European sovereign systemic risk zones

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, GreecePetros Dellaportas, University College London, UK

Roberto Savona, University of Brescia, ItalyMarika Vezzoli, University of Brescia, Italy

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

Definition of systemic risk

“A systemic risk is a risk that an event will trigger a loss ofconfidence in a substantial portion of the financial system thatis serious enough to have adverse consequences for the realeconomy.”

G-10 Report on Financial Sector Consolidation (2001)

According to this definition, the current financial crisis issystemic.


Motivation

Detect sovereign systemic risk zones. The early detectionand the causal identification of such phenomena mayprovide valuable early warning signals to countries thatmove towards dangerous risk paths.

Provide an effective risk mapping in which country-specificfundamentals are mixed together with contagion-basedmeasures, thereby assembling a series of leading indicatorsthat could signal impending sovereign systemic riskabnormalities.


Literature review Ang and Longstaff (2013): Systemic sovereign credit risk in the US and Europe,

multifactor affine framework. Findings: Heterogeneity among US andEuropean issuers, key role of financial market variables.

Reboredo and Ugolini (2015): Systemic risk in European sovereign debtmarkets, conditional value-at-risk measure. Findings: Greek debt crisis wasnot so severe for non-crisis countries, systemic risk increased for countries incrisis.

Considering changes in regimes in CDS dynamics...

Caceres, Guzzo and Segoviano (2010): Primary role in sovereign spreads sharprise, 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 clustersin time and in space.


Data

Daily 5-yr CDS prices for France, Germany, Greece, Ireland, Italy,Portugal, Spain and US from January 1, 2008 to October 7, 2013 (1505daily 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-yrCDS indices.

Macroeconomic factors to investigate their influence to sovereign CDSlevels (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.


Methodology


Copula-based dependencies

Regression Trees (RT)

Heatmap

Ensemble methods

Random Forests

Final Regression Tree (FRT)

Copula-based dependencies

Arakelian and Dellaportas (2012) proposed a flexible threshold model for

estimation of bivariate copulas

where 𝐶𝜃𝑗𝑖 : the copula function, wij: the probability of copula i in the

interval Ij, 𝑖=1𝑙 𝑤𝑖𝑗 = 1 for all j. Thus, our general model (1) allows both

the functional form of the copula and the parameters to change withineach interval Ij .

A RJMCMC algorithm was proposed which obtained samples from theposterior density of these models, and a Bayesian model-averagingestimation approach constructed a posterior density of Kendall's t(Kendall, 1938), marginalised over all models and parameters within eachmodel.


MCMC DetailsSimulation 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: orderedparameters 0 < zl < zl -1 < … < z1 < 1. The densities pl serve as independentMetropolis-Hasting proposal densities for the main chain with targetdensity p.

At each iteration, one auxiliary density pl is chosen at random andtogether with the current sampled point of pl is used at the usualacceptance ratio of the main chain. In the terminology of Jasra et al.(2007), this is an exchange move in the population reversible jumpalgorithm.


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



















































































HeatmapIn order to understand what happens inside each terminal node, we use a graphical representation

HeatmapFor 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



Heatmap (cont’d)

Heatmap on node 1


Heatmap (cont’d)

Heatmap on node 2


Heatmap (cont’d)

Heatmap on node 3


Heatmap (cont’d)

Heatmap on node 4


Heatmap (cont’d)

Heatmap on node 5


Heatmap (cont’d)

Ensemble methodsEnsemble learning techniques (P&C techniques) have been introducedto increase the accuracy of the results:

Combining multiple versions of unstable classifiers increases theaccuracy of the predictors




Data




Data




Data

RT1 RT2 RT… RTN




Data

RT1 RT2 RT… RTN




Data

RT1 RT2 RT… RTN

𝑦1 𝑦2 𝑦… 𝑦𝑁




Data

RT1 RT2 RT… RTN





Data

RT1 RT2 RT… RTN


Ensemble method


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 hasto maximize the differences between the trees. For thisreason, in each tree node a subset of predictors israndomly chosen

RF provide an accuracy level that is in line with Boostingalgorithm with better performance in terms ofcomputational burden (Breiman, 2001)


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 𝑦mitigates the effects of the noisy data on the estimation process that affect both the predictions and the dependent variables itself


Results

Paiwise Kendall's t with Greece


Paiwise Kendall's t with Germany


Sovereign risk dependencies


Sovereign risk dependencies


The results are in line with the recent findings of Gonzalez-Hermosillo and Johnson (2014), that Spain and Italy showa notable co-dependence in explaining each other'svolatility, while Greece assumes a scant role as primarycontagion channel.

