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
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1
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
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2
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
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3
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
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4
Part I: Accounting-based network of
sector-level exposures
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5
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
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Some illustrations of the EEA data
Breakdown of financial instrument
holdings by sector, %
Currency and deposits
Debt securities
Loans
Shares and other equity
Net equity in life insurance and in pension funds
Prepayments of insurance premiums
Evolution of sector-level net
financial wealth
NFC
MFI
OFI
INS
GOV
HH
RoW
12.5
Other accounts
10
100%
7.5
90%
80%
5
70%
60%
2.5
50%
0
40%
30%
-2.5
20%
-5
10%
0%
NFCNFC
A L
MFI MFI
A L
OFI OFI
A L
INS INS
A L
GOVGOV
A L
HH HH L
A
RoWRoW
A L
-7.5
-10
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
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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
 x11
 

X k   xi1

 
 x N1

 x1 j
 
 xij
 
 x Nj
N
x
i 1
ij
 x1N 
  
N
 xiN   xij
 j 1
  
 x NN 
 l j ,k
 ai ,k
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Constructing the network of exposures
Cross-sector gross balance sheet
exposures in the euro area financial
2009 Q1
system
HH
ROW
OFI
The key role played by the
banking sector
NFC
HH
MFI
ROW
GOVT
INS
OFI
NFC
MFI
GOVT
1999 Q1
HH
ROW
OFI
NFC
INS
MFI
GOVT
INS
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9
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
A
A
…
B
A
B
B
…
C
C
C
…
Period
0
1
2
3
10
10
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
Round
NFC
HH
MFI
INS
OFI
GOVT
ROW
Average
EUR bn
783
318
189
122
405
114
278
315.57
1
% of financial
assets
5.54
3.00
0.81
1.98
4.13
3.97
3.34
3.25
EUR bn
632
256
152
98
327
92
224
254.43
2
% of financial
assets
4.47
2.42
0.65
1.60
3.33
3.20
2.99
2.67
EUR bn
541
220
130
84
280
77
192
217.71
3
% of financial
assets
3.83
2.07
0.56
1.37
2.85
2.74
2.78
2.31
Average
% of financial
assets
EUR bn
652.00
4.61
264.67
2.50
157.00
0.67
101.33
1.65
337.33
3.44
94.33
3.30
231.33
3.04
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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
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Part II: Risk-based balance sheets and
transmission of risk
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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
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The contingent claims approach to macrofinancial 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 assets
Bi = 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
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the accounting-based model
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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
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Output: Distance to distress
MFI (banks)
Non-financial firms
14
12
12
10
10
8
8
6
6
4
4
2
0
1999Q1
2
2001Q1
2003Q1
2005Q1
2007Q1
2009Q1
0
1999Q1
2001Q1
2003Q1
2005Q1
2007Q1
2009Q1
Households
Government
30
18
16
25
14
12
20
10
15
8
6
10
4
5
2
0
1999Q1
2001Q1
2003Q1
2005Q1
2007Q1
2009Q1
0
1999Q1
2001Q1
2003Q1
2005Q1
2007Q1
2009Q1
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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.
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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
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Thank you
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Background 1: Output: Market leverage
Non-financial corporations
0.9
OFI
M FI
Households
0.7
0.75
0.3
0.74
0.8
0.73
0.65
0.25
0.72
0.7
0.71
0.6
0.7
0.2
0.6
0.69
0.68
0.55
0.15
0.5
0.67
0.66
0.4
1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4
1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4
INS
1
0.5
0.65
0.1
Govt
0.3
1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4
1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4
NFC
MFI
INS
ROW
RoW
0.55
HH
OFI
GOVT
1
0.95
0.8
0.9
0.25
0.5
0.6
0.85
0.8
0.2
0.45
0.75
0.4
0.2
0.7
1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4
0.15
1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4
0.4
1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4
0
1999Q1 2000Q3 2002Q1 2003Q3 2005Q1 2006Q3 2008Q1
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Background 2: Output: Asset volatility
Non-financial corporations
0.14
M FI
Households
0 .0 6
0.4
OFI
0.1
0.09
0.35
0.12
0 .0 5
0.08
0.3
0.1
0.07
0 .0 4
0.25
0.06
0.08
0 .0 3
0.2
0.05
0.06
0.04
0.15
0 .0 2
0.03
0.04
0.1
0 .0 1
0.02
0.02
0.05
0.01
0
19 9 9 Q1 2 0 0 0 Q3 2 0 0 2 Q1 2 0 0 3 Q3 2 0 0 5Q1 2 0 0 6 Q3 2 0 0 8 Q1
0
0
1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4
1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4
Insurance
0 .14
0 .12
1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4
Government
0 .0 6
0 .0 4
NFC
Rest of the world
0.05
0.2
0.045
0.18
0.04
0.16
0.035
0.14
0.03
0.12
0.025
0.1
0.02
0.08
0.015
0.06
0.01
0.04
HH
MFI
OFI
INS
GOVT
0 .4
0 .3 5
0 .3
0 .1
0 .0 8
0
0 .2 5
0 .2
0 .15
0 .1
0 .0 2
0.005
0
19 9 9 Q1 2 0 0 0 Q3 2 0 0 2 Q1 2 0 0 3 Q3 2 0 0 5Q1 2 0 0 6 Q3 2 0 0 8 Q1
0.02
0
1999Q1
0
2000Q3
2002Q1
2003Q3
2005Q1
2006Q3
2008Q1
1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4
0 .0 5
0
19 9 9 Q1 2 0 0 0 Q2 2 0 0 1Q3 2 0 0 2 Q4 2 0 0 4 Q1 2 0 0 5Q2 2 0 0 6 Q3 2 0 0 7Q4
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ROW
Background 3: Use of networks for broader financial
stability analysis
How the dislocation of a bank’s balance sheet can spread
ROW
Macrofinancial
HH
ii) sectors
OFI
NFC
MFI
GOVT
iii) countries
Firm-level
data
INS
i) interbank
market
Currency
Deposit s
Debt securit ies
Short -term loans
Long-term loans
Shares and other equit y
Other account s
100%
90%
80%
Bank A
70%
60%
50%
40%
30%
20%
10%
0%
Asset s
Liabilit ies
23
23
Background 4:The structure of integrated
accounts
Non-financial accounts
Uses
A
Domestic economy/an invidual sector
Resources
B
All the received transactions from the production
account to the secondary distribution of income
account
All the paid transactions from the production account
to the secondary distribution of income account
B-A=C
Disposable income
D
E
All the paid transactions of the use of disposable
income account
All the received transactions of the use of disposable
income account
I
K=I*J+G
Capital stock in
period t
C-D+E=F
Saving
Capital stock in
period t-1
G
J
All the paid transactions of the capital account
H
Other changes
All the received transactions of the capital account
F-G+H=L
Assets
Net lending/borrowing
Liabilities
M-N=L
All the received (credit) transactions of financial
accounts
M
N
All the paid (debit) transactions of financial accounts
O=R*S+M
P=T*U+N
Asset stock in period t
Liablity stock in period t
Net wealth
R
S
Stock in period t-1
Other changes
O-P=Q
T
U
Stock in period t-1
Other changes
Financial accounts
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Background 5:The CCA model in brief
Key drivers of distress risk:
leverage, volatility and asset return
Distribution of market value of assets
Expected market
value of assets at time h
Distance-to-default
Default point
(value of liabilities)
0
h
Probability
of default
Time
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