nexus between sovereigns and banks amplified strongly until the end of June 2012. However, systemic contributions of Greece, Portugal and Ireland decrease remarkably after the implementation of IMF/EU programs. Nevertheless, Ireland regains its positive net spillover status since the beginning of 2012. The setup of the EFSF and the decision of the two LTROs in December 2011 have a mitigating impact on all four contagion index components. By contrast, nationalization of Bankia in Spain had a further growing impact on all four contagion index components. For future research, we plan to extend our approach along various avenues. We will extend our tool by incorporating extreme realizations and capturing the dynamics using extreme-value-theory as well as Monte Carlo simulations. We will further improve the statistical and econometric framework tool and derive statistical distributions of impulse response functions. With regard to economic applications the next steps will be to extend the model to real economy entities and capture potential spillovers to different sectors in order to shed light on macro-financial interlinkages. Bibliography Acharya, V., I. Drechsler, and P. Schnabl (2011). A Pyrrhic victory? Bank bailouts and sovereign credit risk. NBER Working Paper Series No. 17136. Allen, F. and D. Gale (2000). Financial contagion. Journal of Political Economy 108, 1 33. 82

Chapter 2: A Contagion Index for the Euro Area Alter, A. and Y. Schüler (2012). Credit spread interdependencies of european states and banks during the financial crisis. Journal of Banking and Finance 36(12), 3444 3468. Ang, A. and F. Longstaff (2011). Systemic sovereign credit risk: Lessons from the u.s. and europe. NBER Working Paper No. 16982. Beirne, J. and M. Fratzscher (2012). The pricing of sovereign risk and contagion during the european sovereign debt crisis. Journal of International Money and Finance forthcoming. Bekaert, G., C. Harvey, and A. Ng (2005). Market integration and contagion. Journal of Business Volume 78(1), 39 70. Berndt, A. and I. Obreja (2010). Decomposing European CDS returns. Review of Finance 14, 189 233. Bicu, A. and B. Candelon (2012). On the importance of indirect banking vulnerabilities in the eurozone. Maastricht University Working Paper Series RM/12/033. BIS (2011). The impact of sovereign credit risk on bank funding conditions. Basel: Bank for International Settlements. Caceres, C., V. Guzzo, and M. Segoviano (2010). Sovereign spreads: Global risk aversion, contagion or fundamentals? IMF Working Paper. Caporin, M., L. Pelizzon, F. Ravazzolo, and R. Rigobon (2012). Measuring sovereign contagion in europe. Norges Bank Working Paper 2012/05. Claeys, P. and B. Vašíček (2012). Measuring sovereign bond spillover in europe and the impact of rating news. Working paper. Constâncio, V. (2012). Contagion and the european debt crisis. Banque de France, Financial Stability Review No. 16, 109 121. De Bandt, O., P. Hartmann, and J. L. Peydro (2009). Systemic risk in banking: An update. In In: A. Berger, P. Molyneux & J. Wilson, eds. Oxford Handbook of Banking. Oxford University Press, UK, pp. 633-672. De Bruyckere, V., M. Gerhardt, G. Schepens, and R. Vander Vennet (2012). Bank/sovereign risk spillovers in the european debt crisis. National Bank of Belgium Working Paper Research No. 232. 83

Chapter 2: A Contagion Index for the Euro Area De Santis, R. A. (2012). The euro area sovereign debt crisis: save haven, credit rating agencies and the spread of the fever from greece, ireland and portugal. ECB Working Paper No. 1419. De Socio, A. (2011). The interbank market after the financial turmoil: Squeezing liquidity in a lemons market" or asking liquidity on tap". Banca d Italia Working Paper No. 819. Diebold, F. X. and K. Yilmaz (2009). Measuring financial asset return and volatility spillovers, with application to global equity markets. Economic Journal 119, 158 171. Diebold, F. X. and K. Yilmaz (2011). On the network topology of variance decompositions: Measuring the connectedness of financial firms. PIER Working Paper, 11 031. Diebold, F. X. and K. Yilmaz (2012). Better to give than to receive: Predictive directional measurement of volatility spillovers. International Journal of Forecasting Issue 28, 57 66. Donati, P. (2011). Modelling spillovers and measuring their impact and persistence: Application to cds spreads during the euro area sovereign crisis. ECB unpublished manuscript. Dornbusch, R., Y. Park, and S. Claessens (2000). Contagion: Understanding hoe it spreads. The World Bank Research Observer 15(2), 177 197. Dungey, M., R. Fry, B. Gonzalez-Hermosillo, and V. Martin (2004). Empirical modelling of contagion : A review of methodologies. IMF Working Paper WP/04/78, 1 32. Ejsing, J. and W. Lemke (2011). The Janus-headed salvation: Sovereign and bank credit risk premia during 2008-2009. Economics Letters 110, 28 31. Favero, C. and F. Giavazzi (2002). Is the international propagation of financial shocks non linear? evidence from the erm. Journal of International Economics Vol. 57(1), 231 246. Fontana, A. and M. Scheicher (2010). An analysis of euro area sovereign CDS and their relation with government bonds. ECB Working Paper No. 1271. Forbes, K. (2012). The big C": Identifying and mitigating contagion. MIT Sloan School Working Paper, 4970 12. 84

Chapter 2: A Contagion Index for the Euro Area Forbes, K. and R. Rigobon (2002). No contagion, only interdependence: Measuring stock market co-movements. Journal of Finance 18(4), 2223 2261. Gross, M. and C. Kok (2012). A mixed-cross-section gvar for countries and banks. ECB Working paper forthcoming. Kalbaska, A. and M. Gatkowski (2012). Eurozone sovereign contagion: Evidence from the cds market (2005-2010). Journal of Economic Behaviour and Organization forthcoming. Koop, G., M. H. Pesaran, and S. M. Potter (1996). Impulse response analysis in nonlinear multivariate models. Journal of Econometrics 74(1), 119 147. Longstaff, F., J. Pan, L. Pedersen, and K. Singleton (2011). How sovereign is sovereign credit risk? American Economic Journal: Macroeconomics 3, 75 103. Lütkepohl, H. (2007). New Introduction to Multiple Time Series Analysis (2nd ed.). New York: Springer-Verlag. Merler, S. and J. Pisani-Ferry (2012). Hazardous tango: sovereign-bank interdependence and financial stability in the euro area. Banque de France - Financial Stability Review Issue April. Palladini, G. and R. Portes (2011). Sovereign cds and bond pricing dynamics in the euro-area. NBER Working Paper No. 17586, 1 35. Pesaran, H. H. and Y. Shin (1998). Generalized impulse response analysis in linear multivariate models. Economics Letters 58, 17 29. Segoviano, M. (2006). Consistent information multivariate density optimization methodology. Financial Markets Group Discussion Paper No. 557. Zhang, X., B. Schwaab, and A. Lucas (2011). Conditional probabilities and contagion measures for euro area sovereign default risk. Tinbergen Institute Discussion Paper TI 11-176/2/DSF29. 85

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Chapter 2: A Contagion Index for the Euro Area Appendix 2.A Description of variables and events Table 2.A.1: Composition and description of bank-specific and exogenous variables Name of the Variable Composition or description Endogenous variables AT_bks Erste Group Bank, Raiffeisen Zentralbank Österreich BE_bks DEXIA Group, KBC Group FR_bks BNP Paribas, Credit Agricole, Societe Generale DE_bks Deutsche Bank, Commerzbank, DZ Bank, Landesbank Baden-Württemberg, Landesbank Hessen-Thüringen, HSH Nordbank, WestLB GR_bks EFG Eurobank Ergas, National Bank Of Greece IT_bks Unicredito, Intesa Sanpaolo, Banca Montepaschi Di Siena, Unione Di Banche Italiene (UBI), Banca Popolare Italiana NL_bks ING Bank, Rabobank, SNS Bank ES_bks Banco Santander, Banco Bilbao Vizcaya Argentaria (BBVA), Banco Pastor, Banco Popular Español, La Caixa, Banco Sabadell ES_bks_G1 Banco Santander, Banco Bilbao Vizcaya Argentaria (BBVA) ES_bks_G2 Banco Pastor, Banco Popular Español, La Caixa, Banco Sabadell PT_bks Banco Comercial Portugues, Banco BPI, Banco Espirito Santo, Caixa General De Depositos Exogenous variables SOVXWE itraxx SovX Western Europe * SNRFIN itraxx Europe Senior Financials ITRXEUR itraxx Europe index (125 investment grade companies, all sectors) XOVER itraxx Crossover index (50 sub-investment grade companies, all sectors) EUREON The spread between 3 month EURIBOR and EONIA swap VIX The volatility index of S&P 500 EUROSTOXX The EURO STOXX 50 Index US The 5 year senior CDS of United States of America UK The 5 year senior CDS of United Kingdom UK_bks Royal Bank of Scotland Group, HSBC Holdings, Barclays Bank, Lloyds TSB Bank Note: All endogenous bank variables are computed as asset-weighted averages. All bank components are 5 year senior CDS spreads denominated in euro. Source: CMA (via Datastream) and Bloomberg * For the constituents of these indices please refer to: http://www.markit.com/assets/en /docs/products/data/indices/credit-index-annexes/itraxx_sovx%20we_series%207.pdf and http://www.markit.com/assets/en/docs/products/data/indices/credit-index-annexes/itraxx /%20Europe/%20annex_Series%2017.pdf 87

Table 2.A.2: Descriptive Statistics Endogenous Exogenous Type CDS Sovereigns CDS Banks CDS Indices Other Variable in levels (ln(variable)) Variable name No Obs Mean Median Min Max Std Dev Skew Kurtosis JB Test ADFv1 pvalue ADFv2 pvalue No Obs Mean Median Min Max Std Dev Skew Kurtosis JB Test ADFv1 pvalue ADFv2 pvalue AT 718 107 86 49 239 47,80 0,85 2,33 101 0,618 0,269 717 0,227 0,252-30,75 21,03 3,76-1,01 15,92 5.109 0,001 0,001 BE 718 167 150 32 403 85,90 0,23 2,05 34 0,551 0,118 717 0,143 0,051-32,52 21,36 4,10-0,47 9,31 1.214 0,001 0,001 FI 718 44 33 16 90 21,36 0,71 1,94 95 0,740 0,268 717 0,124 0,081-19,61 32,93 4,22 0,53 9,92 1.466 0,001 0,001 FR 718 109 84 21 247 61,20 0,51 1,94 65 0,671 0,172 717 0,241 0,187-22,05 18,12 4,35-0,09 5,36 167 0,001 0,001 GR 718 3.680 1.010 122 25.961 5512 2,57 9,84 2.189 0,391 0,336 717 0,172 0,026-15,44 17,98 4,02 0,33 4,74 104 0,001 0,001 DE 718 57 46 19 121 25,95 0,57 2,04 66 0,724 0,135 717 0,268 0,089-17,36 19,59 4,15 0,09 4,68 85 0,001 0,001 IR 718 505 582 115 1.287 254,48-0,10 2,03 29 0,526 0,695 717 0,665 0,220-104,45 50,10 8,05-2,84 50,00 66.951 0,001 0,001 IT 718 259 191 68 596 150,19 0,66 1,99 83 0,652 0,157 717 0,191 0,014-18,33 22,22 4,10 0,18 5,63 211 0,001 0,001 NL 718 64 49 25 136 32,55 0,73 2,01 93 0,723 0,344 717 0,179 0,112-35,24 22,11 4,04-0,63 14,16 3.771 0,001 0,001 SP 718 282 256 68 618 130,45 0,34 2,50 21 0,721 0,002 717 0,253 0,219-40,43 21,54 4,84-0,40 11,45 2.154 0,001 0,001 PT 718 639 495 53 1.762 431,89 0,30 1,67 64 0,523 0,317 717 0,168 0,000-18,64 17,49 3,92 0,24 5,12 141 0,001 0,001 At_Bks 718 192 167 121 374 62,78 1,05 2,97 131 0,611 0,516 717 0,048 0,008-20,06 12,04 3,27-0,34 5,93 270 0,001 0,001 BE_Bks 718 338 255 141 744 180,00 0,80 2,18 97 0,915 0,494 717 0,094 0,000-18,54 20,64 3,49 0,68 8,20 864 0,001 0,001 FR_Bks 718 167 131 56 380 83,47 0,74 2,22 83 0,522 0,021 717 0,063 0,000-25,19 15,07 3,01-0,11 11,89 2.361 0,001 0,001 GR_Bks 718 1.166 966 139 3.634 693,84 0,51 2,49 40 0,381 0,001 717 0,188 0,072-17,22 11,34 2,72-0,13 6,79 432 0,001 0,001 DE_Bks 718 145 131 76 319 50,29 0,77 2,74 72 0,530 0,055 717 0,160 0,005-40,79 19,15 4,77-0,61 11,03 1.973 0,001 0,001 IT_Bks 718 253 188 64 690 160,96 0,79 2,35 88 0,748 0,203 717 0,324-0,034-50,70 45,86 6,15 0,54 24,77 14.191 0,001 0,001 NL_Bks 718 132 116 57 251 50,08 0,62 2,18 67 0,702 0,099 717 0,090 0,000-20,28 15,12 3,57 0,06 5,48 184 0,001 0,001 ES_Bks_G1 718 234 228 66 484 101,60 0,38 2,42 27 0,695 0,002 717 0,272 0,114-37,53 19,37 4,27-0,57 12,14 2.535 0,001 0,001 ES_Bks_G2 718 478 426 181 940 206,10 0,45 2,08 50 0,916 0,560 717 0,128-0,011-23,88 13,77 3,42-0,39 7,05 509 0,001 0,001 PT_Bks 718 644 635 74 1.378 372,74 0,08 1,83 42 0,703 0,839 717 0,207 0,050-43,57 19,18 4,68-1,01 14,72 4.224 0,001 0,001 SOVXWE 718 202 183 47 386 97,30 0,17 1,79 47 0,666 0,106 717 0,105 0,000-25,94 16,60 3,52-0,14 8,32 847 0,001 0,001 SNRFIN 718 172 160 64 355 69,27 0,44 2,21 42 0,630 0,027 717 0,068-0,112-14,40 29,07 4,25 0,74 7,32 623 0,001 0,001 ITRX EUR 718 120 109 65 208 34,66 0,75 2,45 76 0,656 0,174 717 0,065 0,029-25,98 15,28 3,24-0,42 9,77 1.389 0,001 0,001 XOVER 718 534 502 352 874 129,20 0,64 2,28 64 0,516 0,280 717 0,004-0,053-20,59 12,65 2,94-0,04 7,14 512 0,001 0,001 EUREON 718 0,61 0,49 0,22 1,35 0,29 0,96 2,87 111 0,447 0,987 717-0,076-0,627-35,06 40,55 7,28 0,85 6,94 550 0,001 0,001 EURSTOXX 718 257 263 201 297 23,75-0,50 2,09 54 0,476 0,252 717-0,080 0,079-17,41 17,78 3,03-0,19 9,63 1.318 0,001 0,001 US CDS 718 43 43 20 64 7,75-0,53 3,35 38 0,631 0,052 717 0,094 0,000-18,54 20,64 3,49 0,68 8,20 864 0,001 0,001 UK CDS 718 72 71 44 103 12,76 0,24 2,56 13 0,551 0,089 717 0,048 0,008-20,06 12,04 3,27-0,34 5,93 270 0,001 0,001 UK_Bks 718 159 143 82 291 51,34 0,60 2,16 65 0,589 0,024 717 0,213 0,002-17,53 10,69 2,97-0,57 8,40 910 0,001 0,001 VIX 718 23 21 14 48 6,24 1,31 4,35 259 0,212 0,020 717-0,016 0,000-5,54 8,67 1,46 0,02 5,82 238 0,001 0,001 Note: JB test refers to the Jarque-Bera test for normality. The JB test statistic is χ 2 -distributed. The null hypothesis is rejected in all cases, for both CDS levels and log first-differences. ADFv1 and ADFv2 refer to the augmented Dickey-Fuller test for unit-roots. ADFv1 has an autoregressive model and ADFv2 refers to the trend stationary model. The null-hypothesis of existence of a unit root cannot be rejected for levels, but can be rejected in the case of log first-differences.

