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Systemic Risk Measurement Challenges and OpportunitiesSerafı́n Martı́nez-Jaramillo
OutlineBackground
Recent history
Relevant concepts and literature
Data
Interbank exposures’ data
Payment system’s data
Network theory
Topological and other measures
Centrality measures
Results
Extended Network of exposures
Systemic Risk Measurement Challenges and Opportunities 2 / 61
Quotes
• In recent years automatic trading has been increasing dramatically in
different markets and financial markets are not the exception. What are the
implications of such trading in financial markets? What is the effect of
increasing intensive computing on the search for arbitrage opportunities? Is
this sort of trading going to increase the volatility of the prices or to increase
the likelihood of financial crashes?
• Financial markets are becoming an ever changing environment with
automatic trading using powerful computer hardware and novel algorithms,
better heuristics, and new statistical methods. Can we feel the presence of
the Red Queen around? Are not financial markets the ultimate laboratory for
competitive co-evolution?
Systemic Risk Measurement Challenges and Opportunities 3 / 61
Systemic risk definitions
• Systemic risk is the risk of experiencing an event which threatens the well
functioning of the system of interest (payments, financial, banking, etc.)
• “Systemic risk is defined as the risk of disruption to financial services that is
caused by an impairment of all or parts of the financial system and has the
potential to have negative consequences on the real economy” (IMF, 2010b)
• Systemic risk can be studied in two components Rochet (2009), Marquez &
Martinez Jaramillo (2009):
• An initial shock
• A contagion process
Systemic Risk Measurement Challenges and Opportunities 4 / 61
Measurement
• Measurement is essential in any scientific discipline
• Why is it important to measure systemic risk?
• Because of social costs
• To design proper regulation
• Why i s it difficult?
• Low frequency high impact events.
• There is still no consensus
Systemic Risk Measurement Challenges and Opportunities 5 / 61
Systemic risk measurement
In July 2010, the U.S. Congress enacted the Dodd Frank Act. The Dodd Frank
Act created the Financial Stability Oversight Council (FSOC). The FSOC has
three broad mandates:
• to identify risks to financial stability arising from events or activities of large
financial firms or elsewhere;
• to promote market discipline by eliminating participants expectations of
possible government bailouts; and
• to respond to emerging threats to the stability of the financial system.
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Systemic risk Methodologies
In Bisias et al 2012, the authors identify 31 measures of systemic risk which can
be classified under the following broad cathegories:
• Macroeconomic measures
• Granular foundations and network measures
• Forward looking risk measures
• Stress tests
• Cross-sectional measures
• Measures of illiquidity and insolvency
Systemic Risk Measurement Challenges and Opportunities 7 / 61
Macroeconomic measures
• Asset prices bubbles
• Property prices, equity prices, credit-gap indicators
• Macroprudential regulation
Systemic Risk Measurement Challenges and Opportunities 8 / 61
Granular foundations and network measures
• The default intensity model
• Network Analysis and financial linkages
• Simulating a credit scenario
• Simulating a credit and funding shock scenario
• Granger causality networks
• Bank funding risk
• Mark-to-market accounting and liquidity pricing
Systemic Risk Measurement Challenges and Opportunities 9 / 61
Forward Looking risk measurement
• Contigent claims analysis
• Mahalanobis distance
• The option iPOD
• Multivariate density estimators
• Simulating the housing sector
• Consumer credit
Systemic Risk Measurement Challenges and Opportunities 10 / 61
Stress tests
• “The banking systems reported financial indicators are above minimum
regulatory requirements and stress tests suggest that the system is resilient”
(IMF, Iceland: Financial Stability Assessment update, 19 August 2008, p 5)
• GDP stress tests
• SCAP
• Iceland/European stress tests
Systemic Risk Measurement Challenges and Opportunities 11 / 61
Cross sectional measures
• CoVaR
• Distressed insurance premium
• Co-Risk
• Marginal and systemic expected shortfall
Systemic Risk Measurement Challenges and Opportunities 12 / 61
Measures of illiquiduty and Insolvency
• Risk topography
• The leverage cycle
• Noise as information for illiquidity
• Crowded trades in currency funds
• Equity market illiquidity
• Serial correlation and Illiquidity in Hedge funds returns
• Broader hedge fund systemic risk measures
Systemic Risk Measurement Challenges and Opportunities 13 / 61
Interconnectedness
• The GHOS, the oversight body of the BCBS, agreed on a consultative
document setting out measures for G-SIBs.
