European sovereign systemic risk zones V. Arakelian, M. Vezzoli Final SYRTO Conference - Université Paris1 Panthéon-Sorbonne February 19, 2016

1. European sovereign systemic risk zones
SYRTO Kick‐Out Meeting
and
First LabEx Réfi Conference on Systemic Risk
February, 19 2016 - Paris
SYstemic Risk TOmography:
Signals, Measurements, Transmission Channels, and
Policy Interventions
Veni Arakelian, Panteion University, Greece
Petros Dellaportas, University College London, UK
Roberto Savona, University of Brescia, Italy
Marika Vezzoli, University of Brescia, Italy

2. Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

3. Definition of systemic risk
“A systemic risk is a risk that an event will trigger a loss of
confidence in a substantial portion of the financial system that
is serious enough to have adverse consequences for the real
economy.”
G-10 Report on Financial Sector Consolidation (2001)
According to this definition, the current financial crisis is
systemic.
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

4. Motivation
Detect sovereign systemic risk zones. The early detection
and the causal identification of such phenomena may
provide valuable early warning signals to countries that
move towards dangerous risk paths.
Provide an effective risk mapping in which country-specific
fundamentals are mixed together with contagion-based
measures, thereby assembling a series of leading indicators
that could signal impending sovereign systemic risk
abnormalities.
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

5. Literature review
 Ang and Longstaff (2013): Systemic sovereign credit risk in the US and Europe,
multifactor affine framework. Findings: Heterogeneity among US and
European issuers, key role of financial market variables.
 Reboredo and Ugolini (2015): Systemic risk in European sovereign debt
markets, conditional value-at-risk measure. Findings: Greek debt crisis was
not so severe for non-crisis countries, systemic risk increased for countries in
crisis.
Considering changes in regimes in CDS dynamics...
 Caceres, Guzzo and Segoviano (2010): Primary role in sovereign spreads sharp
rise, risk aversion (early period of the crisis), country-specific factors, e.g.
public debt and budget deficit (the later stages).
 Arghyrou and Kontonikas (2012): Changes in regime for sovereign debt pricing.
Key role of country-specific macro-fundamentals.
 Ait-Sahalia, Laeven and Pelizzon (2014): Eurozone CDS rates exhibited clusters
in time and in space.
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

6. Data
 Daily 5-yr CDS prices for France, Germany, Greece, Ireland, Italy,
Portugal, Spain and US from January 1, 2008 to October 7, 2013 (1505
daily quotes). For the Greek 5-yr CDS only 1414 quotes were available.
 US and Euro Banks 5-yr CDS indices, US and Euro Other Financials 5-yr
CDS indices.
 Macroeconomic factors to investigate their influence to sovereign CDS
levels (Augustin, 2014):
1. Debt/GDP
2. Exports/GDP
3. GDP growth rate
4. Industrial production
5. Inflation
6. Unemployment
Databases: Markit, Thompson Reuters Datastream, Eurostat.
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

7. Methodology
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
 Copula-based dependencies
 Regression Trees (RT)
 Heatmap
 Ensemble methods
 Random Forests
 Final Regression Tree (FRT)

8. Copula-based dependencies
Arakelian and Dellaportas (2012) proposed a flexible threshold model for
estimation of bivariate copulas
where 𝐶 𝜃 𝑗
𝑖
: the copula function, wij: the probability of copula i in the
interval Ij, 𝑖=1
𝑙
𝑤𝑖𝑗 = 1 for all j. Thus, our general model (1) allows both
the functional form of the copula and the parameters to change within
each interval Ij .
A RJMCMC algorithm was proposed which obtained samples from the
posterior density of these models, and a Bayesian model-averaging
estimation approach constructed a posterior density of Kendall's t
(Kendall, 1938), marginalised over all models and parameters within each
model.
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