Chapter 2: A Contagion Index for the Euro Area Table 2.A.3: Country-specific bank assets and the weight in the country bank index No. Country Bank name Assets* Weight 1 Austria Erste Group 216.709 0,59 2 Austria Raiffeisen Zentralbank 148.798 0,41 3 Belgium Dexia Group 412.759 0,59 4 Belgium KBC Group 290.635 0,41 5 France BNP Paribas 1.965.283 0,40 6 France Crédit Agricole 1.723.608 0,35 7 France Société Générale 1.181.372 0,24 8 Germany Deutsche Bank 2.103.295 0,51 9 Germany Commerzbank 691.014 0,17 10 Germany DZ Bank 388.525 0,09 11 Germany Landesbank Baden-Württemberg 373.059 0,09 12 Germany Landesbank Hessen-Thüringen 163.985 0,04 13 Germany HSH Nordbank 150.930 0,04 14 Germany WestLB 220.179 0,05 15 Greece EFG Eurobank Ergas 73.587 0,41 16 Greece National Bank Of Greece 104.095 0,59 17 Italy Unicredito 926.769 0,44 18 Italy Intesa Sanpaolo 652.630 0,31 19 Italy Banca Montepaschi Di Siena 244.300 0,12 20 Italy Unione Di Banche Italiene 131.511 0,06 21 Italy Banca Popolare Italiana 134.942 0,06 22 Netherlands ING Group 1.241.729 0,72 23 Netherlands Rabobank 404.682 0,23 24 Netherlands SNS Bank 78.918 0,05 25 Portugal Banco Comercial Portugues 92.029 0,27 26 Portugal Banco BPI 44.754 0,13 27 Portugal Banco Espirito Santo 81.265 0,24 28 Portugal Caixa General De Depositos 118.637 0,35 29 Spain Banco Santander** 1.283.349 0,57 30 Spain BBVA** 600.477 0,27 31 Spain Banco Popolar Espnol 158.207 0,07 32 Spain Banco Sabadell 105.321 0,05 33 Spain Caja de Ahorros 70.667 0,03 34 Spain Banco Pastor 30.376 0,01 35 UK Royal Bank of Scotland 1.506.867 0,23 36 UK HSBC 2.555.579 0,38741 37 UK Barclays 1.563.527 0,23702 38 UK LLOYDS TSB Bank 970.546 0,14713 Note: * assets are in thousand euros, Q1 2011. ** In section 4.1, the two Spanish banks (Banco Santander, BBVA) are considered as being part of ES_Bks_G1, and the rest four Spanish banks (Banco Popular Español, Banco Sabadell, La Caixa, Banco Pastor) are part of ES_Bks_G2. 89

Chapter 2: A Contagion Index for the Euro Area Table 2.A.4: Selected events and the cumulative returns of contagion indices 10D cumulative return after the event ±10D cumulative return around the event No. Date Event CI CI CI CI CI CI CI CI bks sovs from from bks sovs from from sovs to bks to sovs to bks to bks sovs bks sovs 1 25.03.2010 EU offers support to Greece 31% 14% 19% 26% -30% 9% 44% 45% 2 10.05.2010 EU sets up the EFSF; ECB starts SMP -5% -5% -24% -2% -29% -16% -45% -40% 3 22.11.2010 Ireland seeks financial support -16% 2% 27% 12% -21% 34% 9% -23% 4 06.04.2011 Portugal requests activation of the aid mechanism -1% 4% -22% -15% 0% -15% 37% -44% 5 15.07.2011 EBA bank stress test results are published -10% 7% -30% 3% -21% 2% -16% 54% 6 06.10.2011 ECB announces second covered bond purchase programme -24% -22% -30% -54% -11% -14% -22% -56% 7 08.12.2011 ECB lowers interest rates by 25 bps -21% -12% -29% -26% -13% 4% -44% -41% 8 22.12.2011 LTRO I 3% 9% 22% 48% -19% -4% -14% 10% 9 01.03.2012 LTRO II 1% -36% 1% 6% 24% -42% -15% -19% 10 10.05.2012 Spain seizes control of Bankia -12% -4% -3% -11% -5% 43% 39% 13% 11 18.06.2012 G20 Summit -10% 3% 34% 1% 14% -3% 68% 16% 12 28.06.2012 EU Summit* 8% -16% 3% -2% -8% -10% 16% 12% Note: * Since our analysis ends on 3 July 2012, the cumulative return around/after the EU Summit is computed only for the next 5 days. ±10D around the event refers to the cumulative return between the values of the index 10 days after the event and 10 days before the event, such that the event is centred. Appendix 2.B The explicit VAR model with exogenous common factors A. Our VAR model with sovereigns, banks, and exogenous variables can be represented as: y AT,t y AT,t 1 u AT,t... α y 1,0 γ ES,t p = y AT _bks,t. + 11,i... γ 1n,i.... y ES,t 1 q u ES,t. + B i=1 y i Exo t i + AT _bks,t 1 i=0 u AT _bks,t α n,0 γ n1,i... γ nn,i... y ES_bks,t y ES_bks,t 1 u ES_bks,t (2.17) where u j,t W N(0, Σ u ). B. The moving average (MA) representation of the VAR model: A VAR (p) model can be represented as: Y t = v + p A i Y t 1 + U t (2.18) i 90

Chapter 2: A Contagion Index for the Euro Area Furthermore, a stable VAR process can be rewritten as: Y t = µ + φ i U t i (2.19) i=0 where φ i are the Moving Average (MA) coefficient matrices. And φ 0 = I k (2.20) Appendix 2.C Other versions of the contagion indices and systemic contribution of sovereigns The four components of contagion index, as defined in eq (2.13) - (2.16), can be weighted and summed as: CI = 100 N(N 1) [M(M 1)CI sovs + P (P 1)CI bks + MP (CI bks sovs + CI sovs bks )] (2.21) The second version of the Contagion Index of sovereigns that we propose is to weight the sum of IN spillover effects (received) by the euro area GDP. In this sense we give a higher importance to whom is affected by the spillover effects coming from other variables: N N CI win = 100 w i y i j (2.22) i=1 j i Where w i is the GDP weight of sovereign i in the Eurozone. 23 The third version of the CI sovereigns is to weight the sum of OUT spillover effects (sent) by the euro area GDP. In this sense we give a higher importance to who affects the others: N N CI wout = 100 w i IR i j (2.23) i=1 j i 23 Since we are not considering in our analysis all euro area countries we adjust these weights, such that they sum up to 1. 91

Chapter 2: A Contagion Index for the Euro Area Similarly, w i is the GDP-adjusted weight of sovereign i in the Eurozone s total GDP. After we have introduced all these measures that derive from the Contagion Matrix, we can re-define our systemic contribution of a sovereign measure: Version 2: SC Sovi = SE OUT,y i + SE IN,y i, CI wout CI win (2.24) Version 3: T SE NET,yi SC Sovi = Ni, T SE NET,yi I T CENET,yi >0 (2.25) where I T CENET,yi >0 is an indicator function that allows only positive net total contagion effects to be summed (since the sum of T CE NET,yi equals zero). Extension 1 - Residuals and IRs from the VARX(2) model with sovereign CDS changes. The aggregation of the impulse responses from a system only with sovereigns, calculated as the expected shock impact in Sov i : SCIS Sovi = EDF Sovi Where: GDP Sovi GDP EA j wt rade ij SovereignResponse j,i wt rade i (2.26) EDF Sovi is the expected default frequency of Sov i (as calculated by Moody s) SovereignResponse j,i is the (average) cumulated response of Sovereign j to a shock in Sovereign i wt rade ij is the Trade weight of Sovereign j in Total Exports of Sovereign i wbis ij is the weight of total holdings of Sovereign j s Banking System towards Sovereign i as reported in the BIS Foreign Claims (ultimate risk basis) database LevG i is the ratio Total Governmental Debt/GDP of Sovereign i LevF i is the ratio Total Assets of Banks/GDP of Sovereign i DomesticBanksAvgResponse, IntBanksAvgResponse are the average responses of financial institutions, domestic and foreign. 92

Chapter 2: A Contagion Index for the Euro Area Extension 2 - Residuals and impulse responses from the VARX(2) model with sovereign and bank CDS changes. The aggregation of IRs from a system with banks and sovereigns:: SCIS Sovi = GDP Sov i j wt rade ij SovereignResponse j,i (2.27) GDP EA wt rade i ExternalDebt i + wbis ij IntBanksAvgResponse T otalf oreignclaims i j + Domestic Debt i Domestic GDP i LevF i DomesticBanksAvgResp Different versions of the Contagion Index and systemic contributions of sovereigns (a comparison) We calibrate differently our contagion index for euro area sovereigns and show that there are no significant differences when we use eqs (20) and (21) instead of (10). In this analysis, we show that when we put more weight on countries with higher GDP, that are being influenced by spillover effects from other countries, the contagion index (CIwOUT, blue line) tops the preceding highest level during the Spanish debt developments (on 10 th April 2012). This index version has the role of highlighting a higher interdependence between big countries and small countries. If the former ones are affected by contagion, it can be considered a red flag for the entire stability of the system. Figure 2.C.1: Different versions of the EA Contagion Index of sovereigns 93

Appendix 2.D Spillover and Net Spillover Matrices Table 2.D.1: The spillover matrix of EA sovereigns and banks (on 18 July 2011) Note: Variables in the first column are the impulse origin. Variables on the top row are the respondents to the shock. Values in the matrix represent the average cumulated spillover effect over the first 5 days. The intensity of a shock on a respondent is marked by different levels of colour (light means no impact and dark means very strong impact). The cumulative impact is bound between 0 and 1. A value of 0.5 means that the response variable will be impacted in the same direction with an intensity of 50% the initial unexpected shock in the impulse variable. If the initial shock has a magnitude of 10 bps then the response variable is expected to increase by 5 bps in the following week. In the last column we have the aggregated impact sent (Sum OUT) by each row variable and on the bottom row the aggregated spillover received (Sum IN) by each column variable. The bottom-right cell (in bold) shows total spillover in the system (by dividing this value to the total number of non-diagonal cells i.e. 20x19 we obtain the contagion index of EA sovereigns and banks, as introduced in eq 2.10).

Table 2.D.2: Net spillover matrix (on 18 July 2011) Note: : If the value in the cell is negative (blue horizontal bar) it means that the row variable is the net receiver and the column variable is the net sender. If the value is positive (red horizontal bar) the column variable is net receiver and the row variable is net sender. The last column shows the sum of net spillover effects of the row variable. In case the NET sum spillover is positive (bold values) then the variable is a net sender of the system.

Chapter 2: A Contagion Index for the Euro Area Appendix 2.E Optimal rolling window size In the last appendix section we provide an ad-hoc procedure and we admit the existence of alternative approaches based for example on grid solutions based on first principle might. Apart from this procedure we have also implemented the contagion index for window sizes varying from 60 days to 120 days. These results show either a higher variance in VAR coefficients or lack to incorporate the developments in the CDS market in a timely manner. These robustness checks are available upon request. The minimum sample size of any estimation period is dependent on the number of variables in the system including the order of lags. For the identification of an optimal rolling window size there is a trade-off between robustness and reliability of estimated VAR coefficients (the longer the sample the better the quality) on the one hand, and gaining information about a build-up of spillover effects over time (the shorter the sample window the larger the weight on more recent information) on the other hand. Against this trade-off we combine the results of the following functions. First, in the estimated VAR in eq (2.1)) at least one of the two γ-coefficients (corresponding to a lag length of two) of a shock variable has to be significant. Since we are interested in the percentage of significant γ-coefficients of the shock variable in the equations of response variables, we apply a joint test under the null hypothesis that γ 1 and γ 2 are simultaneously zero. In Figure 2.E.1 we present the percentage of tests that reject the null hypothesis of the joint test as a function of the window sample size. Second, our aim is that measured spillover effects integrate potentially adverse developments for financial stability. As the sample size of the window increases the weight of new information decreases and spillover effects reflect new developments with a lag effect. We account for this aspect by computing the mean of residual sum of squares (MRSS). Since this function increases with the rolling window size, we are interested in the marginal change of the MRSS. By finding the intersection of these two functions, we obtain an optimal rolling window size between 80 and 85 days. An illustrative representation of the two criteria is presented in Figure 2.E.1. 96

Chapter 2: A Contagion Index for the Euro Area Figure 2.E.1: Optimal size of the rolling window Note: On X-axis: rolling window size in number of days. On Y-axis: percentage of significant γ- coefficients 97

Chapter 2: Centrality-based Capital Allocations and Bailout Funds 98

Chapter 3 Centrality-based Capital Allocations and Bailout Funds

Chapter 3: Centrality-based Capital Allocations and Bailout Funds 3.1 Introduction The difficult task before market participants, policy makers, and regulators with systemic risk responsibilities such as the Federal Reserve is to find ways to preserve the benefits of interconnectedness in financial markets while managing the potentially harmful side effects. Yellen (2013) Systemic risk as a result of market imperfections can be understood as the likelihood of multiple failures of financial institutions that poses significant problems to financial stability (see e.g. De Bandt et al. (2009)). Main causes of the recent financial crisis that had a systemic dimension include: complex securitization transactions, highly leveraged institutions, and highly interconnected financial system (i.e., commercial banks, investment banks, hedge funds, asset managers and insurance companies). Therefore, excessive systemic risk generated by common exposures and interbank interconnectedness is at the center of our analysis to build systemically consistent capital requirements. In this chapter we focus on two main sources of systemic risk: correlated credit exposures and interbank connectivity. First, banks balance sheets can be simultaneously affected by macro or industry shocks since the credit risk of their borrowers is correlated. Second, these shocks can, on the one hand,trigger the default of certain financial institutions and, on the other hand, capital of the entire system is eroded, making the system less resilient and unstable. The latter effect is modeled in the interbank market. Since banks are highly connected through interbank exposures, we focus on those negative tail events in which correlated losses of their portfolios trigger contagion in the interbank market. Our model comes close to the framework proposed by Elsinger et al. (2006) and Gauthier et al. (2012), combining common credit losses with interbank network effects and externalities in the form of asset fire sales. The aim of this chapter is different. We propose a tractable framework to reallocate capital for large financial systems in order to minimize contagion effects and costs of public bailout. We contrast two different capital allocations: the benchmark case, in which we allocate capital based on the risks in individual banks portfolios, and new capital allocations based on some interbank network metrics that capture the potential contagion risk of the entire system. The growth of securitization and derivatives markets as well as increased reliance on wholesale funding has led to a stark increase of the complexity of financial systems and the number of types of interdependencies among financial intermediaries (see e.g. Haldane and May, 2011). As pointed out by Haldane (2009), relationships 100

Chapter 3: Centrality-based Capital Allocations and Bailout Funds between financial institutions foster risk-sharing benefits acting as risk-absorbers up to a certain tipping point. The key concern related to network connectivity is the robust-yet-fragile property. Beyond a certain point, higher connectivity can harm the stability of financial system. This knife-edge property of financial systems is in strong relationship with the capital in the entire system but more importantly with the question at which nodes it is concentrated. When capital is eroded by different common exposure losses, connectivity causes domino effects that flip the system into a bad-state equilibrium. As claimed by Ladley (2013), financial stability cannot be maximized under all scenarios by a certain network structure. When large macro shocks hit the banking system, higher connectivity worsens systemic crises. The opposite effect is observed when shocks are smaller. On the one hand, highly interconnected financial institutions benefit from risk diversification and multiple sources of investment, liquidity and funding opportunities. On the other hand, interconnectedness makes it more difficult for these institutions to assign and monitor risks and to address certain negative externalities. Thus, high interconnectivity exhibits a trade-off: when banks are well diversified, moderate macro shocks are better absorbed by the system and contagion effects are contained; but when large common shocks hit the financial sector, many financial institutions default and spread large losses throughout the entire system, being equivalent to a systemic crisis. During the subprime crisis, asymmetric information among market participants contributed to a sudden stop of market liquidity (e.g., short-term unsecured funding). Scott (2012) presents an analysis of asset-and-liability interconnectedness that fueled contagious spillovers around Lehman Brothers default. He claims that the direct impact of Lehman s insolvency would not have destabilized its counterparties since most of Lehman s liabilities were collateralized. However, the signal sent by policy makers who increased the uncertainty of implicit bailout backstops, by letting Lehman fail, combined with potential risks stemming from asset or liability interconnectedness, generated a wave of spillovers that froze financial markets (e.g. markets for asset backed securities and short-term uncollateralized lending ). In the aftermath of the subprime crisis, regulators and policy makers took several measures to improve public information by publishing results of the stress tests and asking banks to disclose a detailed picture of on- and off-balance sheet positions. Moreover, Basel III regulations and the Dodd-Frank Act, among others, try to address systemic risk by imposing new capital and liquidity requirements and limits on certain asset exposures or liabilities. However, more effort is demanded to reach reasonable financial regulations when it comes to implicit public backstops since some institutions 101

Chapter 3: Centrality-based Capital Allocations and Bailout Funds are too big or too interconnected to let them fail. In this chapter we attempt to provide answers to the following policy-relevant questions: How can different capital reallocations improve the resilience of large financial systems to correlated shocks? Which measures could help us find the optimal allocation? Are network-derived measures helpful for improving financial stability? How can a bailout fund mechanism be optimally designed such that total system losses are minimized? Acharya et al. (2010) and Engle et al. (2012) refer to systemic risk contribution as the susceptibility of a financial institution to be undercapitalized when the entire financial system is undercapitalized. Thus, for the purpose of investigating financial stability under different capital allocations, we focus on correlated tail events of financial institutions by stressing their credit exposures to the real economy sectors. Our credit risk engine is associated to previous work that uses the CreditMetrics framework (see Bluhm et al. (2003), Bonti et al. (2006),Düllmann and Erdelmeier (2009)). Based on a multi-factor credit risk model, this framework helps us to deal with risk concentration caused by large exposures to a single sector or correlated sectors. Even explicit common credit exposures are precisely addressed. CreditMetrics helps us to generate scenarios with large correlated losses across the entire banking system. These events are our main focus since capital across financial institutions is eroded simultaneously and the banking system becomes less resilient to interbank contagion. Allen and Babus (2009) review most of the literature related to financial networks. Contagion is a phenomenon with low probability but high impact on financial stability through several channels. Allen and Gale (2000) and Freixas et al. (2000) are among the first to introduce network features in a contagion-related theoretical framework. The failure of a bank or a group of financial institutions can create domino effects in the interbank market. The risk of contagion is highly dependent on the level of connectivity. As developed in a network-theoretical model by Allen et al. (2012), asset commonality of banks portfolios and their debt structure are two main sources that could trigger information contagion and result in excessive systemic risk. As defined by Kaufman (1995), systemic risk is associated with the probability that cumulative losses will accrue from an event that sets in motion a series of successive losses along a chain of institutions or markets comprising a system.[...] That is, systemic risk is the risk of a chain reaction of falling interconnected dominos. The main innovation of this chapter is that it combines correlated credit exposures, interbank contagion, and network analysis to improve financial stability. In 102

