11

Balance Sheet Contagion and Systemic Risk in the Euro Area Financial System: a Network

Approach

Olli Castrén and Ilja Kavonius

ECB Workshop “Recent Advances in Modelling Systemic Risk using Network

Analysis” 5 October 2009

22

Outline of the presentation

• Key concepts and literature

• Part I: Accounting-based network of sector-level exposures

• Data issues • Constructing the network • Simulating balance sheet contagion

• Part II: Risk-based balance sheets and transmission of risk

• The contingent claims approach • Calculation of sector level credit risk indicators • Contagion of risk exposures in the risk-based

network

• Discussion and outlook for future work

33

Key concepts

• The role of balance sheet interlinkages, leverage and asset volatility as key financial vulnerabilities at the sector level

• At the macro-level, contagion and shock propagation can take place via balance sheet cross-exposures, as someone’s assets are someone else’s liabilities

• But accounting-based balance sheet say nothing about accumulation and transmission of risk exposures

• For a richer analysis, a framework is needed to move to risk-based balance sheets

44

Some related literature

Theory contributions to analysis of balance sheet linkages • Credit chains and balance sheet contagion

• Kiyotaki and Moore (JPE 1997, AER 2002)• Liquidity shocks and systemic risk

• Brunnermeier and Pedersen (RFS, 2009), Shin (JFI 2008)

Empirical applications: • Aikman et al (BoE WP #372, 2009), plus work at BIS, IMF• Interbank contagion literature • Growing literature on financial networks

Work on risk-based balance sheets • Gray, Merton and Bodie (2007), Gray and Malone (2008)

Main contributions of this paper: apply sector level data to balance sheet networks and to analysis of risk contagion

55

Part I: Accounting-based network of sector-level

exposures

66

Data issues

• Euro area financial accounts (EAA): Holdings of various financial instruments by the various sectors, both on the asset and the liability sides

• Use 8 main financial instrument categories and 7 sectors (based on the ESA95 classification)

• Quarterly data for the euro area from 1999 Q1

• A closed system (using the rest of the world sector): each financial liability of a sector is an asset for some other sector

• The financial accounts are linked to the real accounts via the net lending/borrowing positions (net financial wealth)

• Non-financial assets (including housing) have no counterparties on the liability side and are not available on a quarterly basis; excluded from this analysis

77

Some illustrations of the EEA data

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

NFCA

NFCL

MFIA

MFIL

OFIA

OFIL

INSA

INSL

GOVA

GOVL

HHA

HH L RoWA

RoWL

Currency and deposits Debt securities

Loans Shares and other equity

Net equity in life insurance and in pension funds Prepayments of insurance premiums

Other accounts

Breakdown of financial instrument holdings by sector, %

-10

-7.5

-5

-2.5

0

2.5

5

7.5

10

12.5

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

NFC MFI OFI INS GOV HH RoW

Evolution of sector-level net financial wealth

88

Constructing the network of exposures

• The data provide instrument-specific total holdings of assets and liabilities by each sector • Can use information on the relative distribution of the sum elements ai,k and lj,k to estimate the individual elements Xi,j for each instrument category => provides the who-to-whom links• We get bilateral linkages for all 8 instrument categories • Works nicely with non-consolidated data

NNNjN

iNiji

Nj

k

xxx

xxx

xxx

X

1

1

1111

N

jkiij ax

1,

N

ikjij lx

1,

99

Constructing the network of exposures

HH ROW

OFI NFC

MFI GOVT

INS

Cross-sector gross balance sheet exposures in the euro area financial system

The key role played by the banking sector

2009 Q1HH ROW

OFI NFC

MFI GOVT

INS

1999 Q1HH ROW

OFI NFC

MFI GOVT

INS

1010

Propagation of shocks in the network

Transmission of a P&L shock to sector A under mark-to-market accounting

Assets Debt Equity

Disinvestment Loss of equity Channels of transmission

…

…

…

Period 0 1 2 3

C

A

B

C

A

B

C

A

B

1111

Propagation of shocks in the network

Example: a cash-flow shock on the NFC sector that corresponds to a 20% loss in shareholder equity

20% NFC cash flow shock

EUR bn% of financial

assets EUR bn% of financial

assets EUR bn% of financial

assets EUR bn% of financial

assets

NFC 783 5.54 632 4.47 541 3.83 652.00 4.61HH 318 3.00 256 2.42 220 2.07 264.67 2.50MFI 189 0.81 152 0.65 130 0.56 157.00 0.67INS 122 1.98 98 1.60 84 1.37 101.33 1.65OFI 405 4.13 327 3.33 280 2.85 337.33 3.44

GOVT 114 3.97 92 3.20 77 2.74 94.33 3.30ROW 278 3.34 224 2.99 192 2.78 231.33 3.04

Average 315.57 3.25 254.43 2.67 217.71 2.31

Round

Average1 2 3

1212

Propagation of shocks in the network

• In a multi-period framework, agents are expected to balance their accounts after the shock

• In the current context, this would amount to asset dis-investment, or a de-leveraging process

• Need to specify rules for: • Target level of leverage • Assets to be shed • The purchasing party • The impact on the asset price

• The framework allows for simulation of such processes once the rules have been defined

1313

Part II: Risk-based balance sheets and transmission of risk

1414

The role of risk-based balance sheets

• The accounting-based network neatly illustrates shock transmission in the system but it says nothing about risk exposures and systemic risk •Yet financial crises are typically a result of accumulated vulnerabilities in the form of risk exposures, triggered by sudden bursts of volatility

