Das-RiskNetworks MIT Slides

8/20/2019 Das-RiskNetworks MIT Slides

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Risk Networks

Sanjiv R. Das

Santa Clara University

@MITJune 2014

Sanjiv R. Das Risk Networks CSRA 2014 1 / 21


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Systemic Risk from Co-Lending Networks: Overview

Joint work with IBM Almaden1

Focus on financial companies that are the domain for systemic risk(SIFIs).

Extract information from unstructured text (filings).

Information can be analyzed at the institutional level or aggregated

system-wide.Applications: Systemic risk metrics; governance.

Technology: information extraction (IE), entity resolution, mappingand fusion, scalable Hadoop architecture.

1“Extracting, Linking and Integrating Data from Public Sources: A Financial CaseStudy,” (2011), (with Douglas Burdick, Mauricio A. Hernandez, Howard Ho, GeorgiaKoutrika, Rajasekar Krishnamurthy, Lucian Popa, Ioana Stanoi, ShivakumarVaithyanathan), IEEE Data Engineering Bulletin, 34(3), 60-67. [Proceedings

WWW2010, April 26-30, 2010, Raleigh, North Carolina.]Sanjiv R. Das Risk Networks CSRA 2014 2 / 21


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Data

employment, director, officer

insider, 5% owner, 10% owner

h o l d i n g s

,

t r a n s a c t

i o n s

Event

Company Person

SecurityLoan

subsidiaries, insider, 5%,10% owner, banking

subsidiaries

borrower,lender

Forms 8-K

Forms 10-K, DEF 14A, 8-K, 3/4/5

Forms 10-K, DEF14A, 8-K, 3/4/5, 13F,

SC 13D, SC 13G,FDIC Call Report

Reference SEC tableForms 13F, Forms 3/4/5

Forms 3/4/5, SC 13D, SC 13G, 10-K,FDIC Call Report

Forms 3/4/5, SC 13D, SC 13G

Forms 10-K, 10-Q, 8-K

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Loan Extraction

Id Agreement Name Date Total Amount

1 Credit Agreement June 12, 2009 $800,000,000

!

Id Company Role Commitment

1 Charles Schwab Corporation Borrower

1 Citibank, N.A. Administrative Agent

1 Citibank, N.A. Lender $90,000,000

1 JPMorgan Chase Bank, N.A. Lender $90,000,000

1 Bank of America, N.A. Lender $80,000,000

!

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Loan Information

Loan Company Information940)-/ 64%+ 842:&)+0 ;()< =, >?%1()- @2?A%= >41'41%34+ B+ *:C DE FGGH

Extractandcleanseinformationfromheaders,tablesmaincontentandsignatures



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Co-Lending Network

1 Definition: a network based on links between banks that lendtogether.

2 Loans used are not overnight loans. We look at longer-term lendingrelationships.

3 Lending adjacency matrix:

L ≡ {Lij }, i , j = 1...N 4 Undirected graph, i.e., symmetric: L

∈ R N ×N

5 Total lending impact for each bank: x i , i = 1...N



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Centrality

1 Influence relations are circular:

x i =N

j =1

Lij x j ,∀i

2 Pre-multiply by a scalar to get an eigensystem:

λx = L · x3 Principal eigenvector of this system gives the “centrality” score for a

bank.4 This score is a measure of the systemic risk of a bank.



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Data

Five years: 2005 to 2009.

Loans between FIs only.

Filings made with the SEC.

No overnight loans.Example: 364-day bridge loans, longer-term credit arrangement, Libornotes, etc.

Remove all edge weights ¡ 2 to remove banks that are minimallyactive. Remove all nodes with no edges. (This is a choice for the

regulator.)



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Loan Network 2005

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Loan Network 2006–2009

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10/21

Network Fragility

1 Definition: how quickly will the failure of any one bank trigger failuresacross the network?

2 Metric: expected degree of neighboring nodes averaged across all

nodes. E (d 2)/E (d ) ≡ R ,where d stands for the degree of a node.

3 Neighborhoods are expected to “expand” when R ≥ 2.4 Metric: diameter of the network.



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Systemically Important Financial Institutions (SIFIs)



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Extensions

1 Other markets, e.g., CDS exchange. Dodd-Frank mandatesconversion of all OTC contracts to be cleared through central counterparties (CCPs).

2 Inserting risk values at each node. This allows for risk assessmentacross the network based on severity of risk. Overcomes an essentialmissing component of extant network analyses.



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Risk Networks

Assume n nodes, i.e., firms, or “assets.”Let E ∈ R n×n be a well-defined adjacency matrix. This quantifies theinfluence of each node on another.

E may be portrayed as a directed graph, i.e., E ij = E ji .E jj = 1; E ij ∈ {0, 1}.C is a (n × 1) risk vector that defines the risk score for each asset.We define the “risk score” as

S =√

C E C

S (C , E ) is linear homogenous in C .



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ExampleRisk vector C : 0 0 1 2 2 2 2 2 1 0 2 2 2 2 1 0 1 1Risk Score: S = 11.62



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Example: Adjacency Matrix



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Centrality and Fragility

Centrality is the principal eigenvector x of dimension (n × 1) suchthat for scalar λ:

λ x = E x Plot:

Fragility: for each node with degree d j , fragility is the score given by

E (d 2)/E (d )

Values greater than 2 imply a fragile network.



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Risk Decomposition1 Exploits the homogeneity of degree one property of S .2 Risk decomposition (using Euler’s formula):

S = ∂ S

∂ C 1C 1 +

∂ S

∂ C 2C 2 + . . . +

∂ S

∂ C nC n

3 Plot:



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Risk Increments

Increments are simply:

I j =

∂ S

∂ C j , ∀ j Plot:


N li d Ri k S


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Normalized Risk Score

Units of S are free to choose, and determined by the units of vectorC , e.g., rating units, Z-score, expected loss.

S̄ =

√ C E C

C (1)

where C =√

C C is the norm of vector C .When there are no network effects, E = I , the identity matrix, andS̄ = 1, i.e., the normalized baseline risk level with no network(system-wide) effects is unity.Example : For the system in our example, the normalized score is S̄ = 1.81.Now suppose, we add one additional bi-directed link between nodes 6 and12. The risk score S increases from 11.62 to 11.96, and the normalized risk

score S̄ increases from 1.81 to 1.87.Example : If we keep the network unchanged, but re-allocate the compromise

vector by reducing the risk of node 3 by 1, and increasing that of node 16 by

1, we find that the risk score S goes from 11.62 to 11.87, and the

normalized risk score S̄ goes from 1.81 to 1.85.


C Ri k


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Cross Risk

Is the spill over risk from node i to node j material?


C l ti N t k M


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Correlation vs Network Measures

Correlation measures are pairwise and conditional; network measuresare system-wide and unconditional.

Correlations tend to be high in crisis periods but are not early-warningindicators of systemic risk. It is an empirical question as to whether

network measures are predictive.Correlation measures are statistical metrics. Network measuresdirectly model the underlying mechanics of the system because theadjacency matrix E is developed based on physical transactionactivity, and the compromise vector is a function of firm quality thatmay be measured in multivariate ways.


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