Chapter 3: Centrality-based Capital Allocations and Bailout Funds this sense, we propose two solutions: first a capital re-allocation that accounts for systemic contributions in the interbank market and second a bailout fund mechanism that can rescue certain financial institutions based on their relative systemic importance. Both regimes are optimized via some interconnectedness measures calculated from the interbank network, with the intention of making the financial system more robust. To achieve this aim, we use several regulatory databases in combination with market data. Central credit register data is crucial for understanding systemic risk and how bank defaults may spread in the system. The idea of tying capital charges to interbank exposures and interconnectedness to improve the resilience of the banking system, i.e. to minimize expected social costs (e.g. arising from bailouts, growth effects, unemployment) is in the spirit of the regulatory assessment methodology for systemically important financial institutions (SIFIs) proposed by the Basel Committee on Banking Supervision (2011). In contrast to the latter, our study determines an optimal rule based on several interconnectedness measures and the size of total assets and compares the results under different capital allocations. One advantage of our approach is that interbank network topology builds on real balance sheet information of the German Large- Exposures Database, which covers around 99% of the interbank transacted volume. This allows us to identify interbank contagion channels and compute centrality measures accurately. The second policy direction highlighted in this chapter is estimating a proper mechanism and the size of a bailout fund for the financial sector. We start in a benchmark case where capital is allocated based on Value-at-Risk (VaR hereafter) at a security level that would provide comparably high protection against bankruptcy if interconnectedness were irrelevant. The basic idea of the bailout fund is to require less capital instead and to pool the aggregate capital relief in the fund. In the benchmark case, banks are required to hold capital equal to their VaR(α = 99.9%) while the requirement in presence of the bailout fund is the VaR (α = 99%) only. The bailout fund uses its resources to rescue banks. The mechanism of rescuing banks is based on an importance ranking of financial institutions. Banks are ranked based on a trade-off rule between size and centrality measures. We consider several sizes of the bailout fund and compare expected losses with the results obtained from reallocation of capital using centrality measures. We use a framework to assess the impact of different capital allocations on financial stability. We integrate a sound credit risk engine (i.e. CreditMetrics) to generate correlated shocks to credit exposures of the entire German banking system (1764 Monetary financial institutions (MFIs) active in the interbank (IB) market). 103

Chapter 3: Centrality-based Capital Allocations and Bailout Funds This engine gives us the opportunity to focus on correlated tail events (endogenously determined by common exposures to the real economy). Moreover, we model interbank contagion based on Eisenberg and Noe (2001) and extend it to include bankruptcy costs as in Elsinger et al. (2006). This feature allows us to measure expected contagion losses and to observe the propagation process. To empirically exemplify our framework, we use several sources of information: the German central credit register (covering large loans), aggregated credit exposures (to compute small loan portfolios), balance sheet data (e.g. total assets), market data (e.g. to compute sector correlations in the real economy or credit spreads), and data on rating transitions. The framework can be applied in any country or group of countries where this type of information are available. The main advantage of this framework is that policy makers can deal with large banking systems, making the regulation of systemic risk more tractable. Our main contributions are twofold. First, we focus on capital reallocations and try to minimize different target functions with the scope of improving financial stability. We intend to use several target functions: total system losses, second-round contagion effects (i.e. contagious defaults) or losses from fundamental defaults (i.e. banks that default from real-economy portfolio losses). For example, total system losses can be defined as total bankruptcy costs of defaulted banks. Furthermore, we determine capital allocations that improve the resilience of financial system (as defined by our target functions) based on interconnectedness measures from IB network. In order to determine new capital rules and test them on our framework, we utilize several exposure- and network- based connectivity measures: total assets, total interbank assets and liabilities, the degree, eigenvector and weighted eigenvector centrality measures, weighted betweenness, Opsahl centrality, closeness or the clustering coefficient. Second, we implement a bailout fund mechanism that offers a fairly priced insurance against the default of certain entities, however with priorities depending on a ranking constructed based on banks size and centrality in the IB market. We compare measures of the total-system loss across different types of capital allocation and sizes of the bailout fund. Our policy conclusions related to too-interconnected-to-fail versus too-big-to-fail externalities suggest that the latter dominates the former in terms of expected system losses. Finally, this study is related to several strands of the literature including applications of network theory to economics, macro-prudential regulations and interbank contagion. Cont et al. (2010) find that not only banks capitalization and interconnectedness are important for spreading contagion but also the vulnerability of neighbors. Gauthier et al. (2012) use different market- based systemic risk measures 104

Chapter 3: Centrality-based Capital Allocations and Bailout Funds (e.g. MES, DCoVar, Shapley value) to reallocate capital in the banking system and to determine macro-prudential capital requirements. Using the Canadian credit register data for a system of six banks, they rely on an Eisenberg-Noe -type clearing mechanism extended to incorporate fire sales externalities. In contrast to their chapter, we reallocate capital based on centrality measures extracted directly from the network topology of interbank market. Webber and Willison (2011) assign systemic capital requirements optimizing over the aggregated capital of the system. They find that systemic capital requirements are directly related to bank size and interbank liabilities. Tarashev et al. (2010) claim that systemic importance is mainly driven by size and exposure to common risk factors. In order to determine risk contributions they utilize the Shapley value. In the context of network analysis, Battiston et al. (2012) propose a measure closely related to eigenvector centrality to assign the systemic relevance of financial institutions based on their centrality in financial network. Similarly, Soramäki and Cook (2012) try to identify systemically financial institutions in payment systems by implementing an algorithm based on absorbing Markov chains. Employing simulation techniques they show that the proposed centrality measure, SinkRank, highly correlates with the disruption of the entire system. In contrast to the latter two studies, we find that size ( Too-big-to-fail ) dominates centrality measures ( Too-interconnected-to-fail ) obtained from the interbank network. This antithesis might arise from utilizing different target functions in the optimization process. As the subprime crisis has shown, almost any bank can contribute to systemic risk, especially because banks are exposed to correlated risks (e.g. credit, liquidity or funding risk) via portfolios and interbank interconnectedness. Assigning risks to individual banks might be misleading. Some banks might appear healthy when viewed as single entities but they could threaten financial stability when considered jointly. Gai and Kapadia (2010) find that the level of connectivity negatively impacts the likelihood of contagion. Anand et al. (2013) extend their model to include fire sale externalities and macroeconomic feedback on top of network structures, in order to stress-test the resilience of financial systems. These studies illustrate the tipping point at which the financial system breaks down based on the severity of macroeconomic shocks that affect corporate probabilities of default or asset liquidity. Battiston et al. (2012) show that interbank connectivity increases systemic risk, mainly due to a higher contagion risk. Furthermore, Acemoglu et al. (2013) claim that financial network externalities cannot be internalized and thus, in equilibrium, financial networks are inefficient. This creates incentives for regulators to improve welfare by bailing out SIFIs. 105

Chapter 3: Centrality-based Capital Allocations and Bailout Funds The rest of this chapter is structured as follows. In Section 3.2 we describe our methodology and data sources briefly. Section 3.3 refers to our interconnectedness measures and the network topology of German interbank market. In Section 3.4 we describe our risk engine that generates common credit losses to banks portfolios. Section 3.5 gives an overview of the contagion algorithm and Section 3.6 describes how capital is optimized. In Section 3.7 we present our main results and in Section 3.8 we provide some robustness checks. Section 3.9 concludes. 3.2 Data and methodology 3.2.1 Methodology Figure 3.A.1 in Section 3.A offers a helicopter view of our model. It can also be summarized in the following steps: 1. In the initial state, a standard bank portfolio is composed of large and small credit exposures (e.g. loans, credit lines, derivatives) to real economy and interbank (IB) borrowers. On the liability side, banks hold capital, either set to VaR (at α = 99.9%) in the benchmark case, or according to other capital allocations that partly rely on network measures. 1 Furthermore, depositors and other creditors are senior to interbank creditors. We present in Figure 3.1 a standard individual bank balance sheet and the benchmark capital representation based on the credit risk model explained in Section 3.4. 2. In the first stage, we simulate correlated exogenous shocks to banks portfolios that take the form of returns on individual large loans and aggreggated small loans. Due to changes in the value of borrowers assets, their credit ratings migrate (or they default), and banks make profits/losses on their investments in credit to the real-economy sectors. At the end of this stage, in case of portfolio losses, capital is eroded and some banks experience negative capital, i.e. fundamental defaults. Thus, we are able to generate correlated losses that affect the capital of each bank simultaneously. 2 1 VaR at α = 99.9% is calculated for each individual bank from 1 Mn simulations. When we calculate benchmark capital allocations, where contagion effects are ignored, the credit risk of German interbank (IB) loans (as assets) are treated in the traditional way, similarly to large credit exposures to foreign banks (Sector 17, Table 3.A.1). The PDs of German interbank loans banks are set to the mean PD of this sector. In this way, there is a capital buffer to withstand potential losses from interbank defaults, however determined in a way as if interbank loans were yet another ordinary subportfolio. 2 By incorporating credit migrations and correlated exposures, we differ from most of the literature on interbank contagion that usually studies idiosyncratic bank defaults; see Upper (2011). 106

Chapter 3: Centrality-based Capital Allocations and Bailout Funds 3. In the second stage, we model interbank contagion. We apply an extended version of the fictitious contagion algorithm as introduced by Eisenberg and Noe (2001), augmented with bankruptcy costs and fire sales. Fundamental bank defaults generate losses to other interbank creditors and trigger some new defaults. Hence, bank defaults can induce domino effects in the interbank market. We refer to new bank failures from this stage as contagious defaults. 4. Finally, we repeat the previous steps for different capital allocations and for the bailout fund mechanism. We discuss the optimization procedure in Section 3.6. Moreover, Section 3.3 offers an overview of the interconnectedness measures calculated with the help of network analysis and utilized in the optimization process. The bailout fund mechanism, based on a set of assumptions, is detailed in Subsection 3.6.4. 3.2.2 Data sources Our model builds on several data sources. In order to construct the interbank network, we rely on the Large Exposures Database (LED) of the Deutsche Bundesbank. Furthermore, we infer from the LED the portfolios of credit exposures (including loans, bond holdings, credit lines, derivatives, etc.) to the real economy of each bank domiciled in Germany. Since this dataset is not enough to get the entire picture, since especially the smaller German banks hold plenty of assets falling short the reporting threshold of e 1.5 Mn for the LED, we use balance sheet data and the Borrower Statistics. Finally, we rely on stock market indices to construct a sector correlation matrix and we utilize a migration matrix for credit ratings from Standard and Poor s. Rating dependent spreads are taken from Merill Lynch corporate spread indices. Large Exposures Database (LED) The Large Exposures Database represents the German central credit register. 3 Banks report exposures to a single borrower or a borrower unit (e.g., a banking group) which have a notional exceeding a threshold of e 1.5 Mn. The definition of an exposure includes bonds, loans or the market value of derivatives and off-balance sheet items. 4 In this chapter, we use the information available at the end of Q1 2011. The Elsinger et al. (2006) and Gauthier et al. (2012) are remarkable exceptions. 3 Bundesbank labels this database as Gross- und Millionenkreditstatistik. A detailed description of the database is given by Schmieder (2006). 4 Loan exposures also have to be reported if they are larger than 10% of a bank s total regulatory capital. They are not contained in our dataset of large exposures but represent a very small amount 107

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Figure 3.1: Individual bank balance sheet and benchmark capital A L Real Economy Large Loans Real Economy Small Loans Interbank Assets Capital Interbank Liabilities Deposits Other Assets Other Liabilities Benchmark Note: In order to obtain the benchmark capital which equals VaR (α = 99.9%), we use a stylized bank balance sheet. The individual bank portfolio is composed of Large Loans (LL) and Small Loans (SL) to the real economy sectors (this distinction is made for risk modeling purposes). When we calculate benchmark capital, interbank (IB) assets are treated similarly to large credit exposures (LL) to foreign banks (Sector 17, Table 3.A.1). German banks PDs are set to the mean PD of this sector. In this way, there is a capital buffer to withstand potential losses from interbank defaults. Other Assets and Other Liabilities are ignored in our model. 108

Chapter 3: Centrality-based Capital Allocations and Bailout Funds interbank market consists of 1764 active lenders. Including exposures to the real economy, they have in total around 400,000 credit exposures to more than 163,000 borrower units. 5 Borrowers in the LED are assigned to 100 fine-grained sectors according to Deutsche Bundesbank (2009). In order to calibrate our credit risk model, we aggregate them to sectors that are more common in risk management (e.g. like those that fit with equity indices, which are the standard source of information used to calibrate asset correlations of the credit risk model). In our credit risk model, we use EUROSTOXX s 19 industry sectors (and later its corresponding equity indices). Table 3.A.1 lists risk management sectors and the distribution characteristics of the PDs assigned to them. There are two additional sectors (Households, including NGOs, and Public Sector) that are not linked to equity indices. 6 These 21 sectors represent the risk model (RM) sectors of our model. The information regarding borrowers PDs is included as well in LED. We report several quantiles, the mean and variance of the sector-specific PD distributions in Table 3.A.1. Since only Internal-Ratings-Based (IRB) banks report this kind of information, we draw random PDs from the empirical sector-specific distributions for the subset of borrowers without reported PDs. Borrower statistics and balance sheet information While LED is an unique database, the threshold of e 1.5 Mn of notional is a substantial restriction. Although large loans build the majority of money lent by German banks, the portfolios of most German banks would not be well represented by them. That does not come as a surprise if one takes into account that the German banking system is dominated (in numbers) by rather small S&L and cooperative banks. Many banks hold only few large loans while they are, of course, much better divercompared to the exposures that have to be reported when exceeding e 1.5 Mn. Note that loans being reported to the LED but not being part of our set of large loans are captured in the Borrower Statistics and hence are part of our sub-portfolios of small loans ; see Section 3.2.2. It is also important to notice that, while the data are quarterly, the loan volume trigger is not strictly related to an effective date. Rather, a loan enters the database once its actual volume has met the criterion at some time throughout the quarter. Furthermore, the definition of credit triggering the obligation to report large loans is broad: besides on-balance sheet loans, the database conveys bond holdings as well as off-balance sheet debt that may arise from open trading positions, for instance. We use total exposure of one entity to another. Master data of borrowers contains its nationality as well as assignments to borrower units, when applicable, which is a proxy for joint liability of borrowers. We have no information regarding collateral in this dataset. 5 Each lender is considered at aggregated level (i.e. as Konzern ). At single entity level there are more than 4.000 different lending entities reporting data. 6 We consider exposures to the public sector to be risk-free (and hence exclude them from our risk engine) since the federal government ultimately guarantees for all public bodies in Germany. See Section 3.4. 109

Chapter 3: Centrality-based Capital Allocations and Bailout Funds sified. For 2/3 of banks the LED covers less than 54% of the their total exposures. We need to augment the LED by information on smaller loans. Bundesbank s borrower statistics (BS) dataset includes loans to German borrowers by each bank on a quarterly basis. Focusing on the calculation of money supply, it reports only those loans made by banks and branches situated in Germany; e.g. a loan originated in London office of Deutsche Bank would not enter the BS, even if the borrower is German. Corporate lending is structured in eight main industries: agriculture, basic resources and utilities, manufacturing, construction, wholesale and retail trade, transportation, financial intermediation and insurance, and services. Manufacturing and services are further divided into nine and eight sub-sectors, respectively. Loans to households and non-profit organizations are also reported in the BS database. 7 While lending is disaggregated into various sectors, the level of aggregation is higher than in LED, and sectors are different from the sectors in the risk model. Yet, there is a unique mapping from the many LED sectors to the ones of the borrower statistics (BS) sectors. We use this mapping and the one from the LED sectors to the risk model (RM) sectors to establish a compound mapping from BS to RM sectors. They are based on relative weights gained from the LED that are assumed also to hold for small loans. 8 In addition to borrower statistics, we also use some figures from the monthly balance sheet statistics that are also reported to Deutsche Bundesbank. These sheets contain lending to domestic insurances, households, non-profit entities, social security funds, and so-called other financial services companies. Lending to foreign entities is given by a total figure that covers all lending to non-bank companies and households. The same applies to domestic and foreign bond holdings which, if large enough, are also included in LED. Market data Credit ratings migration matrix is presented in Table 3.A.4 and is provided by S&P. Market credit spreads are derived from a daily time series of Merill Lynch option-adjusted euro spreads covering all maturities, from April 1999 to June 2011. Correlations are computed based on EUROSTOXX weekly returns of the European 7 A financial institution has to submit BS forms if it is an monetary financial institution (MFI), which does not necessarily coincide with being obliged to report to LED. There is one state-owned bank with substantial lending that is exempt from reporting BS data by German law. Backed by a government guarantee, we consider this bank neutral to interbank contagion. 8 Detailed information on the mapping is available on request. 110

Chapter 3: Centrality-based Capital Allocations and Bailout Funds sector indices for the period April 2006 - March 2011 covering most of the recent financial crisis. 9 3.3 Interbank network Economic literature related to network analysis has exploded since the beginning of the financial crisis in 2007. For example, focusing on centrality and connectivity measures of the financial network, Minoiu and Reyes (2011) analyze the dynamics of the global banking interconnectedness over a period of three decades. Financial networks are defined by a set of nodes (financial institutions) that are linked through direct edges that represent bilateral exposures between them. Iori et al. (2008) study the micro structure of Italian overnight money market. By looking at different network metrics, they analyze the statistical properties of the emid network (e.g strength, degree, clustering coefficient, average distance, etc). They find different structural breaks and monthly seasonality patterns in the dynamic features of the network. Craig and von Peter (2010) find that a core-periphery model can be well fitted to the German interbank system. Core banks are a subset of all intermediaries (those banks that act as a lender and as a borrower in the interbank market) that share the property of a complete sub-network (there exist links between any two members of the subset). According to their findings, the German interbank market exhibits a tiered structure. As they empirically show, this kind of structure is highly persistent (stable) over time. Sachs (2010) concludes that the distribution of interbank exposures plays a crucial role for the stability of financial networks. She randomly generates interbank liabilities matrices and investigates contagion effects in different setups. She finds support for the knife-edge or tipping-point feature (as mentioned by Haldane (2009)), the non-monotonic completeness property of highly interconnected networks. 3.3.1 German interbank market In Q1 2011, there were 1921 MFIs in Germany, holding a total balance sheet of e 8233 Bn 10. The German banking system is composed of three major types of MFIs: 282 commercial banks (including four big banks and 110 branches of foreign banks) that hold approximately 36% of total assets, 439 saving banks (including 10 Landesbanken) that hold roughly 30% of system s assets and 1140 credit cooperatives 9 We present market credit spreads together with sector correlation matrix in Table 3.A.3 in the Appendix 3.A. 10 According to Deutsche Bundesbank s Monthly Report (March 2011). 111