• To have early warning properties, the framework should include these characteristics • A solution is to construct stochastic risk-based balance sheets which encompass the deterministic accounting-based model

1515

The contingent claims approach to macro-financial risk analysis

• Contingent claims analysis (CCA) measures the expected losses of balance sheet items• Idea: model debt of the sector as a put and equity as a call option, and estimate the market value of assets • The balance sheet of sector i then becomes

Ai= Bi - Pi+ Ji

Ai = market value of assetsBi = book value of debt (distress point)Pi = expected loss on debt (put option)Ji = junior claim (equity, call option)

• The model captures several key financial stability factors: leverage, volatility and non-linearity •By assuming that volatility is zero, the framework collapses to the accounting-based model

1616

Input data

• To estimate the risk-based balance sheets, we need balance sheet data on equity and other liabilities, plus market data on equity volatility, asset returns and interest rates

• Using the techniques developed by Moody’s KMV, market value of assets and asset volatility are estimated at an intermediate stage, once distress points have been estimated

• Equity is measured by shareholder equity plus net financial wealth. Data on equity volatility are implied volatilities of the relevant sector-level stock indices. • For the household and government sector (no equity issued), government bond yield volatility is used

1717

Output: Distance to distress

Households

0

5

10

15

20

25

30

1999Q1 2001Q1 2003Q1 2005Q1 2007Q1 2009Q1

Non-financial firms

0

2

4

6

8

10

12

1999Q1 2001Q1 2003Q1 2005Q1 2007Q1 2009Q1

MFI (banks)

0

2

4

6

8

10

12

14

1999Q1 2001Q1 2003Q1 2005Q1 2007Q1 2009Q1

Government

0

2

4

6

8

10

12

14

16

18

1999Q1 2001Q1 2003Q1 2005Q1 2007Q1 2009Q1

1818

Output: “Network” of pair-wise correlations between sector-level distances-to-distress

2007-2008

HH ROW

OFI NFC

MFI GOVT

INS

1999-2006

HH ROW

OFI NFC

MFI GOVT

INS

Note: The thick link shows correlation between sector-specific distance-to-distress measures that exceeds 0.75, the intermediate link shows correlation between 0.5 and 0.75 and the thin link between 0.25 and 0.5.

1919

Discussion and future work

• Network models applied to the macro level provide new information about sector-level linkages and shock transmission channels

• Can detect important risks and vulnerabilities that might go undiscovered in sector-specific analysis

• Including risk exposures shows how correlations and contagion risk change over time

• Complements the outputs from other models, including those using sector and firm-level information • More work is needed to refine the propagation mechanisms and the CCA balance sheets

2020

Thank you

2121

Background 1: Output: Market leverage

Non-financial corporations

0.4

0.5

0.6

0.7

0.8

0.9

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

Households

0.1

0.15

0.2

0.25

0.3

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

MFI

0.65

0.66

0.67

0.68

0.69

0.7

0.71

0.72

0.73

0.74

0.75

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

OFI

0.5

0.55

0.6

0.65

0.7

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

INS

0.7

0.75

0.8

0.85

0.9

0.95

1

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

Govt

0.15

0.2

0.25

0.3

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

RoW

0.4

0.45

0.5

0.55

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

0

0.2

0.4

0.6

0.8

1

1999Q1 2000Q3 2002Q1 2003Q3 2005Q1 2006Q3 2008Q1

NFC HHMFI OFIINS GOVTROW

2222

Background 2: Output: Asset volatility

Non-financial corporations

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

Households

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

MFI

0

0.01

0.02

0.03

0.04

0.05

0.06

1999Q1 2000Q3 2002Q1 2003Q3 2005Q1 2006Q3 2008Q1

OFI

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

Insurance

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1999Q1 2000Q3 2002Q1 2003Q3 2005Q1 2006Q3 2008Q1

Government

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

1999Q1 2000Q3 2002Q1 2003Q3 2005Q1 2006Q3 2008Q1

Rest of the world

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4

NFC HH MFI OFI INS GOVT ROW

2323

Background 3: Use of networks for broader financial stability analysis

HH ROW

OFI NFC

MFI GOVT

INS

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Assets Liabilit ies

Currency Deposits Debt securit ies

Short -term loans Long-term loans Shares and other equity

Other accounts

How the dislocation of a bank’s balance sheet can spread

Bank A

i) interbankmarket

ii) sectors

iii) countries

Fir

m-l

evel

data

Macro

-fi

nan

cia

l

2424

Background 4: The structure of integrated accounts

Uses Resources

A B

D E

I

K=I*J+G G H

J

Other changes

Assets Liabilities

M N

O=R*S+M P=T*U+N

R S T U

Stock in period t-1 Other changes Stock in period t-1 Other changes

All the received (credit) transactions of financial accounts

Financial accounts

Net wealth

O-P=Q

Non-financial accounts

All the paid transactions of the use of disposable income account

All the received transactions of the use of disposable income account

C-D+E=F

Capital stock in period t

Capital stock in period t-1

All the paid transactions from the production account to the secondary distribution of income account

All the paid transactions of the capital account

All the received transactions from the production account to the secondary distribution of income

account

B-A=C

Disposable income

Liablity stock in period t

M-N=L

All the received transactions of the capital account

Domestic economy/an invidual sector

All the paid (debit) transactions of financial accounts

Asset stock in period t

Net lending/borrowing

F-G+H=L

Saving

2525

Background 5: The CCA model in brief

Distribution of market value of assets Expected market value of assets at time h

Distance-to-default

Default point (value of liabilities)

0 h Time

Probability of default

Key drivers of distress risk: leverage, volatility and asset return