Economics Department
Centre for Computational Finance and Economic Agents
Kiel Institute for the World Economy:6th Kiel Institute
Summer School on Economic Policy Policy,June 24 –
30, 2012
Professor Sheri Markose
Economics Department (University of Essex)
Multi-Agent Financial Network Models (MAFN) For
Systemic Risk Management: A New Complexity
Perspective
Lecture 1 Eigen-Pair Analysis of Financial Systemic Risk
and Design of Super-Spreader Tax To Mitigate Moral
Hazard
scher@essex.ac.uk
The software used in network modelling was developed by
Sheri Markose with Simone Giansante and Ali Rais
Lecture 1 :Roadmap
• New Office of Financial Research in the US Treasury to
put an end to regulators flying blind
Put an end to balkanization of data
• Two methodological problems on financial contagion
and systemic risk : (i)Paradox of Volatility and the
pitfalls of market price data based systemic risk
measures hence structural bilateral data based
networks modeling needed (ii) Negative Externalities
problem the need for holistic visualization
• Two applications used: Systemic Risk From Global
Financial Derivatives Modelled Using Network
Analysis of Contagion and Its Mitigation With SuperSpreader Tax
• Indian Financial System and Bilateral Data based
Modelling: Pioneering first full bilateral analysis
Lecture 1:Roadmap contd Applications to Systemic
Risk from Global Derivatives , Indian Financial System
• Stability of Networks and Eigen-Pair
Analysis: Markose et. al. (2012)
• 3 main questions of macro-prudential
regulation :
• (i)Is financial system more or less stable?
• (ii)Who contributes to Systemic Risk ?
• (iii)How to internalize costs of systemic
risk of ‘super-spreaders’ using Pigou tax
based on eigenvector centrality:
Management of moral hazard
• Furfine Stress Test
• Superspreader Lite Escrow Fund
• Results
Overview Lecture 2:Three major methodological issues
on why policy fails:Why no dogs barked? Robust
Policy Design and monitoring needs to move away
from macro-econometric models to MAFNs
1. Why was the need for macroprudential framework eschewed?
Mainstream Neoclassical ‘Representative Agent’ Models;
Unfortunate Irrelevance of Most State of the Art Monetary
Economics (Buiter 09); evolutionary nature of money and credit
2.Why were there no system wide quantitative models developed for
stress tests of how the financial network would function under these
micro regulatory rules of individual bank behaviour?
Failure of macro-econometric models for policy analysis (Lucas
Critique);we have yet to replace this with multi-agent fine grained
data base driven financial network models
3. Urgent need for modelling tools to monitor liquidity gridlocks,direction
of an ongoing financial contagion, systemic risk : Multi-Agent
Financial Network Models ie. intelligence based models that
can monitor perverse incentives
Answer: Lack of Complex Adaptive System framework- Red Queen
type competitive co-evolution esp between regulator and regulatee
requires constant vigilance and production of countervailing
measures(Markose 2004, 2005) Robert Axelrod on Fragility of
Communication Networks : Overlook Competitive Co-evolution
Methodological Challenges to Measuring Systemic Risk :
Statistical v. Causal Models
• DEFINITION: Economic and financial contagion refers to the
spreading of a negative shock on the solvency conditions of an
economic or financial entity in a physical supply chain or in
terms of generic credit/debt and liquidity obligations governing
interbank, payment and settlement systems and/or claims on
other financial markets
• Structural model based on default causality of chain reactions
governed by the network connections of the financial entities
• In contrast, models made popular by Kaminsky and Reinhart
(2000) view financial contagion as the downward co-movement
of asset prices across different markets and for different asset
classes. This is based on statistical or econometric methods
which measure (amongst other ways) the increased
correlations of asset prices
• Above models complimentary to the causal default models that
use financial network simulations, especially in the use of
contagion models based on CDS price co-movements (Jorge
Chan-Lau et al., 2009)
(i)Paradox of Volatility or Paradox of Stability
Major drawback of market price based systemic risk measures is that they can
suffer from the paradox of financial stability (Borio and Drehman (2009)) or the
paradox of volatility, issues first addressed by Hyman Minsky (1982).
Market based statistical proxies for systemic financial fragility are at their lowest
just before the point of great financial collapse and hence while there may be
some information in the cross-sectional data of FI’s contributions to systemic
risk, the aggregated systemic risk statistics are at best contemporaneous with
the crisis in markets.
As credit growth boosts asset prices, CDS spreads and VIX indices which are
inversely related to asset prices are at their lowest precisely before the crash
when asset prices peak.
Examples of Statistical Measures of Systemic Risk
• To analyze so called interconnectedness risk between
FIs, matrix of bilateral correlations or non-linear copula
based co-movements purported to represent extreme
market conditions is constructed from market price data.
