GDRR Opening Workshop - Network Connectivity and Implications for Systemic Risk - George Michailidis, August 6, 2019

Network Connectivity and Systemic Risk
Network Connectivity and its Implications for Systemic Risk
George Michailidis
Department of Statistics and the Informatics Institute
University of Florida
SAMSI GDRR Workshop
2019
George Michailidis Network Connectivity and Systemic Risk 1 / 36

Concept of Systemic Risk - I
Systemic risk is the possibility that an event at an entity (ﬁrm, component) level
could trigger severe instability or collapse of an entire system (industry, economy)
(Colloquial deﬁnition)

Concept of Systemic Risk - I
Systemic risk is the possibility that an event at an entity (firm, component) level
could trigger severe instability or collapse of an entire system (industry, economy)
(Colloquial definition)
In the case of a financial system, it leads to widespread instabilities that impair its
proper functioning to the point where welfare and economic growth suffer
materially

Concept of Systemic Risk - II
The risk of experiencing a strong systemic event

Such an event adversely aﬀects a number of systemically important intermediaries
or markets (including potentially related infrastructures)

The trigger of the event could be an exogenous shock outside the system under
consideration

consideration
Alternatively, the event could emerge endogenously from within the system

consideration
Alternatively, the event could emerge endogenously from within the system
The systemic event is strong when the intermediaries concerned fail or when the
markets concerned become dysfunctional (in theoretical terms this is often a
non-linearity or a regime change)

Systemic Risk in Financial Systems
There are, in general, three main forms of systemic risk:
1. contagion risk
2. risk of macro shocks causing simultaneous displacements
3. risk of unraveling of imbalances that have built up over time

(1) Contagion
Usually refers to a supposedly idiosyncratic problem that becomes more
widespread in the cross-sectional dimension, often in a sequential fashion
An example is one bank failure causing the failure of another bank, even though
the second bank initially seemed solvent

(2) Large exogenous shock
It negatively aﬀects a range of intermediaries and/or markets in a simultaneous
fashion
For example, it has been observed that banks are vulnerable to economic
downturns

(3) Unraveling of widespread imbalances
It refers to an endogenous shock that was created over time
Example: a lending boom

Drivers of Systemic Risk in Financial Systems
A variety of market imperfections, including asymmetric information, incomplete
markets, externalities and the public-good character of systemic stability
They lead to a greater fragility of financial systems in comparison with other
economic sectors, because of
the information intensity and inter-temporal nature of financial contracts
the balance sheet structures of financial intermediaries (often exhibiting high
leverage and maturity mismatches) and
the high degree of interconnectedness of wholesale financial activities
The combination of the above market imperfections with the three features of
financial systems paves the way for powerful feedback mechanisms, amplification
and non-linearities

Systemic risk in ﬁnancial systems is a complex phenomenon and developing an
aggregate modeling framework that captures realistic features of ﬁnancial
instability remains a very challenging task

Systemic risk in ﬁnancial systems is a complex phenomenon and developing an
aggregate modeling framework that captures realistic features of ﬁnancial
instability remains a very challenging task
In this talk focus on:
contagion risk and the role of interconnectedness for banks

Contagion Risk and Interbank Markets
Iinterbank markets have been a primary locus of systemic risk in the financial
crisis of 2008.
One channel for contagion is through the physical exposures among banks in
these markets.
e.g., in case of differential liquidity shocks (e.g. through depositor withdrawals or
changes in asset valuations that differ across banks), it is beneficial to lend to
each other rather than hoarding liquid assets
Whenever the overall amount of liquid assets in the system may not be sufficient
to honour all interbank market contracts, contagious bank failures may occur
(Allen and Gale, 2000)
Hence, the benefits of sharing risks amongst banks comes at the cost of contagion
risk

Contagion Risk through Information Assymetries
Another channel for interbank contagion emerges through information problems
that lead to adverse selection phenomena (Flannery, 1996)
e.g., the inability of banks to distinguish between good and bad assets or
counterparties leads them to stop lending and hoard liquidity
It represented a powerful transmission mechanism in 2007-08, that also severely
aﬀected non-banking ﬁnancial institutions (e.g. hedge funds) (Ferguson et al.,
2007, Cifuentes, et al., 2005)

Contagion through Endogenously Emerging Risks
When one bank fails, its knowledge about their borrowers gets destroyed making
bank loans more illiquid
As a consequence, the common pool of liquidity shrinks and the resulting shortage
may cause other banks to fail (Diamond and Rajan, 2005)
As the number of bank failures increases, the value of such illiquid bank assets
goes down (cash-in-the-market pricing), worsening the problems in the banking
system (Acharya and Yorulmazer, 2008)

