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Multi-Agent Financial Network Models for Systemic Risk Monitoring and Design of Pigou

Tax for SIFIs

Sheri Markose (scher@essex.ac.uk)Simone Giansante (S.Giansante@bath.ac.uk)Ali Rais Shaghaghi (araiss@essex.ac.uk)

ESRC Conference – Diversity in Macroeconomics University of Essex25th February 2014

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Roadmap• Research Questions & Motivation

• Eigen-Pair Analysis – Target SIFIs – Internalizing Systemic Risk

• Conclusions

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Three Main Questions of Macro-prudential Regulation

1) Is financial system more or less stable?

2) Who contributes to Systemic Risk?

3) How to stabilize and internalizing Systemic Risk of Super-spreaders?

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Multiple Determinant-based Measurement Model of SIFIs

Source: BCBS, 2012; BCBS, 2013a; IMF/BIS/FSB, 2009 reports

Back to basis• Market signals can be misleading• We need to go back to Fundamentals

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Banking Stability Index (Segoviano, Goodhart 09/04) vs Market VIX and V-FTSE Indexes : Sadly market data based

indices spike contemporaneously with crisis ; devoid of requisite info for Early Warning System

“Paradox of Stability” : Stock Index and Volatility Index “Paradox of Volatility” (Borio and Drehman(2009); Minsky

(1982))

RBI Project in mapping the Indian financial system shows the following networks

structures(Sheri Markose & Simone Giansante)

• Project: April 2011 – December 2013– Collection of Bilateral Data of Interbank (Fund, Non-

Fund), Derivatives, etc. as well as Global Flows– Stress Test Contagion Analysis on a Multi-layer

Framework (Solvency & Liquidity)– Eigen Pair Analysis and Design of Pigou Tax for

SIFIs.

FUNDED DERIVATIVES

RTGS • Top RHS Derivatives Exposures : Shows highly tiered core-periphery structure with large numbers of participants in the periphery and a few in the core

• Top LHS Interbank Exposures: Shows a more diffused core with more numbers of banks in the core

• Bottom: network for Indian RTGS shows no marked tiering with few financial institutions in the periphery

Within A larger System with non bank FIs- Net Lenders to Banks Are Mutual Funds and Insurance Companies (Code G-H)

Banks and Non Banks

• The analysis revealed that the largest net lenders in the system were the insurance companies and the Asset Management Companies (AMCs), while the banks were the largest borrowers.

• This renders the lenders vulnerable to the risk of contagion from the banking system. The random failure of a bank which has large borrowings from the insurance and mutual funds segments of the financial system may have significant implications for the entire system

Domestic Banks vs Foreign Borrowers

Source : Data collected from a sample of 50 banks that form 90 per cent of banking sector assets – LHS by Foreign Banks, RHS by Countries

Multilayer Approach to Solvency & Liquidity Contagion

Contagion from Most EVC/ SI Banks

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Three Main Questions of Macro-prudential Regulation

1) Is financial system more or less stable?

2) Who contributes to Systemic Risk?

3) How to stabilize and internalizing Systemic Risk of Super-spreaders?

Eigen Pair Analysis

• Monitoring Systemic Risk : Is the financial system becoming more or less stable ?

• Monitor maximum Eigen-value of the ratio of net liabilities to Tier 1 capital matrix

Why Does Network Structure Matter to Stability ? s < 1.

• My work influenced by Robert May (1972, 1974)• Stability of a network system based on the

maximum eigenvalue lmax of an appropriate dynamical system

• May gave a closed form solution for lmax in terms of 3 network parameters , C : Connectivity , number of nodes N and s Std Deviation of Node Strength : lmax = s A highly asymmetric network such as core periphery, its connectivity has to be very low for it to be stable

Eigen Pair ApproachEigen Pair analysis (Markose 2012, IMF; MarkoseGiansante

Shaghaghi, 2012, JEBO)• Bilateral Gross Matrix X

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0 222.91 138.37 129.28 109.64 105.29 …221.42 0 124.15 116.34 104.96 100.80 …126.66 122.08 0 70.80 60.04 57.66 …118.78 114.48 71.07 0 56.31 54.07 …105.10 101.29 62.88 58.74 0 47.84 … 95.87 92.40 57.36 53.58 45.44 0 … … … … … … … …

X =

M = X – XT : antisymmetric matrix of payablesmij > 0 is net payables by node i from node jmji = – mij is corresponding amount by j to i Considering only matrix of +ve values, i.e., m+ij = mij if mij >0, mij= 0 otherwisewe obtain the weighted adjacency matrix for the directed network

0 1.49 11.71 10.49 4.54 9.42 …0 0 2.08 1.86 3.67 8.40 …0 0 0 0 0 0.30 …0 0 0.27 0 0 0.49 …0 0 2.84 2.44 0 2.40 …0 0 0 0 0 0 …… … … … … … …

M+ =

links point from the net borrower or net protection seller in derivatives to the net buyer (the direction of contagion)

Stability Analysis – SolvencyEigen Pair analysis (Markose 2012, IMF; Markose et al 2012, JEBO)

• Stability of Matrix Θ

)2(

0...)(

....)(.0........

