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Decomposition of systemic risk drivers
in evolving financial networks
Sergio Rubens S. SouzaBanco Central do Brasil – Research Department
The views expressed in this presentation
are those of the authors and do not
necessarily reflect those of the Banco
Central do Brasil.
3Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Introduction
This study has applications in financial networks monitoring. In
this activity, it is essential that systemic risk is correctly
measured and understood.
Motivation: to provide tools to extract richer information on the
contribution of systemic risk sources to systemic risk.
Drivers: network topology (exposures), capital ratios, market
and funding liquidity, nature of shocks (see Gai and Kapadia
(2010), Loepfe et al. (2013), Roukny et al (2013)).
4Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Introduction
We focus on network topology and capital ratios as risk drivers
Regulation has emphasized restrictions over capital ratios of FIs
Contagion literature has emphasized the influence of network topology
They are the basis for many network risk measures proposed by the
literature, that build on a vulnerability matrix. E.g.:
Eisenberg & Noe (2001)’s computation of shock-related losses
Battiston et al. (2012)’s DebtRank
Bardoscia et al. (2015)’s DebtRank with cycles
Silva et al. (2015)’s Impact susceptibility, Network impact fluidity
and Weighted impact diffusion influence.
5Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
What we do
We present a methodology to quantify the influence of the
network topology and capital buffers on systemic risk
measurements in evolving financial networks.
We apply this methodology to analyze global banking network
data from 2005 to 2014, obtained from the BIS-CBS database.
We build counterfactual networks to analyze the influence of isolated
risk drivers.
We decompose the variation of systemic risk measurements along the
period into effects from network topology and capital buffer.
6Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Methodology
Given two financial networks, our methodology consists on
defining transformations that affect one risk driver at a time.
Starting from one of the networks and performing them
sequentially, we reproduce the Vulnerability matrix of the other.
We define: Network topology: Exposures Matrix A = (aij)
Capital buffer: E = (ei )
Vulnerability matrix V (does i propagate default to j?)
7Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Methodology – basics
Let:
Financial network: given by a pair (A, E)
(A, E): initial financial network (from)
(A′, E′): reference financial network (to)
ν: (A, E) → A / E = (aij / ej)
A / E: (aij / ej): vulnerability network
m(A, E): risk measurements that depend only on A / E
8Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Methodology – basics
We define the transformations:
The transformations scale down the levels of the variables of the
reference network to the levels of the initial network total exposures.
Transformations are linear.
9Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Methodology – order of transformations is irrelevant
Consecutive applications of the transformations t and r on the
initial network (A, E) lead to the vulnerability matrix of the
reference network (A′ / E′) regardless of order:
Why this is so:
Transformations t and r are linear
Vulnerability matrix is zero-degree homogeneous in (t, r)
10Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Methodology – decomposing effects of risk-drivers
Order of transformations irrelevant → we can define the effect
of risk drivers as the financial network changes from
(A, E) → (A′ / E′) as:
summing up:
m(A′, E′) - m(A, E) = ΔAm + ΔEm
11Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Methodology – decomposing effects of communities
We extend the methodology to find the effects of groups of
members k;
We define the transformation pk(A, E) as a composition of
transformations tk(A, E) and uk(A, E), similar to t and r;
We show that the order of transformations is also irrelevant:
Thus, the risk variation can be written as:
m(A′, E′) - m(A, E) = 𝑘=1𝑁 ∆𝑘𝑚
12Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Data
Quarterly data on cross-border exposures from the BIS-CBS
database, Mar 2005 – Dec 2014.
Banks’ consolidated positions of worldwide offices, excl inter-office exp
Central banks exposures not informed.
Reporting countries: 26. America, Europe, Asia and Oceania.
Pairwise exposures reported may be:
Immediate borrower basis (claims allocated to the country of the
immediate counterparty)
Ultimate risk basis (claims allocated to whom bears the final risk)
13Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
How we model the financial system network
Pairwise exposures: immediate borrower basis
Our methodology does not support conditional counterparties
Ultimate risk basis: if the guarantor defaults, he is not liable for the
guarantee unless the debtor also fails.
We only consider exposures between reporting countries.
These are 70% of total exposures reported.
We assume this network is a banking system. Each country is
a representative bank.
To estimate the countries’ loss-absorbing capabilities, we use the total
tier 1 capital of the country’s largest banks. We use BvD’s Bankscope.
Medium- and small-sized FIs do not hold significant amount fgn claims.
14Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Risk drivers data
Sep 08 Sep 08 Dec 12Dec 12
15Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Systemic risk measure adopted – intuition
Weighted impact diffusion influence (Silva et al. 2015)
This is a measure of the destructive stress that a country can pose to
the financial system. It is the network members’ vulnerability to
destructive impacts originating or being propagated by the country.
Related to a quantification of default cascade paths from the country.
Computation:
Given the network’s total
communicability, we subtract
from that the communicability
of a network in which q does
not initiate or continue a path.
16Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Systemic risk measures – intuition
Weighted impact diffusion influence (Silva et al. 2015)
It is the network’s communicability shortfall, weighted by the country’s
importance, occurred when q’s power of diffusing impacts is disabled.
Gpq(V) is the communicability p→q (Estrada and Hatano (2008))
17Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Analyses – 2 types
Counterfactual scenarios: fix the reference network at a given
date, varying the initial network along time. Use the initial
network to get the risk driver under study.
What would be the risk evolution had only one risk factor varied along
time? Use this analysis to disentangle effects from different risk drivers
and observe one of them isolated.
Effect decomposition as the network varies along time
How much do individual risk drivers (network topology or capital buffer
distribution) contribute to the evolution of risk measures along time?
18Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Analyses of counterfactual scenarios
How much do network topology and capital buffer
distribution contribute to risk measures along time?
1) Mar 2005 – Dec 2006Fragility increases
2) Mar 2007 – Dec 2009Subprime crisis
3) Mar 2010 – Dec 2012Onset European
sovereign crisis
4) Mar 2013 – Dec 2014Network comparatively
safer
1 23 4
19Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Counterfactual – weighted impact diffusion influence
We fix the reference network at Sep/2008 and check the
effects of network topology alone along time.
Keeping the capital buffer distribu-
tion of Sep 2008, we see that:
• Risk from the US and
European countries increased
fast until Mar 2008.
• Risk from the US kept high
levels until Sep 2010
• Risk from European countries
only decreased significantly
after Dec 2012.
20Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Counterfactual – weighted impact diffusion influence
We fix the reference network at Sep/2008 and check the
effects of capital buffer distribution alone along time.
Keeping the network topology of
Sep 2008, we see that:
• Risk from all countries
decreased fast until Mar 2008.
• After that, risk from all countries
remained mostly constant.
• Exception: risk, for the US and
European countries, increased
until Jun/09.
21Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Effect decomposition – incremental contribution
We compute a period-by-period decomposition of the network
weighted impact diffusion influence into the two risk sources:
More risk than the previous period
Less risk than the previous period
22Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Effect decomposition – incremental contribution
We compute a period-by-period decomposition of the network
weighted impact diffusion influence into the two risk sources:
• Network topology is a more
important volatility contributor
than capital buffer.
• Risk variation from capital buffer
is predominantly negative along
the period.
23Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Effect decomposition
Accumulated effects on network weighted impact diffusion
influence from the two risk sources:
More risk than the first period
Less risk than the first period
24Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
Effect decomposition
Accumulated effects on network weighted impact diffusion
influence from the two risk sources:
• On average, capital buffer
variations have contributed to
reduce risk level compared to
the beginning.
• From Dec 2010, the total capital
buffer increase did not contribute
to reduce risk levels.
• Network topology has been the
main contributor to level
fluctuations.
25Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
To summarize…
We presented a methodology to enhance the network analysis
of financial networks. The methodology allows:
The analysis of the evolution of isolated risk drivers in a given scenario
The quantification of the effects of risk drivers contributions to risk
measures
The quantification of the effects of groups of network members in risk
measures.
26Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
To summarize…
Applying this methodology to the BIS-CBS global claims
networks, we found:
The isolated effects analyses (counterfactual scenario in Sep 2008) show
that prior to the crisis, capital buffers contribute strongly to reducing risks
while exposures increase them. From Sep 2008 onwards, none of the
factors seems, individually, to be able to reduce risk.
The decomposition of systemic risk drivers shows that, after the crisis,
exposures were the main contributor for sharply reducing the systemic risk
measure, in a context in which capital buffers were also varying. Besides,
exposures are responsible for a major share of the risk measure’s volatility,
while capitalization contributed steadily to lowering down the risk measure
level, compared to Mar 2005.
27Decomposition of Systemic Risk Drivers in Evolving Financial Networks
João B Barroso, Thiago C Silva and Sergio R Souza
THANK YOU
Sergio R Stancato de Souza