systemic risk measurement challenges and opportunities · systemic risk measurement challenges and...

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

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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

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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

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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

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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)

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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

Systemic Risk Measurement Challenges and Opportunities 20 / 61

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

Systemic Risk Measurement Challenges and Opportunities 25 / 61

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

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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.

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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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