Multi-Agent Financial Network Models for
Systemic Risk Monitoring and Design of Pigou
Tax for SIFIs
Sheri Markose ([email protected])
Simone Giansante ([email protected])
Ali Rais Shaghaghi ([email protected])
ESRC Conference – Diversity in Macroeconomics
University of Essex
25th February 2014
1
Roadmap
• Research Questions & Motivation
• Eigen-Pair Analysis
– Target SIFIs
– Internalizing Systemic Risk
• Conclusions
2
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?
3
1. Size and
Complexity (20%)
Derivatives
SIZ
Off-Balance Sheet Items (OBS)
SIZ
Tier 1 Ratio
CA
Multiple Determinant-based
Measurement Model of SIFIs
2. Capital (20%)
Determinant and Weight
Indicator
Total Assets
Risk-Weighted Assets (RWA)
Indicator
Units Equity
Sign
Code
SIZE1
LIQ
Liquid assets/ Deposits & Short% of assets Term Funding
5%
LIQ
Equity/ Customer & Short-Term
Funding
LIQ
Basel Leverage Ratio
LEV
1. Size and
Complexity (20%)
Derivatives
Off-Balance Sheet Items (OBS)
SIZE3
CA
Deposits +
& Short-Term
thousands USD
5% Funding
3. Liquidity (20%)
SIZE2
Indicator
weight
% of assets
+
+
4. Leverage (20%)
SIZE4
% of assets
+
5%
5%
Liabilities/ Equity
Tier 1 Ratio
2. Capital (20%)
Equity
CAPITAL1
5. Interconnectedness
(20%)
CAPITAL2
-
%
% of assets
LEV
10%
Interbank Assets/ Interbank
Liabilities
Source: BCBS, 2012;
BCBS,
2013a;
IMF/BIS/FSB,
2009
reports
Deposits
& Short-Term
Funding
LIQ1
% of assets
-
10%
+
6.67%
INT
4
Back to basis
• Market signals can be misleading
• We need to go back to Fundamentals
5
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, NonFund), 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
RTGS
DERIVATIVES
•
•
•
Top RHS Derivatives Exposures
: Shows highly tiered coreperiphery 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
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?
15
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 Approach
Eigen Pair analysis (Markose 2012, IMF; MarkoseGiansante
Shaghaghi, 2012, JEBO)
• Bilateral Gross Matrix X
18
X=
0
221.42
126.66
118.78
105.10
95.87
…
222.91
0
122.08
114.48
101.29
92.40
…
138.37 129.28 109.64 105.29 …
124.15 116.34 104.96 100.80 …
0 70.80 60.04 57.66 …
71.07
0 56.31 54.07 …
62.88 58.74
0 47.84 …
57.36 53.58 45.44
0…
…
…
…
……
M = X – XT : antisymmetric matrix of payables
mij > 0 is net payables by node i from node j
mji = – mij is corresponding amount by j to i
Considering only matrix of +ve values, i.e., m+ij = mij if mij >0, mij= 0 otherwise
we obtain the weighted adjacency matrix for the directed network
M+ =
0 1.49 11.71 10.49 4.54
0
0 2.08 1.86 3.67
0
0
0
0
0
0
0 0.27
0
0
0
0 2.84 2.44
0
0
0
0
0
0
…
…
…
…
…
9.42 …
8.40 …
0.30 …
0.49 …
2.40 …
0…
……
links point from the net
borrower or net
protection seller in
derivatives to the net
buyer (the direction of
contagion)
Stability Analysis – Solvency
Eigen Pair analysis (Markose 2012, IMF; Markose et al 2012, JEBO)
• Stability of Matrix Θ


( x12  x21 )  ( x13  x31 ) 
0
.0.

C2 t
C3t

( x23  x32 ) 

0
0
....

C3t

.
.
0
....


 ( xi1  x1i )
.
...
0
 C1t

.
.
...
...



(
x

x
)
(
x

x
)
Nj
jN
 N 1 1N
.
...
 C1t
C jt
....
....
....
...
0
...

0



( x3 N  xN 3 ) 

C Nt

.
 (2)
( xiN  xNi ) 

C Nt

.


0

Eigenvector Centrality
A variant is used in the Page Ranking algorithm used by Google
Centrality: a measure of the relative importance of a node within a network
Eigenvector 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
The vector v, containing centrality values of all nodes is obtained by solving the
eigenvalue equation Θ 𝒗𝟏 = λmax 𝒗𝟏 .
λmax is a real positive number and the eigenvector 𝒗𝟏 associated with the
largest eigenvalue has non-negative components by the Perron-Frobenius
theorem (see Meyer (2000))
Right Eigenvector Centrality : Systemic Risk Index Θ
Left Eigenvector centrality Leads to vulnerability
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 Losses
2011
Q1
Q2
Q3
Q4
Pearson Correlation
0.948
0.980
0.989
0.930
Furfine Losses rank order
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
80
70
60
50
40
30
20
10
0
0
10
20
30
40
EVC rank order
50
60
70
80
Application to Macro-Networks
Source Castren and Racan, 2013 (BIS data)
25
Application to Macro-Networks
The 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
26
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).
27
Questions n.3
How to stabilize and internalizing Systemic
Risk of Super-spreaders?
28
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
Initial Untaxed System
Max impact = 56% Tier 1
capital loss
1
0.9
max eigen value
0.8
MAX EIGEN VALUE
THRESHOLD
0.7
Tax Fund 20%for SIFIs
Max impact = 4% Tier 1
Capital Loss
0.6
0.5
0.4
0.3
0.2
0.1
Tax Fund 36%
Max impact 0%
0
0
0.1
0.2
0.3
0.4
0.5
alpha
0.6
0.7
0.8
0.9
1
Super Spreader PigouTax: To Mitigate
Socialized Losses
0.4
%TAX ON CAPITAL
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.1
0.2
0.3
0.4
0.5
ALPHA
0.6
0.7
0.8
0.9
1
Contagion from Most EVC/ SI Banks :
(LHS before Stabilization; RHS after Stabilization)
Concluding Remarks
• 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)
THANK YOU!
35