9. MCMC Details
Simulation Annealing
Adopt Jasra et al. (2007) to generate L parallel-sampled auxiliary Markov
chains with target densities
where p: posterior density needed to obtain samples from, zl: ordered
parameters 0 < zl < zl -1 < … < z1 < 1. The densities pl serve as independent
Metropolis-Hasting proposal densities for the main chain with target
density p.
At each iteration, one auxiliary density pl is chosen at random and
together with the current sampled point of pl is used at the usual
acceptance ratio of the main chain. In the terminology of Jasra et al.
(2007), this is an exchange move in the population reversible jump
algorithm.
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

10.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

11.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

12.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
 They deal with qualitative/quantitative variables
 They are robust in case of missing values and outliers
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

13.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
 They deal with qualitative/quantitative variables
 They are robust in case of missing values and outliers
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

14.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
 They deal with qualitative/quantitative variables
 They are robust in case of missing values and outliers
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

15.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
 They deal with qualitative/quantitative variables
 They are robust in case of missing values and outliers
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

16.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
 They deal with qualitative/quantitative variables
 They are robust in case of missing values and outliers
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

17.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
 They deal with qualitative/quantitative variables
 They are robust in case of missing values and outliers
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

18.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
 They deal with qualitative/quantitative variables
 They are robust in case of missing values and outliers
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

19.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
 They deal with qualitative/quantitative variables
 They are robust in case of missing values and outliers
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

20.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
 They deal with qualitative/quantitative variables
 They are robust in case of missing values and outliers
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

21.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
 They deal with qualitative/quantitative variables
 They are robust in case of missing values and outliers
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

22.  Regression Trees are non parametric methods that partition the predictor
space X into homogeneous subsets with respect to the dependent variable Y
 They explain non-linear patterns between dependent variable and covariates
 The main advantages are:
 They identify the most important variables and corresponding split points
thereby finding risky/non risky final zone (and their paths)
 They deal with qualitative/quantitative variables
 They are robust in case of missing values and outliers
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Regression Trees (RT)

23. Heatmap
In order to understand what happens inside each terminal node, we use a
graphical representation
Heatmap
For each region, we visualize the values of all covariates by means of
colors: from blue (low values) to red (high values)
In this way we have an idea of how variables are “expressed” in each
node
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

24. Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Heatmap (cont’d)

25. Heatmap on node 1
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Heatmap (cont’d)

26. Heatmap on node 2
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Heatmap (cont’d)

27. Heatmap on node 3
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Heatmap (cont’d)

28. Heatmap on node 4
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Heatmap (cont’d)

29. Heatmap on node 5
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Heatmap (cont’d)

30. Ensemble methods
Ensemble learning techniques (P&C techniques) have been introduced
to increase the accuracy of the results:
 Combining multiple versions of unstable classifiers increases the
accuracy of the predictors
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

31. Ensemble methods
Ensemble learning techniques (P&C techniques) have been introduced
to increase the accuracy of the results:
 Combining multiple versions of unstable classifiers increases the
accuracy of the predictors
Data
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

32. Ensemble methods
Ensemble learning techniques (P&C techniques) have been introduced
to increase the accuracy of the results:
 Combining multiple versions of unstable classifiers increases the
accuracy of the predictors
Data
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

33. Ensemble methods
Ensemble learning techniques (P&C techniques) have been introduced
to increase the accuracy of the results:
 Combining multiple versions of unstable classifiers increases the
accuracy of the predictors
Data
RT1 RT2 RT… RTN
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

34. Ensemble methods
Ensemble learning techniques (P&C techniques) have been introduced
to increase the accuracy of the results:
 Combining multiple versions of unstable classifiers increases the
accuracy of the predictors
Data
RT1 RT2 RT… RTN
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

35. Ensemble methods
Ensemble learning techniques (P&C techniques) have been introduced
to increase the accuracy of the results:
 Combining multiple versions of unstable classifiers increases the
accuracy of the predictors
Data
RT1 RT2 RT… RTN
𝑦1 𝑦2 𝑦… 𝑦 𝑁
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

36. Ensemble methods
Ensemble learning techniques (P&C techniques) have been introduced
to increase the accuracy of the results:
 Combining multiple versions of unstable classifiers increases the
accuracy of the predictors
Data
RT1 RT2 RT… RTN
𝑦1 𝑦2 𝑦… 𝑦 𝑁
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

