DebtRank: Too Central to Fail?

Chair of Systems Design www.sg.ethz.ch

DebtRank: Too Central to Fail?

Stefano BattistonCoupled Climate-Economics Modelling and Data Analysis, ENS Paris

November 23, 2012

Stefano Battiston Chair of Systems Design www.sg.ethz.chDebtRank: Too-Central-to-Fail?

Acknowledgments

1 ETH Chair of Systems Design; OTC - Swiss National Fund

2 FOC - Forecasting Financial Crisis (FET-OPEN)www.focproject.net

3 INET - Systemic Risk Task Force

4 R. Kaushik, M. Puliga, M. Tasca, S. Vitali, J. Glattfelder, F.Schweitzer (ETH Zurich), G. Caldarelli (IMT Lucca),

5 J. Stiglitz and B. Greenwald (Columbia Univ.)

Coupled Climate-Economics Modelling and Data Analysis, ENS Paris November 23, 2012 2 / 41

www. focproject.net

Stefano Battiston Chair of Systems Design www.sg.ethz.chDebtRank: Too-Central-to-Fail? Introduction

Financial Crises and Financial Networks

1 We live in an interconnected global economy

2 Benefits but also major threats

Systemic crises

1 large social and economiccosts

2 can emerge endogenously,without external shocks


Stefano Battiston Chair of Systems Design www.sg.ethz.chDebtRank: Too-Central-to-Fail? Financial Networks

Financial Networks and Systemic Risk



Interacting Networks and Systemic Risk

General Vision

1 Links or varying nature

2 Frictions: feedback loops and amplifications

3 Individual Risk VS Global risk:

1 emerging properties2 often unexpected3 socially desirable? The role of regulation.

Research Questions as in the following slides:



RQ: Empirical: Topological Structure

Bow-tie, core-peripheryHeterogeneity, extreme concentra-tion

Cross-country, all firms[Glattfelder, Battiston 2009 PRE]

Global, TNC (e.g. financial)[Vitali, Glattfelder, Battiston 2011 PLOS-ONE]



RQ: Empirical: Interdependence

Empirical analysis of FEDemergency loans data. DebtRank[Puliga, Battiston, Kaushik, Tasca, Caldarelli (2012) Sci.

Rep. 2: 451]

Pearson, Tail-Correlation and Jointdraw-up probability in CDS’s andbonds[Kaushik, Battiston, http://arxiv.org/abs/1205.0976]

[Puliga, Battiston, Kaushik, Caldarelli, Veredas (2012) in

progress ]



RQ: Models of Distress and Defaults

Amplifications and feedbacks:Trade-off: Liaisons can be dangerous

Default Propagation (w/woliquidity)

Distress Propagation -Time-to-Default

[Battiston, Delli Gatti, Gallegati, Stiglitz, Greenwald, 2012 JEDC,

2012 JFS]



Q4: Models of Procyclicality of Leverage

Bank-bank + bank-assetnetwork, time to default

Positive feedback: leverage -asset price

Roles of: (1) connectivity, (2)capital requirements, (3) pricereaction

[Tasca, Battiston 2011 WP ECSS, 2012 WP ETH Risk

Center]



Models of Efficiency vs Stability

Incentive to form Links:

Stable networks are notefficient

Tension: Individual profitvs social welfare.

[Koenig, Battiston, Napoletano, Schweitzer,

2011 JEBO, 2012 GEB]



Empirical examples

SOCIET ELETTRICA

INVESTOR AB

CAPITAL GROUP COMPANIES INC,

ANDRE HOFFMAN AND ANDREA

ABB LTD

SCHWEIZERISCHE

NORTRUST NOMINEES LIMITED

NOVARTIS FOUNDATION FOR EMPLOYEE PARTICIPATION

BZ GRUPPE HOLDING

CANTON OF SAINT GALL

SYNGENTA AG

FRANKLIN RESOURCES, INC.

JP MORGAN CHASE BANK, NA

ADECCO SA

PARGESA HOLDING SA

BRANDES

KUEHNE UND NAGEL INTERNATIONAL AG

PUTNAM INVESTMENT MANAGEMENT INC

CREDIT SUISSE GROUP

ST. GALLER KANTONALBANK

FIDELITY INVESTMENTS LIMITED

CHASE NOMINEES LIMITED

HOLCIM LTD.

AXA

COMPAGNIE FINANCIERE RICHEMONT

ROCHE HOLDING AG

PARJOINTCO NV

ALLIANZ AKTIENGESELLSCHAFT

MFS INVESTMENT MANA

EMASAN AG

SWISS REINSURANCE COMPANY

DR. H.C. THOMAS SCHMIDHEINY

ZURICH FINANCIAL

SWISSCOM AG

NESTLE S.A.