• Measures include:
• methodology for assessing systemic importance
• additional required capital
• arrangements by which they will be phased in
• Objectives:
• strengthen the resilience of G-SIBs
• create incentives to reduce systemic importance
Systemic Risk Measurement Challenges and Opportunities 14 / 61
Interconnectedness
• Assessment methodology based on an indicator-based approach:
• size
• interconnectedness
• lack of substitutability
• global (cross-jurisdictional) activity
• complexity
• Additional loss absorbency requirements are to be met with a progressive
CET1 ranging from 1% to 2.5%.
• An additional 1% surcharge would be applied.
Systemic Risk Measurement Challenges and Opportunities 15 / 61
Network models and payment systems.
• Studies describing payment systems around the world:
• Soramki et al. (2006)
• Bech & Atalay (2008)
• Becher et al. (2008)
• Rordam & Bech (2008)
• Propper et al. (2008)
• Wetherilt et al. (2010)
Systemic Risk Measurement Challenges and Opportunities 16 / 61
Network models and financial contagion.
• Direct contagion through the interbank market widely studied by central
banks in several countries, Upper(2007).
• maximum entropy assumption
• individual idiosyncratic failures
• Contagion has been studied by simulating networks in Nier et al. (2007) and
Gai & Kapadia (2010). They use randomly generated networks.
• random models use scale free properties which interbank exposures
networks exhibit
Systemic Risk Measurement Challenges and Opportunities 17 / 61
Network models and systemic risk.• More recently contagion and systemic risk have been studied:
• Muller (2006)
• Nier et al (2006)
• Babus (2007)
• Mistrulli (2007)
• Markose et al (2009)
• Others include contagion within a wider simulation framework:
• Boss et al. (2006)
• Aikman et al. (2009)
• Alessandri et al. (2009)
• Marquez-Diez-Canedo et al. (2009)
• Martinez-Jaramillo et al. (2010b & 2010b)
• Gauthier et al. (2010a & 2010b)Systemic Risk Measurement Challenges and Opportunities 18 / 61
Other Related Works.
• Empirical analysis of the Italian interbank market, Iori et al. (2008)
• Simulation to model interbank lending and study contagion, Iori et al. (2006)
• Coupled stochastic processes, Battiston et al. (2012)
• Cascade processes on networks, Lorenz et al. (2009)
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Interbank’s data
• daily data from January 2004 onwards
• a time window contemplating data from the 3rd of January 2005 to 31st
December 2010
• comprises deposits and loans, securities, and foreign exchange
Three type of networks:
• Interbank
• Interbank - CLS
• Interbank - FX
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SPEI’s data
• daily data from January 2004 onwards
• a time window contemplating data from the 3rd of January 2005 to 31st
December 2010
Three types of networks:
• Low value
• Large value
• Total value
Network built accumulating the daily payments between each pair of banks in
both directions.
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Topological measures
• Topological measures
• Degree
• Clustering coefficient
• Reciprocity
• Affinity
• Completeness Index
• Other measures
• Strength
• Flow
• Herfindahl-Hirschman Index (HHI)
• Preference Index
Systemic Risk Measurement Challenges and Opportunities 22 / 61
Centrality measures• Concept commonly used in social networks
• Several important interpretations
• power
• influence
• independence
• control
• Characteristics of a relevant financial institution (Henggeler-Muller (2006)):
• possesses many linkages to other members (degree)
• Amount of assets, liabilities or flow is very large (strength)
• its failure could transmit contagion rapidly (closeness)
• its counterparties are also relevant (eec & pagerank)
• there are many paths which passes through it (betweenness)
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Centrality measures
• Strength centrality
• The sum of its interbank assets and liabilities.
