Eindhoven University of Technology

MASTER

Assigning sovereign credit ratings in the Eurozone using CDS spreads

van de Ven, R.E.J.

Award date:2017

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Eindhoven, February 2017

Assigning Sovereign Credit Ratings in the

Eurozone using CDS spreads

by R.E.J. (Rick) van de Ven

Bsc. Industrial Engineering and Innovation SciencesStudent identity number 0738742

in partial fulfillment of the requirements for the degree of

Master of Science

in Operations, Management & Logistics

Eindhoven University of Technology

Supervisors:Dr. A. ChockalingamProf. Dr. K-K. Kim (KAIST)Dr. S. DabadghaoCompany supervisor (KPMG):S. Bush

TUE. School of Industrial EngineeringSeries Master Theses Operations, Management & Logistics

Subject headings: Sovereign credit risk, Forecasting, Credit Rating Agencies, Credit risk, Euro debt cri-sis, European Monetary Union, Risk management.

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Quote

“There are two superpowers in the world today in my opinion. There’s the United States and there’s Moody’sBond Rating Service. The United States can destroy you by dropping bombs, and Moody’s can destroy you bydowngrading your bonds. And believe me, it’s not clear sometimes who’s more powerful.” (Friedman, 1996).

”Independence is a very subjective assessment.”(Chidambaram, unknown).

”Some of the most interesting research that I did was about risk assessment and how ordinary citizenslike me handle risk assessment and how irregular our risk assessments are.”(Biss, unknown)

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Abstract

Assigning Sovereign Credit Ratings in the Eurozone using CDS spreadsby R.E.J. (Rick) van de Ven

The credit ratings issued by the Big Three ratings agencies (S&P, Moody’s, Fitch) were evaluated as notaccurate and tend to respond slow to market changes. In order to have an alternative rating procedure, thisresearch develops a regression-based model utilizing CDS data, and data on financial and macroeconomicvariables to estimate sovereign CDS spreads. Using the CDS spreads, the default probabilities of eightsovereigns in the Eurozone can be estimated. The new ratings scheme is then used in conjunction withthese default probabilities to assign credit ratings to sovereigns. The ratings assigned by the new schemeresponds quick to market changes, while the ratings issued by the Big Three tend to respond slow to marketchanges. The transparency and rigor of the new scheme will result in better and trustworthy indications ofa sovereign’s financial health. Investors and monetary authorities can make better informed decisions, sincethe level of information asymmetry will decrease.

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Management Summary

In this report the process and the outcome of the master thesis conducted at KPMG regarding sovereigncredit risk is presented. This management summary provides a brief overview of the master thesis.

Problem definition

It became evident during the credit crisis of 2008 that there were several major issues with sovereign creditratings issued by the big three (S&P, Moody’s and Fitch). The big three are three credit rating agenciesthat control 95 % of the market (Naciri, 2015): S&P, Moody’s and Fitch. The main issues were a misuse oftheir position (Klein, 2004; Eijffinger, 2012; Taylor et al., 2011), a conflict of interest (EC, 2013; Larosiereet al., 2009; Ozturk et al., 2016), not being transparent about the rating procedure (Iyengar, 2010; Katzet al., 2009; Benmelech and Duglosz, 2009) and a slow response to market changes (Eijffinger, 2012; Ozturket al., 2016). Due to these issues, the sovereign credit ratings that were issued did not reflect credit risk inan adequate manner. Since there was an over-reliance on these credit ratings (Eijffinger, 2012; White, 2010),external parties such as investors were mislead which caused tremendous chaos. To deal with this situation,an alternative rating procedure has to be developed (EC, 2013), which could serve as a possible replacement.

Research question

The starting point of the new procedure is the AL-CDS model (Ang and Longstaff, 2013), in which thedefault probability of a sovereign can be calculated based upon the CDS spread. The model splits sovereigncredit risk into a systemic risk part, which affects every sovereign, and an idiosyncratic risk part, which issovereign specific. However, the model has been designed for backward looking in which it is not clear howthe model performs for future predictions. Second, the model is solely based upon the CDS spread and doesnot take into account financial nor macro economic variable. Third, the authors investigate the relationshipbetween systemic risk and financial factors, finding that there is a significant relationship. They mentionthat more attention has to be paid to this relationship, since they test a limited set of financial variablesand other financial variables could provide more insight. Furthermore, several researchers point out that oneshould include macro economic variables if one investigates the Euro debt crisis (Gibson et al., 2014; Afonsoet al., 2014; Bernoth et al., 2012; Hagen et al., 2011). Since the model is retrospective in nature and doesnot include financial and/or macroeconomic data for the calculation, the question arises whether the modelis accurate for future predictions and specifically when one tries to model the Euro debt crisis. The researchquestion is as follows:Can the AL-CDS model be extended by including the factors that represent systemic and non-systemic risk?

Calibration of the models

The AL-CDS model has been calibrated over a timespan of 3 years before the peak of the Euro debt crisisusing non-linear least squares optimization. Based upon the calibration outcome, regression analyses overboth the systemic and idiosyncratic risk outcome have been performed. The outcome indicates what factorsdrive sovereign credit risk on both a systemic and idiosyncratic level, such as that the VIX index is a major

v

indicator of systemic risk.

Three alternative models have been designed based using the outcome of the regression analyses, which areas follows:

1. The Sys-model includes financial data for the calculation of systemic risk.2. The Idio-model includes both financial and macro economic data for the calculation of idiosyncratic

risk.3. The Reg-model uses financial data for the calculation of systemic risk and both financial and macro

economic data for the calculation of idiosyncratic risk.

The three models have been compared over the peak of the Euro debt crisis (which is a time period of 3years). The outcome can be seen in Table 1, in which it can be seen that the usage of the AL-CDS modelresults into the least accurate fit since the RMSE values are the highest of the four models. This is in contrastto the usage of the Reg-model, which has the lowest RMSE values and results into the most accurate fit.The Reg-model is used to develop an alternative rating procedure.

Table 1: RMSE outcome

RMSE

Germany Portugal Spain Italy Ireland Netherlands Belgium FranceAL-CDS model 48 743 331 315 563 58 168 112

Sys-model 30 732 303 306 504 46 159 107Idio-model 48 410 272 193 380 40 96 90Reg-model 30 399 246 185 321 30 88 85

Comparison of ratings

An alternative rating procedure has been developed, which is based upon the expected default probability.The ratings issued by the Reg-model have been compared with ratings issued by the big three. As an extrabenchmark, the 1 year sovereign bond yields are also included. The situation for Portugal is shown in Figure1, in which it can be seen that the ratings issued by the big three tend to respond slow to market changes.This is in contrast with the ratings issued by the alternative scheme, which react quick to market changes.A similar situation can be found for most of the other sovereigns.

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012

Date

Ba3

Ba1

Baa2

A3

A1

Aa2

0

1

2

3

4

5

6

7

8

9

10

Yie

ld (

%)

Reg-model

Moodys

S&P

Fitch

Yield(%)

Ra

tin

g

Figure 1: Ratings for Portugal

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Conclusion

The ratings that are issued by the Reg-model react quick to changes in the market, while the ratings issuedby the big three tend to respond slow to market changes. This shows that the new rating procedure can beused as an early warning indicator. Second, the ratings issued by the Reg-model have a single quantitativemetric, in which a reliable comparison can be made. This is more complex for the ratings issued by the bigthree, since they use a qualitative metric which differs between the big three. Third, this research points outwhat factors drive both systemic and idiosyncratic risk in the Eurozone. This insights will help to understandwhat drives sovereign credit risk.

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Acknowledgements

A master thesis might be written by a single person, but there were many people that contributed to thisresearch. I would like to use this opportunity to thank everyone that helped me.

I would like to thank my first supervisor, Arun Chockalingam, for his help to structure my ideas and toset a clear direction for my research. I would like to thank my second supervisor, Kyoung-Kuk Kim, forhis use full insights in the interesting world of credit risk and his passion for mathematical models. I wouldlike to thank my third supervisor, Shaunak Dagabdhao, for his insights in CDS spreads and his analyticalquestions which helped me to guide my research. I would like to thank my company supervisor, Scott Bush,for the market insights that he shared with me which helped me to make my work applicable for financialinstitutions. I would also like to thank Steven, Jeroen, Martijn and the other colleagues for all their questionsand comments, which helped me to understand credit risk.

I would like to thank my family, which have always supported me during my life and were eager to listento all my good and not so applicable ideas. You have always unconditionally loved me, which still impressesme. I would like to thank my friends, who encouraged me to get the most out of my student life. You mightnot always know it, but the interesting conversation and the fun we had made my life interesting. I wouldalso like to thank both the Technical University of Eindhoven and the Korea Advanced Institute of Scienceand Technology, without the Dual Degree program and all the help this thesis wouldn’t be possible. Aspecial thanks goes to the unknown man that I met in the train one day who had to ask the most importantquestion: Why do you like your work? You’re simple question helped me to understand that I truly like thefinancial sector and that I shouldn’t give up. Last but not least, I want to thank God who always helped myon my journey in life. Even though many people struggle to understand life and you, you create somethingbeautiful out of all this complex mess.

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Contents

List of Tables xi

List of Figures xii

1 Introduction 1

1.1 The credit crisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Theoretical background 3

2.1 Relevance of sovereign credit ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 An introduction to Credit Rating Agencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3 Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.4 Basel agreements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.5 Credit risk model classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.6 Comparison of credit risk models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.7 Sovereign credit risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.8 Credit Default Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.9 Sovereign credit risk models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Methodology 10

3.1 Research question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2 Problem Solving Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3 Conceptual project design & project plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Data 14

4.1 CDS data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.2 Explanatory variables for systemic risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.3 Explanatory variables for Idiosyncratic risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5 Models 17

5.1 AL-CDS model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.3 Alternative models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.3.1 Regression for Systemic risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.3.2 Regression for Non-systemic risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.3.3 Model design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

ix

6 Comparison 266.1 Default probability forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266.2 New rating scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

7 Conclusion 327.1 Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327.2 Research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337.3 Scientific contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337.4 Business impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347.6 Suggestions for future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347.7 Personal reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Bibliography 36A Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41B CDS spread graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42C Summary statistics CDS data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43D Summary statistics Systemic Risk data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44E Summary statistics Idiosyncratic Risk data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45F Forecast results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47G Ratings assigned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

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List of Tables

1 RMSE outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi2 Risk classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii3 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

1.1 Credit ratings of Iceland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

5.1 Parameter estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195.2 Share of systemic risk over the calibration period . . . . . . . . . . . . . . . . . . . . . . . . . 195.3 Systemic risk regression outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.4 Idiosyncratic risk regression results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.5 Overview of the different models. Note that MC simulation stands for Monte Carlo simulation. 225.6 RMSE outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

6.1 Rating scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1 three years maturity CDS spread calibration period . . . . . . . . . . . . . . . . . . . . . . . . 432 five years maturity CDS spread calibration period . . . . . . . . . . . . . . . . . . . . . . . . 433 three years maturity CDS spread testing period . . . . . . . . . . . . . . . . . . . . . . . . . . 434 five years maturity CDS spread testing period . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Systemic risk variables- Part 1 (calibration period) . . . . . . . . . . . . . . . . . . . . . . . . 446 Systemic risk variables- Part 2 (calibration period) . . . . . . . . . . . . . . . . . . . . . . . . 447 Systemic risk variables- Part 1 (testing period) . . . . . . . . . . . . . . . . . . . . . . . . . . 448 Systemic risk variables- Part 2 (testing period) . . . . . . . . . . . . . . . . . . . . . . . . . . 449 Summary Statistics Portugal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4510 Summary Statistics Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4511 Summary Statistics Spain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4512 Summary Statistics Ireland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4613 Summary Statistics the Netherlands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4614 Summary Statistics Belgium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4615 Summary Statistics France . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

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List of Figures

1 Ratings for Portugal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

3.1 This figure shows the conceptual project design of the graduation project . . . . . . . . . . . . . . 123.2 This figure shows a con size version of the project plan. . . . . . . . . . . . . . . . . . . . . . . . . 13

4.1 five years CDS spreads from April 2007 until April 2010 . . . . . . . . . . . . . . . . . . . . . 154.2 five years CDS spreads from May 2010 until April 2013 . . . . . . . . . . . . . . . . . . . . . 15

5.1 λ and ζ intensity values over the calibration period . . . . . . . . . . . . . . . . . . . . . . . . 205.2 3 years maturity CDS spread for the Netherlands . . . . . . . . . . . . . . . . . . . . . . . . . 235.3 3 years maturity CDS spread for Portugal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

6.1 Estimated default probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276.2 Ratings vs. yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286.3 Ratings for Germany . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306.4 Ratings for Spain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306.5 Ratings for Portugal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1 3 years maturity CDS spread for the calibration period . . . . . . . . . . . . . . . . . . . . . . . . 422 3 years maturity CDS spread for the testing period . . . . . . . . . . . . . . . . . . . . . . . . . . 423 5 years maturity CDS spread the Netherlands . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 5 years maturity CDS spread Portugal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 3 years maturity CDS spread Belgium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 5 years maturity CDS spread Belgium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 5 years maturity CDS spread France . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 3 years maturity CDS spread France . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 5 years maturity CDS spread Spain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5010 3 years maturity CDS spread Spain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5011 3 years maturity CDS spread Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5112 3 years maturity CDS spread Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5113 5 years maturity CDS spread Ireland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5214 3 years maturity CDS spread Ireland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5215 5 years maturity CDS spread Germany . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5316 3 years maturity CDS spread Germany . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5317 Ratings the Netherlands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5418 Ratings France . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5419 Ratings Belgium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5520 Ratings Ireland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5521 Ratings Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

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Definition and abbreviations

The definitions are derived from the book Quantitative Risk Management (McNeil et al., 2005), the web incase of the definition of sovereign credit risk (QFinance, 2013) or are defined by the author in case of thetwo types of sovereign risk (systemic and idiosyncratic).