• Market-based systemic risk measures that have been
proposed: Conditional VaR (CoVaR) Adrian and
Brunnermeier (2009); System Expected Shortfall (SES)
Acharya et al. (2010); Co-risk by Chau-Lan (2010); DIP
(Distress Insurance Premium) by Huang et al. (2010);
POD (Probability that at least one bank becomes
distressed) by Segoviano and Goodhart (2009),
Shapley-Value by Tarashev et. al. (2010) and Macroprudential capital by Gauthier et. al (2009).
Banking Stability Index (Segoviano, Goodhart 09/04) v
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))
(ii) Fallacy of Composition In the Generation of
Systemic Risk/Negative Externalities: Holistic
Visualization Needed
Systemic risk refers to the larger threats to the financial system as a whole that
arise from domino effects of the failed entity on others.
At the level of the individual user these schemes appear plausible but at
the macro-level may lead to systemically unsustainable outcomes.
Example 1 : Risk sharing in advanced economies uses O-T-C derivatives.
Success of risk sharing at a system level depends on who is providing
insurance and structural interconnections involved in the provision of
guarantees.
Only 5% of world OTC derivatives is for hedging purposes
Credit Risk Transfer in Basel 2 gave capital reductions from 8% to 1.6% capital
charge if banks got CDS guarantees from ‘AAA’ providers . Most of this held
in trading accounts
Example 2: Outsourcing of Pension Fund Management
Example 3: Indian banks’ exposure to foreign LCFIs
Digital Mapping of Financial Sector: For over two decades central
bankers and monetary/financial academics have had no incentives to
study the financial system in a quantitative integrated way (Gary Gorton
Real
Estate
(V)ICT
Non-Bank
Peer to
Peer
Lending
(I)
Household
/Borrowers
Real estate
Mortgage
(RMBS);
Savings and
indirect
Investments
(II)
Deposit
Banks/
Regional
Originate
and
distribute
(X) Regulatory
Framework
Central Banks; Basel
II &II I; Solvency II
(VI)Repo
and
Interbank
Markets
(III)Large
Complex
Financial
Intermediaries
(LCFI)
Cross
Border
Asset
Cash
(IX) Government
Debt/Bonds and
Deficit ; Sovereign
Risk
(VII)Financial
Derivatives Credit
Default Swaps (on
Sovereign and LCFI s)
Private
Sector Investment
Securiti
zation
(AAA,
Securities
AA, BBB)
BBB
Ratings Agencies
(VIII)Stock
Market;
Equity Investment
(IV)Life
Assurance and
Pension Funds
(LAPFs)
______________
Hedge Fund
Re-Insurance
Structure of Global Financial Derivatives Market
(2009,Q4 204 participants): Green(Interest Rate), Blue (Forex), Maroon (
Equity); Red (CDS); Yellow (Commodity); Circle Broker Dealers in all markets
Total Value and Market Share of Financial Derivatives for Banks Q4 2009
(1)The total value of financial derivatives is in billions of US dollars. (2) The
market shares are in parenthesis. (3) Banks are ranked using Gross Notional
Gross Notional
All FIs
674.369
Gross Positive Fair
Value (GPFV)
Gross Negative
Fair Value
(GNFV)
Derivatives Assets
10.465
Derivatives
Liabilities
Total Assets
0.889
37.252
Tier 1 capital
1.413
10.144
1.168
Top 16 FIs
659.263
(97.76%)
10.254
(97.98%)
9.934
(97.92%)
Top 26 FIs
673. 827
(99.92%)
10.453
(99.89%)
10.134
(99.89%)
1.068
(91.39%)
0.816
(91.78%)
27.863
(74.80%)
1.014
(71.60%)
1.15
(98.52%)
0.874
(98.33%)
32.837
(88.15%)
1.207
(85.48%)
UK Fund Management 1984 and 2004 (Source Blake et.