SONATA SECURITIES SA

UBS AG

THE DEPOSITORY

NOVARTIS AG

KUEHNE KLAUS-MICHAEL

NEUE AARGA

Zurich Stock Market: ownership network and its backbone1.



Empirical examples

UK (left) and US (NYSE) (right) stock market networks2.



Empirical Examples

China (left) and Japan (right) stock market networks



The financial core of the TNC network

Ownership network around TNC worldwide Left: The core ( 1300nodes). (Right) An example of few top financial institutions involvedin many cycles. [Vitali ea., PLoS-ONE 2011]



Political Economy and the Art of Pipe Plumbing

Distress propagation: key issue for the stability of financial systems

direct channel: balance sheet interlock (unipartite graph)indirect channel: common asset (bipartite graph)

“Plumbing” aspects

improving stress-test techniques utilized at central banks to designfinancial system more robust to endo/exo shocks

Political economy aspects

distorsion of incentives leading to e.g. excessive risk takingeconomic concentration, influence on enforcement of existing policiesand design of new policies



From Too-Big-to-Fail to Too-Central-to-Fail

Too-big-to-fail: balance sheet size

Too-connected-to-fail: number of financial inter-linkages

Too-correlated-to-fail: similar portfolios and/or strategies

Too-central-to-fail: impacting those who are important via networkeffects


Stefano Battiston Chair of Systems Design www.sg.ethz.chDebtRank: Too-Central-to-Fail? Network Effects

Balance Sheet Structure

Fundamental identity: Assets = Liabilities + Equity

Equity < 0 implies default



Default Cascade



Devaluation Effect



Distress Propagation: DebtRank



Shock to a Common External Asset


Stefano Battiston Chair of Systems Design www.sg.ethz.chDebtRank: Too-Central-to-Fail? DebtRank

DebtRank

DebRank is a novel indicator to identify

SIFI (Systemically Important Financial Institutions)groups of SIFI

Propagation of distress from an institution to another is a key issuefor the stability of financial systems.

Propagation channels

direct: balance sheet interlock (unipartite graph)indirect: common asset (bipartite graph)

DebtRank overcomes some limitations in

standard stress-test techniques at central banksstandard complex network mesures (e.g. betweenness, centrality etc.)



DebtRank


SIFI

(Systemically Important Financial Institutions)groups of SIFI








DebtRank


SIFI (Systemically Important Financial Institutions)groups of SIFI








DebtRank

more central = moresystemically important

not just a ranking

systemic economic loss(e.g., euros) due to distresson one or more nodes

extension/adaptation tosocial/biological contagion?

[Battiston, Puliga, Kaushik, Tasca, Caldarelli, DebtRank:Too-central-to-fail? (2012) Sci Rep. 2:541]



Impact Matrix and Debtrank definition

exposure of i to j , Aij (e.g. lending, bond, stock shares).core capital of i , Ei .

1 Relative exposure of i to j , w.r.t. total exposure,Aij∑j Aij

, is generally

small (sum up to 1)

2 Relative exposure of i to j , w.r.t. core capital: Zij =Aij

Ei, (sum can

easily exceed 1)

Direct Impact of i on j defined as the exposure that j has towardsi : Wij = Zji , W = ZT

DebtRank: A node i is more central if it impacts strongly (largeWij) many other central nodes: recursive!Each node propagates its distress only once (we tamereverberations)all formulas at doi:10.1038/srep00541widgets and infographics at:http://ethz.focproject.net:8080/widgetCoupled Climate-Economics Modelling and Data Analysis, ENS Paris November 23, 2012 27 / 41

http://ethz.focproject.net:8080/widget


Inspired by Network Centrality

Adapting notion of Feedback Centrality to financial distress: a nodeis more important if it impacts on many high value and importantnodes

ci =∑j

Wijvj +∑j

Wijcj

c = (I −W )−1Wv

where v = e.g. total asset

Issues: need λ(W ) < 1, but imposing row-stochasticity we couldnot compare values across time

Strategy: keep impact matrix as is and tame cycles by excludingwalks already visited

Result: we obtain not just a ranking but an estimate of fraction oftotal economic value in distress



Debt Rank Dynamics

A node i is more central if it impacts strongly (large Wij) manyother central nodes: recursive!