Chapter 3: Centrality-based Capital Allocations and Bailout Funds (including 2 regional institutions) that hold around 12%. Other banks (i.e. mortgage banks, building and loan associations and special purpose vehicles) are in total 60 MFIs and represent approx. 21% of system s balance sheet. Our interbank (IB) network consists of 1764 active banks (i.e. aggregated banking groups). These banks are actively lending and/or borrowing in the interbank market. They hold total assets worth e 7791 Bn, from which 77% represent large loans and 23% small loans. Table 3.1 presents the descriptive statistics of the main characteristics and network measures of the German banks utilized in our analysis. 11 The average size of a bank s total IB assets is around e 1 Bn. As figures show, there are few very large total IB exposures, since the mean is between quantiles 90 th and 95 th, making the distribution highly skewed. Similar properties are observed for Total Assets, Large Loans and the Out Degrees, sustaining the idea of a tiered system with few large banks that act as interbank broker-dealers connecting other financial institutions (see Craig and von Peter (2010)). 12 3.3.2 Centrality measures In order to assign the interconnectedness relevance/importance to each bank of the system we rely on several centrality characteristics. The descriptive statistics of our centrality measures are summarized in Table 3.1. The information content of an interbank network is best summarized by a matrix X in which each cell x ij corresponds to the liability amount of bank i to bank j. As each positive entry represents an edge in the graph of interbank lending, an edge goes from the borrowing to the lending node. Furthermore, the adjacency matrix (A) is just a mapping of matrix X, in which a ij = 1 if x ij > 0, and a ij = 0 otherwise. In our case, the network is directed, and our matrix is weighted, meaning that we use the full information regarding an interbank relationship, not only its existence. We do not net bilateral exposures. Our network has a density of 0.7% given that it includes 1764 nodes and 22,752 links. 13 This sparse characteristic is typical for interbank networks (see for 11 In Section 3.8, we discuss in detail the properties of interbank liabilities distribution and compare them over time. Moreover, we provide a discussion over the dynamics of network measures. 12 One aspect that needs to be mentioned here is that the observed interbank network is not the complete picture, since interbank liabilities of German banks raised outside Germany are not reported to LED. For example, LED does not capture a loan made by Goldman Sachs to Deutsche Bank in London. This aspect might bias downwards exposures and centrality measures of big German banks that might borrow/lend outside the German interbank market. 13 The density of a network is the ratio of the number of existing connections divided by the total number of possible links. In our case of a directed network, the total number of possible links is 1764 1763 = 3, 109, 932 112

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Table 3.1: Interbank (IB) market and network properties Number of banks 1764** Number of links 22,752 Quantile mean std dev 5% 10% 25% 50% 75% 90% 95% Total IB Assets * 7591 13,089 35,553 100,450 310,624 868,299 1,647,666 990,433 7,906,565 Total IB Liabilities * 2640 6,053 19,679 61,450 180,771 527,460 1,212,811 990,433 7,782,309 Total Assets * 37,798 63,613 160,741 450,200 1,290,698 3,412,953 7,211,608 4,416,920 37,938,474 Total Large Loans * 8719 17,293 60,692 208,475 675,199 2,054,840 4,208,323 3,424,445 30,221,363 Total Small Loans * 8906 34,932 85,741 217,516 550,855 1,287,390 2,253,149 992,475 8,748,757 Out Degree 1 1 1 2 4 9,1 16 13 82 In Degree 1 1 4 9 14 19 25 13 37 Total Degree 2 3 5 11 18 27 38 26 111 Opsahl Centrality 51.5 80.6 165.8 345.9 791.6 2071.2 4090 3342 24,020 Eigenvector Centrality 0.000003 0.000019 0.000078 0.000264 0.001092 0.004027 0.009742 0.003923 0.023491 Weighted Betweenness 0 0 0 0 0 401.5 6225.8 10,491 82,995 Weighted Eigenvector 0.000004 0.000012 0,000042 0,000142 0.000611 0.002217 0.004839 0.003148 0.023607 Closeness Centrality 253.2 328.8 347.8 391.8 393,6 411.5 427.4 371.22 69.13 Clustering Coefficient 0 0 0 0.00937 0.04166 0.12328 0.16667 0.0379 0.0677 No of obs 88 176 441 882 1323 1587 1675 1764 1764 Note: ** no of banks active in the interbank market. * in thousand e; Data point: 2011 Q1 113

Chapter 3: Centrality-based Capital Allocations and Bailout Funds example Soramäki et al., 2007). As outlined by Newman (2010), the notion of centrality is associated with several metrics. In economics the most-used measures are: out degree (the number of links that originate from each node) and in degree (the number of links that end at each node), the strength (the aggregated sum of interbank exposures), betweenness centrality (the inverse of number of shortest paths that pass through a certain node), Eigenvector centrality (centrality of a node given by the importance of its neighbors) or clustering coefficient (how tightly connected is a node to its neighbors). The strength of a link is defined by the size (volume) of exposure and the direction (ingoing or outgoing) shows whether money has been lent/borrowed (i.e. out degree refers to borrowing relationships and in degree to lending ones). 14 Out Degree is one of the basic indicators and it is defined as the total number of direct interbank creditors that a bank borrows from: k i = N a ij (3.1) j Similarly, we can count the number of lending relationships from i to j (in degree). Since is a directed graph, we distinguish in our network analysis between out degrees and in degrees, referring to borrowing and lending. Degree is the sum of out degree and in degree. In economic terms, for example in case of a bank default, a certain number (the out degree) of nodes will suffer losses in the interbank market. Given that our matrix is weighted, we are able to compute each node s strength, that is its total amount borrowed from other banks: N s i = x ij (3.2) j The strength of a node is represented in Table 3.1 as total IB liabilities. Similarly, we construct the strength of the interbank assets. The degree distribution shows a tiered interbank structure. A few nodes are connected to many banks. For example, 20 banks (around 1%) lend to more than 100 banks each. On the borrowing side, 30 banks have a liability to at least 100 banks. These banks are part of the core of the network as defined by Craig and von Peter (2010). In terms of strength of interbank borrowing, 158 banks have a total IB borrowed amount in excess of e 1 Bn while only 27 banks have total interbank liabilities in excess of e 10 Bn. On the assets side, 103 banks lend more than e 1 14 For a detailed description of centrality measures related to interbank markets see Gabrieli (2011) and Minoiu and Reyes (2011). 114

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Bn and 25 financial institutions have German interbank assets in excess of e 10 Bn. Opsahl et al. (2010) introduce a novel centrality measure that we label Opsahl centrality. This measure combines the out degree (eq. 3.1) with the borrowing strength (total IB liabilities, eq. 3.2) of each node, using a tuning parameter ϕ: 15 OC i = k (1 ϕ) i s ϕ i (3.3) The intuition of a node with high Opsahl centrality is that, in the event of default, this node is able to infect many other banks with high severity. This translates into a higher probability of contagion (conditional on the node s default) compared with other nodes. Eigenvector centrality is a recursive concept. A bank is considered an important IB borrower if it borrows from many banks and they are themselves considered important (as IB borrowers). Eigenvector centrality is defined as the principal eigenvector of the adjacency matrix (see for example Bonacich (1987)). The centrality of each node corresponds to its component in the eigenvector. It tends to be large if the node has a high number of outbound connections (i.e., a high out degree) or has such connections to other important nodes or both, of course. In our analysis we use both an unweighted and a weighted version of eigenvector centrality. The latter uses full information of the liabilities matrix X, and the former only the existence of links, i.e., the adjacency matrix. 16 Betweenness centrality is a path-type measure that takes into account the number of shortest paths that pass through a certain node. A higher betweenness coefficient is related to a more strategically positioned node that acts as a bridge in connecting other nodes. In terms of lending, a bank with high betweenness will cut off a lot of intermediation in case of its default. We are using the weighted centrality version similar to the case of eigenvector centrality. Closeness centrality summarizes the shortest distances between any two nodes of the network. A node is regarded as closer to the center if its total distance to the other nodes is lower (compared to others), so information flow spreads fast in the network. So-called super-spreaders have the capacity of contaminating the core institutions in relatively short time, causing the collapse of the entire system. The clustering coefficient measures the likelihood of a certain node to be in a complete graph with its neighbors. Using these centrality measures, we intend to assign capital buffers to those nodes which create externalities to the banking system by being able to contaminate 15 In our analysis we set ϕ = 0.5, leading to the geometric mean between strength and degree. 16 We provide in Appendix 3.B a technical description of centrality measures. 115

Chapter 3: Centrality-based Capital Allocations and Bailout Funds the entire network. As we will discuss in Section 3.6 we intend to shift capital from the periphery to more central financial institutions according to alternative definitions of centrality such that contagion is contained and system losses are minimized. 3.4 Credit risk model Our credit risk engine is a one-period model, and all parameters are calibrated to a 1-year time span. In order to model credit risk, we utilize lending information from two data sources at different levels of aggregation: large loans and small loans. These loans are given to the real economy. Since borrowers of large loans are explicitly known, along with various parameters such as the loan volume, probability of default and sector, we can model their credit risk with high precision. When simulating defaults and migrations of individual borrowers, we can even account for the fact that loans given by different banks to the same borrower should migrate or default simultaneously. We cannot keep this level of precision for small loans because we only know their exposures as a lump-sum to each sector. Accordingly, we simulate their credit risk on portfolio level. 17 3.4.1 Modeling the returns of large loans In modeling credit portfolio risk we closely follow the ideas of CreditMetrics. 18 We start with a vector Y N (0, Σ) of systematic latent factors. Each component of Y corresponds to the systematic part of credit risk in one of the risk modeling (RM) sectors. The random vector is normalized such that the covariance matrix Σ is actually a correlation matrix (see Table 3.3(a)). In line with industry practice, we estimate correlations from co-movements of stock indices. 19 For each borrower k in RM sector j, the systematic factor Y j assigned to the sector is coupled with an independent idiosyncratic factor Z j,k N (0, 1). Thus, the stylized asset return of borrower (j, k) can be written as: X j,k = ρy j + 1 ρz j,k. 17 The parameters of our model are presented in Table 3.A.2 in Section 3.A. 18 For a detailed description of this model see Gupton et al. (1997). 19 Our correlation estimate is based on weekly time series of 19 EUROSTOXX industry indices from April 2006 to March 2011. The European focus of the time series is a compromise between a sufficiently large number of index constituents and the actual exposure of the banks in our sample, which is concentrated on German borrowers but also partly European wide. 116

Chapter 3: Centrality-based Capital Allocations and Bailout Funds The so-called intra-sector asset correlation ρ is common to all sectors. 20 The latent factor X j,k is mapped into rating migrations via a threshold model. We use 16 S&P rating classes including notches AAA, AA+, AA,...,B, plus the aggregated junk class CCC C. Moreover, we treat the default state as a further rating (D) and relabel ratings as numbers from 1 (AAA) to 18 (default). Let R 0 denote the initial rating of a borrower and R 1 the rating one period later. A borrower migrates from R 0 to rating state R 1 whenever X [θ(r 0, R 1 ), θ(r 0, R 1 1)], where θ is a matrix of thresholds associated with migrations between any two ratings. For given migration probabilities p(r 0, R 1 ) from R 0 to R 1, the thresholds are chosen in a way such that 21 P (θ(r 0, R 1 ) < X j,k θ(r 0, R 1 1)) = p(r 0, R 1 ), which is achieved by formally setting θ (R 0, 18) =, θ (R 0, 0) = + and calculating θ (R 0, R 1 ) = Φ 1 p (R 0, R), 1 R 0, R 1 17. R>R 1 The present value of each non-defaulted loan depends on notional value, rating, loan rate, and time to maturity. In this section we ignore the notional value and focus on D, the discount factor. A loan is assumed to pay an annual loan rate C until maturity T, at which all principal is due. We set T equal to a uniform value of 4 years, which is the digit closest to the mean maturity of 3.66 estimated from the borrower statistics. 22 Payments are discounted at a continuous rate r f +s (R) where r f is the default-free interest rate and s(r) is the rating-specific credit spread; see Table 3.A.3.(b). The term structure of spreads is flat. We ignore the risk related to the default-free interest rate and set r f = 2% throughout. The discount factor for a 20 This could be relaxed but would require the inclusion of other data sources. 21 In our model we use the 1981 2010 average one-year transition matrix for a global set of corporates from Standard and Poor s (2011). 22 The borrower statistics report exposures in three maturity buckets. Exposure-weighted averages of maturities indicate only small maturity differences between BS sectors. If we wanted to preserve them, the differences would shrink even more in the averaging process involved in the mapping from BS sectors to RM sectors. By setting the maturity to 4 years we simplify loan pricing substantially, mainly since calculating sub-annual migration probabilities is avoided. 117

Chapter 3: Centrality-based Capital Allocations and Bailout Funds non-defaulted, R-rated loan at time t is T ( ) D (C, R, t, T ) C + I{u=T } e (r f +s(r))(u t). (3.4) u=t+1 If the loan is not in default at time 1, it is assumed to have just paid a coupon C. The remaining future cash flows are priced according to eq 3.4, depending on the rating at time t = 1, so that the loan is worth C + D (C, R 1, 1, T ). If the loan has defaulted at time 1, it is worth (1 + C) (1 LGD), where LGD is an independent random variable drawn from a beta distribution with expectation 0.39 and standard deviation 0.34. 23 This means, the same relative loss is incurred on loan rates and principal. The spreads are set such that each loan is priced at par at time 0: C (R 0 ) e r f +s(r 0 ) 1, D (C (R 0 ), R 0, 0, T ) = 1. Each loan generates a return equal to D (C (R 0 ), R 1, 1, T ) + C (R 0 ) if R 1 < 18 ret (R 0, R 1 ) = 1 +, (1 + C (R 0 )) (1 LGD) if R 1 = 18 which has an expected value of Eret (R 0, R 1 ) = 1 + R 1 <18 p(r 0, R 1 ) [D (C (R 0 ), R 1, 1, T ) + C (R 0 )] +p (R 0, 18) (1 + C (R 0 )) (1 ELGD). Besides secure interest, the expected return incorporates credit risk premia that markets require in excess of the compensation for expected losses. We assume that the same premia are required by banks and calibrate them to market spreads, followed by slight manipulations to achieve monotonicity in ratings. 24 Having specified migrations and revaluation on a single-loan basis, we return to 23 Here we have chosen values reported by Davydenko and Franks (2008), who investigate LGDs of loans to German corporates, similar to Grunert and Weber (2009), who find a very similar standard deviation of 0.36 and a somewhat lower mean of 0.275. 24 Market spreads are derived from a daily time series of Merill Lynch euro corporate spreads covering all maturities, from April 1999 to June 2011. The codes are ER10, ER20, ER30, ER40, HE10, HE20, and HE30. Spreads should rise monotonically for deteriorating credit. We observe that the premium does rise in general but has some humps and troughs between BB and CCC. We smooth them out as they might have substantial impact on bank profitability but lack economic reason. To do so, we fit Ereturn (R 0 ) by a parabola, which turns out to be monotonous, and calibrate spreads afterwards to make the expected returns fit the parabola perfectly. Spread adjustments have a magnitude of 7bp for A and better, and 57bp for BBB+ and worse. Final credit spreads are presented in Table 3.A.3.(b). 118

Chapter 3: Centrality-based Capital Allocations and Bailout Funds the portfolio perspective. Assuming that k in (j, k) runs through all sector-j loans of all banks, we denote by R j,k 1 the rating of loan (j, k), which is the image of asset return X j,k at time 1. If bank i has given a (large) loan to borrower (j, k), the variable LL i,j,k denotes the notional exposure; otherwise, it is zero. Then, the euro return on the large loans of bank i is ret LL i = j,k LL i,j,k ret ( R j,k 0, R j,k ) 1. (3.5) This model does not only account for common exposures of banks to the same sector but also to individual borrowers. If several banks lend to the same borrower, which may concern a large exposure, they are simultaneously hit by its default or rating migration. 3.4.2 Modeling the returns of small loans As previously described, for each bank we have further information on the exposure to loans that fall short of the e 1.5 Mn reporting threshold of the credit register. However, we know the exposures only as a sum for each RM sector so that we are forced to model its risk portfolio-wise. However, as portfolios of small total volume tend to be less diversified than larger ones, we steer the amount of idiosyncratic risk adding to the systematic risk of each sector s sub-portfolio by its volume. Central limit theorem In this section, we sketch the setup only; details are found in Section 3.C. We consider the portfolio of a bank s loans belonging to one sector; they are commonly driven by that sector s systematic factor Y j, besides idiosyncratic risk. If we knew all individual exposures and all initial ratings, we could just run the same risk model as for the large loans. It is central to notice that the individual returns in portfolio j would be independent, conditional on Y j. Hence, if the exposures were extremely granular, the corresponding returns would get very close to a deterministic function of Y j, according to the conditional law of large numbers. 25 We do not go that far since small portfolios will not be very granular; instead, we utilize the central limit theorem for conditional measures, which allows us to preserve an appropriate level of idiosyncratic risk. Once Y j is known, the total of losses on an increasing number of loans converges to a (conditionally) normal random variable. This conditional 25 This idea is the basis of asymptotic credit risk models. The model behind Basel II is an example of this class. 119