al 2010) Fund sponsors think they are diversifying by
outsourcing to specialist fund managers:
concentration and herding at system level
Financial network models to date have yielded mixed
results : None about propagators of 2007 crisis C:
Core; P Periphery (see Fricke and Lux (2012)
Properties of Networks
Diagonal Elements Characterize Small World Networks
Watts and Strogatz (1998), Watts (2002) See Markose et. al. (2004)
Properties Clustering
Coefficient
Average Path
Length
Degree
Distribution
High
Equal and fixed
In-degrees to each
node
Networks
Regular
High
Random
Low
Low
Scale Free/Power
Law
Low
Variable
Exponential/
Poisson
Fat Tail
Distribution
Some Networks: A graphical representation of random
graph (left) and small world graph with hubs, Markose
et. al. 2004
Sheri Markose and Simone Giansante RBI
Project in mapping the Indian financial
system shows the following networks
structures
• Top RHS Derivatives Exposures : Shows highly tiered
core-periphery structure with large numbers of
participants in the periphery and a few in the core
• Characterization of Too Interconnected to Fail
• 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
FUNDED
RTGS
DERIVATIVES
Bank-Bank Within A larger System with non bank FIs- Net
Lenders to Banks Are Mutual Funds and Insurance Companies
(Code G)
Global Derivatives Market (Θ matrix) : JP and BoA
central Tier; 22 other banks in Tier 2 all banks in the
top tiers will fail if any other fails of this group
Markose et. al. 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
Gross Exposures : Row Bank are Borrowers (Protection
Sellers in Derivatives) ; Column Banks are Lenders
(Protection Buyers in Derivatives)
Constructing the network of bilateral exposures
X=
0
221.42
126.66
118.78
105.10
95.87
…
222.91 138.37 129.28 109.64 105.29 …
0 124.15 116.34 104.96 100.80 …
122.08
0 70.80 60.04 57.66 …
114.48 71.07
0 56.31 54.07 …
101.29 62.88 58.74
0 47.84 …
92.40 57.36 53.58 45.44
0…
…
…
…
…
……
M = X – XT : antisymmetric matrix of derivatives 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
0
0 2.08 1.86
0
0
0
0
0
0 0.27
0
0
0 2.84 2.44
0
0
0
0
…
…
…
…
4.54
3.67
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)
Contagion and Stability of Matrix Θ’ :
Impact of i on j relative to j’s capital


0



0


.


(
x

x
)
 i1 1i

C1t

.


(
x

x
)
 N 1 1N

C1t
( x12  x21 ) 
C2 t
.
( x13  x31 ) 
C3t
( x23  x32 ) 
C3t
0
.
...
0
...
.
...
0
.
...
...
( xNj  x jN ) 
0
.0.
....
....
....
....
....
C jt
...

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
 is maximum
eigenvalue of Θ
The vector v, containing centrality values of all nodes is obtained by solving
the eigenvalue equation Θ v = λmax v : Right Eigenvector Centrality :
Systemic Risk Index
Left Eigenvector centrality Leads to vulnerability index
𝒗 Θ = λmax 𝒗
Positive values for the centralities are guaranteed by Perron-Frobenius thm:
The eigenvector of the largest eigenvalue of a non-negative matrix Θ’
Stability of the dynamical network λsystem
:
is
maximum
max
eigenvalue of Θ
Eigen Pair (λmax, v)
Dynamics of bank failures given
Ut +1 = [´ + (1- )I] Ut = S Ut (10)
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 Condition max(´) < 
After q iterations
Too Interconnected To Fail :
Stress Test
• Objective: Build CDS Network and Conduct Stress Tests
There is very high correlation between the dominance of market
share in CDS and CDS network connectivity
• Stress Tests: Follow Furfine (2003) Algorithm
• The loss of derivatives cover/receivables due to the failed bank as
counterparty suspending its guarantees will have a contagion like
first and multiple order effects. Full bilateral tear up assumed; No
possibility for Novation
• There is a power iteration Mq where q is the qth power of the netted
matrix. At each q, weighted paths of length q between
each i and j nodes is obtained
•
We use 6% reduction of core capital to signal bank failure
Contagion from JP Morgan (LHS; 12
direct counterparties) BoA (RHS; 7 direct
counterparties )
Contagion from
Deutsche Bank (LHS; 4 direct c-parties
demised) Standard Charter (RHS; 1 direct cparties)
Contagion when JP Morgan Demises in Clustered CDS Network 2008
Q4 ( Left 4 banks fail in first step and crisis contained) v
In Random Graph (Right 22 banks fail !! Over many steps)
Innoculate some key players v Innoculate all ( Data Q4 08)
Mitigation of Systemic Risk
Impact of Network Central
Banks: How to stabilize ?
To date the problem of how to have banks internalize
their systemic risk costs to others (and tax payer) from
failure has not been adequately solved
In particular penalty for being too interconnected has
not been dealt with from direct bilateral network data
There are 5 ways in which stability of the
financial network can be achieved
(i)Constrain the bilateral exposure of financial intermediaries (Ad
hoc constraints do not work)
(ii) Ad hocly increase the threshold rho in (11),
(iii) Change the topology of the network
(iv) Directly deduct a eigenvector centrality based prefunded buffer
in matrix
Si # =
#
𝑗 𝜃𝑗𝑖 =
1
𝐶𝑖
(
𝑗 (𝑥𝑗𝑖
− 𝑥𝑖𝑗 )+ −  vi 𝐶𝑖 ) .