• Degree centrality
• A vertex is more important if it is connected to many other vertices.
• Betweenness centrality
• A vertex with high betweenness centrality can stop or distort the
information that passes through it.
• Closeness centrality
• A node with high centrality would depend less on others.
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Centrality measures
• Entropic Eigenvector Centrality (Bonacich (1972))
• Based on Perron’s eigenvector (ePF )
• Considers the relevance of its neighbors.
• PageRank centrality (Page et al. (1999))
• Based on the Google’s algorithm
• Considers the centrality of its neighbors.
• A principal components unified measure of centrality
• different measures equally important
• preserve most informatino provided by such measures
• from the policy making perspective, it is important to have only one
measure of importance enabling to rank vertices
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Scale-free Networks
Interbank Interbank - CLS Interbank - FX
p-value < .05 < .1 < .05 < .1 < .05 < .1
Degree 77% 60% 81% 65% 54% 41%
In Degree 81% 66% 83% 67% 84% 76%
Out Degree 80% 60% 80% 64% 56% 45%
Exposures 57% 50% 63% 54% 83% 76%
Table : Percentage of days in which the exposures network exhibited power law
distributions.
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SPEI Network
Figure : January the 3rd 2005 Figure : July the 27th 2010
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Interbank exposures network
Figure : January the 3rd 2005 Figure : December the 31st 2010
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SPEI
Number of arcs
2005 2006 2007 2008 2009 2010 2011150
200
250
300
350
400
450
500
550
600
650
Num
ber
of A
rcs
Time
Average degree
2005 2006 2007 2008 2009 2010 20118
10
12
14
16
18
20
Ave
rage
Deg
ree
Time
Systemic Risk Measurement Challenges and Opportunities 29 / 61
SPEI
Completeness index
2005 2006 2007 2008 2009 2010 2011
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
Com
plet
enes
s In
dex
Time
Systemic Risk Measurement Challenges and Opportunities 30 / 61
SPEI
Affinity vs. degree
0 5 10 15 20 25 30 35 400
5
10
15
20
25
30
35
40
Degree
Affi
nity
Reciprocity
2005 2006 2007 2008 2009 2010 20110.68
0.72
0.76
0.8
0.84
0.88
0.92
Rec
ipro
city
Time
Systemic Risk Measurement Challenges and Opportunities 31 / 61
SPEI
Borrowing HHI for bank 12
2005 2006 2007 2008 2009 2010 20110.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
HH
IB
Time
High ValueLow Value
Lending HHI for bank 3
2005 2006 2007 2008 2009 2010 2011
0.2
0.25
0.3
0.35
0.4
0.45
0.5
HH
ILTime
High valueLow value
Systemic Risk Measurement Challenges and Opportunities 32 / 61
Interbank
Volume
2005 2006 2007 2008 2009 2010 20110.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2x 10
8
Tot
al V
olum
e
Time
Core size
2005 2006 2007 2008 2009 2010 201118
20
22
24
26
28
30
32
34
Cor
e S
ize
Time
Systemic Risk Measurement Challenges and Opportunities 33 / 61
Interbank
Bank 13’s flow
2005 2006 2007 2008 2009 2010 2011−1
0
1
2
3
4
5
Time
Flo
w
LPI bank 7