Chapter 3: Centrality-based Capital Allocations and Bailout Funds randomness accounts for the presence of idiosyncratic risk in the portfolio. Correspondingly, our simulation of losses for small loans involves two steps. First, we draw the systematic factor Y j. Second, we draw a normal random variable, however with mean and variance being functions of Y j that match the moments of the exact Y j -conditional distribution. The Y j -dependency of the moments is crucial to preserve important features of the exact portfolio distribution, especially its skewness. Also, it preserves the correlation between the losses of different banks in their sector-j portfolios. Portfolio granularity An exact fit of moments is not achievable for us as it would require knowledge about individual exposures and ratings of the small loans, but an approximate fit can be achieved based on the portfolio s Hirschman-Herfindahl Index (HHI) of exposures. As we also do not explicitly know the portfolio HHI, we employ an additional large sample of small loans provided by a German commercial bank, to estimate the relationship between portfolio size and HHI. The estimate is sector specific. It provides us with a forecast of the actual HHI based on the portfolio s size and the sector. The forecast is the second input to the function that gives us Y j -conditional variances of the (conditionally normal) portfolio losses. Details are described in Section 3.C.1. 3.5 Modeling contagion As introduced in Section 3.2, we differentiate between fundamental defaults and contagious defaults (see Elsinger et al. (2006) or Cont et al. (2010), for instance). Fundamental defaults are related to losses from the credit risk of real economy exposures, while contagious defaults are related to the interbank credit portfolio (German only). 26 Moreover, we construct an interbank clearing mechanism based on the standard assumptions of interbank contagion (see e.g.upper, 2011): 1. Banks have limited liability. 2. Interbank liabilities are senior to equity but junior to non-bank liabilities (e.g. deposits). 26 Foreign bank exposures are included in Sector 17 of the real economy portfolio, since we have to exclude them from the interbank network. Loans made by foreign banks to German financial entities are not reported to LED. 120

Chapter 3: Centrality-based Capital Allocations and Bailout Funds 3. Losses related to bank defaults are proportionally shared among interbank creditors, based on the share of their exposure to total interbank liabilities of the defaulted bank. In other words, its interbank creditors suffer the same loss-given-default. 27 4. Non-bank assets of a defaulted bank are liquidated at a certain discount. This extra loss is referred to as fire sales and is captured by bankruptcy costs, defined below. The clearing mechanism closely follows Eisenberg and Noe (2001) and the extension by Elsinger et al. (2006) to bankruptcy costs. 3.5.1 Losses and bankruptcy costs In our analysis, we are particularly interested in bankruptcy costs since they represent a dead-weight loss to the economy. We model them as the sum of two parts. the first one is a function of bank s total assets, because there is empirical evidence for a positive relationship between size and bankruptcy costs of financial institutions; see Altman (1984). The second part incorporates fire sales and their effect on the value of the defaulted bank s assets. For their definition, recall eq 3.5 which determines the return ret LL i (in euros) made by each bank i on its large loans. Similarly, we define in eq 3.16 in Appendix 3.C bank s return on small loans. We switch the sign and define losses L real i ret LL i ret SL i, highlighting that, so far, we deal with losses related to the real economy. If these losses exceed the bank s capital K i, we label them as fundamental defaults, and the bank s creditors suffer a loss the extent of which equals max ( 0, L real ) i K i. Note that this is a loss before bankruptcy costs and contagion. In the whole economy, the fundamental losses add up to L real i ( max 0, L real ) i K i We intend to proxy lump-sum effects of fire sales to the total fundamental loss in the system. The larger L real, the more assets will the creditors of defaulted banks try to sell quickly, which puts asset prices under pressure. We proxy this effect by a system-wide relative loss ratio λ being monotonic in L real. 27 We do not have any information related to collateral or the seniority of claims. 121

Chapter 3: Centrality-based Capital Allocations and Bailout Funds In total, if bank i defaults, we define bankruptcy costs as the sum of two parts related to total assets and fire sales: ( BC i φ T otalassets i L real i ) + λ ( L real ) max ( 0, L real i K i ) (3.6) We consider φ the proportion of assets lost due to litigation and other legal costs. In our analysis we set φ = 5%. 28 It is rather for convenience than for economic reasons that we set the function λ equal to the cumulative distribution function of L real. Given this choice, the more severe total fundamental losses in the system are, the closer λ gets to 1. 29 3.5.2 Eisenberg and Noe - interbank contagion algorithm When a bank defaults (or a group of them), it triggers losses in the interbank market. If interbank losses (plus losses on loans to the real economy) exceed the remaining capital of the banks that lent to the defaulted group, this can develop into a domino cascade. At every simulation when interbank contagion arises, we follow Elsinger et al. (2006), who build on Eisenberg and Noe (2001), to compute losses that takes into account the assumptions (1) (3) at the beginning of Section 3.5. However, we describe the mechanism in terms of losses rather than of a clearing payment vector. 30 The following set of definitions and equations describe an equation system. Each bank incurs total portfolio losses L i, which consists, first, of its fundamental losses made in the real economy 31, and second, of losses on its interbank loans, defined below in eq 3.10: L i = L real i + L IB i. (3.7) A bank defaults if its capital K i cannot absorb the real-economy and interbank 28 Our results remain robust also for other values φ {1%, 3%, 10%}. Alessandri et al. (2009) and Webber and Willison (2011) use contagious bankruptcy costs as a function of total assets, and set φ to 10%. Given the second term of our bankruptcy costs function that incorporates fire sales effects, we reach at a stochastic function with values between 5% and 15% of total assets. 29 We acknowledge that real-world bankruptcy costs would probably be sensitive to the amount of interbank credit losses, which we ignore. This simplification, however, allows us to calculate potential bankruptcy costs before we know which bank exactly will default through contagion, so that we do not have to update bankruptcy costs in the contagion algorithm. If we did, it would be extremely difficult to preserve proportional loss sharing in the Eisenberg-Noe allocation. 30 The clearing payment vector is not a sufficient statistic for the payoffs to all claimants. It is so for the interbank market but, for instance, it does not contain information on the size of losses to non-bank debtors or equity holders. 31 This loss can also be negative, i.e.,the bank makes a profit on these assets. 122

Chapter 3: Centrality-based Capital Allocations and Bailout Funds credit losses. We define the default indicator as 1 if K i < L i, D i = 0 otherwise. (3.8) We have modeled bankruptcy costs such that their (potential) extent BC i is known before contagion; i.e., they are just a parameter of the equation system. Yet, whether they become real is captured by D i. Total portfolio losses and bankruptcy costs are now distributed to the bank s claimants. If capital is exhausted, further losses are primarily borne by interbank creditors since their claim is junior to other debt, as stated in assumption (4) at the beginning of Section 3.5. Bank i causes its interbank creditors an aggregate loss of Λ IB i = min (l i, max (0, L i + BC i D i K i )), (3.9) which is zero if the bank does not default. The greek letter signals that Λ IB i is a loss on the liability side of bank i, which causes a loss on the assets of its creditors. Recall that x ij denotes interbank liabilities of bank i to bank j. The row sum l i = N j=i x ij defines total interbank liabilities of bank i. This gives us a proportionality matrix π to allocate losses, given by x ij l π ij = i if l i > 0; 0 otherwise. If the loss amount Λ IB i is proportionally shared among the creditors, bank j incurs a loss of π ij Λ IB i due to the default of i. Also bank i may have incurred interbank losses; they amount to L IB i = N k=1 π ji Λ IB j, (3.10) which provides the missing definition in eq 3.7. This completes the equation system eq 3.7 eq 3.10. We can either consider the vector of L i as a solution or, equivalently, L i +BC i D i. The algorithm proposed by Eisenberg and Noe (2001) gives us a unique result. 3.6 Optimization This paper compares losses in the system, according to some loss measure and subject to different capital and bailout rules. The comparison allows us to minimize 123

Chapter 3: Centrality-based Capital Allocations and Bailout Funds the loss measure. However, an optimal bailout or capital rule is not the sole focus of this paper. There are two reasons for this. First, the loss functions that would be optimized are only few of many that could be the optimal outputs of the system. We discuss different target functions (i.e. system losses) in Section 3.6.2. Our emphasis is on how the different loss functions interact with the different capital or bailout rules, to provide insights into how the rules work. Second, the rules themselves are subject to a variety of restrictions. These include the fact that the rules must be simple and easily computed from observable characteristics, and they must be smooth to avoid the threshold phenomenon that have been noted in the banking literature with capital requirements based on step functions. Simplicity is important not just because of computational concerns. Simple formal rules are necessary to limit discretion on the ultimate outcome of capital rules. Too many model and estimation parameters set strong incentives for banks to lobby for a design in their particular interest. While this is not special to potential systemic risk charges, it is clear that those banks who will most likely be confronted with increased capital requirements are the ones with the most influence on politics. Vice versa, simplicity can also help to avoid arbitrary punitive restrictions imposed upon individual banks. In this sense, the chapter cannot offer deliberately first-best solutions for capital requirements. In our analysis we keep the total amount of capital in the system constant; otherwise, optimization would be straightforward: more capital for all, ideally 100% equity funding for banks. 32 As a consequence, when we require some banks to hold more capital, we are willing to accept that others may hold less capital as in the benchmark case. Taken literally, there would be no lower limit to capital except zero. However, we also believe that there should be some minimum capital requirement that applies to all banks for reasons of political feasibility, irrespective of their role in the financial network. Implementing a uniform maximum default probability for all banks might be one choice. Finally, there are also technical reasons for simplicity. Each evaluation step in the optimization requires a computationally expensive full-fledged simulation of the financial system. We therefore restrict ourselves to an optimization over one parameter, focusing on whether the various network measures analyzed are able to capture aspects actually relevant for total system losses at all. 3.6.1 Capital allocations In this subsection, we introduce a range of simple capital rules over which we minimize the total system loss. The range represents intermediate steps between two 32 We are aware that are also costs associated with holding more capital. Thus, in this exercise we are optimizing our target function subject to total capital in the system being constant. 124

Chapter 3: Centrality-based Capital Allocations and Bailout Funds extremes. One extreme is our benchmark case, by which we understand capital requirements in the spirit of Basel II, i.e., a system focused on a bank s portfolio risk (and not on network structure). For our analysis we require banks to hold capital equal to its portfolio VaR on a high security level α=99.9%, in line with the level used in Basel II rules for the banking book. There is one specific feature of our VaR measure, however. In line with Basel II again, the benchmark capital requirement treats interbank loans just as other loans. For the determination of bank i s benchmark capital K α,i (and only for this exercise), each bank s German interbank loans (on the asset side) are merged with loans to foreign banks into portfolio sector 17 where they contribute to losses just as other loans. 33 capital adds up to T K α i K α,i. In the whole system, total required The other extreme has one thing in common with the benchmark case: total required capital in the system must be the same. On bank level, required capital consists of two components in this case. One is given by a comparably low amount K min,i derived under a mild rule, which we set to the portfolio VaR on a moderate security level of 99%, again treating interbank loans as ordinary loans. This limits bank PDs to values around 1%, which could be a politically acceptable level. 34 The other component is allocated by means of a centrality measure. Given Centrality i to be one of the measures introduced in Section 3.3, the simple idea is to allocate the system-wide capital relief from the mild capital rule proportionally to the centrality measure: K centr,i K min,i + (T K α T K min ) Centrality i i Centrality i, (3.11) where T K min i K min,i. Having defined the two extremes K α and K centr (now understood as vectors), the range of regimes we optimize over is given by a linear combination between them, which automatically keeps total required capital constant and guarantees that bank individual capital is always positive, since both 33 Default probabilities for these loans are taken from the Large Exposure Database in a similar way as for the loans to the real economy. 34 Actual bank PDs can be below or above 1 percent, depending on whether defaults in a risk model, where interbank loans are directly stressed by systematic factors, are more frequent than in presence of contagion (but without direct impact of systematic factors). However, the probability of fundamental losses cannot exceed 1%. 125

Chapter 3: Centrality-based Capital Allocations and Bailout Funds extremes are positive: 35 K (β) βk α + (1 β) K centr, 0 β 1. The parameter β is subject to optimization. In general, the approach is not limited to one centrality measure. We could define multiple corner regimes based on a subset of centrality measures and optimize over the convex hull of them and the benchmark case. This procedure is numerically expensive and not yet carried out. Clearly, re-allocating capital implies that some banks will have to hold higher capital (lower PDs) and some lower capital (higher PDs) than in the benchmark case. This might be politically undesirable, requiring a modification of our approach. For example, regulators could agree on a total amount of additional capital to be held in the system, compared to T K α, that would be allocated using centrality-based rules. 3.6.2 Target function(s) The optimization process tries to minimize a measure of expected system loss (i.e. the target function). The mechanism of contagion proposed by us has several sets of agents, each of whom suffers separate losses. Initially, the portfolio of assets outside the interbank market is shocked to give a loss to the real economy. Bankruptcy can ensue which causes losses to the interbank sector (which being a junior claimant on the residual, is the primary recipient of the loss) and possible losses to the nonbanking sector (to the extent that the losses to the banking sector are limited by the its liabilities to the defaulting bank). One can define the expected total loss, which is just the sum of the bankruptcy costs of the defaulted banks: ET L = E i BC i D i (3.12) where BC i is the bankruptcy cost of bank i, if the bank goes bankrupt, and where D i is the default indicator function, and (L i K i ) is just the loss of bank i in excess of its capital. 36 This presumes that the bank goes bankrupt if its losses, L i exceed 35 We could also intermediate between the two extremes in other ways, e.g. by flooring at K min and appropriate subsequent rescaling, to keep total capital constant. However, we would expect more interesting results from a (yet outstanding) optimization over linear combinations of multiple centrality measures, than of such kind of modification. In addition, our approach has the advantage that is is differentiable in β rather than being Lipschitz continuous only, as it would be the case with flooring. 36 L i refers to portfolio losses of both interbank and real-economy assets as introduced in eq 3.7. 126

Chapter 3: Centrality-based Capital Allocations and Bailout Funds its capital K i. This is a total social deadweight loss that does not include the initial portfolio loss due to the initial shock. Since these losses are attributed to bank share holders, and they are rewarded for bearing this risk we are not counting them in this initial version. In our empirical analysis we use this first version of the system losses. While this is a compelling measure of social loss, there are distributional reasons that it might not be the only measure of interest. We minimize the expected loss function with respect to different capital rules, in the above example exemplified by K i. The optimal routine requires as inputs the losses that are associated with each bank from the credit risk model and contagion algorithm. The optimization process is repeated for various initial capital requirements imposed by the VaR for each bank (e.g.v ar(α = 99.9%)) and the measures of both balance sheet and network bank characteristics that the capital allocation rule is based on. 37 3.6.3 Setting capital allocation(s) procedure In summary, the main steps in setting capital allocations are: 1. Compute different network measures based on interbank exposures and the network topology. (presented in Table 3.1) 2. Set minimum capital. In our analysis it is set at the VaR (α = 99%) where interbank loans are treated as ordinary loans. It (imperfectly) implements a cap of 1% on bank PDs. 3. The difference between benchmark capital (i.e. VaR(α = 99.9%)) and minimum capital (i.e. VaR(α = 99%)) is pooled and divided based on a capital allocation rule. 4. In each capital allocation rule, given the centrality measure chosen and the coefficient β, calculate required capital for each bank. This amount is assumed to be actually held by banks. 5. Generate a large simulation sample of losses to real-economy bank portfolios. For each capital allocation and each simulation scenario, let the interbank contagion mechanism run. This gives, for each allocation, a sample of aftercontagion losses from which the target function (total expected losses) and further measures are calculated. 38 37 We refer to other target functions in Appendix 3.D. 38 During simulation procedure, we select scenarios where we have at least one fundamental bank default, i.e., when there exists and at least one i for which L real i > K i. Otherwise, interbank contagion does not exist. This selection is a simple form of importance sampling, in a purely numeric mean. Expectation values are not conditional on it. 127

Chapter 3: Centrality-based Capital Allocations and Bailout Funds 6. For each centrality measure, perform a simple grid search over β to minimize the target function. In Section 3.7 we provide an empirical analysis of this methodology using centrality measures discussed in Section 3.3. 3.6.4 Bailout fund mechanism Our second direction to improve the resilience of financial system reflects a bailout fund mechanism. The fund acts a lender of last resort, covering negative equity resulting from portfolio losses and recapitalizing the bank (with an amount related to its interbank assets). In our proposed policy tool, the bailout fund obtains resources directly from banks. Banks receive a capital relief and these resources are pooled in a bailout fund. The bailout fund main features follow some basic ad hoc rules designed by us. These rules can be relaxed or extended. The focus of the bailout mechanism is to provide a simplified framework for policy makers when deciding to rescue or not some financial institutions. Up to now this implicit blanket guarantee was given by the tax payer to systemically important institutions without a clear definition of who qualifies or not. The bailout fund has the following features: i) it has limited resources; ii) it saves banks based on a ranking rule, obtained from a centrality-based index; iii) it utilizes funds to rescue and recapitalize banks before the interbank contagion takes place. When a bank is saved by the bailout fund, it is also recapitalized with a buffer ɛ = 20% of total interbank assets, such that it can sustain further losses on its interbank assets generated by contagious defaults. These funds are deducted from the resources of the bailout fund. In case that the remaining resources are not sufficient to cover 20% of bank s IB assets, the capital buffer absorbs all resources (due to compliance with rule (i)). First, similarly to capital re-allocation as defined in Section 3.7.1, we choose a parameter β [0, 1] which now, however, defines a trade-off between a centrality measure and capital in the benchmark case, and compute an index for each financial 128