(v)Levy a capital surcharge commensurate to the eigenvector
centrality in denominator
Si# =
𝑗 𝜃𝑗𝑖 # =
1
(1+𝜏 (vi𝑖 )𝐶𝑖
𝑗 (𝑥𝑗𝑖
− 𝑥𝑖𝑗 )+
(i) & (ii) do not price in negative externalities and systemic risk of
failure of highly network central nodes. Network topologies emerge
endogenously and are hard to manipulate exogenously.
.Design
of Pigou Tax To Internalize Systemic Risk Costs:
Proportional to Damage
Too Interconnected To Fail :
Stress Test RBI Case, Contagion Analysis
• Stress Tests: Follow Furfine (2003) Algorithm
• Criteria of failure of a bank in the contagion analysis is based on the
Basel rule that
(Tier 1 capital – LGD)/ RWA < 0.06 = TRWA.
• Here LGD is loss given default and the threshold for bank failure in
terms of RWA is denoted as TRWA.
• However, as the practical aspects of insolvency requires
recapitalization, it is important to see the equivalence of the above
Basel rule with a Tier 1 capital threshold criteria (Tc) for failure :
•
Tc
= 1 - TRWA
𝑅𝑊𝐴
𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙
.
Socialization of Losses: Global
Derivatives
Sergoviano and Singh (IMF 2008) Based on March 2008
data, in the case of a single institution failure, the total
loss could be as high as $300–$400 billion depending
on the FI; but when cascade effects are taken into
account, the total loss could rise to over $1,500 billion.
Our 2009 Q4 results show direct domino losses
$ 350.6bn constituting 25% loss of Tier 1 capital of
banks ; this does not include non-banks or nonUS/European banks; that closet to $750 bn
Alpha
0.2
Bank Name
T ier 1 Capital
0.3
0.5
EVC T ax% T ax $s T ax % T ax $s T ax%
1.00
1.5
T ax
$s
T ax% T ax $s T ax%
6.64
T ax
$s
T ax%
T ax
9.96
0.77
13.28
Goldman Sachs
17.15
0.39
0.08
1.33
0.12
1.99
0.19
3.32
0.39
Deutsche Bank
49.42
0.32
0.06
3.20
0.10
4.80
0.16
7.99
0.32 15.99
0.49 23.98
0.65
31.98
JPMorgan
96.37
0.31
0.06
6.04
0.09
9.06
0.16 15.09
0.31 30.19
0.47 45.28
0.63
60.37
Credit Suisse
39.49
0.30
0.06
2.39
0.09
3.58
0.15
5.97
0.30 11.94
0.45 17.91
0.60
23.87
Morgan Stanley
46.67
0.30
0.06
2.80
0.09
4.20
0.15
7.00
0.30 14.00
0.45 21.00
0.60
28.00
HSBC Group
35.48
0.30
0.06
2.13
0.09
3.19
0.15
5.32
0.30 10.63
0.45 15.95
0.60
21.26
Societe Generale
34.69
0.24
0.05
1.64
0.07
2.46
0.12
4.10
0.24
8.20
0.35 12.30
0.47
16.41
Barclays
77.56
0.23
0.05
3.64
0.07
5.46
0.12
9.10
0.23 18.20
0.35 27.29
0.47
36.39
Bank of America
111.92
0.21
0.04
4.61
0.06
6.92
0.10 11.53
0.21 23.05
0.31 34.58
0.41
46.11
Standard Chartered
24.58
0.19
0.04
0.94
0.06
1.40
0.10
2.34
0.19
0.29
7.02
0.38
9.36
Citibank
96.83
0.18
0.04
3.52
0.05
5.29
0.09
8.81
0.18 17.62
0.27 26.43
0.36
35.25
Wachovia
39.79
0.17
0.03
1.38
0.05
2.08
0.09
3.46
0.17
6.92
0.26 10.38
0.35
13.84
BNP Paribas
90.37
0.15
0.03
2.70
0.04
4.06
0.07
6.76
0.15 13.52
0.22 20.28
0.30
27.03
Credit Agricole
44.53
0.14
0.03
1.27
0.04
1.90
0.07
3.17
0.14
0.21
9.50
0.28
12.67
Lloyds
74.27
0.14
0.03
2.09
0.04
3.14
0.07
5.23
0.14 10.45
0.21 15.68
0.28
20.90
Uni Credit
56.07
0.13
0.03
1.45
0.04
2.18
0.06
3.63
0.13
7.26
0.19 10.89
0.26
14.52
UBS
42.32
0.13
0.03
1.09
0.04
1.63
0.06
2.72
0.13
5.45
0.19
8.17
0.26
10.90
New York Mellon
10.15
0.11
0.02
0.22
0.03
0.33
0.05
0.55
0.11
1.11
0.16
1.66
0.22
2.21
RBS
98.28
0.07
0.01
1.35
0.02
2.03
0.03
3.39
0.07
6.77
0.10 10.16