Table 2: Risk classification

Type of risk Explanation

Credit Risk The risk of not receiving promised repayments on outstanding investments,such as loans and bonds, due to the ’default’ of a borrower.

Sovereign credit risk The risk that a government may refuse to repay or be unable to repay moneyit has borrowed.

Model Risk The risk associated with using a misspecified (inappropriate) model for mea-suring risk.

Liquidity Risk The risk stemming from the lack of marketability of an investment that cannotbe bought or sold quickly enough to prevent or minimize a loss.

Default risk The risk of the situation in which an obligator defaults.Downgrade risk The risk associated with a possible downgrade of the classification of a financial

product or party.

Systemic risk The risk that influences all governments jointly, which is depending on themacro-economic conditions.

Idiosyncratic risk The risk associated with an individual government, which is independent fordifferent governments.

Table 3: Abbreviations

Abbreviation Explanation

CDS Credit Default SwapAL-CDS Model designed by Ang & Longstaff to estimate the CDS spreadReg-model Model which includes the outcome of the regression analyses to calculate the

CDS spreadCRA Credit Rating AgencyBig Three Three major CRA’s (S&P, Moody’s & Fitch)IRB Internal Rating Based

xiii

Chapter 1

Introduction

1.1 The credit crisis

The credit crisis which started in August 2007 with bankruns in several short-term markets (Gorton andMetrick, 2012), is regarded as one of the biggest crises since the Great Depression (Bash, 2015). Thefirst public notion of this liquidity problem appeared in August 2007, when the French bank BNP Paribasannounced that customers were not allowed to withdraw money from one of the hedge funds (Elliott, 2012).The tipping point occurred when Lehmann Brothers filed for bankruptcy in August 2008, which started arun on money. During the credit crisis many institutions faced liquidity problems, which resulted in thefollowing situations:

1. Many companies had to ask for financial support from the government, such as Fanny Mea (Sorkin,2008) and RBS (BBC, 2008).

2. A large number of companies defaulted worldwide (Linnane and Adler, 2008), such as the WashingtonMutual of Henderson, Nevada and Park City, Utah with 307 billion dollar in assets (Douglas, 2009)and Northern Rock (BBC, 2009).

3. Governments also became part of this worldwide crisis and asked from liquidity support from otherstates and/or financial institutions. Examples are the governments of Greece (Featherstone, 2011),Cyprus and Iceland (Anderson, 2015).

To understand why this happened, one has to look to the main drivers of the event which are:

1. The decrease of the housing prices in the United States of America, which became evident at the endof 2006 (Simkovic, 2013). This affected households and especially investors, since they invested infinancial products who were related to the mortgages who became less worth.

2. ‘The systemic vulnerabilities that occurred in the financial sector with the rise of shadow banks’(Bernanke, 2010). Shadow banks are defined by Bernanke (2010) as ‘financial entities other thanregulated depository institutions that serve as intermediaries to channel savings into investment’.

3. The role that Credit Ratings Agencies (CRAs) played in the credit crisis (Naciri, 2015; Larosiere et al.,2009; SEC, 2011). CRAs issue credit ratings which were designed to evaluate the credit risk of financialproducts, companies and governments and were issues by CRAs. However, these credit ratings turnedout to be not accurate nor reliable(Eijffinger, 2012; Naciri, 2015; De Haan and Amtenbrink, 2011;Klinz, 2011; Haspolat, 2015), which created even more fear and uncertainty (Becker and Milbourn,2009; Naciri, 2015; De Haan and Amtenbrink, 2011; Klinz, 2011). Since there was an over-relianceon these credit ratings (Eijffinger, 2012; White, 2010), external parties such as investors were misleadwhich caused chaos.

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The first two reasons have been studied quite extensively, therefore this report will focus on the third aspect:The role of the Credit Rating Agencies. Even though credit risk has already been investigated extensively,during the credit crisis new problems appeared. The situation of Iceland shows what can happen if the creditratings of a government are not a good indicator. Before the 29th of September the credit ratings for Icelandby most of the credit rating agencies were positive (which can be seen in Table 1.1, which indicates thatIceland should have enough liquidity to withstand a mild to severe crisis). However, within just three days,after the 29th of September, the three major banks defaulted on 62 billion dollar of external debt and werenationalized by the government (Amadeo, 2015). It is remarkable that the credit ratings for Iceland wereso positive just the day before the crisis started, since at the end of the second quarter the external debtwas 7 times the GDP of 2007 (Iceland Statistics, 2008). As a comparison, the ratio of debt (both internaland external) to GDP in the USA in 2013 was 1,045 (IMF, 2014), at that time the USA was rated AAA byMoody’s (2013) which is just one step above the rating that was assigned by Moody’s for Iceland before thecrisis. As a result of the chaos that occurred, the currency dropped 50 % in just one week (Central Bankof Iceland, 2008), the stock market fell 95 % (Amadeo, 2015) and many business went bankrupt (Anderson,2015). After the nationalization was finished, the credit ratings had to down rate Iceland to keep up withthe current situation (which can be seen in Table 1.1 but it was already too late. This example shows thatcredit ratings of a government are quite relevant and should be precise and accurate.

Table 1.1: Credit ratings of Iceland

Agency 29-sep-08 10 Oct 2008

Fitch A+ BBB–Moody’s Aa1 A1

S&P A– BBB

1.2 Contents

As mentioned before, there were serious issues with the credit ratings of governments, named sovereign creditratings, since they were not accurate. The European Commission stated a new procedure has to be devel-oped to issue sovereign credit ratings. This report has been made to be able to develop a new procedure toevaluate sovereign credit risk. Sovereign credit risk can be split up into two different types of risk: systemicrisk, which affects every government jointly, and idiosyncratic risk, which is government specific. Sovereigncredit risk is a subpart of credit risk, credit risk is the most dominate type of risk in the financial sector (vanDeventer and Imai, 2003; Tasche, 2005).

The report starts with an explanation of the theory behind sovereign credit risk, which is listed in Chapter2. The methodology to develop an alternative rating procedure is listed in Chapter 3. The data that hasbeen used is explained in Chapter 4. The AL-CDS model and the three alternative models that have beendeveloped are explained in Chapter 5. A comparison of the ratings issued by the Reg-model with ratingsissued by the big three is listed in Chapter 6. A conclusion regarding this research is listed in Chapter 7,which also includes a reflection on the research.

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Chapter 2

Theoretical background

There are several theoretical topics that were covered in this research, which will be explained in this section.As a starting point, the relevance of sovereign credit ratings is explained in Section 2.1. An introduction tothe agencies behind the sovereign credit ratings is explained in Section 2.2. A summary of the issues regardingsovereign credit ratings is listed in Section 2.3. The main financial regulation that deals with financial issuesis explained in Section 2.4. Due to this financial regulation, financial institutions were allowed to developcredit risk models internally. An overview of the main credit risk model is listed in Section 2.5. A comparisonof the different models is listed in Section 2.6. The specific models that can be used for sovereign credit riskare explained in Section 2.9.

2.1 Relevance of sovereign credit ratings

As mentioned before, it became evident during the credit crisis that credit ratings of governments were notreliable (Eijffinger, 2012; De Haan and Amtenbrink, 2011; Klinz, 2011; Naciri, 2015). This imposes a majorproblem, due to several reasons:

1. Governmental bonds are key financial products since they account for 40% of the bond market(AFME,2016; Hill et al., 2012). The credit risk is expressed by the credit rating of it’s government, but if theinformation is not accurate nor reliable, a huge loss could occur on government bonds which will havea negative worldwide impact.

2. Credit Ratings have a huge impact on the cost of funding for a government (Eijffinger, 2012). Theimpact of the ’downgrade of a sovereign borrower may jeopardize the achievements of implementedausterity measures.’(Eijffinger, 2012). This could happen if the credit rating of a government is wronglydowngraded, due to a non-correct method.

3. Government bonds are seen as reliable and risk-free investments (Hill et al., 2012) and are thereforetraded by many investors, but what could happen if there is more risk associated that is currentlyknown at the moment? This would change the current way of thinking, since government bonds areseen as risk-free investments.

4. As seen in the case of Iceland the credit ratings should warn external parties of possible losses thatcould occur in a certain economy, which in turn could help to protect an economy to collapse. If theratings reflect a different viewpoint on its credit risk compared to reality, the situation could becomeeven worse due to confusion.

To understand where the criticism towards credit ratings of governments arises, one first need to understandthe institutions that express credit ratings which are named Credit Rating Agencies. This is explained inthe next section.

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2.2 An introduction to Credit Rating Agencies

Credit ratings are expressed by Credit Ratings Agencies (CRAs), which are legal entities allowed to evaluatecredit risk (Naciri, 2015). If a company or government expresses that it wants to be evaluated in terms ofcredit risk, it will have to pay a fee for the service. The credit rating expresses its credit risk, depending onthe classification (such as AAA, BB+ etc.). It was reported that there were 121 Credit Rating Agencies by2015 (Naciri, 2015), but 95% of the credit rating market is dominated by the so-called ’big three’ (Naciri,2015). The ’big three’ are three Credit Ratings Agencies from the USA: Standard & Poor’s (S&Ps), Moodys& Fitch. The big three use a ordinal categorization in which each of them has its own labels (Naciri, 2015).One of the advantages is that a rating provides a quick insight which can also be used as a benchmark. Oneof the main disadvantages of this system is that the classifications do not reflect the credit risk in a linearscale which make a simple comparison difficult, i.e. a downgrade from the highest scale to one scale lower isnot equal to a downgrade from a middle scale to one scale lower.

Even though the CRAs express that their ratings are merely ‘an opinion’ (Ferguson, 2010; Standard &Poor’s (S&P), 2012), they still have a major impact on the financial market since ‘big investors incorporatethem into their investment guidelines,... In either case, a weak rating costs money.’ (The Economist, 2012).There is an interesting case in which the US government filed a lawsuit with a claim of 5 billion dollar againstS&Ps since they lowered the credit rating of the USA(Naciri, 2015), which heavily impacted the decisionmaking on the US treasury bill for many investors. This example shows that credit ratings can not simplebe seen as ‘an opinion’, why would a government issue a lawsuit if the credit rating is only seen as a simpleopinion with no major impact? This is not the only issue that arises concerning credit ratings. The nextsection summarizes the issues related to credit ratings.

2.3 Issues

As mention before, many people blame the role CRAs had in the credit crisis. To understand what happenedand what caused their behaviour, a large number of investigations have been conducted. An overview ofthe major issues is listed in this section, based upon reports from governments and financial institutions(Larosiere et al., 2009; SEC, 2011; Katz et al., 2009; De Haan and Amtenbrink, 2011) and investigations byseveral researchers (Naciri, 2015; Benmelech and Duglosz, 2009; Partnoy, 2006; Klinz, 2011; Eijffinger, 2012;Ozturk et al., 2016):

1. CRAs are blamed for their oligopoly, the big three have a market share of 95% in which they misusetheir position (Naciri, 2015; Larosiere et al., 2009; Klinz, 2011). An example of this situation iswhen Moody’s send a ’unsolicited’ rating to Hanover Re in 2004 with a letter to ask to pay for acertain service (Naciri, 2015). Since the company didn’t pay as Moody’s requested, they kept loweringthe credit rating even though this wasn’t done by other credit ratings. This lead to confusion forshareholders and resulted in a loss of 175 million dollar for the company (Klein, 2004).This shows thatthe big three misuse the credit ratings they express.

2. CRAs are ’insufficient transparent’ (Naciri, 2015) about the reasoning behind their attribution ofratings. This makes it difficult to assess the ratings given by the big three, since detailed informationsuch as the factor weights are not provided (Eijffinger, 2012). In response with this criticism, the bigthree published in-house publications to convince outside parties of their objectivity and accuracy. Anexample is a publication by Moody’s (2011) in which their model is compared to the Altman Z-scoremodel (Altman, 1968), which is one of the first developed models to assess credit risk and still appliedtoday (Naciri, 2015). They find out that the assessment of Moody’s is more accurate compared to theAltman Z-score. This is quite interesting, since why would one wants to prove the reliability if thechairmen express that the ratings are merely ’opinions’? (Ferguson, 2010; Standard & Poor’s (S&P),2012). Independent investigations point out that the methodologies used by the big three are not as

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accurate nor reliable as they tend to present (Partnoy, 2006; Hunt, 2009; Iyengar, 2010; Becker andMilbourn, 2009; Klein, 2004). Hunt (2009) points out that: ’the fact that agencies are willing to givetheir models suggests that someting is wrong with the reputational capital model. It suggests that therating agencies credit-assessment techniques are not valuable, so that ratings derive their value fromsomething other than high quality.’