Chapter 3: Centrality-based Capital Allocations and Bailout Funds institution as a β-weighted average:; both variables are transformed such that they are in a comparable range. More formally, we set index i = β log (V ar α,i ) Centrality i + (1 β) max i (log (V ar α,i )) max i (Centrality i ). This index is then mapped into a ranking. necessary in the order down the rank. The bailout fund rescues banks if Second, we vary the maximum resources of the bailout fund: Resources BF = η i (K α, i K min, i ) where η ranges between 0 to 100%. Banks get a capital release that sums up for the entire system to i(k α, i K min, i ). At the same time banks pool the amount Resources BF into the bailout fund. On the one hand, banks hold less capital compared to the benchmark capital allocation but on the other hand there is a targetedbailout fund that is able to inject fresh capital into banks whenever it is needed (banks default) and there are still resources left in the fund. 3.7 Results In this section we show case our framework in both policy directions discussed above: first, Subsection 3.7.1 outlines our results for capital re-allocations using centrality measures and, second, Subsection 3.7.2 presents an empirical application of the bailout fund mechanism. 3.7.1 Capital allocations Our main results from capital re-allocation exercise are depicted in Figure 3.2. As defined in Equation 3.12, the target function that we compare across centrality measures and within one measure is the total expected bankruptcy cost. Our benchmark allocation (based only on VaR) is represented by the point where β = 1. As observed, some centrality measures help to improve the stability of banking system in terms of expected total losses. Among them are Total Assets (TA), Opsahl centrality, IB Liabilities, Out Degrees, Weighted Eigenvector and Eigenvector centrality. In contrast, capital allocations based on Clustering coefficient, Closeness, Weighted Betweenness, IN degrees and IB Assets have a higher expected loss than in the benchmark allocation (when weight β on VaR measure is 100%), for any β < 1. 129

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Opsahl Centrality (Equation 3.3) dominates any other network measures apart from Total Assets. By setting a 70% weight on the difference between initial capital allocation (VaR (α = 99.9%)) and minimum capital (VaR(α = 99%)) and the rest on Opsahl Centrality measure, we obtain a improvement of around 20% of expected system losses, from e 1211 Mn to e 977 Mn. The allocation based on TA beats any network based measure, improving the expected loss by almost 40%, reducing it from e 1211 Mn to e 730 Mn. 39 Figure 3.2: A comparison of different capital allocations across network measures Expected Total System Losses Thousand eur 4 3.5 3 2.5 2 1.5 x 10 6 Clustering Closeness Wei Eigen Wei Betweenness Eigen Opsahl Total Degrees In Degrees Out Degrees Total Assets IB Liabilities IB Assets 1 0.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 β Note: On Y-axis is represented the size of Total Expected System Loss (as measured by Equation 3.12) from all defaults (both fundamental and contagious) under different capital allocations. On X-axis, β represents the weight on VaR (whereas (1-β) represents the weight on centrality measure). Figure 3.3 (a) and Figure 3.3 (b) present expected loss functions under best performing centrality measures: Opsahl Centrality and Total Assets. In the case of Opsahl centrality (Fig. 3.3 (a)), on one hand, expected losses of fundamental defaults are always above the benchmark case and, on the other hand, losses from contagion reach a minimum when β = 0.4. This allocation does not coincide with the best allocation in terms of total system losses (β = 0.7). The non-linearity 39 Since bankruptcy costs (BC) are directly linked to TA (eq 3.6), this might be one factor that explains the good performance of TA in minimizing system losses. 130

Chapter 3: Centrality-based Capital Allocations and Bailout Funds observed in the case of Opsahl centrality is similar to other centrality measures (e.g. weighted eigenvector, total liabilities or Out Degrees). This is not true in the case of TA allocations (Fig. 3.3 (b)). TA have a rather monotonous effect on total expected system losses. Although varying the weight between TA and VaR has no impact on expected losses from fundamental defaults, it has a strong mitigating effect on expected losses from contagion. In this case, the best allocation is β = 0, meaning all weight on TA apart from the minimum capital (K min ) that was set based on VaR (at a lower quantile, i.e. α = 99%). Figures 3.4 (a) and 3.4 (b) reflect the frequency distributions before and after contagion based on three allocation rules: the benchmark case (all weight on VaR measure), the best allocation based on the combination between VaR measure and Total Assets (TA), and the best allocation based on the combination between VaR measure and Opsahl centrality, respectively. These results are obtained with 20,000 simulations employing importance sampling. 40 On one hand, results depicted in Figure 3.4 (a) show that the best allocation based on both Total Assets (TA) and VaR gives a frequency distribution of fundamental defaults (before IB contagion) with longer and fatter tail than in the case based only on VaR. Best allocation based on Opsahl centrality is something in between. There are less banks with a PD very close to 0 than in the case of benchmark allocation (VaR) but PDs of several banks increase relative to the benchmark case. On the other hand, the frequency distributions of PDs observed in Figure 3.4 (b) after IB contagion show a completely different picture. Best allocations based on TA and Opsahl perform much better in terms of overall distribution of probability of defaults than in the benchmark case. Figure 3.5 (a) depicts the relationship between total number of fundamental defaults and contagious results (out of 20,000 simulations, with importance sampling) of each individual bank. In the case of the benchmark allocation (i.e. VaR), the relationship is clearly non-linear. Some banks, although have a low fundamental PD experience much higher rates of default due to contagion. In contrast, when using Opsahl centrality some banks have a higher probability of default that can be close to 0.5% in some cases before contagion and 0.7% after contagion, but there is a linear relationship between fundamental and contagious defaults, sign that the incidence of contagious systemic collapses has decreased. We observe also a two tier structure, and we investigate further which bank characteristics can be distinguished between the two groups. Similar results are shown for the best allocation under TA when we compare them with the benchmark case in Figure 3.5 (b). Thus, we claim 40 We select simulations that result in at least one interbank default and weight them by their expected probability. 131

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Figure 3.3: Expected system losses: All defaults, fundamental defaults and contagious defaults 2 x 10 6 All Defaults Fundamental Defaults Contagious Defaults 15 x 10 5 All Defaults Fundamental Defaults Contagious Defaults 1.8 1.6 1.4 10 Expected Losses Thousand eur 1.2 1 0.8 Expected Losses Thousand eur 5 0.6 0.4 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 β 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (a) Capital allocations under rules based on Opsahl(b) Capital allocations under rules based on Total Centrality Assets Note: On Y-axis is represented the size of Expected System Loss (as measured by Equation 3.12) from fundamental, contagious defaults, and all defaults under different capital allocations. On X-axis, β represents the weight on VaR (α = 99.9%), whereas (1-β) represents the weight on centrality measure. β that allocations based on TA and Opsahl centrality shift capital from smaller or less interconnected nodes to bigger or more interconnected, respectively, and therefore the system becomes more resilient to interbank contagion. In order to get the full picture, instead of focusing on unconditional expected bankruptcy costs we now switch to tail expectations. 41 First we provide the distributions under benchmark, TA and Opsahl best allocations conditional that losses exceed the 99% quantile. Conditional expected losses under benchmark allocation are equal to around e 115 Bn, while under TA allocation are almost half. With Opsahl centrality best allocation conditional expected losses are around e 89 Bn. Total system losses reach a maximum around e 900 Bn. This amount is equivalent to a total system collapse (approx. 10% of the total system assets). Zooming further into the conditional tail and measuring losses above 99.9% reinforces the idea that TA and Opsahl centrality perform better than the benchmark allocation. Top.1% losses exceed on average e 435 Bn in the case of TA, e 589 Bn under the best allocation using Opsahl centrality and around e 663 Bn under the benchmark case. We present these results in Figure 3.E.2(a) and Figure 3.E.2 (b) in Appendix 3.E. 41 In Figure 3.E.1 we present the unconditional distributions of system losses, as defined in eq 3.12. The unconditional mean under benchmark allocation (VaR) equals e 1211 Mn while under best TA allocation it is e 730 Mn and under best Opsahl centrality allocation it is e 977 Mn. 132

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Figure 3.4: Frequency distributions of individual bank PDs 4500 5000 TA VaR Opsahl 4000 3500 TA VaR Opsahl 4000 3000 pdf 3000 pdf 2500 2000 2000 1500 1000 0 * * 0 0.5 1 1.5 2 2.5 3 3.5 4 x 10-3 (a) Before IB contagion 1000 500 0 0 0.5 1 1.5 2 2.5 3 3.5 x 10-3 (b) After IB contagion Note: On Y-axis is presented the frequency distribution (no of occurrences) of individual bank PDs. On X-axis, are represented PDs (per bank). Sign * denotes that the distribution has a longer tail but has been truncated and observations after that threshold are aggregated at that point. Capital allocations are: i) BLUE based on Total Assets (TA) (with min capital VaR (α = 99%)), ii) GREEN based on VaR (α = 99.9%) [our benchmark allocation], iii) ORANGE based on Opsahl centrality. Results obtained with 20,000 simulations (using importance sampling). * * Finally, Figure 3.6 shows ratios between best capital allocations under Total Assets (TA), Opsahl centrality, and Weighted Eigenvector centrality, respectively, to VaR benchmark allocation. The first observation is that ratios of TA to VaR allocations have a maximum around two. That implies that for some banks capital doubles under this allocation. On the lower side, some banks give up capital floored by a minimum of 20% of the initial capital allocation. The ratios of Opsahl best allocation to benchmark allocation looks more dispersed (a higher variance). There is one bank that receives 13 times more capital than in the benchmark case, and several that hold around four times more. On the lower side, banks hold around 60% of initial allocation. The third allocation, that involves a tradeoff between Weighted Eigenvector centrality and VaR measure, shows one outlier with around seven times more capital than in the benchmark case and another node with twice the initial capital. On the lower side, results are similar to the Opsahl best allocation. To conclude, we infer that TA allocation performs the best also because the extra capital allocated to some banks is not much more in excess. In other words. it is the most closely related allocation to the benchmark one. Hence, TA best allocation outperforms any other allocation with respect to our target function. Another intuitive inference is that the other centrality measures might mis-reallocate capital. For example, let s say that benchmark capital for a bank represents 8% of the total assets. If under the new allocation rule this bank receives 13 times more 133

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Figure 3.5: Occurrences of individual bank defaults (a) Opsahl vs VaR (b) Total Assets (TA) vs VaR Note: On X-axis - Fundamental defaults; on Y-axis - Contagious defaults. Results obtained with 20,000 simulations (using importance sampling). 134

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Figure 3.6: Comparison of different capital allocations based on: Total Assets, Opsahl and Weighted Eigenvector 14 12 Total Assets Opsahl Wei Eigen 10 8 6 4 2 0 1 1.2 1.4 Note: On Y-axis are represented ratios of best performing capital allocations (from each measure) to VaR benchmark allocation (i.e. K/Kα ) capital, that represents 104% of the total assets. Due to this misallocation likelihood, we infer that more constraints should be design in order to achieve better performing allocations using centrality measures. We leave this extra mile for future research. 3.7.2 Bailout fund mechanism As we discussed in Section 3.6.4, we design a second policy direction to deal with SIFIs in form of a bailout fund mechanism. Figure 3.7 depicts the probability distributions of bank defaults at different levels of total available resources of the bailout fund using a ranking of banks based on Opsahl centrality (top row) and using a ranking based on Total Assets (bottom row) in contrast to a ranking based only on VaR measure. As we increase the size of the bailout fund, the bank ranking looses importance. In the case of a bailout fund with 100% resources, rankings that consider VaR, TA or Opsahl centrality lead to very similar PD distributions. The difference is made when the bailout fund has less resources. Thus, targeting them plays an important role. With 10% resources of the maximum size, the ranking based on Opsahl centrality combined with the size delivers the best results. Rankings are actually very similar. Compared with capital re-allocations, the bailout fund mech- 135

Chapter 3: Centrality-based Capital Allocations and Bailout Funds anism targets resources when they are needed (losses exceed existing capital) and to whom is more systemically important (based on the bank ranking). This method gives less room to misuse resources. Still the difference is made by which entities to save or not, given the limited amount of resources. Using maximum amount of resources, the expected system losses are close to 0. With 40% of the funds, the expected system losses are similar to the optimal capital allocation obtained above under Opshal centrality. Figure 3.8 shows us how the expected total system loss evolves, at different levels of expected bailout funds and at different weights on centrality measure as compared to VaR. Expected bailout funds increase as the bailout fund has more resources (i.e. as η increases). Intuitively, as resources of the bailout fund increase (X-axis) the expected system losses decrease (Y-axis). Fund resources increase from e 54 Bn (20% of the maximum resources) to nearly e 270 Bn (100% of the maximum bailout fund). This effect is non-linear. On the Z-dimension, in the case of the maximum bailout fund, there is a minimum at the ranking based on 90% weight on VaR and 10% weight on Opsahl centrality. The optimal bailout rule changes as bailout fund size decreases, with the weight on Opsahl centrality gaining in importance. 136

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Figure 3.7: Pdfs of bank defaults AFTER contagion using a bailout fund mechanism with rules based on: Opsahl (Ops) versus VaR (upper level); Total Asstets (TA) versus VaR (lower level). 0.2 1 0.9 Ops Ops 0.18 VaR 0.9 VaR 0.8 0.16 0.8 0.7 Ops VaR 0.14 0.7 0.6 0.12 0.6 0.5 0.1 0.5 pdf 0.08 0.4 0.06 0.3 0.04 0.2 0.02 0.1 0 40 60 80 100 120 140 160 (a) Bailout funds: 10% 0 10 15 20 25 30 35 * * pdf pdf 0.4 0.3 0.2 0.1 (b) Bailout funds: 50% 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 (c) Bailout funds: 100% 1 0.9 0.2 TA TA 0.18 VaR 0.9 VaR 0.8 0.16 0.14 0.8 0.7 0.7 0.6 TA VaR 0.12 0.6 0.5 0.1 0.5 0.04 0.02 0 40 60 80 100 120 140 160 * * pdf pdf 0.4 0.08 0.4 0.3 0.06 0.3 0.2 0.2 (d) Bailout funds: 10% 0.1 0 10 15 20 25 30 35 (e) Bailout funds: 50% 0.1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 * * pdf Note: Results obtained with 10,000 simulations (with importance sampling). (f) Bailout funds: 100% 137

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Figure 3.8: Bailout efficiency surface: Opsahl centrality x 10 6 4.5 4 Expected System losses 3.5 3 2.5 2 1.5 1 0.5 0 1 1.2 1.4 1.6 1.8 x 10 6 0 Expected Bailout Funds 0.2 0.4 0.6 0.8 1 weight on VaR versus Centrality Note: Expected bailout funds are the expected value of the utilized resources, as we increase the capital of Bailout fund from e 54 Bn to e 270 Bn in steps of e 54 Bn (20% of e 270 Bn) from the maximum amount pooled (i.e. ( V ar 99.9% +V ar 99% ) over all 1764 banks is e 270 Bn). Results obtained with 10,000 simulations (using importance sampling). 3.8 Robustness checks In this section we provide an analysis of the stability of centrality measures, liabilities distributions and robustness checks of the parameters utilized throughout this chapter. 3.8.1 Interbank liabilities In Table 3.1 we have shown the properties of the interbank assets and liabilities for our empirical application using the data reported at the end of Q1 2011. Since the utilized data is highly confidential, we describe in this section the distributional properties of the interbank liabilities. In Figure 3.F.1 we attempt to compare the goodness-of-fit for a power law distribution versus a log normal distribution. The power law α-coefficient is 0.45 while the constant term around 4. 138

Chapter 3: Centrality-based Capital Allocations and Bailout Funds As a standard convention, the minus in front of α corresponds to the negative slope. Figure 3.F.2 shows ranked liabilities for each of 2005, 2007, 2009, and 2011 first quarter reported data. 42 We find that the α-coefficient changes from 0.51 in 2005 to 0.45 in 2011. Similar the constant decreases from 4.7 in 2005 to 4 in 2011. At the top of exposures we observe an increase in volumes over time. Number of interbank liabilities decreases from 29,000 in 2005 to 22,000 in 2011. This effect is probably 43 also a consequence of mergers and acquisitions in the German banking sector. Most of the interbank volume moves into intra-group transactions. 3.8.2 Network structure As a robustness check of our results, we compare interbank properties, liabilities and centrality measures over the period 2005-2011. Tables 3.F.1, 3.F.2, and 3.F.3 are similar to Table 3.1. As mentioned before both number of banks and number of interbank exposures decrease by 11% and around 21%, respectively, from 2005 to 2011. The average individual bank total IB exposure increased from e 900 Mn to almost e 1 Bn. The average number of lending and borrowing connections (i.e. total degree) decreases from 29 to 26. The distributions of centrality measures are very similar over this time span. For example, looking at different quantiles, mean or standard deviation of Opsahl centrality distributions we observe similar ranges across the four snapshots presented in this chapter. At the higher end of the distribution, connectivity as measured by Opsahl centrality peaks in 2007 Q1, meaning that big banks are trading less in the interbank market. Very small banks show a lag in this behavior, with a peak in 2009 Q1. Weighted betweenness and clustering coefficient show a very skewed distribution. Most of the banks have a zero coefficient in this case. We infer that this feature has an impact on our results when we try to re-allocate capital based on these network measures. Over time, these two indicators show a less clustered network structure and rather a tiered one. This feature is strengthen by the dynamics of closeness centrality, that decreases over the period 2005-2011. On average, eigenvector-type centrality bottoms in 2009 Q1, in the midst of the financial crisis. At the top of the distribution, the most recent results reveal that important banks became even more interconnected compared to before the crisis period. This comparison over time leaves room for a dynamic re-adjustment process of the capital re-allocations. Since interbank network properties do not change 42 Due to confidentiality reasons, we have transformed real data into a simple moving average using three consecutive data points. 43 The number of active banks decreases from 1.989 in 2005 to 1.764 in 2011. 139