0.14
13.54
Dexia
25.24
0.06
0.01
0.31
0.02
0.46
0.03
0.76
0.06
1.53
0.09
0.12
3.06
4.68
6.34
0.58
2
2.29
Network Statistics –Scaling exponent (alpha)
for outdegrees and for flows/exposures : those
with higher connectivity have even higher
liabilities (V1 204 nodes; V2 202 nodes)
Connectivity
Outdegree (V1)
Clustering
0.018
0.48
Flows (V1)
Outdegree(V2)
Flows (V2)
0.013
0.45
Tail
MaxExponent Xmin Likelyhood
2.1
1 -225.806
2.49
7.95 -167.081
2.15
1 -209.727
3.38
7.95 -97.2634
How to stabilize: Superspreader tax
quantified : tax using Evcentrality of each
bank Vi or vi^2 to reduce max eigenvalue of
matrix
Superspreader tax rate
Table 7 Super-Spreader Tax Raised From Top 20 LCFIs (All
columns other than EVC $bns) PTO
Note EVC is Eigenvector Centrality ; Tax % = EVC x alpha;
Tax$s= Tax Rate x Tier 1 Capital
• Super-spreader fund works like an escrow
account; amounts escrowed as in a CCP or by
regulator to be disbursed when default occurs
• Super Spreader Fund lite : Secure funds to
cover max losses of 1st tier (q=1) from any
trigger bank failure
• Full stabilization for λmax < 1, costly implies tax
rates of 77% of Tier 1 capital of Goldman Sachs
etc
Conclusion :Systems are unstable and superspreader taxes aim to mitigate instability
• Too interconnected to fail addressed only if systemic risk from
individual banks can be rectified with a price or tax reflecting the
negative externalities of their connectivity
• Lessons to be learnt : Disease Transmission in scale free networks
(May and Lloyd (1998), Barthelemy et. al : With higher probabilities
that a node is connected to highly connected nodes means disease
spread follows a hierarchical order.
• Highly connected nodes become infected first and epidemic dying
out fast and often contained in first two tiers
• Cold comfort for financial networks as failure of superspreaders
destroys bulk of Tier 1 capital and history as we know it is over !
• Innoculate a few rather than whole population; Strengthen hub;
Reduce variance of node strength in dominant eigenvalue formula
• Changes in eigenvector centrality of FIs can give early warning of
instability causing banks
Ongoing tests and Concluding Remarks
• Derivatives do not complete markets; excessive
use causes tail risk; extant size a threat
• Super spreader tax and fund recommended over
ad hoc breakup of banks
• Can eigenvector centrality based on adjacency
matrix ie. unweighted eigenvector centrality be a
sufficient proxy ?; less information is needed
• Capital for CCPs to secure system stability can
use same calculations
• Further stress tests for robustness of ICE to see
if .0013% capital is sufficient
Other Issues :Do Real World Financial
Networks Satisfy Nash Equilibrium ?
Babus (2009) states that in “an equilibrium network the
degree of systemic risk, defined as the probability that
a contagion occurs conditional on one bank failing, is
significantly reduced”. The premise of too
interconnected to fail is that the failure of a big bank
will increase the failure of another big bank, which we
find to be the empirical characteristic of the network
topology of the derivatives market involving US banks,
indicates that the drivers of network formation in the
real world are different from those assumed in
economic equilibrium models.