3. CRAs use an issuer-pay model, in which the CRAs receive a fee from the issuer in return for a creditrating. This results into a conflict of interest (EC, 2013; Ozturk et al., 2016), since each issuer wants tohave the highes credit rating possible. It is mentioned in the paper by Partnoy (2006) that managers ofthe big three met with the management of their clients to discuss how they could keep reach or maintaina certain rating. This shows that the objectivity and independent position of CRAs can be doubted.Another issue with the conflict of interest is that issuers may seek to hire CRAs that provide morefavourable credit ratings (Naciri, 2015). As a result, ’agencies whose rating methodologies requiredlower levels of credit enhancement to reach a given rating lower than competitors tended to increasetheir market share (Cantor and Packer, 1996). Plus, the present of a new CRA could result in anincrease of ’issuer-friendly’ ratings by already established CRAs (Becker and Milbourn, 2009).

4. CRAs are generally slow to respond to market changes (Eijffinger, 2012; Ozturk et al., 2016; Naciri,2015). Even when analysts and other financial institutions expressed that there was a crisis coming,they still didn’t updated the ratings. And when the CRAs responded, they tended to overreact (Naciri,2015; Ozturk et al., 2016). Many investors almost blindly trusted the CRAs expertise (The Economist,2012), which created even more instability during the financial crisis (Bank of England et al., 2013)due to the combination of a late and overreacted response.

5. As mentioned before, CRAs use an ordinal scale of rating symbols to represent the credit risk of anissuer. However, it has not been proven yet that this concept is as accurate as they suggest. Instead,various studies have pointed out that one can seriously doubt the accuracy due to the usage of theordinal scale (Cantor and Packer, 1996; Blinder, 2007; Benmelech and Duglosz, 2009). They point outthat replacing the ordinal rating system by a linear rating system could improve the current situation.

6. A lack of independence for CRAs (Naciri, 2015). The big three were ’perceived to be hesitatingin downgrading companies in which they were in consulting business’(Naciri, 2015), such as Enron,Freddie Mac and many other clients that defaulted. The big three seem to have become victims of thesystem they created themselves, since ’in a crisis a downgrade can be like firing a bullet in company’sheart’ (Fons and Partnoy, 2009). During the AIG bailout in 2009, US officials made sure that CRAswould not downgrade the company (Naciri, 2015).

7. CRAs were not able to adequately incorporate the correlation between pools of assets which were linkedtogether (Katz et al., 2009). Since many financial products and institutions, such as governments, arelinked together in real-life, one has to incorporate the relationship. Since this was not done properly, thesnowball effect that was happening was not included in the models which created even more confusion.

8. CRAs underestimated the credit risk of both financial products (De Haan and Amtenbrink, 2011;Larosiere et al., 2009; Benmelech and Duglosz, 2009) and institutions, such as Iceland (which wasexplained in the introduction). If several ratings of both financial products and institutions are toopositive one can seriously doubt the current methodology that is used by the ’big three’.

In general, all the criticism can be summarized into one main issue (Naciri, 2015): ’the poor governance ofagencies followed in producing ratings, mainly deterred by subprime debacle and suggesting that the existinggovernance framework for the operation of CRAs needs to be significantly reinforced, as it may not produceaccurate ratings (EC, 2013)’. To be able an alternative, insights in the Basel agreements is necessary sincethey are the international guidelines for credit risk models. This is explained in the next section.

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2.4 Basel agreements

There are three Basel agreements, each one focusses on a different aspect. Basel I (BCBS, 1988) categorizedproducts in several categories, depending on their risks, and required that banks should reserve capital forpossible losses due to credit risk. It also mentioned that government bonds can be seen as risk-free products,a viewpoint that became later under discussion and is also stressed in this report. Basel II (BCBS, 2006)gave banks permission to (re)develop their own models to analyze credit risk, in which the foundation IRBapproach restricted banks to use credit ratings from CRAs while under the advanced IRB approach bankswere allowed to find all relevant parameters themselves. Basel II insists that they should test their mod-els on a regular basis, to assure that the parameter values were valid, and that more emphasis has to bepaid to models that include macroeconomic conditions.Lopez (2004) used a model to reveal the impact ofmacroeconomic conditions, in which was found out that a higher correlation yields a lower default proba-bility in general and that the size of a company has a negative relationship with the impact of a change inthe macroeconomic conditions. Basel III (BCBS, 2010) ensured that banks had to increase their capital towithstand shocks and introduced liquidity ratio.

There is quite some criticism towards the Basel agreements, since due to Basel II there was an increasingdependency on CRAs and there tends to be a pro-cyclical effect in which the capital requirements wouldnegatively affect a bank during a crisis. To understand this criticism, insight in credit risk models is needed.The next section provides information on credit risk models, which could be be used to replace the currentcredit rating procedure of governments.

2.5 Credit risk model classification

Several institutions have developed mathematical models to analyze the liquidity position of a financialproduct or institution. An overview of the three different types of models that exists is listed underneath(Kliestik and Cug, 2015; Caouette et al., 2008):

1. Structural models,which ‘consider business failures to be endogenous event, which is also affected bycapital structure’ (Kliestik and Cug, 2015). This implies that the default probability mainly dependson the capital structure. The models in this group assume that default occurs as soon when thecompany asset value falls below a given threshold. Structural variables are used to explain creditspreads. Examples of models in this group are the Merton model (Merton, 1974) and the Black andScholes Model (Black and Scholes, 1973). Advantages of these models are that they are precise andconsistent. Disadvantages of these models are that they are not very accurate and that they assume aconstant interest rate, which does not hold in reality.

2. Reduced models, models in which default is interpreted as an exogenous variable in which creditspreads are used as an input. Within this group, there is a separation within models based on intensityand credit migration models. The intensity based models emphasise the modeling of the random timeof defaults as a time of jump in a jump random process (Kliestik and Cug, 2015). The credit migrationmodels model the transitions between credit ratings by a Markov process (Kliestik and Cug, 2015),default occurs when the obligator has the lowest credit rating (usually labelled as ’default’). Examplesof reduced models are the model made by Duffie and Singleton (Duffie and Singleton, 1999) and CreditPortfolio View. Advantages of these models are that the default probability can be derived from creditderivatives prices and debt prices, which are perhaps the most sensitive sectors (van Deventer andImai, 2003) and that they have less parameter estimation risk. An disadvantage is that these modelsare more complex to derive than structural models.

3. Hybrid models, models in which aspects from both the structural as reduced models are combined(Zhou, 2001). Within this group there is a subgroup called ‘Value at Risk’ models, such as CreditMetrics and Credit Risk Plus. These models ‘aim to measure the potential loss, with a predeter-mined confidence level, that a portfolio of credit exposures could suffer within a specified time horizon’

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(Kliestik and Cug, 2015) and are more dominant within the group of hybrid models. An advantage ofhybrid models is that they combine the advantages of the two different type of models. The disadvan-tages depend on the specific model itself and are therefore explained at the corresponding section.

In the case of the first group of reduced models and hybrid models, default is defined as ”the situationwhere an obligator cannot make a payment related to a bond or a loan obligation, whether it is a couponpayment or the redemption or principal”(Kliestik and Cug, 2015). A selection of six models that are wellknown in literature and applied in the industry (Crouhy et al., 2000; Gordy, 2000; Kliestik and Cug, 2015;McNeil et al., 2005; Bluhm et al., 2003; Rosch, 2003) will be discussed in the next section chapter, which arethe Merton model, the KMV model, Credit Risk Plus, Credit Metrics, Credit Portfolio View and the factormodel.

2.6 Comparison of credit risk models

The Merton model is the first credit risk model that has been developed, it’s main strengths are it’s simplicityand the usage for any publicly traded company. However, there are some issues related to the assumptionsof the model. In real life, one can not assume that constant interest rates apply for a long time period sincethey tend to change over time. Besides, companies can default at any time in reality, not only at a giventime period which is modelled in the model. The KMV model and Credit Metrics have been developedto deal with some of these issues, as a result institutions in both models able to default at any moment.Besides, the KMV model is capable to react quick to changes in the economic prospect of a firm, has astrong empirical testing and is capable of dealing with large databases. However, there some drawbacksto the KMV model, since it is quite sensitive to changes in the economic prospect of a firm and can onlybe applied for firms with publicly traded stocks. The drawbacks and strengths of the KMV model are op-posite to Credit Metrics, the strengths of Credit Metrics are the weaknesses of the KMV model and viceversa. Besides, Credit Metrics is not able to distinguish between firms in the same credit rating and creditratings have to be used as input, which has been shown in the previous chapter to be not reliable nor accurate.

Credit Risk Plus is different to the models described before since the cause of default is not considered.Just as the Merton model, it is easy to implement and it requires few inputs. However, the model doesnot incorporate migration risk and the cause of default is not taken into account, which makes it difficultto predict defaults in the future. The model has limited capability and can be only considered as a quickbut not thorough indication. Credit Portfolio View does only consider macroeconomic factors. The strengthof this model is that each factor has a specified weight, which allows a detailed insight in the importanceof each factor. However, the model does not include internal factors who can also influence the potentialcredit risk of a company. Since the internal capital structure is not included, this model is not considered toprovide a full insight in the main default drivers.

As mentioned before, the KMV model and CreditMetrics have overlap, since their weaknesses are thestrengths of the other model. It would be interesting to combine the KMV model and Credit Metrics tohave a model who addresses the weaknesses of the both models and combines the strengths, which wouldresult in an optimal model (since the KMV model and CreditMetrics are the two most optimal models of thefive models mentioned). Since the advanced IRB approach allowed banks to (re)develop credit risk models,research has been conducted on the so called ’factor models’ (Bluhm et al., 2003; Rosch, 2003; Jakubık, 2006),which are credit risk models who are classified as hybrid models. Factor models are derived from the KMVmodel and Credit Metrics and consider both the internal risk of company and the impact of macroeconomicchanges. These factor models are in line with the recommendation from Basel II that more attention hasto be paid to credit risk models who incorporate the influence of external factors. The models take careof the weaknesses of the two models, in a factor model one can distinguish between institutions within thesame credit rating and factor models can be used for each type of institution. A factor model is capable ofsplitting the sovereign credit risk into a systemic and non-systemic risk part, which allows a more preciseinsight and is thus preferred above the five listed model. Based upon the factor model, other models or

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procedures will be used to specify the systemic risk and non-systemic risk to understand what the driversbehind these types of risk are.

2.7 Sovereign credit risk

As mentioned before, a factor model can split the risk into a systemic and non-systemic part (henceforthnamed: Idiosyncratic part). The systemic part affects every sovereign, examples of events that result into anincrease of the systemic risk are a global financial crisis, a world war etc. The idiosyncratic part is sovereignspecific, in which several sovereigns can have a different behavior. Examples of events that drive idiosyncraticrisk are a recession, a political crisis etc.

It has been found out that for emerging countries, the share of the systemic risk is higher than the idiosyn-cratic risk (Longstaff et al., 2011; Alper et al., 2012). This can be explained since they are highly dependingon external investments. This is in contrast with developed countries, in which the share of idiosyncraticrisk is higher than systemic risk (Longstaff et al., 2011). An analysis of the USA by the authors showed thatsystemic risk in the USA can be explained by the VIX index an the stock index. This analysis provides ananswer to what type of risk is primarily driving sovereign credit risk. Most investigations that investigatesovereign credit risk use the CDS spread. More information regarding the CDS spread is explained in thenext section.

2.8 Credit Default Swaps

A CDS is a financial instrument which acts as a insurance. If a sovereign issues a bond, there might bethe possibility that the sovereign defaults in which the investor will loose its investment (the par value ofa bond). If the investors purchases a CDS, the issuer of the CDS pays out the par value of the bond. Inreturn for this insurance, the buyer pays a percentage of the par value which is denoted as the CDS spread.The spread is usually denoted in base points.

The concept of a CDS has been invented by Blythe Masters in 1994, who worked for J.P. Morgan at thattime. The CDS market increased in size until 62.2 trillion dollar in 2007 (Weistroffer, 2009), but decreasedin size 25.5 billion dollar in 2012 (Weistroffer, 2009). ”The collapse of Lehman finally confronted marketparticipants and supervisors with the failure of a relevant CDS counterparty that was also an important ref-erence entity. Market reactions were heavy, owing to the fuzziness of information on actual credit exposuresin a market where trading takes place over-the-counter (OTC)” (Weistroffer, 2009). The main issuers andbuyers of CDS products are banks and hedge funds (Weistroffer, 2009).

Most research conduced before the financial crisis regarding the CDS market was focused on emergingcountries (Arce et al., 2012). There was a shift in the focus since the financial crisis, in which more attentionwas paid to developed countries and especially sovereigns in the Eurozone (Arce et al., 2012; Alper et al.,2012). Sovereigns such as Portugal and Greece faced severe financial problems, which was also reflected inthe CDS spreads. The CDS spread values were quite stable and low (below 500 basepoints) before the EuroDebt crisis but increased steeply during the Euro Debt crisis and even reached 1710 base points for the 3years maturity CDS spread of Portugal. Special attention has to be paid to Greece, since the CDS spreadeven went over 55,000 base points for the 1 year maturity. This is an extreme situation, since one wouldassume that a sovereign defaults if the spread reaches 10,000 base points. This shows that it’s complex tomodel sovereign credit risk.