Chapter 3: Centrality-based Capital Allocations and Bailout Funds overnight, we consider a one-two year gap between re-estimations as adequate. 3.8.3 Credit risk parameters Regarding the robustness of the parameters of the credit risk model, we have rerun several times the computation of VaR measures at quantile α = 99.9%. For this computation we employed a new set of 1 Mn. simulations, and kept the same generated PDs. Results are very similar, the average standard deviation of the individual VaR measures at this quantile is under 2%. For the 99% VaR, the variance decreases drastically (i.e. under.5%). 3.9 Conclusion In this chapter we present a tractable framework to assess the impact of different capital allocations on the financial stability of large banking systems. Furthermore, we attempt to provide some empirical evidence of the usefulness of network-based centrality measures. Combining simulation techniques with confidential bank balance sheet data of the Deutsche Bundesbank, we test our framework for different capital re-allocations. Our aim two fold. First, to provide regulators and policy makers with a stylized framework to assess capital for SIFIs. And second, to give a novel direction to future research in the financial stability field using network analysis. Our main results show that there are certain capital allocations that improve financial stability, as defined in this chapter. Focusing on the system as a whole and assigning capital allocations based on networks metrics produces outperforming results compared with the benchmark capital allocation, that is based solely on the individual bank balance sheet. Commonalities among bank portfolios make the financial system vulnerable to large macro-shocks. Our findings come with no surprise when considering a stylized contagion algorithm. The improvement comes from getting the big picture of the entire system with interconnectedness and centrality playing a major role in triggering and amplifying contagious defaults. What is interesting is that capital allocations based on total assets dominate any other centrality measure tested. These results strengthen the findings that systemic capital requirements should depend mainly on total assets as proposed by Tarashev et al. (2010). Combining total assets and network metrics on top of individual bank asset riskiness (given for example by VaR measure), one could improve even further system s stability. 140

Chapter 3: Centrality-based Capital Allocations and Bailout Funds We find our work also relevant for the forthcoming micro-prudential mandate of the ECB, to supervise the entire European banking system with a focus on SIFIs. In order to apply our methodology, an harmonized European credit register is necessary. Micro-prudential supervision should incorporate a macro-prudential view. The information regarding both interconnectedness, that could fuel interbank contagion, and correlated credit exposures, that show vulnerability to common shocks, are strongly dependent on the availability of this kind of dataset. As shown by Löffler and Raupach (2013), market-based systemic risk measures seem unreliable when willing to assign capital surcharges for systemically important institutions (or other alternatives like for example the systemic risk tax proposed by Acharya et al. (2010)). Thus, what we propose in this chapter is a novel tractable framework to improve financial system s resilience based on network and balance sheet measures. Our study complements the methodology proposed by Gauthier et al. (2012). Since market data for all financial intermediaries does not exist when dealing with large financial systems, we propose a methodology that relies mainly on the information extracted from the central credit register. At this moment, we are not providing technical details on how capital re-allocation in the system could be implemented by policy makers. One proposal could be the acquisition of equity stakes by banks that receive a capital release into those banks that need a higher capital buffer. This aspect is complex and practical application involves legal and political consensus. Future research includes several directions. First, we would like to refine the allocation rule to combine more centrality measures in our optimization process. Second, the methodology can be extended by including information regarding other systemically important institutions (e.g. insurance companies, hedge funds or other shadow banking institutions). In order to accomplish this direction further reporting requirements are necessary. Last, we intend to calculate the insurance premium for each bank based on the expected bailout resources utilized. 141

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Chapter 3: Centrality-based Capital Allocations and Bailout Funds Appendix 3.A Risk and contagion mechanism Table 3.A.1: Risk model (RM) sectors No Risk Model Sector No of Borrowers Volume Weight PDs Distribution Characteristics 5% 25% 50% 75% 95% mean 1 Chemicals 3200 0.88% 0.00008 0.0019 0.0059 0.0154 0.0666 0.0166 2 Basic Materials 14,419 1.49% 0 0.0027 0.0085 0.0205 0.1000 0.0220 3 Construction and Materials 17,776 1.34% 0 0.0012 0.0066 0.0185 0.0795 0.0199 4 Industrial Goods and Services 73,548 15.06% 0 0.0023 0.0077 0.0207 0.1300 0.0257 5 Automobiles and Parts 1721 0.67% 0.00001 0.0031 0.0105 0.0300 0.1498 0.0291 6 Food and Beverage 13,682 0.76% 0.00001 0.0027 0.0082 0.0185 0.0800 0.0192 7 Personal and Household Goods 21,256 1.26% 0 0.0017 0.0074 0.0199 0.1490 0.0275 8 Health Care 16,460 0.95% 0 0.0003 0.0012 0.0086 0.0384 0.0098 9 Retail 25,052 1.62% 0 0.0017 0.0079 0.0267 0.1140 0.0237 10 Media 2,534 0.24% 0 0.0017 0.0045 0.0171 0.0790 0.0181 11 Travel and Leisure 8,660 0.68% 0 0.0036 0.0117 0.0292 0.2000 0.0316 12 Telecommunications 299 0.75% 0 0.0012 0.0036 0.0232 0.0632 0.0182 13 Utilities 15,679 3.22% 0 0.0009 0.0039 0.0126 0.0677 0.0162 14 Insurance 1392 4.12% 0.00029 0.0003 0.0009 0.0066 0.0482 0.0115 15 Financial Services 23,634 22.48% 0.00021 0.0003 0.0005 0.0057 0.0482 0.0107 16 Technology 2249 0.16% 0 0.0020 0.0050 0.0160 0.0468 0.0131 17 Foreign Banks 3134 22.06% 0.00003 0.0003 0.0009 0.0088 0.0795 0.0140 18 Real Estate 56,451 11.39% 0 0.0010 0.0051 0.0168 0.0831 0.0182 19 Oil and Gas 320 0.48% 0.00038 0.0022 0.0081 0.0296 0.1286 0.0303 20 Households (incl. NGOs) 79,913 1.26% 0 0.0005 0.0035 0.0124 0.0600 0.0134 21 Public Sector 1948 9.15% 0 0 0 0 0 0 TOTAL 388,327 100% 0.015 Note: Volume weight refers to the credit exposure of sector into the aggregated portfolio. Table 3.A.2: Model parameters Section Parameter Description Value Robustness Portfolio Credit Risk Σ correlation matrix of systematic factors Y Table 3.A.3.(a) ρ intra-sector asset correlation 0.1995 e LGD LGD beta distribution: expectation 0.39 v LGD LGD beta distribution: standard deviation 0.34 r f risk free rate 2% s(r) rating specific credit spreads Table 3.A.3.(b) T loan maturity 4 yr Centrality measures ϕ Opsahl centrality coefficient 0.5 0.2; 0.8 Bankruptcy costs φ potential costs associated with Total 5% 1%; 3%; 10% Assets λ fire sales costs associated with the severity [0, 1] of total losses in the system Capital allocation rule β weight on VaR [0, 1] α benchmark benchmark capital:v ar α is the euro value 99.9% at quantile α of the losses distribution α min minimum capital:v ar α is the euro value at 99% 98%; 99.5% quantile α of the losses distribution Bailout mechanism β weight on VaR [0, 1] η maximum bailout size proportion [0, 1] ɛ new capital buffer as a proportion of IB assets 20% 10% 146

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Figure 3.A.1: Risk model sketch INITIAL PORTFOLIO AND CAPITAL CREDIT PORTFOLIO EXOGENEOUS SHOCKS INTERBANK CONTAGION Bank 1 Capital Benchmark case: K = VaR(99.9%) Bank 1 Bank 1 Bank 1 Bank 2 or New Allocations: K ~ = K min + f(var,centrality) Fundamental Default Bank 2 Bank 2 Bank 2 Bank 3 Shocks Bank 3 Bank 3 Contagious Default Bank 3 Real Economy Loans Bank N 2 CreditMetrics Capital Bank N 2 Contagious Default Bank N 2 Bank N 2 Bank N 1 Bank N Timeline Fundamental Default Profit/Loss = Δ Real economy Assets (REA) 1st stage K = K ~ + REA Bank N 1 Bank N Round 1 Bank N 1 Bank N 2nd stage IB Profit/Losses = ΔInterbank Assets (IBA) K = K + IBA Round K Bank N 1 Bank N Note: Capital is identified by the color of parentheses around banks: green (well capitalized), yellow (medium capitalized), orange (low capitalized), red (default status). 147

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Table 3.A.3: Credit risk parameters (a) Sector correlation matrix S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 S21 S1 1 0.81 0.81 0.87 0.56 0.58 0.78 0.44 0.62 0.64 0.67 0.56 0.68 0.71 0.78 0.71 0.67 0.60 0.74 0 0 S2 0.81 1 0.80 0.86 0.56 0.47 0.69 0.26 0.61 0.60 0.64 0.49 0.58 0.64 0.77 0.69 0.64 0.59 0.80 0 0 S3 0.81 0.80 1 0.91 0.68 0.55 0.79 0.38 0.74 0.74 0.79 0.55 0.60 0.78 0.86 0.77 0.75 0.69 0.70 0 0 S4 0.87 0.86 0.91 1 0.65 0.61 0.86 0.41 0.75 0.76 0.82 0.60 0.66 0.78 0.88 0.84 0.75 0.71 0.77 0 0 S5 0.56 0.56 0.68 0.65 1 0.37 0.60 0.23 0.55 0.49 0.52 0.38 0.36 0.52 0.60 0.51 0.47 0.52 0.42 0 0 S6 0.58 0.47 0.55 0.61 0.37 1 0.76 0.56 0.63 0.65 0.59 0.55 0.59 0.53 0.62 0.52 0.50 0.51 0.54 0 0 S7 0.78 0.69 0.79 0.86 0.60 0.76 1 0.58 0.79 0.81 0.79 0.64 0.69 0.74 0.84 0.77 0.72 0.67 0.71 0 0 S8 0.44 0.26 0.38 0.41 0.23 0.56 0.58 1 0.39 0.51 0.39 0.58 0.54 0.47 0.49 0.46 0.41 0.31 0.41 0 0 S9 0.62 0.61 0.74 0.75 0.55 0.63 0.79 0.39 1 0.70 0.81 0.48 0.52 0.66 0.76 0.68 0.66 0.64 0.56 0 0 S10 0.64 0.60 0.74 0.76 0.49 0.65 0.81 0.51 0.70 1 0.80 0.63 0.66 0.71 0.77 0.72 0.67 0.66 0.61 0 0 S11 0.67 0.64 0.79 0.82 0.52 0.59 0.79 0.39 0.81 0.80 1 0.51 0.54 0.74 0.84 0.75 0.74 0.76 0.58 0 0 S12 0.56 0.49 0.55 0.60 0.38 0.55 0.64 0.58 0.48 0.63 0.51 1 0.67 0.58 0.62 0.58 0.53 0.48 0.56 0 0 S13 0.68 0.58 0.60 0.66 0.36 0.59 0.69 0.54 0.52 0.66 0.54 0.67 1 0.65 0.68 0.62 0.61 0.53 0.72 0 0 S14 0.71 0.64 0.78 0.78 0.52 0.53 0.74 0.47 0.66 0.71 0.74 0.58 0.65 1 0.86 0.70 0.92 0.73 0.66 0 0 S15 0.78 0.77 0.86 0.88 0.60 0.62 0.84 0.49 0.76 0.77 0.84 0.62 0.68 0.86 1 0.79 0.87 0.82 0.74 0 0 S16 0.71 0.69 0.77 0.84 0.51 0.52 0.77 0.46 0.68 0.72 0.75 0.58 0.62 0.70 0.79 1 0.67 0.60 0.68 0 0 S17 0.67 0.64 0.75 0.75 0.47 0.50 0.72 0.41 0.66 0.67 0.74 0.53 0.61 0.92 0.87 0.67 1 0.75 0.67 0 0 S18 0.60 0.59 0.69 0.71 0.52 0.51 0.67 0.31 0.64 0.66 0.76 0.48 0.53 0.73 0.82 0.60 0.75 1 0.52 0 0 S19 0.74 0.80 0.70 0.77 0.42 0.54 0.71 0.41 0.56 0.61 0.58 0.56 0.72 0.66 0.74 0.68 0.67 0.52 1 0 0 S20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 S21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 Note: Sectors are in the same order as in Table 3.A.1. (b) Credit spreads by rating Rating Credit spread AAA 0.4740% AA+ 0.5417% AA 0.6588% AA 0.7901% A+ 0.9802% A 1.2236% A 1.4902% BBB+ 1.8653% BBB 2.2476% BBB- 2.8046% BB+ 3.3978% BB 4.1033% BB 4.9980% B+ 6.3089% B 8.3518% B 10.3230% CCC/C 16.3980% 148

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Table 3.A.4: S&P s credit ratings transition matrix, in percent AAA AA+ AA AA A+ A A- BBB+ BBB BBB- BB+ BB BB- B+ B B- CCC D AAA 90.867 4.879 2.770 0.703 0.165 0.248 0.145 0.000 0.052 0.000 0.031 0.052 0.000 0.000 0.031 0.000 0.052 0.006 AA+ 2.654 78.891 12.151 4.075 0.923 0.674 0.311 0.124 0.124 0.062 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.010 AA 0.510 1.375 83.962 8.352 2.999 1.479 0.448 0.427 0.146 0.094 0.052 0.042 0.021 0.000 0.000 0.021 0.052 0.021 AA- 0.052 0.136 4.493 80.439 10.428 2.957 0.731 0.282 0.146 0.073 0.042 0.000 0.000 0.042 0.115 0.021 0.000 0.042 A+ 0.000 0.115 0.607 4.666 81.021 9.196 2.689 0.743 0.418 0.094 0.094 0.126 0.010 0.094 0.042 0.010 0.000 0.073 A 0.052 0.063 0.294 0.588 5.269 81.528 7.168 2.834 1.207 0.294 0.157 0.157 0.105 0.126 0.031 0.010 0.021 0.094 A- 0.063 0.011 0.116 0.211 0.643 7.092 79.937 7.893 2.487 0.717 0.169 0.158 0.169 0.148 0.042 0.011 0.053 0.084 BBB+ 0.000 0.011 0.074 0.096 0.329 1.114 7.344 77.672 9.403 2.122 0.499 0.424 0.180 0.276 0.159 0.021 0.106 0.170 BBB 0.011 0.011 0.064 0.043 0.182 0.515 1.319 7.551 79.631 6.747 1.738 0.890 0.397 0.333 0.182 0.043 0.097 0.247 BBB- 0.011 0.011 0.011 0.075 0.075 0.259 0.431 1.498 9.239 76.639 5.908 2.781 1.110 0.604 0.367 0.237 0.334 0.410 BB+ 0.077 0.000 0.000 0.055 0.022 0.154 0.132 0.694 2.502 12.809 69.290 7.044 3.538 1.378 0.904 0.209 0.584 0.606 BB 0.000 0.000 0.066 0.022 0.000 0.111 0.089 0.254 0.819 2.843 9.470 71.092 8.541 2.987 1.516 0.509 0.797 0.885 BB- 0.000 0.000 0.000 0.011 0.011 0.011 0.078 0.145 0.334 0.535 2.295 9.158 71.078 9.369 3.409 1.081 1.036 1.448 B+ 0.000 0.011 0.000 0.045 0.000 0.045 0.101 0.056 0.079 0.112 0.382 1.773 7.754 72.966 8.607 2.963 2.188 2.918 B 0.000 0.000 0.023 0.023 0.000 0.102 0.079 0.045 0.125 0.045 0.261 0.443 1.908 9.641 65.478 8.994 6.155 6.677 B- 0.000 0.000 0.000 0.000 0.046 0.081 0.000 0.163 0.081 0.163 0.209 0.244 0.697 3.625 11.921 59.719 12.455 10.596 CCC 0.000 0.000 0.000 0.000 0.058 0.000 0.164 0.105 0.105 0.105 0.058 0.269 0.655 1.625 3.414 10.173 51.239 32.028 149

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Appendix 3.B Centrality measures - technical details In this part, we follow the technical details provided by Newman (2010) to define centrality measures used in our analysis. 3.B.1 Eigenvector centrality Let A be the adjacency matrix, with a ij = 1 if there is a credit exposure of bank j to bank i, and a ij = 0 otherwise. And κ 1 be the first eigenvector of matrix A. Then eigenvector centrality is given by the following relation (in matrix notation): Ax = κ 1 x. Eigenvector centralities of all nodes are non-negative. In the case of weighted eigenvector centrality, the adjacency matrix A is replaced by the weighted liabilities matrix X = X/ j x, where each row is normalized to sum up to 1. This measure ij was firstly proposed by Bonacich (1987). 3.B.2 Betweenness centrality The geodesic distance between any two nodes is given by the shortest path. Let g ij be the number of possible geodesic paths from i to j (there might be more than a single shortest path) and n q ij be the number of geodesic paths from i to j that pass through node q, then the betweenness centrality of node q is: B q = i,j j i n q ij g ij, where by convention nq ij g ij = 0 in case g ij or n q ij are zero. 150