A C D E F G H0
5
10
15
20
25
30
35
40
45
Bank%
LP
I
Systemic Risk Measurement Challenges and Opportunities 34 / 61
Interbank
2005 2006 2007 2008 2009 2010 20110
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
HH
IL
Time
Figure : Lending HHI bank B
Systemic Risk Measurement Challenges and Opportunities 35 / 61
Interbank’s centrality
2005 2006 2007 2008 2009 2010 20110
2
4
6
8
10
12
14
16
18
20
Time
Ran
king
PCStrengthClosenessDegreePageRankEECBetweenness
Figure : Principal components centrality
Systemic Risk Measurement Challenges and Opportunities 36 / 61
Pairwise correlations
0
0.5
1Degree vs. Strength
0
0.5
1Degree vs. Closeness
0
0.5
1Degree vs. Betweenness
0
0.5
1Degree vs. PageRank
0
0.5
1Degree vs. EEC
0
0.5
1Strength vs. Closeness
0
0.5
1Strength vs. Betweenness
0
0.5
1Strength vs. PageRank
0
0.5
1Strength vs. EEC
0
0.5
1Closeness vs. Betweenness
0
0.5
1Closeness vs. PageRank
0
0.5
1Closeness vs. EEC
0
0.5
1Betweenness vs. PageRank
0
0.5
1Betweenness vs. EEC
0
0.5
1PageRank vs. EEC
Systemic Risk Measurement Challenges and Opportunities 37 / 61
SPEI’s centrality
2005 2006 2007 2008 2009 2010 20110
5
10
15
20
25
30
35
Time
Ran
king
TotalLow valueLarge value
Figure : Low vs large centrality bank C
2005 2006 2007 2008 2009 2010 20116
8
10
12
14
16
18
Time
Ran
king
TotalLow valueLarge value
Figure : Low vs large centrality bank D
Systemic Risk Measurement Challenges and Opportunities 38 / 61
Interbank’s centrality
2005 2006 2007 2008 2009 2010 20111
2
3
4
5
6
7
8
Time
Ran
king
Bank’s A rankingBank’s B ranking
Figure : Changes in ranking for banks A
& B
2005 2006 2007 2008 2009 2010 20110
2
4
6
8
10
12
14
16
18
20
Time
Ran
king
BorrowerLender
Figure : Changes in behavior bank C
Systemic Risk Measurement Challenges and Opportunities 39 / 61
PC centrality ranking vs. Asset size ranking
Systemic Risk Measurement Challenges and Opportunities 40 / 61
Congruence: Low value vs. Large value networkNumber of banks Top 1 Top 3 Top 10 Average Overlaping
27 0.53 0.97 0.97 0.7028 0.60 1.00 1.00 0.6929 0.48 1.00 1.00 0.6830 0.58 1.00 1.00 0.6431 0.57 1.00 1.00 0.5832 0.52 1.00 1.00 0.6133 0.33 1.00 1.00 0.6735 0.62 1.00 1.00 0.6336 0.62 1.00 1.00 0.6837 0.60 0.98 0.98 0.6238 0.26 1.00 1.00 0.6439 0.43 0.94 0.94 0.6240 0.51 1.00 1.00 0.6041 0.52 0.98 0.98 0.58
Systemic Risk Measurement Challenges and Opportunities 41 / 61
Congruence: Exposures vs. payments networkNumber of banks Top 1 Top 3 Top 10 Average Overlaping
27 0.16 1.00 1.00 0.7328 0.12 0.98 0.98 0.7629 0.12 1.00 1.00 0.7430 0.36 1.00 1.00 0.7031 0.27 0.97 0.97 0.6032 0.23 0.98 0.98 0.6433 - 1.00 1.00 0.7735 - 1.00 1.00 0.7136 0.15 1.00 1.00 0.7137 0.12 0.97 0.97 0.6938 0.05 1.00 1.00 0.7239 0.15 0.92 0.92 0.6440 0.27 0.98 0.98 0.6841 0.03 0.98 0.98 0.65
Systemic Risk Measurement Challenges and Opportunities 42 / 61
Average correlations1 on rankings
Exposures vs. Payments Low vs. Large
Maximum 0.77 0.65Minimum -0.29 -0.38Average 0.25 0.06
1Correlations were computed for the largest time-window when the number of banks was constantat 40.