37. Ensemble methods
Ensemble learning techniques (P&C techniques) have been introduced
to increase the accuracy of the results:
 Combining multiple versions of unstable classifiers increases the
accuracy of the predictors
Data
RT1 RT2 RT… RTN
𝑦1 𝑦2 𝑦… 𝑦 𝑁
Ensemble method
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

38. Random Forests
 RF grow a non pruned tree on a training set which is a
different bootstrap sample drawn from the data
 An important issue of RF is about the use of Out-Of-Bag
(OOB) predictions, where for each observation zi=(xi; yi) the
algorithm computes the predictions by averaging only
those trees grown using a training set not containing zi
 For improving the accuracy, the injected randomness has
to maximize the differences between the trees. For this
reason, in each tree node a subset of predictors is
randomly chosen
 RF provide an accuracy level that is in line with Boosting
algorithm with better performance in terms of
computational burden (Breiman, 2001)
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

39. Final Regression Tree (FRT)
RF increase the accuracy of the predictions but loose the
interpretability of a single tree
A possible simple solution is the FRT (Savona, Vezzoli 2013)
 The results of the RF are combined with RT. More precisely,
we fit a RT using the RF predictions in place of the original
dependent variable Y
 The substitution of y with 𝑦 mitigates the effects of the noisy
data on the estimation process that affect both the predictions
and the dependent variables itself
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

40. Results

41. Paiwise Kendall's t with Greece
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

42. Paiwise Kendall's t with Germany
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

43. Sovereign risk dependencies
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

44. Sovereign risk dependencies
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
The results are in line with the recent findings of Gonzalez-
Hermosillo and Johnson (2014), that Spain and Italy show
a notable co-dependence in explaining each other's
volatility, while Greece assumes a scant role as primary
contagion channel.
The challenging issue is to separate all these central factors
then understanding all possible risk patterns and
corresponding triggers
Non parametric tools (RT, RF and Heatmap) help us to
detect systemic sovereign risk zones shedding lights on
their deep causes, dynamics, and risk signals.

45. Risk mapping
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
It is of particular interest to investigate all data
simultaneously, in a panel-data regression tree
approach. We used as response variable all the
CDS levels, stacked together on a 10,444 × 1
dimensions response variable Y, and used as
covariates all Kendall's t estimates, taking care
again to avoid reverse causality. The predictor
matrix had dimension 10,444 × 21.

46. Risk mapping - Covariates
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
 Contagion-based measures, Kendall's t capturing the co-movement of:
1. Core countries: tFr,Ger
2. Peripheral countries: tGIIPS
3. Pairwise combinations of Euro countries: tEuroSvgn,EuroSvgn
4. Sovereign CDS and Euro Banks 5-yr CDS index: tsvgn,EUBanks
5. Sovereign CDS and the Euro Other Financials 5-yr CDS index: tsvgn;EUOther
6. Sovereign Euro and US CDS: tsvgn,US
7. Sovereign CDS and US Banks 5-yr CDS index: tsvgn,USBanks
8. Sovereign CDS and US Other Financials 5-yr CDS index: tsvgn,USOther
 Country-specific fundamentals:
1. Debt/GDP ratio
2. Exports/GDP ratio
3. GDP growth
4. Industrial production
5. Inflation

47. Sovereign Risk Mapping
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
medcorr_GIIPS
≥0.3167
medcorr_other
<0.5209
vs_EU Fin
≥ 0.4606
inflation
≥ 0.019
GDP growth
<0.0685
inflation
≥ 0.0295
inflation
< - 0.0025
1515 4731
2156 9328
7726 2470614888
unempl. rate
< 0.1175
Debt/GDP
< 1.196
inflation
< 0.0315
Debt/GDP
< 0.9365
Debt/GDP
< 0.6645
medcorr_other
<0.4872
medcorr_GIIPS
≥0.4924
vs_svgnUS
<0.08706
vs_EU Fin
≥ 0.3546
717 1217575 842
285
160 370
219 445
76
The «Financial Greek Tragedy»