Results of Systemic Risk Monitoring
Q1- Q4 2011 for Indian Banking Sector
Table 1: Total Borrowing and Lending for 76 Indian Banks
(Q1,Q2, Q3, Q4 2011; Rs crores) Codes A (PSB); B(Old
Pvt);C(New Pvt); D(Foreign)
MAR
JUNE
TOTAL
BORROWING
322,360
25,819
113,258
169,933
631,370
SEP
TOTAL
LENDING
352,412
35,372
78,591
164,996
631,370
TOTAL
BORROWING
287,780
22,934
126,621
156,646
593,981
DEC
TOTAL
LENDING
344,946
34,578
69,744
144,714
593,981
TOTAL
BORROWING
TOTAL
LENDING
TOTAL
BORROWING
TOTAL
LENDING
PSB
OLD PVT
337721
27276
371072
47720
353002
24698
393493
40449
NEW PVT
154027
82272
143336
98394
FOREIGN
TOTAL
147336
666361
165298
666361
184005
705040
172705
705040
PSB
OLD PVT
NEW PVT
FOREIGN
TOTAL
RBI Funded Sector (Q1-Q4 2011) Top 25 Banks Systemic
Importance Measures : Net Liabilities , Eigen vector
Centrality, Tiering
Banks
C001
A010
C004
A015
C007
A013
A008
A001
A027
A023
A016
A002
A018
C006
A012
D018
C005
A011
A017
A024
A006
C003
B005
A022
A020
Net Position (Rs Crores;+Liabilities, - Assets)
Q1
Q2
Q3
Q4
13553.080 19590.740 28859.910 24564.990
16972.130 15073.100 17886.350 18039.150
-4684.180 -1038.790 5003.490 4619.860
10269.390 9568.660
-1.170 -6306.230
2032.650 5036.800 7628.780 9408.210
6226.400 7769.360 9647.920 9565.900
9851.610 5785.090 5490.330 7636.960
4183.980 4643.230 8728.300 8325.170
972.490 4777.160 7586.210 6146.000
2257.380 2162.780 1511.650 -2618.810
2946.890 2644.700 1544.860 6007.520
4276.630 4983.230 5342.360 5016.420
-44132.990 -43068.050 -20927.530 -18373.800
1835.640 2929.740 7127.080 5527.660
357.970 2274.000 2776.180 5791.040
-2904.000 -3134.930 -4432.480
-980.260
2254.170 5341.930 5369.730 3934.640
-1793.610
-96.030 1995.760 1654.730
5144.420 5227.960 6785.620 3566.400
7836.120 2390.120 6836.660
440.770
9403.200 8945.670 9525.720 -2300.260
457.910 3665.500 4863.870 3680.250
1682.770 2039.060 2367.580 2971.870
1970.450 2796.430 2621.420 2911.610
2375.870 2019.740 2721.100 3191.910
Eigen Vector Centrality (right)
Q1
Q2
Q3
Q4
0.234
0.303
0.501
0.451
0.471
0.401
0.349
0.401
0.148
0.214
0.163
0.323
0.443
0.366
0.168
0.234
0.093
0.105
0.139
0.221
0.099
0.190
0.203
0.199
0.313
0.167
0.093
0.199
0.115
0.159
0.317
0.192
0.115
0.140
0.263
0.176
0.136
0.118
0.121
0.176
0.081
0.085
0.041
0.166
0.125
0.156
0.205
0.153
0.068
0.108
0.088
0.147
0.075
0.085
0.128
0.134
0.062
0.072
0.133
0.122
0.021
0.105
0.000
0.113
0.085
0.152
0.132
0.108
0.042
0.057
0.062
0.094
0.109
0.137
0.233
0.094
0.207
0.099
0.137
0.092
0.231
0.310
0.222
0.092
0.074
0.089
0.091
0.089
0.049
0.059
0.083
0.088
0.032
0.102
0.062
0.084
0.055
0.065
0.090
0.080
Q1
0.817
0.859
0.873
0.901
0.704
0.690
0.761
0.704
0.648
0.704
0.535
0.606
1.000
0.423
0.775
0.620
0.690
0.676
0.535
0.718
0.831
0.845
0.408
0.493
0.521
Tiering
Q2
0.838
0.853
0.912
0.882
0.662
0.750
0.765
0.691
0.721
0.676
0.559
0.662
1.000
0.529
0.809
0.632
0.706
0.735
0.632
0.750
0.853
0.853
0.456
0.559
0.485
Q3
1.000
0.937
0.984
0.968
0.651
0.841
0.778
0.778
0.651
0.762
0.778
0.746
0.952
0.460
0.810
0.667
0.746
0.778
0.603
0.857
0.952
0.968
0.508
0.603
0.619
Q4
1.000
0.800
0.900
0.871
0.686
0.700
0.743
0.671
0.629
0.686
0.500
0.657
0.886
0.471
0.743
0.643
0.643
0.771
0.700
0.714
0.886
0.871
0.500
0.514
0.586
Table 2 RBI Annual Growth (%) in 2011 by 76 Banks
Classified by Bank Type in the Funded and Non-Funded
Sectors
Percentage change over the one year period (March 2011 to December 2011)
Public Sector Banks Old Private Banks New Private Banks Foreign Banks Banking Sector
Fund Based
Borrowings
17.8
22.5
51.9
-18.1
19.9
Non Fund
Based
Borrowings
-12.5
-37.1
-3.4
16.2
1.4
Total
Borrowings
9.5
-4.3
26.6
8.3
11.7