The challenging issue is to separate all these central factorsthen understanding all possible risk patterns andcorresponding triggers

Non parametric tools (RT, RF and Heatmap) help us todetect systemic sovereign risk zones shedding lights ontheir deep causes, dynamics, and risk signals.

Risk mapping


It is of particular interest to investigate all datasimultaneously, in a panel-data regression treeapproach. We used as response variable all theCDS levels, stacked together on a 10,444 × 1

dimensions response variable Y, and used ascovariates all Kendall's t estimates, taking careagain to avoid reverse causality. The predictormatrix had dimension 10,444 × 21.

Risk mapping - Covariates


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

Sovereign Risk Mapping


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



vs_svgnUS<0.08706

vs_EU Fin≥ 0.3546

717 1217575 842

285

160 370

219 445

76

The «Financial Greek Tragedy»

Safe Zone Pathmedcorr_GIIPS

≥0.3167


Debt/GDP< 1.196

inflation< 0.0315

Debt/GDP< 0.9365

Debt/GDP< 0.6645



vs_svgnUS<0.08706

vs_EU Fin≥ 0.3546

717 1217575 842

285

160 370

219 445

76

un

emp

l. R

ate

Deb

t/G

DP

Exp

/GD

P

GD

P g

row

th

vs_U

SB

anks

vs_E

U_O

ther

med

corr

_oth

er

med

corr

_FrG

er

vs_E

UB

anks

me

dco

rr_G

IIP

S

vs_s

vgn

US

vs_U

S_O

ther

Infl

atio

n

Ind

. Pro

d


Risky Zone Pathmedcorr_GIIPS

≥0.3167


Debt/GDP< 1.196

inflation< 0.0315

Debt/GDP< 0.9365

Debt/GDP< 0.6645



vs_svgnUS<0.08706

vs_EU Fin≥ 0.3546

717 1217575 842

285

160 370

219 445

76


Low unemployment rate with high Debt/GDP ratio or with a high unemployment rate

High Risky Zonemedcorr_GIIPS

≥0.3167


Debt/GDP< 1.196

inflation< 0.0315

Debt/GDP< 0.9365

Debt/GDP< 0.6645



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


Evolution of risk indicators importance


PC-CONTAGION: ↑ importance from Q32008 (LB collapse) ▸ peak atQ42011 ▸ ↓ Q22012 ▸ high values. Thereafter, both importance metricsshowed a downtrend. The time-varying importance assumed byfundamentals is also confirmed becoming relevant with the Greek crisisand contagion-based factors.

Summary - Concluding remarks


First, Greece is a “world apart” from July 2011 to end ofperiod, i.e. when the country started showing very lowdependencies with other peripheral Euro countries with veryhigh levels of CDS quotations mapped onto extremely highvalues for unemployment rate and Debt/GDP ratio.

Second, we identified three main systemic risk zones basedon contagion and specific country fundamentals, namely:

1. A safe zone (Unemployment rate < 11.75% andDebt/GDP ratio < 119.6%);

2. A risky zone with high Unemployment rate, or with lowUnemployment rate coupled with high Debt/GDP ratio

3. A high risk zone (Unemployment rate > 11.75%,Debt/GDP ratio > 93.65% and significant sovereigncontagion).

Summary - Concluding remarks (cont’d)


Third, we provided evidence on time-varying importanceassumed by fundamentals, which became relevant with theGreek crisis. Instead, contagion-based factors assumed a keyimportance with the Lehman Brothers collapse, nextachieving a new emphasis with the Euro debt crisis erupted in2010, finally showing the same importance as thefundamental-based variables.

These results have important policy implications for earlydetection and the causal identification of sovereign systemicrisk.

Future work is needed to connect systemic sovereign risk toother systemic risk dimensions, such as banking and otherfinancial intermediaries, and non-financial firms as well.

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.

Appendix

Kendall's quantiles


Prior Elicitation


MCMC Details - Laplace Approximation


Economy & Finance

European sovereign systemic risk zones