48. Safe Zone Path
medcorr_GIIPS
≥0.3167
unempl. rate
< 0.1175
Debt/GDP
< 1.196
inflation
< 0.0315
Debt/GDP
< 0.9365
Debt/GDP
< 0.6645
medcorr_other
<0.4872
medcorr_GIIPS
≥0.4924
vs_svgnUS
<0.08706
vs_EU Fin
≥ 0.3546
717 1217575 842
285
160 370
219 445
76
unempl.Rate
Debt/GDP
Exp/GDP
GDPgrowth
vs_USBanks
vs_EU_Other
medcorr_other
medcorr_FrGer
vs_EUBanks
medcorr_GIIPS
vs_svgnUS
vs_US_Other
Inflation
Ind.Prod
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

49. Risky Zone Path
medcorr_GIIPS
≥0.3167
unempl. rate
< 0.1175
Debt/GDP
< 1.196
inflation
< 0.0315
Debt/GDP
< 0.9365
Debt/GDP
< 0.6645
medcorr_other
<0.4872
medcorr_GIIPS
≥0.4924
vs_svgnUS
<0.08706
vs_EU Fin
≥ 0.3546
717 1217575 842
285
160 370
219 445
76
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
Low unemployment rate with high Debt/GDP ratio or with a high unemployment rate

50. High Risky Zone
medcorr_GIIPS
≥0.3167
unempl. rate
< 0.1175
Debt/GDP
< 1.196
inflation
< 0.0315
Debt/GDP
< 0.9365
Debt/GDP
< 0.6645
medcorr_other
<0.4872
medcorr_GIIPS
≥0.4924
vs_svgnUS
<0.08706
vs_EU Fin
≥ 0.3546
717 1217575 842
285
160 370
219 445
76
High unemployment rate together with high Debt/GDP ratio and signicant sovereign contagion
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

51. Evolution of risk indicators importance
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
PC-CONTAGION: ↑ importance from Q32008 (LB collapse) ▸ peak at
Q42011 ▸ ↓ Q22012 ▸ high values. Thereafter, both importance metrics
showed a downtrend. The time-varying importance assumed by
fundamentals is also confirmed becoming relevant with the Greek crisis
and contagion-based factors.

52. Summary - Concluding remarks
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
 First, Greece is a “world apart” from July 2011 to end of
period, i.e. when the country started showing very low
dependencies with other peripheral Euro countries with very
high levels of CDS quotations mapped onto extremely high
values for unemployment rate and Debt/GDP ratio.
 Second, we identified three main systemic risk zones based
on contagion and specific country fundamentals, namely:
1. A safe zone (Unemployment rate < 11.75% and
Debt/GDP ratio < 119.6%);
2. A risky zone with high Unemployment rate, or with low
Unemployment rate coupled with high Debt/GDP ratio
3. A high risk zone (Unemployment rate > 11.75%,
Debt/GDP ratio > 93.65% and significant sovereign
contagion).

53. Summary - Concluding remarks (cont’d)
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones
 Third, we provided evidence on time-varying importance
assumed by fundamentals, which became relevant with the
Greek crisis. Instead, contagion-based factors assumed a key
importance with the Lehman Brothers collapse, next
achieving a new emphasis with the Euro debt crisis erupted in
2010, finally showing the same importance as the
fundamental-based variables.
These results have important policy implications for early
detection and the causal identification of sovereign systemic
risk.
Future work is needed to connect systemic sovereign risk to
other systemic risk dimensions, such as banking and other
financial intermediaries, and non-financial firms as well.

54. This project has received funding from the European Union’s
Seventh Framework Programme for research, technological
development and demonstration under grant agreement n° 320270
www.syrtoproject.eu
This document reflects only the author’s views.
The European Union is not liable for any use that may be made of the information contained therein.

55. Appendix

56. Kendall's quantiles
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

57. Prior Elicitation
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones

58. MCMC Details - Laplace Approximation
Arakelian, Dellaportas, Savona, Vezzoli - European sovereign systemic risk zones