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2.9 Sovereign credit risk models

Factor models have already been extensively used for corporate credit risk, but limited for sovereign creditrisk. Since there is a limited number of defaults and the characteristics differ per default case, the usage ofhistorical default data is limited. However, there are two alternatives that can be used as a proxy. The firstalternative is to use the sovereign bond yield, in which a increase in the yield indicates a rise in the impliedsovereign credit risk. A second alternative is to use the CDS spread, in which a rise in the spread indicatesa rise in the implied sovereign credit risk. It is assumed that a higher CDS spread indicates that the marketperceives that there is a higher level of sovereign credit risk. Since the CDS market is more liquid than thebond market and the CDS spread is a direct measure of sovereign credit risk, the usage of the CDS spreadis preferred.

Within the CDS model, there is a classification into two types of models. The first category consists ofmodels that split the CDS spread into a default and risk premium part. The default part is the share ofthe spread that represents the implied default probability, while the risk premium part can be seen as theimplied market value. The advantage of this model is that it is capable of deriving a clear implied sovereigncredit risk default value, but not what the factors are that change this value. Examples of such models canbe found in articles by (Pan and Singleton, 2008; Longstaff et al., 2011; Duffie and Singleton, 2003). Thesecond category consists of models that split the CDS spread into a systemic risk part, which affects eachborrower, and an idiosyncratic risk part, which is sovereign specific. This type of model provides a more indepth analysis of what drives sovereign credit risk and more specifically, to what extent it is dependent on thestatus of other sovereigns. There are a limited number of articles available in this category, but an exampleof such a model can be found in Ang and Longstaff (2013). Since this type of model allows a comparison ona national level, the usage of the second type of model is preferred.

The model that is tested by Ang and Longstaff (2013) (henceforth: AL-CDS model) is quite accurate whenone looks back over the period till the Euro debt crisis. It has been designed for backward looking, it is notclear how the AL-CDS model performs for future predictions It would be interesting to see how the AL-CDSmodel performs over data of the Euro debt crisis. The model is solely based upon the CDS spread anddoes not take into account financial and/or macro economic data for the calculation. However, the authorsinvestigate the relationship between systemic risk and financial factors, finding that there is a significantrelationship. They also mention that more attention has to be paid to this relationship, since they testa limited set of financial variables and other financial variables could provide more insight. Furthermore,several researchers point out that one should include macro economic variables if one investigates the Eurodebt crisis (Gibson et al., 2014; Afonso et al., 2014; Bernoth et al., 2012; Hagen et al., 2011). Since the modelis retrospective in nature and does not include financial and/or macroeconomic data for the calculation, thequestion arises whether the model is accurate for future predictions and specifically when one tries to modelthe Euro debt crisis.

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Chapter 3

Methodology

3.1 Research question

This research aims to extend the current AL-CDS model by including the representative factors for bothsystemic and non-systemic risk. The current factor model assigns parameter values for both the systemicrisk and non-systemic risk based upon historical data, which provides an insight whether a country is moresensitive to systemic or non-systemic risk. If the factors behind these two types of sovereign credit risk areknown, future predictions can be made. This might be more complex in the current AL-CDS model, sinceit has been designed to look backward. The advantage of a more advanced model is that the the impact ofchanges in the macro economic and financial environment can be quantified. Based upon the information sofar, the research question is defined as follows:

Can the AL-CDS model be extended by including the factors that represent systemic and non-systemic risk?The sub questions are as follows:

1. What are the parameter values needed for the AL-CDS model? The first step is to find the mainparameter values that can be used for the basic factor model to separate the risk into systemic andnon-systemic risk. The three main parameter values are systemic risk shock intensity, conditionaldefault probability due to this systemic shock and the individual shock intensity of a country.

2. What are the financial factors that represent systemic risk? As mentioned before, more attention needsto be paid to the relationship between financial factors and systemic risk. Therefore, more financialfactors will be tested to reveal what factors could represent systemic risk within the Euro zone, suchas the interest rate. The values of these financial factors will be compared with the first parameter,systemic risk shock intensity. If it turns out that the systemic risk shock intensity can be representedby financial factors, the model will be adjusted by replacing the systemic risk shock intensity by therepresentative factors. In case this is not possible the systemic risk shock intensity will not be replacedin the model.

3. What are the factors that represent non-systemic risk? Macro economic and financial factors will betested to reveal what factors do represent non-systemic risk for each of the selected countries. Thevalues of the factors will be compared with the individual shock intensity of each country. If it turnsout that the non-systemic risk shock intensity of a country can be represented by financial factorsand/or macro economic factors, the model will be adjusted by replacing the non-systemic risk shockintensity by the factors. In case this is not possible, the non-systemic risk shock intensity will not bereplaced in the model.

4. How can this model be validated? The factors provide a more detailed insight in the two types of risk,which can make the factor model more specific. The model has to be tested to validate it.

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Based upon the main research question and the sub questions, the methodology can be developed which isstated in the next section. Based upon this methodology, the conceptual project design and project plan aremade which are listed in section three. The main deliverables are listed in section four, while a timeline forthe project is listed in section five. The data gathering setup is listed in section six.

3.2 Problem Solving Cycle

The methodology that will be used for this research is the problem-solving cycle (van Aken et al., 2008),which consists of the following steps:

1. Problem definition, which is summarized as follows: ’The current rating procedure of Credit RatingAgencies to assess sovereign credit risk is not accurate’. More information about the problem can befound in Chapter 2.

2. Analysis and diagnosis, in which the analysis of the current situation is described in Chapter 2. Thesecond step is the diagnosis, which should give an answer to the second and third sub question.

3. Solution design, in which a model should be designed which could be used for predictions for the future.This model can be used for the set of countries that is selected and will answer the fourth question.More information regarding this model can be found in Chapter 5.

4. Intervention, in which the main person applies the solution to change the current business procedure.The intervention part is out of scope for this research.

5. Learning and evaluation, which is an ongoing process during the project in which the student learnsand reflects on the progress. Discussion with supervisors play an important role for this aspect andshould not be underestimated by the student.

3.3 Conceptual project design & project plan

The conceptual project design contains the outline of the project (van Aken et al., 2008), which can helpthe student to have a clear direction to follow. It consists of three elements (van Aken et al., 2008) whichcan be seen in Figure 3.1:

1. The subject of analysis, which is represented in the right side of Figure 3.1. In this case, it is a businessprocess namely the current rating procedure used by the big three to assess sovereign credit risk.

2. The set of theoretical perspectives, which provide a theoretical background for the project to developthe diagnosis of the current business situation. This has already been conducted, the complete findingscan be found in the literature study conducted by the student while a summary can be found in Chapter2.

3. The deliverables of the project, in which the main deliverable is a model to assign sovereign creditratings in the Eurozone.

Based upon the conceptual project design, a project plan can be made. The project plan consists of thetwelve steps (van Aken et al., 2008) that the student has to follow to be able to finally design the maindeliverable of the graduation project. The steps are as follows:

1. Literature study on the topics defined in the left side of the conceptual project design. This has alreadybeen done, the findings can be found in this report and more extensively in the literature study (van deVen, 2016).

2. Empirical analysis of the business problem, in which information about the business problem shouldbe gathered to be able to gather the full picture. For more information, see Chapter 2.

11

Figure 3.1: This figure shows the conceptual project design of the graduation project

3. Formulation of the diagnosis of the main problem. For more information, see Chapter 2

4. Exploration of solution directions, in this case the author has investigated credit risk models in whichfactor models seem to be possible solution due to their unique characteristics.

5. Feedback of the results of the former steps from the supervisors, in this case academic supervisorsand one company supervisors. This should be done after the design of the project plan but also on acontinuous basis during the project.

6. Further detailing of the project plan for solution design and implementation, in which a more detailedplan is made to cover all the relevant details.

7. A further literature search regarding topics on solution design, resulting in design specifications etc.This will be done to be able to apply the proper tools and methods to be able to provide an answer tothe sub questions.

8. Elaboration of one direction into a redesign, in this case a credit risk model that can be applied to thegovernments that have been selected.

9. Development of organizational support for the redesign, as described before this step will be evaluatedlater during the project.

10. Presentation and authorization of the solution, which is the final stage of the project. This will beprobably held at the end of February 2017, however the first academic supervisor should give greenlight before the student can plan a presentation.

11. Implementation of the solution, which will be evaluated later if this should be part of the project.Since the model will be developed in such a way that it can be applied for four to five governments, themodel could already be implemented. However, this depends to which extent the word implementationshould be applied.

12. Evaluation, which should not only be done at the end of the project but also during the project on aregulatory basis to keep on track.

A graphical and concise overview of the project plan can be found in Figure 3.2.

12

1. Collect the data

2. Develop several models

in MATLAB

3. Investigate Systemic risk

4. Investigate Idiosyncratic

risk

5. Model validation

Figure 3.2: This figure shows a con size version of the project plan.

13

Chapter 4

Data

There are two time periods considered for this research: 4-2007 until 4-2010 (the calibration period) and5-2010 until 4-2013 (the testing period). Some characteristics about the data is discussed in this chapteras well as the rest of this research. The CDS spreads, and financial and macro-economic data have beencollected over the two time periods.

4.1 CDS data

The three years and five years CDS spread of eight sovereigns in the Euro zone for both time periodshave been collected from Bloomberg. The eight countries are Portugal, Italy, Spain, Ireland, France, Bel-gium, Germany and the Netherlands. This comparison of eight sovereigns allows for an in-depth analysis ofsovereign credit risk in the Euro zone, since this selection includes sovereigns that have less fluctuation inthe CDS spread (such as Germany) and sovereigns that have a higher fluctuation in the CDS spread (suchas Portugal). We are also able to analyze the dependency of a sovereign’s credit risk on its own performanceand macro-economic variables as well as other sovereigns. We do not include Greece in our data-set since theCDS spread of both the three year and five year maturity are extremely high (over 30,000 base points). Thisexplanation provides an answer to sub questions 1. The five year CDS spread for the calibration period canbe seen in Figure 4.1 and for the testing period in Figure 4.2. The corresponding three year CDS spreads canbe found in Appendix section B. The summary statistics of the CDS data can be found in Appendix section C.

There are a couple of observations to note regarding the data from the calibration period (2007-2010). Thereis no data available on Ireland’s CDS spreads before the first of January 2008, when they started to issueCDS contracts. Ireland also has the highest CDS spreads for most of the time period under study (averagefive years maturity value for the CDS spread of 129 base points and a maximum of 367 base points) andalso the highest implied sovereign credit risk. For all the European sovereigns, we see an increase in theCDS spread from the beginning of 2010, which marks the start of the Euro debt crisis. Note that among theeight countries under consideration, Portugal has the highest standard deviation due to the high fluctuationin its CDS spread. It is of interest to note that for both Portugal and Ireland, the three years CDS spreadis higher than the five years CDS spread for about a third of the time span.

During the testing period, the CDS spread is much higher compared to the calibration period for allsovereigns. Portugal has the highest implied credit risk (average five years CDS spread of 663 basis points),much higher compared to the calibration period. Portugal and Ireland still show the reverse behavior withthe three and five year maturity CDS spread. Germany continues to have the lowest CDS spreads and isthus perceived to have the lowest implied sovereign credit risk. We see that for all the countries, the highestCDS spread was in 2011 which marks the peak of the Euro debt crisis. From 2012, a downward trend in theCDS spreads is observed for all the sovereigns, implying that sovereign credit risk starts to diminish.

14

20 April 2007 7 September 2007 5 January 2008 13 June 2008 31 October 2008 20 March 2009 7 August 2009 25 December 2009 30 April 2010

Date

0

50

100

150

200

250

300

350

400C

DS

spre

ad (

basepoin

ts)

Germany

Portugal

Spain

Italy

Ireland

Netherlands

France

Belgium

Figure 4.1: five years CDS spreads from April 2007 until April 2010

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 4 January 2013 26 April 2013

Date

0

200

400

600

800

1000

1200

1400

CD

S s

pre

ad (

basepoin

ts)

Germany

Portugal

Spain

Italy

Ireland

Netherlands

France

Belgium

Figure 4.2: five years CDS spreads from May 2010 until April 2013

15

4.2 Explanatory variables for systemic risk

”More attention has to be paid to the relationship between systemic risk and financial” factors(Ang andLongstaff, 2013). We refer to several articles such as (Rosch, 2003; Ang and Longstaff, 2013; Koopmanet al., 2012; Wegener et al., 2016) to come up with a comprehensive list of financial variables to use. Wealso use corporate financial data since they are highly correlated with the performance of the country andalso because limited information is available on the factors for sovereigns. We collect the following variablesfrom Bloomberg:

• FX rates (Euro-Dollar ratio, Euro-Pound ratio, Euro-Yen ratio, Euro-RMB ratio)• Stock indices (NASDAQ index, S&P500 index, Eurostoxx index)• VIX indix (EU VIX Eurostoxx)• Commodities (Brent Oil price per barrel in Euro, Gold price per ounce in Euro)• Interest rates (one month, three months and six months Euribor, ECB interest rate, Euro-Dollar

deposit interest rate)• Bond prices (one year, three years and five years Euro-bond bid prices)• Swap rates (one year, three years and five years swap rates)

The FX rates are the ones used in the IMF basket of the SDR valuation. The US stock indices are includedsince the US is the biggest economy in the world and the biggest trading partners of the European Union(Directorate General for Trade, 2016). The VIX index has been included since it is a strong indicator forsystemic risk, also mentioned in (Ang and Longstaff, 2013). The Oil price has been included since ”positiveoil price shocks lead to lower sovereign CDS spreads” (Wegener et al., 2016). The summary statistics canbe found in Appendix section D.