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Figure 3.B.1: Centrality measures (a) Betweenness (b) Eigenvector Note: The scale-free random graphs were generated with igraph toolbox in R. The red nodes have the highest centrality values. 3.B.3 Closeness centrality For the definition of closeness centrality we follow Dangalchev (2006): C i = 2 d ij, j j i where d ij the lenght of the geodesic path from i to j. This formula is also appropriate for disconnected graphs. centrality equal to 0. Disconnected components have a closeness 3.B.4 (Local) Clustering coefficient Watts and Strogatz (1998) show that in real-world networks nodes tend to establish clusters with a high density of edges. Global clustering coefficient refers to the property of the overall network while local measure refers to individual nodes. This property is related to the mathematical concept of transitivity. Cl i = number of pairs of neighbors of i that are connected. number of pairs of neighbors of i The local clustering coefficient shows the average probability that a pair of i s neighbors are connected to each other (i.e. are neighbors as well). The local clustering coefficient of a node with the degree 0 or 1 is equal to zero. 151

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Appendix 3.C Modeling returns of small loans Let s consider a portfolio with loans from one sector only. Assume there we have N r loans in each rating class, which make up N in total. Each one is assigned to a latent asset return X i,r (sector index omitted). Conditionally on the single systematic factor Y of the sector, the X i,r are independent and so are corresponding rating migrations R i,r 0 = r R i,r 1. All loans have the same uniform maturity T = 4 yr as the large loans. The notional of loan (i, r) has a weight w i,r relative to the total of all loans in the sector s portfolio. If not in default, its rating specific discount factor is the same as in 3.4.1, i.e., D (r, r) = 1 at the beginning of the risk horizon and D ( r, R i,r ) 1 one period later. As for large loans, the return on loan (i, r) is determined as D ( C (r), R i,r 1, 1, T ) + C (r) if R i,r 1 < 18 i,r = 1 +, (1 + C (r)) (1 LGD) if R i,r 1 = 18 where C (r) was the loan rate. The corresponding return in the small-loans portfolio of one sector is then = 17 N r r=1 i=1 w i,r i,r. As we want to approximate by a Y conditionally normal random variable, we now determine the conditional expectation E ( Y ) and variance var ( Y ). further approximation is that these moments are not to be based on all weights w i,r (which we do not know for small loans) but instead on two aggregates that we can estimate: the Herfindahl index, H = 17 Nr r=1 i=1 wi,r, 2 and exposure weights w r N r i=1 w i,r of the rating classes. To start with, the conditional migration probability, i.e., the probability of the asset return X i,r to fall between two neighbored thresholds, is A p (r, R Y ) P ( R i,r 1 = R ) Y = P (θ (r, R) < Xi,r θ (r, R 1) Y ) ( θ (r, R) ρy = P < Z i,r θ (r, R 1) ) ρy Y 1 ρ 1 ρ ( ) ( ) θ (r, R 1) ρy θ (r, R) ρy = Φ Φ 1 ρ 1 ρ (3.13) 152

Chapter 3: Centrality-based Capital Allocations and Bailout Funds with θ (r, 18) = and θ (r, 0) = +. The conditional expectation in each rating class immediately calculates as µ r (Y ) E ( i,r Y ) (3.14) = 1 + 17 R=1 [D (r, R) + C (r)] p (r, R Y ) + (1 + C (r)) (1 E (LGD)) p (r, 18 Y ) (which does not depend on i in fact) and, summing up over ratings, E ( Y ) = The conditional variance of a single i,r is 17 r=1 w r µ r (Y ). v r (Y ) var ( i,r Y ) = var ( i,r + 1 Y ) (3.15) = E ( ( i,r + 1) 2 ) Y (µr (Y ) + 1) 2 = 17 R=1 [D (r, R) + C (r)] 2 p (r, R Y ) + (1 + C (r)) 2 p (r, 18 Y ) [ var (LGD) + (1 ELGD) 2] (µ r (Y ) + 1) 2 where we utilize that LGD is independent of the other variables. Recall that migrations are conditionally independent, from which we immediately obtain for the whole sector s portfolio: var ( Y ) = 17 N r r=1 i=1 w 2 i,rv r (Y ). If v r (Y ) were rating independent, we could extract it from the sum and would obtain H v r (Y ) as result. Because it is not, we make the weaker assumption that the distribution of e loan sizes does not depend on the rating (but well on the sector). If that holds, there is a relationship between H and the Herfindahl indices of the rating buckets that can be used to derive the approximation var ( Y ) H 17 r=1 w r v r (Y ). To sum up, returns for the small loans are simulated in the following way. Input data: For each bank b, the exposure to sector j is SL b,j. From the SL b,j we infer on the Herfindahl index H b,j of its loans as described in (see Section 3.C.1). Furthermore, for each sector j the (bank-independent) rating distribution (w r,j ) r=1...17 153

Chapter 3: Centrality-based Capital Allocations and Bailout Funds is gathered from the sample of large loans and assumed to be the same for small loans. The matrix of discount factors D (r, R) r=1...17,r=1...18 can be calculated once at the beginning. Steps of one simulation round: 1. Draw systematic factors Y j ; they affect both large and small loans. 2. Calculate the matrices (p (r, R Y j )) r=1...17,r=1...18 according to eq 3.13 for all sectors j. 3. Calculate the vectors (µ r (Y j )) r=1...17 from eq 3.14 and (v r (Y j )) r=1...17 from eq 3.15 for all j. Based on them, calculate µ sect j (Y j ) 17 r=1 w r,j µ r (Y j ) and σj sect (Y j ) 17 w r,j v r (Y j ) for all j. r=1 4. For each bank b, the euro return on small loans is ret SL b = 21 j=1 SL b,j ( H b,j σj sect (Y j ) Zb,j small + µ sect j (Y j ) ) (3.16) where the Z small b,j are independent N (0, 1) random variables. 3.C.1 Estimating the granularity of small-loans exposures (Herfindahl Index) In Appendix 3.C we quantify the granularity of a small-loans subportfolio by its Herfindahl index H. We cannot estimate it directly as we know only the total exposure SL for each bank and sector. Although individual exposures cannot exceed e 1.5 Mn by construction so that a small-loans portfolio of size SL cannot have an H in excess of 1.5 Mn/SL, this upper bound will often be very imprecise, especially in the case of loans to households. We therefore perform estimations and a simulation exercise based on a sample of individual loans made by a large German bank. We assign all exposures to risk management sectors and exclude all above e 1.5 Mn. This gives us between 86 and 43,000 loans by sector, with a median of 6156 observations. While it would be critical to assume that the loan sizes of our full sample, which stems from a large bank, follow the same distribution as those of small banks, we hope that any such difference is not substantial when only small loans are concerned. 154

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Let now U denote the random loan size in a certain sector. If the total exposure SL is large relative to EU so that probably many loans are in the portfolio, elementary arguments lead to the following approximation; cf. Hart (1975). H E ( U 2) / (E (U) SL) (3.17) This relationship is used for large SL. For smaller values of SL, we rely on simulations and subsequent curve fitting: we define a sequence of exposure buckets [SL k, SL k+1 ] and, for each of them, randomly collect loans from the sample until the total exposure falls into the bucket; this generates one possible H assigned to SL k+1. Repeating the procedure provides us with a sample of such H for each exposure bucket. The bucket specific average H k is our approximation of the size dependent Herfindahl index. It turns out that eq 3.17 works well for SL > 5.9 Mn. For smaller values, a sector-specific cubic function (of logarithms) is fitted to the averages H k. Some data entries are equal to the minimum reporting unit 1000. We assume they arise from a single loan. To sum up, we define 1 if SL 1000 H (SL) exp { a ln 3 SL + b ln 2 SL + c ln SL + d } if 1000 < SL 5, 844, 325 E (U 2 ) / (E (U) SL) else where a, b, c, d, E (U 2 ), and E (U) are sector specific parameters. Appendix 3.D Other target functions First, the deadweight loss can be distributed to the banking sector and to the nonbanking sector in the sense that those bankruptcy costs not covered by the interbank liabilities accrue to the outside sector. Second, the initial losses of the sectors outside of banking are distributed to the banks through the capital losses. Thus, a case can be made that the loss minimized should have the capital losses to the banks subtracted from them: ET L1 E i D i (BC i + L i K i ). The fact that the bankruptcy costs are distributed among the banks only partially, and the rest are absorbed in the non-bank sector indicates another loss measure which is ET L1, above, but with the bankruptcy costs modified so reflect the 155

Chapter 3: Centrality-based Capital Allocations and Bailout Funds non-banking sector share: ET L2 E i D i [I(BC i > l i )(BC i l i ) + L i K i ], where l i are the total interbank liabilities of bank i. In this case, bankruptcy costs in excess of interbank liabilities are counted. Appendix 3.E Other results Figure 3.E.1: Unconditional distribution of total system losses x 10 4 2 TA Unconditional mean=7.3011e+05 number 1 0 x 10 4 2 0 1 2 3 4 5 6 7 8 VaR x 10 8 Unconditional mean=1.2115e+06 number 1 0 x 10 4 2 0 1 2 3 4 5 6 7 8 Opsahl x 10 8 Unconditional mean=9.7777e+05 number 1 0 0 1 2 3 4 5 6 7 8 x 10 8 156

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Figure 3.E.2: Conditional distributions of losses for best capital allocation under rule based on: Total Assets (TA), Value-at-Risk (VaR), and Opsahl centrality (Opsahl) TA TA 600 40 Conditional mean (q=99%) = 58.929.917 Conditional mean (q=99.9%) = 435.768.013 400 200 20 number 0 0 1 2 3 4 5 6 7 8 9 x 10 8 VaR 1000 Conditional mean (q=99%) = 115.250.380 0 2 3 4 5 6 7 8 9 x 10 8 VaR 500 number 0 0 0 1 2 3 4 5 6 7 8 9 x 10 8 Opsahl 800 Conditional mean (q=99%) = 88.685.892 600 400 200 0 0 1 2 3 4 5 6 7 8 9 x 10 8 number number 30 Conditional mean (q=99.9%) = 663.615.840 20 10 number (a) Conditional Distribution of Losses (1% quantile) 40 20 0 2 3 4 5 6 7 8 9 x 10 8 Opsahl Conditional mean (q=99.9%) = 589.768.804 2 3 4 5 6 7 8 9 x 10 8 number (b) Conditional Distribution of Losses (q=99.9%) 157

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Appendix 3.F Liabilities and network properties Figure 3.F.1: Power law vs log-normal diagnostics Note: For confidentiality reasons liabilities were transformed with a simple moving average consisting of three consecutive liabilities (ranked by size). 158

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Figure 3.F.2: Comparison between ranked interbank liabilities (by size) Note: For confidentiality reasons liabilities were transformed with a simple moving average consisting of three consecutive liabilities (ranked by size). 159

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Table 3.F.1: Network properties - 2009 Q1 No of banks** 1780 No of links 23,475 Quantile mean std dev 5% 10% 25% 50% 75% 90% 95% Total IB Assets * 7779 13,407 35,610 106,684 330,323 930,469 1,861,787 990,894 6,385,872 Total IB Liabilities * 3310 6264 18,287 56,581 182,849 568,604 1,228,837 990,894 8,170,345 Total Assets * 46,238 73,476 168,061 440,785 1,233,332 3,157,769 5,984,005 4,763,593 58,325,883 Out Degree 1 1 1 2 4 10 15 13 83 In Degree 1 1 4 9 14 19 24 13 39 Degree 2 3 6 12 19 27 37 26 114 Opsahl centrality 107.5 141.6 246.3 472.9 1088.7 2432.7 4375.7 3484 26,597 Eigenvector centrality 5.99E-06 1.30E-05 4.25E-05 0.000137 0.000699 0.002755 0.006942 0.00306 0.02351 Weighted betweenness 0 0 0 0 0 694.5 7877.75 9522 77,055 Weighted eigenvector 0.000012 0.000017 0.000037 0.000112 0.000523 0.001900 0.003801 0.002913 0.023520 Closeness centrality 317.3125 317.3125 368.4375 402.5 404 422.1875 438.625 387.8771 53.8038 Clustering coefficient 0 0 0 0.0099 0.05 0.1445 0.2008 0.0438 0.0825 No of obs 89 178 445 890 1335 1602 1691 1780 1780 Note: ** no of banks active in the interbank market. * in thousand e 160

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Table 3.F.2: Network properties - 2007 Q1 No of banks** 1822 No of links 25,346 Quantile mean std dev 5% 10% 25% 50% 75% 90% 95% Total IB Assets * 6235 11.593 29,307 86,765 249,302 735,171 1,621,935 941,918 6,280,025 Total IB Liabilities * 3526 6020 16,897 50,463 167,960 524,639 1,377,271 941,918 7,005,688 Total Assets * 43,016 71,051 156,391 407,544 1,146,350 3,037,258 5,635,412 4,867,551 58,588,305 Out Degree 1 1 1 2 5 12 18 14 82 In Degree 1 1 4 9 15 21 27.4 14 42 Degree 2 3 6 12 19 29 43 28 116 Opsahl centrality 104.9 140.1 239.7 475.1 1096.7 2499.4 4546.9 3406 22,514 Eigenvector centrality 0.000012 0.000024 0.000077 0.00024 0.000966 0.003547 0.008665 0.0037 0.0231 Weighted betweenness 0 0 0 0 0 109.6 6009.8 9145 75,048 Weighted eigenvector 0.000021 0.000028 0.000056 0.000149 0.000558 0.001958 0.004772 0.0031 0.0232 Closeness centrality 312.6 327.375 367.375 414.75 417.875 437.45 451.8 398.21 56.93 Clustering coefficient 0 0 0 0.01389 0.05357 0.15486 0.20467 0.0484 0.0868 No of obs 91 182 456 911 1367 1640 1731 1822 1822 Note: ** no of banks active in the interbank market. * in thousand e 161

Chapter 3: Centrality-based Capital Allocations and Bailout Funds Table 3.F.3: Network properties - 2005 Q1 No of banks** 1989 No of links 28,976 Quantile mean std dev 5% 10% 25% 50% 75% 90% 95% Total IB Assets * 6034 10,662 28,607 82,385 222,942 637,407 1,483,345 904,305 6,252,776 Total IB Liabilities * 2846 5389 15,751 48,197 161.576 486,450 1,108,158 904,305 6,858,284 Total Assets * 27,890 50,648 127,479 336,441 929,702 2,538,967 4,483,895 3,145,409 25,946,202 Out Degree 1 1 1 2 5 12 18 15 88 In Degree 1 1 4 9 15 21 27.05 15 45 Degree 2 3 6 13 20 30 43.05 29 123 Opsahl centrality 82.1 115 210.2 442.5 1023.4 2276.5 4080.9 2972 18,568 Eigenvector centrality 0.000012 0.000024 0.000079 0.00025 0.000974 0.0032994 0.007708 0.00356 0.02214 Weighted betweenness 0 0 0 0 0 574.8 8639.9 10,151 82,861 Weighted eigenvector 0.000021 0.000029 0.000061 0.000165 0.000550 0.001851 0.004124 0.003034 0.0223 Closeness centrality 337.325 339.8125 399.1875 452.625 457 475.325 487.275 432.29 62.58 Clustering coefficient 0 0 0 0.01428 0.0585 0.15909 0.2 0.0513 0.093 No of obs 99 199 497 995 1492 1790 1890 1989 1989 Note: ** no of banks active in the interbank market. * in thousand e 162

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Complete Bibliography Tarashev, N., C. Borio, and K. Tsatsaronis (2010). Attributing systemic risk to individual institutions. BIS Working Papers No. 308. Upper, C. (2011). Simulation methods to assess the danger of contagion in interbank markets. Journal of Financial Stability 7, 111 125. Watts, D. J. and S. Strogatz (1998). Collective dynamics of small-world networks. Nature 393(6684), 440 442. Webber, L. and M. Willison (2011). Systemic capital requirements. Bank of England Working Paper No. 436. Yellen, J. L. (2013). Interconnectedness and systemic risk: Lessons from the financial crisis and policy implications. Speech at the American Economic Association/American Finance Association Joint Luncheon, San Diego, California. Zhang, X., B. Schwaab, and A. Lucas (2011). Conditional probabilities and contagion measures for euro area sovereign default risk. Tinbergen Institute Discussion Paper TI 11-176/2/DSF29. 171

Complete Bibliography 172

Erklärung Ich versichere hiermit, dass ich die vorliegende Arbeit mit dem Thema Three Essays on Systemic Risk and Financial Contagion ohne unzulässige Hilfe Dritter und ohne Benutzung anderer als der angegebenen Hilfsmittel angefertigt habe. Die aus anderen Quellen direkt oder indirekt übernommenen Daten und Konzepte sind unter Angabe der Quelle gekennzeichnet. Weitere Personen, insbesondere Promotionsberater, waren an der inhaltlich materiellen Erstellung dieser Arbeit nicht beteiligt. Die Arbeit wurde bisher weder im In- noch im Ausland in gleicher oder ähnlicher Form einer anderen Prüfungsbehörde vorgelegt. Konstanz, den 19. Juni 2013 Adrian Alter Siehe hierzu die Abgrenzung auf der folgenden Seite.

Eigenabgrenzung Kapitel 1 entstammt einer gemeinsamen Arbeit mit Yves S. Schüler (Universität Konstanz). Meine individuelle Leistung bei der Erstellung dieser Arbeit beträgt 50%. Kapitel 2 entstammt einer gemeinsamen Arbeit mit Andreas Beyer, PhD (European Central Bank). Meine individuelle Leistung bei der Erstellung dieser Arbeit beträgt 60%. Kapitel 3 entstammt einer gemeinsamen Arbeit mit Dr. Peter Raupach (Deutsche Bundesbank) und Ben Craig, PhD (Deutsche Bundesbank). Meine individuelle Leistung bei der Erstellung dieser Arbeit beträgt 50%. 174