Fund Based
Lending
Non Fund
Based
Lending
Total
Lending
32.5
-11.3
-7.1
3.1
19.9
-24.0
33.2
64.8
5.8
1.4
11.7
14.4
25.2
4.7
11.7
Table 3 RBI: Total Tier 1 Capital and Risk Weighted Assets
for 76 Indian Banks (Q1,Q2, Q3, Q4 2011; Rs crores)
Mar-2011
Jun-2011
Sep-2011
Dec-2011
Tier I RWA Tier I RWA
Tier I RWA Tier I RWA
503567.72 5402595.86 479329.04 4883406.81 488063.41 5096607.27 492639.37 5261735.23
Ratio
0.093
0.098
0.096
0.094
Systemic Risk from Multi-Sector: Funded and Unfunded
Track Max Eigen-Value To see If Network System is More or
Less Unstable ; Some Seasonality Q4 reduction in Instability
Total non sector netting leads to high Instability
FUND
Banks
Q1 Q2
Nodes
76
76
Q3
76
NON - FUND
Q4
76
Q1
76
Q2
76
Q3
76
DERIVATIVES
Q4
76
Q1
76
Q2
76
Q3
76
TOTAL No Cross
sector netting
TOTAL Netted
Q4
76
Q1
76
Q2
76
Q3
76
Q4
76
Q1
76
Q2
76
Q3
76
Q4
76
127
Edges
9 1258 1274 1269 1152 1125 1159 1076 995 981 961 908 1605 1595 1624 1573 1948 1925 1978 1915
Conne
ct
0.22 0.22 0.22 0.22 0.20 0.20 0.20 0.19 0.17 0.17 0.17 0.16 0.28 0.28 0.28 0.28 0.34 0.34 0.35 0.34
CC
0.38 0.40 0.39 0.41 0.40 0.39 0.40 0.40 0.41 0.39 0.40 0.40 0.41 0.41 0.42 0.42 0.52 0.51 0.53 0.54
Eigen
Value 0.32 0.36 0.24 0.38 0.26 0.23 0.23 0.27 0.18 0.18 0.20 0.20 0.66 0.61 0.57 0.64 0.92 0.87 0.82 0.91
Is Basel II criteria far too lenient as
solvency threshold ?
• For the Indian banks for Q4 2011, for
example, the Basel criteria implies that the
median Tc is around 40%
• On average percentage Tier 1 capital they
can lose before declared a failed bank is
46%.
Contagion from Most EVC/ SI Bank : C001 Q4
2011(LHS before Stabilization;
RHS after Stabilization)
Contagion Losses from top 20 Systemically
Important (Eigen-vector centrality) Banks :Total
Banks
C001
C004
A018
D031
C003
A010
D011
A015
D020
A001
A004
A006
A013
A008
D014
C007
D017
D006
A025
A023
Contagion 25% Capital
%C loss = Contagion 6%RWA
EVC(r)
%RWA
Global
n. DB
Global
n. DB
Loss (Rs
Loss(Rs
cr)
cr)
0.35 0.27
195116.8
39.6%
24 287288.2
58.3%
0.34 0.54
103433.1
21.0%
12 120968.2
24.6%
0.31 0.25
80107.17
16.3%
7 248875.9
50.5%
0.30 0.26
42956.94
8.7%
4 270333.1
54.9%
0.28 0.46
33293.35
6.8%
3 118993.8
24.2%
0.26 0.30
33293.35
6.8%
3 275405.3
55.9%
0.22 0.52
25595.52
5.2%
1 137228.5
27.9%
0.20 0.25
24860.58
5.1%
2 18176.84
3.7%
0.18 0.58
21665.42
4.4%
1 248875.9
50.5%
0.16 0.20
15762.16
3.2%
0 15762.16
3.2%
0.16 0.36
21924.74
4.5%
1 90302.43
18.3%
0.15 0.15
10396.85
2.1%
0 12837.97
2.6%
0.15 0.10
11459.66
2.3%
0 11459.66
2.3%
0.15 0.23
11835.92
2.4%
0 11835.92
2.4%
0.12 0.60
28356.22
5.8%
2 67498.46
13.7%
0.12 0.35
11868.24
2.4%
0 12706.82
2.6%
0.12 0.21
8049.73
1.6%
0 23597.42
4.8%
0.11 0.57
16026.55
3.3%
1 74189.87
15.1%
0.10 0.25
9953.73
2.0%
0 12394.85
2.5%
0.10 0.28
17392.21
3.5%
1 17601.8
3.6%
30% Capital
Global
Loss(Rscr
)
41 283061.5
20 119979.2
39 110902
42 86857.98
20 113411.6
42 88469.26
21 83732.85
3 18176.84
39 79802.75
0 15762.16
14 12589.6
2 12837.97
0 11459.66
0 11835.92
10 19021.08
3 12053.01
2 14262.28
11 16026.55
2 12394.85
2 17601.8
n. DB
57.5%
24.4%
22.5%
17.6%
23.0%
18.0%
17.0%
3.7%
16.2%
3.2%
2.6%
2.6%
2.3%
2.4%
3.9%
2.5%
2.9%
3.3%
2.5%
3.6%
38
16
14
12
18
10
10
3
10
0
0
2
0
0
1
2
1
1
2
2
How to stabilize ? Superspreader tax escrow fund: tax
using E-Vcentrality 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 Rs 20,000 crores
Max impact = 4% Tier 1
Capital Loss
0.6
0.5
0.4
0.3
0.2
Tax Fund Rs
36,000 crores
Max impact 0%
0.1
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
0.6
0.7
0.8
0.9
1
ALPHA
C001
C004
A018
D031
C003
A010
D011
A015
D020
A001
A004
A006
A013
A008
D014
C007
D017
D006
A025
A023