4.3 Explanatory variables for Idiosyncratic risk

A selection of fourteen financial and macro economic variables has been made to assess non-systemic sovereigncredit risk. We chose these variables since they are good indicators of idiosyncratic risk for both sovereignsand corporate institutions, as mentioned in (Koopman et al., 2012; Rosch, 2005; Jakubık, 2006; Gestel et al.,2006). The data is collected from Bloomberg, ECB and Eurostat at a sovereign level. The variables collectedare:

• Finance (High Yield 10 years treasury bond bid price, stock index, interest rate on deposits, long-terminterest rate, inflation ratio)

• Unemployment ratios (Total unemployment, unemployment over 25 years, unemployment under 25years)

• Industry indices (Production index construction, Manufacturing turnover index)• Balances (Real effective exchange rate, International trade ratio, Index of deflated turnover)• Economic indices (Generic economic situation over the next year of customers, Financial situation over

the last year of customers).

No data is available for the production index construction for both Ireland and Spain. The summary statisticscan be found in Appendix section E.

16

Chapter 5

Models

In this section we first explain the backward looking model developed in Ang and Longstaff (2013), whichforms the base of our framework and model. We calibrate it using data from 2007-2010 and test its perfor-mance on data from 2010-2013. Seeing the deficiencies in the AL-CDS model’s performance, three alternativemodels have been developed. This is explained in Section 5.3, while a comparison of the models can be foundin 5.4.

5.1 AL-CDS model

The AL-CDS model is based on the classical framework presented in (Duffie and Singleton, 2003). Themodel assumes two kinds of shocks - a systemic shock that affects every sovereign and an idiosyncraticshock which only affects the default of an individual sovereign. The systemic and non-systemic shocks areassumed to be independent of each other. The idiosyncratic shock is the same as the underlying standardreduced-form credit models used by (Pan and Singleton, 2008; Duffie and Singleton, 1999). In the AL-CDSmodel the idiosyncratic default is triggered by ‘the first jump of a sovereign-specific Poisson process’(Angand Longstaff, 2013). This intensity process follows a standard square-root process for sovereign i :

dζi,t = (ai − biζi,t)dt+ ci√ζi,t dZi,t (5.1)

where ai, bi, ci are constants and Zi,t is a standard Brownian motion, all sovereign specific. This settingallows for mean reversion and conditional heteroskedasticity in the intensity process and guarantees thatthe intensity process never becomes negative. It has to be noted that there is no restriction placed on thecorrelation between the Brownian motions across sovereigns, since this is partially taken into account by thesystemic risk intensity process.Systemic risk affects every sovereign, but each sovereign experiences its impact differently. This impact is

modeled by the parameter γi which is sovereign specific and is assumed to be constant. The intensity processfor systemic risk is also modeled as a Poisson intensity process, which follows a standard square-root process:

dλt = (α− βλt)dt+ σ√λi,t dZλ,t, (5.2)

where α, β, σ are constants and Zλ,t is the Brownian motion of the systemic risk intensity process in Equation(5.2). The Brownian motion for systemic risk and the Brownian motions driving the idiosyncratic risk areuncorrelated. Similar to the idiosyncratic risk intensity process, the systemic risk intensity process can neverbecome negative. The probability that there is no default by sovereign i by time t can be expressed asfollows:

P (no default by time τ) = exp

(−∫ τ

o

(γiλt + ζi,t)dt

). (5.3)

The total default intensity is the sum of the idiosyncratic shock intensity ζi,t and the systemic risk intensity λtmultiplied by the exposure (or impact) γi. Sovereign credit risk thus depends on the two intensity processes

17

and the exposure. These values can be derived from the CDS spread (si,τ ) of sovereign i and maturity τusing the following formula:

si,t,τ =

ω

∫ τ

t

D(t, τ)(A(λ, t)C(ζi, t) + γiB(ζi, t)F (λ, t)

)dt∫ τ

t

(D(t, τ)A(λ, t)B(ζi, t)

)dt

, (5.4)

where ω is the recovery rate and D(t, τ) is the value of a risk-free zero-coupon bond with maturity τ attime t. The formulas for A(λ, t), B(ζi, t), C(ζi, t), F (λ, t) can be found in Appendix A and have been derivedfrom the paper by (Ang and Longstaff, 2013). The constants α, β, σ denote the slope and curvature of thesystemic risk part of the CDS term structure, while the value of λt reflects the systemic risk level of theCDS spread of a sovereign. The constants ai, bi, ci denote the slope and curvature of the idiosyncratic partof the CDS term structure, while the values of ζi,t reflect the idiosyncratic risk level of the CDS spread of asovereign. The value of ω has been set at 50%, which is in line with Duffie and Singleton (2003); Ang andLongstaff (2013).We make the following assumptions. A sovereign default event is assumed to occur upon the first arrival

of the Poisson process, but in reality, a default is triggered by credit events described in the CDS contracts.The precise legal definition of a sovereign default is thus not fully captured by the model. We work with therisk-neutral measure, since there are almost no historical cases of sovereign defaults. We take the countrywith the lowest CDS spread to be the comparison country - and its default depends only on systemic risk.In this paper, Germany is set as the comparison country since it has the lowest CDS spread, in addition tobeing the biggest economy in the Eurozone.

5.2 Calibration

The constants and the intensity processes have been estimated using the 3 and 5 year CDS spread over thecalibration time period. The values for the zero coupon bonds D(t) have been bootstrapped using the 1,3, and 6 month Euribor rates and the 1, 3 and 5 year swap rates, collected from Bloomberg. The cubicspline interpolation algorithm (Longstaff et al., 2005) has been used to calculate these values. To be able tofind the constants and the intensity process values, the estimated CDS spread si,t,τ has been compared withthe original CDS spread si,t,τ . The parameters have been estimated using the nonlinear least squares method.

Since Germany is the country that represents systemic risk in the Eurozone, the systemic risk constantsand the systemic risk intensity values λt have been estimated using a nonlinear least squares algorithm overdata of Germany. Note that γGermany = 1 since Germany is the base for systemic risk. The second stepis to estimate the constants ai, bi, ci, γi and the idiosyncratic risk intensity process ζi,t for each of the sevensovereigns using a nonlinear least squares algorithm. The outcome of the calibration of the parameters canbe found in Table 5.1, in which the standard error is listed within brackets.As can be seen in Table 5.1, almost all parameter estimates are quite reliable since the standard error is

very small. The standard error for Germany is high, but still within an acceptable range. The RMSE valuesfor each country are small and within 10 basis points. Thus, we can conclude that the model has a reliableand accurate fit for the calibration period. The calibration results corroborate actual observations. Mostcountries have γ < 1, indicating a higher dependency on idiosyncratic risk. However, this is not the casewith Spain and Ireland - they exhibit γ > 1 indicating a higher dependency on systemic risk. The CDSspread of Portugal is quite volatile, and the calibration sets a high value for cPortugal.

The values of λ and ζ over the calibration period can be seen in Figure 5.1, while the share over timeof systemic and idiosyncratic risk can be seen in Table 5.2. As can be seen in the Figure, the ζ values ofIreland are high until mid 2008 and tend to become smaller afterwards. Ireland has the highest values untilmid 2008, which indicates that Ireland has the highest level of idiosyncratic risk. Afterwards, Italy has thehighest zeta values for one year. Portugal has the highest ζ values for the last timer period, in which even

18

Table 5.1: Parameter estimates

Systemic Risk α β σ RMSEGermany -0.0763 -1.01225 0.6890 2.9751

(0.2263) (0.8280) (0.1348)

Idiosyncratic risk a b c γ RMSEPortugal 0.7506 -2.4049 0.6252 0.6037 5.4192

(0.2478) (0.7436) (0.2146) (0.4847)Spain 0.2137 -0.2708 0.4924 1.3295 5.5228

(0.0076) (0.1108) (0.0957) (0.1539)Italy 0.2091 0.1647 0.4822 0.4633 6.6835

(0.0698) (0.1070) (0.1877) (0.3494)Ireland 0.5427 -0.0824 0.1015 3.0176 8.3658

(0.1467) (0.0134) (0.0401) (0.0013)Netherlands 0.2142 -0.6143 0.2676 0.6002 3.2370

(0.0110) (0.1281) (0.0634) (0.0005)France 0.0963 -0.4039 0.4767 0.2580 3.8622

(0.0506) (0.2223) (0.1229) (0.1693)Belgium -1.0445 0.2590 0.1944 0.6412 4.1714

(0.0094) (0.0076) (0.0034) (0.0006)

intensity values over 500 are reached which indicates that there is a serious level of idiosyncratic risk forPortugal. The smallest values can be found for Germany and the Netherlands, which have the lowest levelof sovereign credit risk. The γ values in Table 5.1 that are above 1, such as for Spain and Ireland, indicatethat these countries have a pattern similar to Germany. As can be seen in Table 5.2, Ireland has a highshare of systemic risk over time (67% on average). The Netherlands also has a high share of systemic risk(67% on average), which indicates that it is more affected by systemic risk than idiosyncratic risk. It wasexpected that a similar situation would also occur for Spain, since the values of γ is above one. However,as can be seen the share of idiosyncratic risk is still higher than systemic risk. For the other countries, theshare of idiosyncratic risk is quite small compared to the share of systemic risk. This explanation providesan answer to subquestion 1.

Table 5.2: Share of systemic risk over the calibration period

Share Min Max Median Average

Portugal 2% 100% 19% 22%Spain 6% 100% 37% 43%Italy 2% 59% 12% 14%

Ireland 0% 100% 68% 67%Netherlands 6% 100% 68% 67%

France 1% 100% 19% 23%Belgium 1% 100% 31% 35%

19

20 April 2007 7 September 2007 5 January 2008 13 June 2008 31 October 2008 20 March 2009 7 August 2009 25 December 2009 30 April 2010

Date

0

100

200

300

400

500

600

Inte

nsitie

s)

Germany

Portugal

Spain

Italy

Ireland

Netherlands

France

Belgium

Figure 5.1: λ and ζ intensity values over the calibration period

5.3 Alternative models

As mentioned before, the AL-CDS model was designed for backward calculation. To check how it performsfor future predictions, three alternative models have been designed. The results of the AL-CDS modelare compared with the results of the three alternative models. These alternative models have a differentprocedure to calculate λ and ζ. A reliable estimation for λ and ζ is important since they are the keycomponents to calculate the survival probability, as can be seen in Equation 5.3. These are regressed againstthe financial and macro-economic variables and a model that returns the closest fit is used to estimatesovereign credit risk. The next two sections describe the regression process. The model’s performance isobserved over the testing period and the results can be seen in Section 5.4.

5.3.1 Regression for Systemic risk

We start with a principle component analysis of the financial variables using the Varimax technique. Thevariables that turned out to be independent and are able to explain a major share of the variance and havebeen used as input for a regression analysis. Several lagged time series (1 week, 2 weeks, 3 weeks, 1 month,3 months) have been tested to design a model which is able to explain the behavior of the systemic riskintensity process. EU VIX with two weeks lag, 1 month Euribor and Euro-Dollar FX rate provide the bestfit, explaining 83% of the variance (see Table 5.3). These three variables are used to calculate lambda forthe alternative procedure. All variables are significant at 99% level. The outcome of the regression analysesprovide an answer to sub question 2.

20

Table 5.3: Systemic risk regression outcomeVariable lag coefficient standard error R2

EU VIX two weeks 1.641 0.1241m Euribor no lag -10.383 0.934Euro-Dollar no lag 10.005 3.416

0.829

5.3.2 Regression for Non-systemic risk

For each of the sovereigns (excluding Germany), the following procedure has been followed. A principalcomponent analysis of the explanatory variables was conducted using the Varimax technique. The variablesthat turned out to be independent and able to explain the major share of the variance have been used asinput for a regression analysis. Several lagged time series (1week, 2 weeks, 3 weeks, 1 month, 3 months) anddifferent sets of variables have been tested to find a model for each sovereign that captures its idiosyncraticrisk. The outcome can be seen in Table 5.4.