Systemic Risk Measurement Challenges and Opportunities 43 / 61
Extended network
Figure : Interdependency between the Mexican financial system and its foreign
counterparts
Systemic Risk Measurement Challenges and Opportunities 44 / 61
Exposures
0
100
200
300
400
500
600
700
800
Jul2008
Oct Jan2009
Apr Jul Oct Jan2010
Apr Jul Oct Jan2011
Apr Jul
FX Deposits & loans
Derivatives Securities
Figure : Exposures by type of exposure
Systemic Risk Measurement Challenges and Opportunities 45 / 61
Exposures II
0
100
200
300
400
500
600
J2008
O J2009
A J O J2010
A J O J2011
A J
Pension funds Banks
Brokerage firms Investment funds
Figure : Exposures by type of intermediarie
Systemic Risk Measurement Challenges and Opportunities 46 / 61
Exposures III
0
1
2
3
4
5
6
7
8
9
2007 2008 2009 2010 2011
USA Europe Japan Others
Figure : Exposures by region of the counterpart
Systemic Risk Measurement Challenges and Opportunities 47 / 61
Loans
0
1
2
3
4
5
6
7
8
9
2007 2008 2009 2010 2011
USA Europe Japan Other
Figure : Loans by region of the counterpart
Systemic Risk Measurement Challenges and Opportunities 48 / 61
Net exposures
-10
-5
0
5
10
15
2007 2008 2009 2010 2011
Figure : Net Exposures
Systemic Risk Measurement Challenges and Opportunities 49 / 61
Over-Exposure for Banks
0
5
10
15
20
25
30
J2008
O E2009
A J O E2010
A J O E2011
A J
Total No deposits No securities
No FX No derivatives
Figure : Number of banks which are overexposed
Systemic Risk Measurement Challenges and Opportunities 50 / 61
Over-Exposure for Brokerage houses
0
2
4
6
8
10
12
14
16
18
20
J2008
O E2009
A J O E2010
A J O E2011
A J
Total No deposits No securities
No FX No derivatives
Figure : Number of brokerage houses which are overexposed
Systemic Risk Measurement Challenges and Opportunities 51 / 61
Over-exposure and contagion I
Figure : Original Network.Systemic Risk Measurement Challenges and Opportunities 52 / 61
Over-exposure and contagion II
Figure : Network after the initial shock.Systemic Risk Measurement Challenges and Opportunities 53 / 61
Over-exposure and contagion III
Figure : Network after contagion.
Systemic Risk Measurement Challenges and Opportunities 54 / 61
Over-exposure and contagion IV
Figure : Over-exposure.Systemic Risk Measurement Challenges and Opportunities 55 / 61
Stress testing conceptual framework
Scenario generator
Contagion phase Loss distribution
----- After contagion …… After the shock
Figure : Banco de Mexico stress testing framework.
Systemic Risk Measurement Challenges and Opportunities 56 / 61
What to do when there is no supervisory data
Figure : Adrian and Brunnermeier CoVaR network.
Systemic Risk Measurement Challenges and Opportunities 57 / 61
Summary• The payments system network is more connected than the interbank
exposures network.
• Importance in the payments network is different than in the exposures
network.
• The unified centrality measure can be employed on the methodology
proposed by the BCBS to determine G-SIBs.
• Bank’s importance changes depending on the type of payment and
depending if they are acting as lenders of borrowers.
• Bank’s behavior can change over time.
• Determining systemic importance based only on asset’s size could be
misleading.
• Most centrality measures are robust.
• Topology of the network is not enough to characterize systemic importance.Systemic Risk Measurement Challenges and Opportunities 58 / 61
Future work:
• Network formation models
• Studying other financial networks, like the securities settlement network
• Bank’s behavior in distress
• Bank’s funding strategies
• Link to economic variables
Systemic Risk Measurement Challenges and Opportunities 59 / 61
Thanks
Thank you!
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