Super-Spreader Escrow Fund : Ball Park Figure
Note EVC is Eigenvector Centrality ; Tax % = EVC x alpha;
Tax$s= Tax Rate x Tier 1 Capital
• Super-spreader fund works like an escrow
account; amounts escrowed as in a CCP or by
regulator to be disbursed when default occurs
• Super Spreader Fund lite : Secure funds to
cover max losses of 1st tier (q=1) from any
trigger bank failure
• Full stabilization for λmax < 0.25, costly implies
surcharge rates of 35% of Tier 1 capital of high
EVC banks to cover Rs 36,000 crores
• A small amount of escrow fund of Rs20,000
crores can prevent potential losses of Tier 1
Conclusion :Systems are unstable and
operationalizing of Eigen-vector Pigou Tax aim to
mitigate instability
• Too interconnected to fail addressed only if systemic risk
from individual banks can be rectified with a price or tax
reflecting the negative externalities of their connectivity
• Lessons to be learnt : Disease Transmission in scale
free networks (May and Lloyd (1998), Barthelemy et. al :
With higher probabilities that a node is connected to
highly connected nodes means disease spread follows a
hierarchical order. Knowledge of financial
interconnectivity essential for targetted interventions
• Highly connected nodes become infected first and
epidemic dying out fast and often contained in first two
tiers
• Innoculate a few rather than whole population;
Strengthen hub; Reduce variance of node strength in
dominant eigenvalue formula
Concluding Remarks - contd
• Changes in eigenvector centrality of FIs can give
early warning of instability causing banks
• 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)
References:
2012 (Forthcoming)IMF Working Paper, Monetary and Capital
Markets Department
Systemic Risk From Global Financial Derivatives: A Network
Analysis of Contagion and Its Mitigation With SuperSpreader Tax , Sheri Markose
Multi-Agent Financial Network (MAFN) Model of US
Collateralized Debt Obligations (CDO): Regulatory Capital
Arbitrage, Negative CDS Carry Trade and Systemic Risk
Analysis
Sheri M. Markose, Bewaji Oluwasegun and Simone
Giansante, Forthcoming as a Chapter in Simulation in
Computational Finance and Economics: Tools and Emerging
Applications Editor(s): Alexandrova-Kabadjova B., S.
Martinez-Jaramillo, A. L. Garcia-Almanza, E. Tsang, IGI Global,
August 2012.
http://www.acefinmod.com/CDS1.html
More Readings
Borio, C and M. Drehmann (2009a), “Towards an operational framework for financial
stability: 'fuzzy' measurement and its consequences”, in Banco Central de Chile (ed),
Financial stability, monetary policy and central banking; also available as BIS Working
Papers, no 284.
Craig, B and von Peter, G. (2010) “Interbank Tiering and Money Center banks”, BIS
Working Paper No. 322.
Fricke, D. And T. Lux (2012) “Identifying a Core-Periphery Structure in the Italian Interbank
Market”,Kiel Institute for the World Economy, Mimeo.
Haldane Andrew G (April 2009), “Rethinking the financial network”, Speech delivered at th
Financial Student Association, Amsterdam.
Minski, H. ( 1982) "The Financial-Instability hypothesis: Capitalist processes and the
behavior of the economy", 1982, in Kindleberger and Laffargue, editors, Financial Crises.
http://www.acefinmod.com/CDS1.html
S. Markose , 2012 , 'Too Interconnected To Fail' Financial Network of US CDS Market:
Topological Fragility and Systemic Risk (Online May 2012, Journal of Economic Behaviou
and Organization, JEBO)
Markose, S. (2012) “Systemic Risk From Global Financial Derivatives: A Network Analysis
of Contagion and Its Mitigation With Super-Spreader Tax” IMF Working Paper (Under
review)