Table 5.4: Idiosyncratic risk regression resultsCountry Variable lag co-efficient std error R2

Portugal Generic economic situation no lag -2.585 0.415 0.887Index of deflated turnover no lag -8.837 1.077HY 10yrs treasury bond no lag 73.932 18.759Unemployment ratio Total no lag 57.192 4.167

Spain Unemployment ratio Total no lag 6.212 0.349 0.838Generic economic situation 1 week 0.672 0.187

Italy Index of deflated turnover no lag -11.918 1.519 0.892Real effective exchange rate no lag -8.253 2.636Int trade ratio no lag -8.462 0.840Inflation ratio no lag 28.004 2.088

Ireland Long term interest rate no lag 87.836 11.020 0.899Unemployment ratio over 25 year no lag 6.268 2.275Manufacturing turnover index adj no lag -3.608 0.384

Netherlands Unemployment ratio Youth 1 week -4.657 1.629 0.782Stock index no lag -0.260 0.017Inflation ratio no lag 1.635 0.174

Belgium Interest rate deposit no lag -17.728 2.559 0.801Financial situation over the last year no lag -6.856 0.533Production index construction no lag 0.295 0.090

France Unemployment ratio Total 3 weeks 18.982 1.341 0.860Int trade ratio no lag -1.542 0.118Generic economic situation no lag -1.158 0.100

As can be seen, the standard errors of the parameter estimations are low and the estimations are highlysignificant, from which it follows that the outcome can be classified as reliable. The R-squared values arebetween 0.782 and 0.899 which indicates that the behavior of the idiosyncratic risk intensity process can bewell explained by macroeconomic data. All variables are significant at 99% level. Portugal is highly sensitiveto a change in either the 10 years high yield treasury bond (co-efficient of 73.932) or the unemployment ratioof the total population (co-efficient of 57.192). Ireland is very sensitive to a change in the long term interestrate (co-efficient of 87.836). These values are quite high, since most absolute co-efficient values are smallerthan 10. The Netherlands has the lowest co-efficient values of all sovereigns (maximum absolute co-efficientvalue of 4.657). The high co-efficient values correspond with the high CDS values, while the low co-efficient

21

values for the Netherlands correspond with the low CDS values. The outcome is used to calculate zeta foralternative procedure. The outcome of the regression analyses provide an answer to sub question 3.

5.3.3 Model design

Besides the CDS model, three alternative models have been designed based upon the regression outcomes.The three alternative models use the same constants (γi, α, β, σ, ai, bi, ci) as the CDS model. However, thedifference is in the use of the systemic and idiosyncratic risk intensity processes. While in the CDS modelthe intensity processes are simulated using the constants for the testing time span, the alternative modelsincorporate the outcome of the systemic risk and idiosyncratic risk regression models to calculate zeta andlambda. This procedure is named variable calculation. The other procedure is to simulate the lambda andzeta values over the testing period using Monte Carlo simulation of the formula 5.1 for lambda and formula5.2 for zeta.

For the first alternative model, instead of using the outcome of the Monte Carlo simulation to calculatelambda, the outcome of the systemic risk regression model has been used. This model is named Sys-Modelhenceforth. This can be seen in the following formula:

λt = (EU Vix at t) × 1.614 + (1 momth Euribor at t) ×−10.383 + (Euro-Dollar at t) × 10.005 (5.5)

Note that the values for the zeta have been calculated using Monte Carlo simulation of formula 5.1.

For the second alternative model, the values of the zeta have been replaced by the idiosyncratic risk regressionmodels.This model is named Idio-Model henceforth. This can be be seen in the following formula:

ζi,t =

zi∑1

Variable value at t × impact factor (5.6)

In which zi is the number of variables included for sovereign i. The variables can be found in 5.4.Note thatthe values for the lambda have been calculated using Monte Carlo simulation of formula 5.2.

For the third alternative model, the values of both lambda and zeta have been calculated using the regres-sion models. This model is named Reg-Model henceforth. No Monte Carlo simulation has been used.

An overview of the AL-CDS model and the three alternative models can be seen in Table 5.5.

Table 5.5: Overview of the different models. Note that MC simulation stands for Monte Carlo simulation.

Model Explanation Systemic risk Idiosyncratic risk

CDS Model designed to look backward MC simulation MC simulationSys-model Model which replaces lambda calculation Variable calculation MC simulation

Idio-model Model which replaces zeta calculation MC simulation Variable calculationReg-model Model which replaces both lambda and zeta calculation Variable calculation Variable calculation

22

5.4 Results

Based upon the settings for the AL-CDS model and three alternative models, the CDS spreads of the threeyear and five year maturity have been simulated for the testing time period. Note that the actual data overthe testing period has been used, since forecast data was not available. The most accurate fit and leastaccurate fit for the sovereign which has both systemic and idiosyncratic risk are respectively shown in Figure5.2 and 5.3. The figures for the other sovereigns can be found in Appendix F.

30-4-2010 17-9-2010 4-1-2011 24-6-2011 11-11-2011 30-3-2012 17-8-2012 25-12-2012 26-4-2013

Time

0

20

40

60

80

100

120

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Sys-model outcome

Idio-model outcome

Figure 5.2: 3 years maturity CDS spread for the Netherlands

As can be seen in Figure 5.2, which shows the values for the 3 years maturity CDS spread for the Nether-lands, the AL-CDS model outcome is not close to the actual CDS spread while the outcome of the Reg-modelis quite close to the actual CDS spread. This shows that the Reg-model for the Netherlands results in abetter estimation compared to the AL-CDS model.

23

30-4-2010 17-9-2010 4-1-2011 24-6-2011 11-11-2011 30-3-2012 17-8-2012 25-12-2012 26-4-2013

Time

0

200

400

600

800

1000

1200

1400

1600

1800

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Sys-model outcome

Idio-model outcome

Figure 5.3: 3 years maturity CDS spread for Portugal

As can be seen in Figure 5.3, which shows the values for the 3 years maturity CDS spread for Portugal,there is a similar situation in which the Reg-model returns a better fit. However, there is still some deviationbetween the actual CDS spread and the outcome of the Reg-model. This can be explained by the differentbehavior of the CDS spread before and during the crisis. Before the crisis, the CDS spread of the five yearsmaturity CDS spread for Portugal was under 300 base points with a mean value of 60 base points, whileduring the crisis the the CDS spread of the five years maturity was on average 663 base points and reachedeven 1380 base points. This similar situation can also be found for Spain, Ireland and Italy. This is alsoreflected in their high CDS spreads, which indicates a higher level of implied sovereign credit risk. Due tomatters of simplicity, only the outcome of the AL-CDS model and the most optimal model (Reg-model) areshown.

Table 5.6: RMSE outcome

RMSE

Germany Portugal Spain Italy Ireland Netherlands Belgium FranceAL-CDS model outcome 48 743 331 315 563 58 168 112

Sys-model 30 732 303 306 504 46 159 107Idio-model 48 410 272 193 380 40 96 90Reg-model 30 399 246 185 321 30 88 85

The RMSE between the actual and the estimated CDS spread from the models is shown in Table 5.6 anddenoted in base points. We can conclude that the Reg-model does better than the AL-CDS model sinceit incorporates the financial and macro-economic data. The smallest RMSE values can be found for thecountry with the lowest CDS values, which is Germany with a RMSE value of 48 base points. The highestRMSE values are for Portugal (743 bp) and Ireland (563 bp), are also the countries with the highest CDSspread. The Reg-model results in lower RMSE values compared with the outcome of the AL-CDS model,in the case of Spain, even a decrease of 46%. Thus, the Reg-model can be used for forecasting, which isnecessary to assign a credit rating for a sovereign.

As mentioned before, there is a clear difference in the CDS spread behavior before and during the Eurodebt crisis. The CDS spread was much higher during the crisis than before, which explains why there is a

24

difference between the outcome of the Reg-model and the actual CDS spread. It would be of interest to seewhat the outcome of the Reg-model would be, if stress testing would be applied. Stress testing is requiredby Basel III (BBC, 2009) and reveals the impact of a negative scenario on the outcome of the model. One ofthe type of stress testing that can be applied is to test the vulnerability of a sovereign to a macro economicshock (Wong et al., 2008). The Reg-model in capable of including the possibility of a macro economic shock,both on a systemic and idiosyncratic level.

25

Chapter 6

Comparison

To be able to compare the outcome of the forecasting model with the ratings assigned by the big three,a classification scale has to be designed to assign a rating based upon the estimated default probability.However, there are a couple of issues to notice. First, the big three do not release information regardingwhat default probability is assigned to a credit rating. There is a qualitative definition for each rating, but noquantitative expression in terms of default rates nor default probability over time. Since the rating proceduresused by the big three are different, different ratings are issued for the same sovereign. Furthermore, datafrom S&P (Standard & Poor’s (S&P), 2012) and Moody’s (Moody’s, 2008) show a discrepancy between thesovereign credit rating assigned by a credit rating agency and the default rate that is observed over timeby the credit rating agency. One would assume that a higher rating would result into a lower default rate,but the opposite situation can be seen. These observations show that is it not clear what the quantitativeimpact is of a rating in terms of the observed default rate.To be able to compare the ratings, we first calculate the estimated default probability using the Reg-model,

as shown in Section 6.1. Based upon the default probabilities, a rating scheme is developed shown in Section6.2. A comparison of the ratings assigned by the Reg-model and the ratings assigned by the big three isshown in Section 6.3. As an extra benchmark, the sovereign 1 year bond yields are also included in thecomparison. This explanation provides an answer to sub question 4.

6.1 Default probability forecast

To be able to calculate the default probability, one needs to have the values of lambda, zeta and gamma. Sincethese values are known for the calibration time period, the default probability for the eight countries can becalculated. There are two main approaches to calculate the default probability (BCBS, 2005). The first isthe Through The Cycle approach, which can be used in case one considers the stressed default probability.In this situation, the probability of default is not heavily affected by the economic circumstances, such asan economic downturn or a global crisis. The second approach is the Point In Time approach, in which theunstressed default probability is calculated. In this approach the default probability the impact of macroeconomic changes is taken into account. The second approach is used by the big three and should also beused for the Reg-model, since the impact of macro economic changes is taken into account. Therefore, thePoint In Time approach will be applied to calculate the default probability which is calculated as:

P (Default within one year from time t) = 1 − exp

(−∫ t+1

t

(γiλt + ζi,t

)dt

)(6.1)

The time span has been set to 1 year, since assets are commonly values on a yearly basis. The lambda andzeta values are known on a weekly basis for a time span of 3 years, but 1 year data is needed to calculate thedefault probability. Thus, the default probabilities values within one year from time t have been calculated

26

per week for two years, which includes the peak of the Euro debt crisis. The default probabilities can befound in Figure 6.1.

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012

Time

0

0.02

0.04

0.06

0.08

0.1

0.12

P (

Defa

ult w

ithin

1 y

ear

from

tim

e t)

Germany

Portugal

Spain

Italy

Ireland

Netherlands

France

Belgium

Figure 6.1: Estimated default probability

The default probability is the highest for Portugal and Ireland and matches with their high CDS spread.Thus, the model reflects the implied sovereign credit risk in an adequate manner. The default probability forPortugal decreases from the beginning of 2012, which points out that Portugal is perceived by the market totake adequate steps to lower it’s credit risk. The default probability for Ireland is decreasing from the startof 2011, which shows that Ireland is quicker to deal with the crisis that appeared than Portugal. Irelandand Portugal can be classified as high risk sovereigns. Germany has the lowest default probability, closelyfollowed by the Netherlands; they can be classified as stable and safe sovereigns since their default probabilityvalues are very low and stable. Belgium and France follow a similar pattern in which their values are betweenthe relatively stable sovereigns and the risky sovereigns. Thus, they can be classified as low risk sovereigns.

6.2 New rating scheme

To be able to understand the relationship between the ratings assigned by the big three and the marketperception by the sovereign 1 year maturity yield, a scatter plot has been made which can be seen in Figure6.2. Since there is no data available for the sovereign 1 year maturity bond of Portugal and the Netherlands,the 1 year yield has been calculated from the corresponding 2 year maturity bond. The same procedurehas been used for Spain for May 2010 until mid October 2010, since there was not data available for thesovereign 1 year maturity bond for this time period. both a linear and exponential fit have been applied, inwhich the exponential fit is a closer fit compared to the linear fit. However, as we see in the plot, there is awide range for the yield for ratings below Aa2; especially for Ba2 where yields range between 2% and 10%.This shows that while the market is perceiving a higher level of risk, the sovereigns have the same creditrating. Hence, using bond yields alone would not be sufficient to set up a rating scheme.To complement a bond yield based rating scheme, we can make use of our model and the default probabilities

we obtain. This allows a more reliable comparison of sovereigns, since there is a metric which applies to eachsovereign. When a sovereign defaults, the default probability value should have a value of 1 and it shouldhave the lowest possible rating. Since Germany is the sovereign which is used as comparison and it’s implieddefault probability is low, Germany is assigned the highest credit rating which is Aaa. We use just one ratingfor default, similar to Moody’s and S&P and unlike Fitch which includes three different default categories.

27

0 2 4 6 8 10 12 14

Yield (%)

Ba3

Ba1

Baa2

A3

A1

Aa2

Aaa

Ra

tin

g

M: Germany

M: Portugal

M: Spain

M: Italy

M: Ireland

M:Netherlands

M: France

M: Belgium

S: Germany

S: Portugal

S: Spain

S: Italy

S: Ireland

S:Netherlands

S: France

S: Belgium

F: Germany

F: Portugal

F: Spain

F: Italy

F: Ireland

F:Netherlands

F: France

F: Belgium

Exponential fit

Linear fit

Figure 6.2: Ratings vs. yield

The probability of default in which a sovereign is still included in the highest bucket is set to be maximumdefault probability value of Germany. An exponential scale has been applied to represent the increasingimpact of a lower rating. We have a total of 22 buckets, each one representing a rating. The bucket rangeincreases as we go towards the default rating, with 1.279 being the range multiplier ensuring that the lastbucket ends with default probability of 1. The first bucket includes sovereigns with a default probabilitybetween 0% and 0.0057%, the second bucket contains sovereigns with a default probability between 0.0058%and 0.0073%. A similar classification to Moody’s has been used for this rating scheme. The buckets can beseen in Table 6.1.