)(...0....)(.........0..

)(........)(00

0.....0.)()(0

1

11

1

11

33

3

3223

3

3113

2

2112

jt

jNNj

t

NN

Nt

NiiN

t

ii

Nt

NN

t

tt

Cxx

Cxx

Cxx

Cxx

Cxx

Cxx

Cxx

Cxx

The vector v, containing centrality values of all nodes is obtained by solving the eigenvalue equation Θ = λmax . λmax is a real positive number and the eigenvector associated with the largest eigenvalue has non-negative components by the Perron-Frobenius theorem (see Meyer (2000))Right Eigenvector Centrality : Systemic Risk Index ΘLeft Eigenvector centrality Leads to vulnerability

Eigenvector Centrality

Centrality: a measure of the relative importance of a node within a networkEigenvector centrality

Based on the idea that the centrality vi of a node should be proportional to the sum of the centralities of the neighbors

l is maximum eigenvalue of Θ

A variant is used in the Page Ranking algorithm used by Google

 

Stability of the dynamical network system : Eigen Pair (λmax , v)

In matrix algebra dynamics of bank failures given Ut +1 = [´ + (1- )I] Ut = Q Ut

I is identity matrix and is the % buffer• U0 with elements (u1t , u2t, ..... unt) = (1,0,......0) to

indicate the trigger bank that fails at initial date, t=0, is bank 1 and the non-failed banks assume 0’s

STABILITY: λmax(Q) < 1; λmax(´ ) <

Stability Condition: lmax(´) < • is the % capital buffer• The criteria of failure of a bank in the contagion

analysis is based on the Basel rule that

(Tier 1 Capital – Loss)/ RWA < 0.06 = TRWA

• Equivalence of the above Basel rule with a Absolute Tier 1 capital threshold criteria (Tc) for failure

TC = 1 - TRWA(RWA/Tier 1 Capital) =

How Useful is the Eigen Vector Centrality Rank Order As a Proxy for Furfine Losses of Capital ?

Table 5 : Pearson Correlation in the Rank Order of EVC and that of Furfine Losses2011 Q1 Q2 Q3 Q4

Pearson Correlation 0.948 0.980 0.989 0.930

Figure 3 Scatter Plot of Pearson Correlation of 0.98993 in the Rank Order of Eigenvector centrality (EVC) and that of Furfine Losses (1 being the highest and 76 is lowest) Q3 2011

0 10 20 30 40 50 60 70 800

1020304050607080

EVC rank order

Furfi

ne L

osse

s ra

nk o

rder

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Application to Macro-Networks

Source Castren and Racan, 2013 (BIS data)

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Application to Macro-NetworksThe high EVC of the French and Italian Non Bank Sector and that of French Public Sector signalling their foreign indebtedness is worrying In turn Spanish and Turkish banking systems are most vulnerable to global exposures

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Loss Multiplier vs EigenPair

Loss multiplier (BLUE) is very low in the run up to the crisis in 2007-2009 and peaks well after the crisis (Paradox of Volatility) vs EigePair (GREEN).

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Questions n.3

How to stabilize and internalizing Systemic Risk of Super-spreaders?

There are 5 ways in which stability of the financial network can be achieved

 

Design of Pigou Tax To Internalize Systemic Risk Costs: Proportional to Damage

How to stabilize ? Superspreader tax escrow fund: tax using EV centrality of each bank vi to reduce max eigenvalue of

matrix from .91 to closer to threshold 0.25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1MAX EIGEN VALUE

THRESHOLD

alpha

max

eig

en v

alue

Tax Fund 20%for SIFIsMax impact = 4% Tier 1 Capital Loss

Initial Untaxed SystemMax impact = 56% Tier 1 capital loss

Tax Fund 36% Max impact 0%

Super Spreader PigouTax: To Mitigate Socialized Losses

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

ALPHA

%TA

X O

N C

API

TAL

Contagion from Most EVC/ SI Banks : (LHS before Stabilization; RHS after Stabilization)

• Changes in eigenvector centrality of FIs can give early warning of instability

• These banks will, like Northern Rock, be winning bank of the year awards ; however potentially destabilizing from macro-prudential perspective

• Capital for CCPs to secure system stability can use same calculations

• Insights and how to quantify systemic risk from multiple clearing platforms for derivatives products (point made by Manmohan Singh, IMF)

Concluding Remarks

THANK YOU!

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