Each node propagate its distress only once (we tamereverberations).

hi (t) = min

{1, hi (t − 1) +

∑j

Wjihj(t − 1)

}, where j | sj(t − 1) = D

si (t) =

D if hi (t) > 0 & si (t − 1) 6= II if hi (t − 1) > 0U otherwise,



Applications: SIFI

In several countries, Central Banks maintain a database of:

Balance sheet interlocking exposures between banksExposures to external assetsCore capital

Build the impact matrix under various scenarios possibly taking intoaccount market values

Run DebtRank and GroupDebtRank to assess systemic impact ofone or more institutions



Applications: Counterparty Risk

Investors usually do not know the mutual exposures amongcounterparties. However,

One can generate an ensemble of viable networks of exposuresusing available information

Run DebtRank and GroupDebtRank on each network of theensemble

Obtain distribution of losses across counterparties, conditional to agiven shock



Application: an exercise on FED data + BvDdata

Take banks’ investment in each others equity share as a proxy of allexposures

Focus on the largest borrowers from the FED in 2008-2010

22 inst., peak lending 1.2 USD trillions, total assets 20 USD trillions)

Incorporate dynamics of core capital (take market capitalization asa proxy of core capital)

Recipe

1 market capitalization as proxy of core capital

2 investments in equity as proxy of financial exposures

3 rescaling factor α, conservative scenario: in good the times everybank can sustain the default of at least 5 counterparties



Application: an exercise on FED data + BvDdata



Debt Rank vs other Measures

200 400 600 800 10000

0.1

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Time (days)

De

btR

an

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fau

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200 400 600 800 10000

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200 400 600 800 10000

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Time (days)

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Ce

ntr

alit

y



Group DebtRank

Recipe

1 A selected group of institutions is hit by a shock: for each a certainfraction φi < 1 of equity vanishes

2 Propagate distress according to impact matrix as before (closedwalks traversed only once)

3 Test various values of φ and impact scaling factor α



GroupDebtRank

100 200 300 400 500 600 700 800 900 10000

0.2

0.4

0.6

0.8

1G

roup D

ebtR

ank

100 200 300 400 500 600 700 800 900 1000

40

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Avg. M

ark

et C

ap. (U

SD

bill

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Time(Days)



Conclusions

Network effects matter for distress propagation: SIFI andcounterparty risk

DebtRank is a centrality-inspired algorithm to assess SIFI innetwork context, overcoming some limitations of state-of-the-artstress-testing

From Too-Big-to-Fail to Too-Central-to-Fail

Currently: a new method to evaluating VAR and ES in a networkcontext



Financial Networks: a research agenda

1 Empirics: network structure

2 Link formation: evolution to stable/efficient structures

3 Node dynamics: propagation (e.g., information, distress)




1 Empirics: network structure

2 Link formation: evolution to stable/efficient structures

3 Node dynamics: propagation (e.g., information, distress)

Meta-level

1 Feedback from structure onto incentives: political economy aspect




Financial networks

1 Topology, Link formation, Node dynamics:e.g., FOC, various INET grants

2 Interacting networks: MULTIPLEX

3 Feedback from structure onto incentives:INET TaskForce on Systemic Risk (Stiglitz) - Working Group onFinancial Interlinkages (Haldane, Battiston)



The FOC Project

Forecasting Financial Crises (FOC)

European project funded by FET-OPEN

13 partners (including ECB), coordinated by Guido Caldarelli atIMT Lucca

Information:www.focproject.netwidgets: http://ethz.focproject.net:8080/

Related events

FOC-CRISIS School on Complex Financial Networks, IMT Lucca,October 24-27 2012

INET Conference False Dichotomies, Waterloo, November 15-172012

NetSci 2013



Debt Rank Dynamics

Centrality computation plus contraints on walks is equivalent tofollowing algorithm.

continuous variable hi ∈ [0, 1].

3 possible states, undistressed, distressed, inactive: si ∈ {U, D, I}.Sf : set of nodes in distress at time 1. hi (1) = ψ ∀i ∈ Sf ;hi (1) = 0∀i /∈ Sf , and si (1) = D , ∀i ∈ Sf ; si (1) = U ∀i /∈ Sf .

hi (t) = min

{1, hi (t − 1) +

∑j

Wjihj(t − 1)

}, where j | sj(t − 1) = D

si (t) =

D if hi (t) > 0 & si (t − 1) 6= II if hi (t − 1) > 0U otherwise,



43

1

2

65

7 8

h=1

h=0

h=0

h=0

h=0 h=0

h=0 h=0

43

1

2

65

7 8

h=1

h=0.5

h=0.5

h=0.5

h=0 h=0

h=0 h=0

43

1

2

65

7 8

h=1

h=0.5

h=0.5

h=0.5

h=0.25 h=0.25

h=0 h=0

43

1

2

65

7 8

h=1

h=0.5+

0.125

h=0.5

h=0.5

h=0.25+

0.125

h=0.25

h=0.125 h=0.125

43

1

2

65

7 8

h=1

h=0.5+

0.125

h=0.5

h=0.5

h=0.25+

0.125

h=0.25

h=0.125 h=0.125


DebtRank: Too Central to Fail?

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