28

Table 6.1: Rating schemeBig 3 Reg-model

Moody’s S&P Fitch PD (default) Nr Label

Aaa AAA AAA 0.0000 - 0.0057 1 AaaAa1 Aa+ Aa+ 0.0058 - 0.0073 2 Aa1Aa2 Aa AA 0.0074 - 0.0093 3 Aa2Aa3 Aa- AA- 0.0094 - 0.0119 4 Aa3

A1 A+ A+ 0.0120 - 0.0152 5 A1A2 A A 0.0153 - 0.0195 6 A2A3 A- A- 0.0196 - 0.0249 7 A3

Baa1 BBB+ BBB+ 0.0250 - 0.0319 8 Baa1Baa2 BBB+ BBB+ 0.0320 - 0.0408 9 Baa2Baa3 BBB- BBB- 0.0409 - 0.0522 10 Baa3

Ba1 BB+ BB+ 0.0523 - 0.0667 11 Ba1Ba2 BB BB 0.0668 - 0.0854 12 Ba2Ba3 Bb- Bb- 0.0855 - 0.1092 13 Ba3

B1 B+ B+ 0.1093 - 0.1396 14 B1B2 B B 0.1397 - 0.1786 15 B2B3 B- B- 0.1787 - 0.2284 16 B3

Caa1 CCC+ CCC 0.2285 - 0.2922 17 Caa1Caa2 CCC CCC 0.2923 - 0.3737 18 Caa2Caa3 CCC- CCC 0.3738 - 0.4780 19 Caa3

Ca CC CCC 0.4781 - 0.6113 20 Ca1Ca C CCC 0.6114 - 0.7819 21 Ca2

C D DDD 0.7820- 1.0000 22 DDD 23

D 24

6.3 Results

The ratings assigned by the Reg-model are compared with the ratings assigned by the big three, which canbe seen in Figures 6.3 through 6.5. The sovereign 1 year bond yield is also included as a benchmark, inwhich an increase in the yield indicates that the market perceives that the level of sovereign credit risk in-creases. One could categorize the eight countries in 3 groups based upon the ratings issued by the forecastingmodel. The first group consist of Germany and the Netherlands, which have a low level of sovereign creditrisk. The second group consist of Belgium, France, Spain and Italy, which have a small level of sovereigncredit risk. The third group consist of Portugal and Ireland, which have a serious level of sovereign credit risk.

The Reg-model gives Germany the highest possible rating, similar to the Big 3. Germany’s bond yieldsare low, under 3.5%, and have a low fluctuation which indicates that there is less implied sovereign creditrisk. A similar situation can be found for the Netherlands, but note that the Reg-model downgraded theNetherlands during the peak of the crisis.

29

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012

Date

Aa1

AAA

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Yie

ld (

%)

Reg-model

Moodys

S&P

Fitch

Yield(%)

Ra

tin

g

Figure 6.3: Ratings for Germany

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012

Date

Ba1

Baa2

Aa3

Aa1

0

1

2

3

4

5

6

7

Yie

ld (

%)

Reg-model

Moodys

S&P

Fitch

Yield(%)

Ra

tin

g

Figure 6.4: Ratings for Spain

For Spain, the credit rating issued by the Reg-model until mid 2011 is Baa1, while it is downgraded to Baa2afterwards. The credit ratings issued by the big three show a lag, since they start to downgrade Spain atthe end of 2011. The yield values indicate a rise in the implied sovereign credit risk at the begin of 2011,while a second increase at the end of 2011. The CDS spread indicates that there is an increase in the impliedsovereign credit risk from the start of 2011. This market behavior is captured by the Reg-model and not bythe credit ratings issued by big three. Thus, it can be concluded that the ratings issued by the Reg-modelprovide better insights than the ratings issued by the big three. The same situation applies to Italy, Franceand Belgium.

30

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012

Date

Ba3

Ba1

Baa2

A3

A1

Aa2

0

1

2

3

4

5

6

7

8

9

10

Yie

ld (

%)

Reg-model

Moodys

S&P

Fitch

Yield(%)

Ra

tin

g

Figure 6.5: Ratings for Portugal

For Portugal, the credit rating issued by the Reg-model follows a decreasing trend. Portugal is rated Ba2from the beginning of 2011, indicating a serious level of sovereign credit risk. This can easily be inferredby looking at the yield values, which increase over time reaching a high of 13%. The Big 3 also downgradePortugal over time, a sharp decrease in March 2011 and again at the end of 2011. However, the CDS spreadand the yield was already an early indication of high sovereign risk - which the Big 3 were slow to respondto. Their update at the end of 2011 was late, since the yield was already quite high before. This is an-other example why the rating issued by the Reg-model provides better insight and faster market responsecompared to the Big 3. A similar situation in which big three are slow to respond can also be found for Ireland.

The figures for the other sovereigns can be found in Appendix G. It can be concluded that the ratings issuedby the Big 3 tend to be slow to respond to market changes. The ratings are not downgraded at the momentwhen both the CDS spread and the sovereign bond yield increase. This is in contrast with the ratingsissued by the Reg-model, which responds quicker to changes in the markets. Second, our rating scheme isa quantitative measure based on the the Reg-model, allowing for a more reliable comparison between thesovereigns. This is in contrast with the rating procedure used by the big three which is qualitative in natureand allows for different ratings for the same sovereign.Thus, this new procedure can be used to replace thecurrent sovereign credit risk procedure.

31

Chapter 7

Conclusion

7.1 Outcome

The credit ratings assigned to sovereigns play a crucial role in indicating the financial health of thesesovereigns.The inadequacies of the ratings assigned by the big three (S &P, Moody’s, Fitch) became ap-parent during the financial crisis of 2008. Several issues were found, such as a lack of transparency, a conflictof interest, a slow respond to market changes etc. This resulted into the complex situation in which thesovereign credit ratings did not reflect sovereign credit risk into an adequate manner. To deal with thissituation, a transparent, rigorous, and responsive model to accurately evaluate the creditworthiness of asovereign, and a rating scheme to assign credit ratings using this model are urgently required.

In this research, we develop a regression-based model (named Reg-model), to estimate the CDS spreadsof sovereigns. The model adopts the notion that sovereign credit risk is composed of both systemic andidiosyncratic risk. The model is designed from the AL-CDS model. The Reg-model uses historical CDS dataand data on other financial and macroeconomic variables to estimate CDS spreads. With these estimates,the values of the systemic and idiosyncratic risk intensity processes can be calculated. These values in turnyield estimates of the default probability of a sovereign. The developed ratings scheme can be used to assignaccurate credit ratings to sovereigns. Our results show that the Reg-model provides accurate estimates ofCDS spreads, while the original AL-CDS model results into less accurate estimations. Furthermore, thecredit ratings assigned to sovereigns using our model and ratings scheme reflect reality better, as opposed tothe credit ratings issued by the big three. The proposed model is transparent, responsive (since the modelallows users to adjust factors and/or add new information easily) and demonstrably accurate. Furthermore,the model also allows for stress testing to be performed, a key requirement for financial models in currenteconomic conditions. This shows that the current AL-CDS model can be extended by incorporating financialand macro economic data, as part of an alternative rating procedure. This is the answer to the main researchquestion.

There are a couple of business advantages when the Reg-model is used. First, the Reg-model is capable ofdealing with different levels of stress testing loading. This results into a more reliable future predictions,which reduces the information asymmetries (IMF, 2010) and improves the transparency (Katz et al., 2009).Second, since the Reg-model returns a more reliable outcome one can allocate the capital buffers more ade-quately. This will result into a cost saving for sovereign credit risk and a better credit risk management.

32

7.2 Research questions

The research questions and a short reflection on the answer is provided.

Sub Question A: What are the parameter values needed for the basic factormodel?

The parameter values can be found in Chapter 5, which have been calibrated over a timespan of 3 yearsbefore the crisis. The values were found using the Non-Linear Least Squares algorithm for the AL-CDSmodel. As can be seen, the sovereigns with a high CDS spread have higher values for the constants. Mostgamma values are below one, which indicates that a sovereign is more affected by idiosyncratic risk, expectfor Spain and Ireland, which are more depending on systemic risk.

Sub Question B: What are the financial factors that represent systemic risk?

There are three financial factors that represent systemic risk, namely the VIX index (2 weeks lag), theEuro-Dollar ratio and the 1 month Euribor rate. The factors have been found from a sample of differentframeworks. Of this sample, a Principal Component Analysis has been conducted to reveal what factorsrepresent the variance with the lowest level of correlation. The factors that quality have been tested using aregression analysis, in which lagged time series have been evaluated. The outcome can be seen in Chapter 5.

Sub Question C: What are the factors that represent non-systemic risk?

A sample of different frameworks has been made. Similar to systemic risk, out of this sample a PrincipalComponent Analyses and Regression Analyses have been conducted on a sovereign level. The outcome canbe seen in Chapter 5. For more sovereigns, the unemployment rate is a factor that is representative. Theother factors depend on the sovereign itself.

Sub Question D: How can this model be validated?

The ratings issued by the model have been validated by comparing them with the ratings issued by the bigthree. As an extra benchmark, the sovereign 1 year bond yields have been included which represent themarket perception. Based upon this dual comparison, it can be concluded that the Reg-model serves as anearly indicator compared to the ratings issued by the big three. This shows that the model is valid to beused.

Main Question : Can the factor model be extended by including the factors thatrepresent systemic and non-systemic risk?

As can be seen in the conclusion, the factor model can be extended by including external data. Thisinformation improves the accurateness of the forecasts, in which a more accurate ratings can be issued. Thisshows that the factor model indeed can be extended.

7.3 Scientific contribution

This research several scientific contributions, which are as follows:

1. Alternative procedure for issueing sovereign credit ratings. The rating procedure explained in thisresearch can replace the current rating procedure used by the big three.

The other contributions are as follows:

33

1. Insight in the drivers of both idiosyncratic and systemic risk. This research shows that variables canrepresent systemic risk, such as the VIX index, and what variables represent idiosyncratic risk for eightsovereigns in the Eurozone.

2. More evidence that the ratings issued by the big three tend to respond slow to market changes. Thiscan be seen in the figures, in which the ratings issued by the big three do not keep up with the changesin the market.

7.4 Business impact

There are two main aspects that affect businesses:

1. The alternative rating procedure can be used to indicate when the CRAs tend to downgrade a sovereign.This information can be used to make a decision whether a sovereign bond is still kept or sold.

2. The alternative rating procedure shows what factors might affect sovereign credit risk. This informationcan be used by a goverment to change its financial polity to improve it’s credit ratings.

7.5 Limitations

There are a couple of limitations for this research that are worth to mention:

1. Since there was no prediction data available for the financial and macro economic data, actual data hasbeen used. If prediction data was available, a fairer comparison between the models would be possible.

2. In the CDS mode, sovereign credit risk is mainly driven by the CDS spread. The CDS spread capturescredit risk, but is also affected by market risk. An increase in the CDS spread could also happen sincethe product is traded more frequently by trades.

7.6 Suggestions for future research

There are a couple of suggestions for future research on this topic:

1. Try to develop a framework of what factors might affect sovereign credit risk. A framework has beendesigned in this research by combining frameworks from different fields. However, if a widely acceptedframework could be developed more clarity on what might affect sovereign credit risk can be gained.

2. Calibrate the model using sovereigns from another continent, since the model has been designed forsovereigns in the Eurozone. It would be of interest to see how the model would perform for sovereignsfrom other monetary unions.

3. Calibrate the model over the peak of the Euro debt crisis and use the outcome to make future predictionsfor the coming five years. Since the CDS spread before and during the crisis is quite different, it wouldbe interesting to find out what variables influence the strong increase in the CDS spread during thecrisis.

4. Include the political influence. In case the political situation of a sovereign changes, it might affect thecredit rating. It would be of interest to identify the political impact and to quantify this.

7.7 Personal reflection

There are a couple of lessons learned that are worth sharing:

1. Share issues earlier and more often. Sometimes I noticed that when I don’t understand or struggle tofind a solution, I try to fix it myself. If I share my thoughts with someone else more often, they mighthelp me to structure my thoughts and can help me to find a solution.

34

2. Never go to quick. I tend to move quick and to think about the next step, but sometimes it can helpto make sure the current step is worked out well enough. This prevents the situation in which I haveto go back in the process and do quite some work again. By paying a bit more attention and to try tounderstand the situation complete, I can prevent this situation.

35

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Wong, J., Choi, K.-F., and Fong, T. P.-W. (2008). A Framework for Stress Testing Banks’ Credit Risk,pages 240–260. Palgrave Macmillan UK, London.

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40

Appendix

A Formulas

Please note that for reasons of simplicity, the subscript i on ξi, ai, bi, ci, and γi is suppressed in this appendix.There are three layers of equations for equation 8. The first layer is as follows:

A(λ, t) = A1(t) exp(A2(t)λ),

B(ξ, t) = B1(t) exp(B2(t)ξ),

C(ξ, t) = (C1(t) + C2(t)ξ) exp(B2(t)ξ),

F (λ, t) = (F1(t) + F2(t)λ) exp(A2(t)λ),

The second layer of formulas is as follows:

A1(t) = exp

(α(β + ψ)t

σ2

)(1 − ν

1 − ν eψt

)2α/σ2

,

A2(t) =β − ψ

σ2+

2ψ

σ2(1 − ν eψt)

B1(t) = exp

(a(b+ φ)t

c2

)(1 − θ

1 − θ eφt

)2a/c2

,

B2(t) =b− φ

c2+

2φ

c2(1 − θ eφt),

C1(t) =a

φ

(eφt − 1

)exp

(a(b+ φ)t

c2

)(1 − θ

1 − θ eφt

)2a/(c2+1)

,

C2(t) = exp

(a(b+ φ)t

c2+ φt

)(1 − θ

1 − θ eφt

)2a/(c2+2)

,

F1(t) =α

ψ

(eψt − 1

)exp

(α(β + ψ)t

σ2

)(1 − ν

1 − ν eψt

)2α/(σ2+1)

,

F2(t) = exp

(α(β + ψ)t

σ2+ ψt

)(1 − ν

1 − ν eψt

)2α/(σ2+2)

,

The third and last layer is as follows:

ψ =√β2 + 2γσ2,

ν = (β + ψ)/(β − ψ),

φ =√b2 + 2c2,

θ = (b+ φ)/(b− φ). (1)

41

B CDS spread graphs

20 April 2007 7 September 2007 5 January 2008 13 June 2008 31 October 2008 20 March 2009 7 August 2009 25 December 2009 30 April 2010

Date

0

50

100

150

200

250

300

350

CD

S s

pre

ad

(b

ase

po

ints

)

Germany

Portugal

Spain

Italy

Ireland

Netherlands

France

Belgium

Figure 1: 3 years maturity CDS spread for the calibration period

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 4 January 2013 26 April 2013

Date

0

200

400

600

800

1000

1200

1400

1600

1800

CD

S s

pre

ad

(b

ase

po

ints

)

Germany

Portugal

Spain

Italy

Ireland

Netherlands

France

Belgium

Figure 2: 3 years maturity CDS spread for the testing period

42

C Summary statistics CDS data

Table 1: three years maturity CDS spread calibration period

country Portugal Spain Germany France Belgium Netherlands Italy Ireland

min 0,420 0,130 0,100 0,040 0,130 0,330 1,000 13,220median 41,710 49,170 12,060 16,640 28,670 19,050 47,960 129,350

max 280,370 161,230 77,900 80,400 135,770 117,550 187,470 347,300mean 52,597 51,539 16,310 20,157 32,170 24,193 57,188 115,824

std 52,499 42,532 16,737 18,018 30,249 26,603 49,202 81,462N 157 157 157 155 155 153 158 121

Table 2: five years maturity CDS spread calibration period

country Portugal Spain Germany France Belgium Netherlands Italy Ireland

min 2,962 1,965 3,240 1,000 0,100 0,100 4,562 17,300median 49,090 59,922 20,041 22,090 32,420 27,670 66,134 146,310

max 280,703 161,919 86,503 97,901 144,300 125,310 194,033 366,600mean 60,389 59,340 22,227 26,121 38,557 29,013 68,742 128,806

std 51,540 44,167 17,182 22,228 32,549 29,018 51,795 86,243N 158 158 146 154 155 153 156 121

Table 3: three years maturity CDS spread testing period

3 year maturity (testing period)

country Portugal Spain Germany France Belgium Netherlands Italy Irelandmin 233.190 169.700 6.530 11.320 20.330 16.140 110.840 97.830

median 522.370 271.395 29.535 64.095 123.985 35.325 209.175 578.465max 1710.530 593.340 82.470 201.170 384.910 101.360 557.060 1382.590

mean 727.450 308.663 34.554 83.206 140.731 44.644 274.684 534.464std 422.579 109.635 16.999 44.795 80.965 21.550 134.765 290.891N 156.000 156.000 156.000 156.000 156.000 156.000 156.000 156.000

Table 4: five years maturity CDS spread testing period

5 year maturity (testing period)

country Portugal Spain Germany France Belgium Netherlands Italy Irelandmin 223.086 155.927 21.995 62.019 66.620 26.500 125.502 153.240

median 524.340 299.718 46.976 91.104 151.060 53.005 265.475 557.745max 1389.809 598.227 114.452 252.500 396.690 132.490 561.995 1102.490

mean 663.065 328.369 57.531 120.094 168.529 65.884 302.388 485.375std 310.137 105.247 23.833 52.179 74.916 28.565 127.659 214.687N 156.000 156.000 156.000 156.000 156.000 156.000 156.000 156.000

43

D Summary statistics Systemic Risk data

Table 5: Systemic risk variables- Part 1 (calibration period)

Type Eu-Po Eu-Ye Eu-Do Eu-Rm NASDAQ S&P500 Eurostoxx EU VIX Gold price Oil price

min 0.672 115.040 1.254 8.573 1,293.850 683.380 1,817.240 12.450 15.294 646.040median 0.807 137.680 1.414 10.045 2,265.210 1,182.395 2,971.730 24.160 26.265 910.150

max 0.960 169.470 1.589 11.094 2,810.380 1,561.800 4,556.970 79.130 81.034 1,178.650mean 0.813 144.421 1.417 9.961 2,183.271 1,184.304 3,243.904 27.900 29.561 898.418

std 0.083 17.444 0.085 0.706 389.861 241.301 786.777 12.699 12.198 140.978N 158 157 157 158 158 158 158 158 158 157

Table 6: Systemic risk variables- Part 2 (calibration period)

Type Euribor rate Eurobond bid price Swap rateDuration 1 month 3 months 6 months 1 year 3 years 5 years 1 year 3 years 5 years ECB Deposit

min 33.730 0.400 0.635 0.280 0.558 1.111 1.968 1.072 1.713 0.945 0.250median 3.868 4.069 4.187 2.750 2.600 2.704 2.890 3.228 4.000 3.769 3.896

max 143.680 5.130 5.381 6.000 4.592 4.637 4.674 5.410 5.315 5.431 3.250mean 78.840 2.717 3.027 2.492 2.521 2.851 3.217 3.162 3.406 3.170 1.843

std 23.675 1.788 1.798 1.990 1.604 1.179 0.879 1.633 1.172 1.712 1.314N 151 158 158 153 158 158 158 158 158 158 158

Table 7: Systemic risk variables- Part 1 (testing period)

Type Eu-Po Eu-Ye Eu-Do Eu-Rm NASDAQ S&P500 Eurostoxx EU VIX Gold price Oil price

min 0.778 95.420 1.197 7.780 2,091.790 1,022.580 2,026.030 11.300 14.909 1,176.650median 0.844 110.195 1.319 8.478 2,785.685 1,318.750 2,616.750 18.185 23.843 1,592.450

max 0.904 129.870 1.481 9.635 3,294.945 1,588.850 3,068.000 43.050 49.794 1,882.410mean 0.842 109.785 1.330 8.566 2,759.420 1,305.154 2,584.906 20.695 26.197 1,543.003

std 0.029 7.624 0.063 0.482 299.449 131.372 245.612 6.966 7.804 178.495N 156 156 153 156 156 156 153 156 156 156

Table 8: Systemic risk variables- Part 2 (testing period)

Type Euribor rate Eurobond bid price Swap rateDuration 1 month 3 months 6 months 1 year 3 years 5 years 1 year 3 years 5 years ECB Deposit

min 0.107 0.184 0.316 0.000 0.200 0.005 -0.038 0.240 0.289 0.408 0.745median 0.623 0.895 1.154 0.250 0.310 0.505 0.576 1.054 1.200 1.497 1.892

max 1.458 1.611 1.831 0.750 0.450 1.487 2.203 2.805 1.988 2.755 3.206mean 0.658 0.877 1.114 0.266 0.310 0.555 0.702 1.205 1.133 1.401 1.801

std 0.442 0.472 0.496 0.227 0.055 0.454 0.627 0.721 0.520 0.648 0.690N 156 156 156 155 156 156 156 156 156 156 156

44

E Summary statistics Idiosyncratic Risk data

Table 9: Summary Statistics Portugal

Portugal

Type Gen. Eco. situation Index of deflated turnover Bond yield Unemp. totalmin -54.90 97.50 3.77 8.40

median -28.20 100.60 4.42 9.05max -10.30 105.40 5.14 11.90

mean -28.67 100.68 4.40 9.78std 11.94 1.69 0.31 1.15N 158 158 158 158

Table 10: Summary Statistics Italy

Italy

Type Index of deflated turnover Real eff. exc. rate Int. trade ratio Inf. ratiomin 97.70 99.37 86.40 103.90

median 100.55 101.73 103.00 108.30max 104.00 104.56 108.30 110.90

mean 101.00 101.90 101.95 107.68std 1.66 1.50 4.71 1.90N 158 158 158 158

Table 11: Summary Statistics Spain

Spain

Type Gen. Eco. situation Unemp. totalmin -48.20 7.80

median -17.10 12.80max -8.40 20.20

mean -23.63 13.71std 12.79 4.48N 158 158

45

Table 12: Summary Statistics Ireland

Ireland

Type Long term int. rate Unemp. over 25 yrs Man. indexmin 4.17 3.60 83.90

median 4.61 5.80 107.70max 5.76 11.70 113.40

mean 4.75 7.18 103.70std 0.42 3.05 8.72N 158 158 158

Table 13: Summary Statistics the Netherlands

the Netherlands

Type Int. rate deposit Unemp. under 25 years Infl. ratiomin 2.65 7.60 102.77

median 4.00 9.35 105.82max 4.56 12.20 108.45

mean 3.90 9.60 105.59std 0.52 1.20 1.51N 158 158 158

Table 14: Summary Statistics Belgium

Belgium

Type Int. rate deposit Fin. situation Pro. Index constructionmin 2.21 -16.50 57.00

median 3.88 -12.40 108.60max 4.53 -2.50 126.10

mean 3.45 -11.58 103.09std 0.82 4.11 18.38N 158 158 158

Table 15: Summary Statistics France

France

Type Unemp. total Int. Trade ratio Gen. Eco. situationmin 6.80 87.50 -46.50

median 8.00 97.70 -24.30max 10.10 103.20 5.70

mean 8.29 96.84 -24.15std 0.96 3.84 14.28N 158 158 158

46

F Forecast results

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

20

40

60

80

100

120

140

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 3: 5 years maturity CDS spread the Netherlands

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

200

400

600

800

1000

1200

1400

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 4: 5 years maturity CDS spread Portugal

47

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

50

100

150

200

250

300

350

400

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 5: 3 years maturity CDS spread Belgium

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

50

100

150

200

250

300

350

400

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 6: 5 years maturity CDS spread Belgium

48

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

50

100

150

200

250

300

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 7: 5 years maturity CDS spread France

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

50

100

150

200

250

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 8: 3 years maturity CDS spread France

49

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

100

200

300

400

500

600

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 9: 5 years maturity CDS spread Spain

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

100

200

300

400

500

600

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 10: 3 years maturity CDS spread Spain

50

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

100

200

300

400

500

600

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 11: 3 years maturity CDS spread Italy

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

100

200

300

400

500

600

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 12: 3 years maturity CDS spread Italy

51

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

200

400

600

800

1000

1200

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 13: 5 years maturity CDS spread Ireland

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

200

400

600

800

1000

1200

1400

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 14: 3 years maturity CDS spread Ireland

52

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

20

40

60

80

100

120

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 15: 5 years maturity CDS spread Germany

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012 17 August 2012 25 December 2012 26 april 2013

Time

0

10

20

30

40

50

60

70

80

90

CD

S s

pre

ad

(b

ase

po

ints

)

Actual CDS spread

AL-CDS model outcome

Reg-model outcome

Figure 16: 3 years maturity CDS spread Germany

53

G Ratings assigned

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012

Date

Aa2

Aa1

AAA

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Yie

ld (

%)

Reg-model

Moodys

S&P

Fitch

Yield(%)

Ra

tin

g

Figure 17: Ratings the Netherlands

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012

Date

A3

A1

Aa2

AAA

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Yie

ld (

%)

Reg-model

Moodys

S&P

Fitch

Yield(%)

Ra

tin

g

Figure 18: Ratings France

54

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012

Date

A3

A1

Aa2

AAA

0.5

1

1.5

2

2.5

3

3.5

4

Yie

ld (

%)

Reg-model

Moodys

S&P

Fitch

Yield(%)

Ra

tin

g

Figure 19: Ratings Belgium

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012

Date

Ba2

Baa3

Baa1

A2

Aa3

Aa1

0

2

4

6

8

10

12

14

Yie

ld (

%)

Reg-model

Moodys

S&P

Fitch

Yield(%)

Ra

tin

g

Figure 20: Ratings Ireland

55

30 April 2010 17 September 2010 4 February 2011 24 June 2011 11 November 2011 30 March 2012

Date

Baa2

A3

A1

Aa2

1

2

3

4

5

6

7

Yie

ld (

%)

Reg-model

Moodys

S&P

Fitch

Yield(%)

Ra

tin

g

Figure 21: Ratings Italy

56