Contagion Risk and Interconnectedness - I
A fairly large body of economic/ﬁnance literature has emerged in the last 20
years, studying the role of networks in the propagation of shocks and hence their
relationship to contagion risk
For example, Allen and Gale (2000), Upper (2006), Braverman and Minca
(20014) consider network linkages as the result of common holdings or direct
contractual agreements
A second stream of literature, examines linkages through equity returns. For
example, Cont and Wagalath (2013, 2014) examine such correlations during the
ﬁnancial crisis and attribute it to liquidation of large positions by market
participants
De Vries (2005) and Acharya and Yorulmazer (2008) show that if banks hold
stakes in the same companies, bank equities are necessarily interdependent

Contagion Risk and Interconnectedness - II
A third thrust in the literature examines the role that the degree of connectivity
and the topology of the network play in vulnerability/resilience of the banking
(ﬁnancial) system to withstand shocks (Allen and Gale, 2000; Freixas et al., 2000;
Gai et al., 2011; Elliott et al., 2014; Acemoglu et al., 2015; Glasserman and
Young, 2015)

Analysis of Physical and Correlation Networks
Physical networks ← interbank lending
Correlation network ← common asset holdings
Key questions of interest:
How did these two networks behave over time and during the 2008 crisis?
What is their information content and how their structure is correlated to
exogenous shocks?
Implications for systemic risk and macro-prudential dimension of ﬁnancial
supervision

An Accounting Framework for linking the two networks
Leveraging work by Shin (2009) and Elliott et al. (2014)
Soem notation:
yi,k denotes the market value of bank i’s assets including loans to ﬁrms and
households as well as k asset classes (equities, bonds, commodities, etc.)
wi,k is the weight invested in each of the k assets by bank i; k wi,k = 1
xi denotes the total value of liabilities of bank i held by other banks
xi,j is the value of bank i’s liabilities held by bank j
πi,j is the share of bank i’s liabilities held by bank j.
ei indicates the market value of bank i’s equity
di is the total value of liabilities of bank i held by non-banks

Accounting Framework - II
and bank’s i balance sheet identity satisﬁes
k
wi,k yi,k +
j
xj πi,j = ei + xi + di

Accounting Framework - III
So, the vector of interbank debt can be rewritten as
X = ΠX + WY − E − D ⇐⇒ (I − Π)X = WY − E − D
The left hand side represents the interbank market that depends on the market
value of the portfolio of assets held by banks, the market value of bank equities,
and the value of bank liabilities held by non-banks.
The interbank market is dynamic with a high volume of daily trading
On the other hand, D (debt claims on the banking sector by households, mutual
and pension funds, and other non-bank institutions) changes at much slower time
scales (Shin, 2008)
So, changes to D are less likely to drive interbank lending

Accounting Framework - IV
Aggregating across all banks, the balance sheet becomes
and hence
E = WY − D

Accounting Framework - V
Physical Network (I − Π)X = WY − E − D →
directly obtained from transaction data and closely captures liquidity in the
banking system
Correlation Network E = WY − D →
needs to be inferred from market prices, and its behavior is driven by
investors, whereas physical networks are driven by the actions of banks

Constructing Correlation Networks
In such networks, edges correspond to statistical associations between bank equity
returns
Let ri,t = log(
ei,t
ei,t−1
)
Following, Billio et al. (2012) it is customary to ﬁlter the log-returns through a
GARCH(1,1) model
Then, one can construct Pearson correlation, partial correlation (Brownlees et al.,
2018), or partial auto-correlation networks (Billio et al., 2012; Diebold and
Yilmaz, 2014; Basu et al., 2018)

Focus on Partial Auto-Correlation Networks 1
They can be constructed in a pairwise fashion by regression the log-returns of
bank i on its past history and on those of bank j
A better approach is to use a vector autoregression (VAR) model
However, since there are usually more parameters than time points (data), one
needs to resort to regularization
1
Also referred to in the literature as Granger causal networks (see Basu and Michailidis, 2015;
Basu, Shojaie and Michailidis, 2015

Detour: VAR in High Dimensions
The VAR model:
p-dimensional, discrete time, stationary process Xt
= {Xt
1 , . . . , Xt
p }
Xt
= A1Xt−1
+ . . . + Ad Xt−d
+ t
, t i.i.d
∼ N(0, Σ ). (1)
A1, . . . , Ad : p × p transition matrices (solid, directed edges).
Σ−1
: contemporaneous dependence (dotted, undirected edges).
stability: Eigenvalues of A(z) := Ip − d
t=1 At zt
outside {z ∈ C, |z| ≤ 1}.
Key challenge: parameter space grows as O(dp2
).

Estimating VARs through regression
data: {X0
, X1
, . . . , XT
} - one replicate, observed at T + 1 time points
construct autoregression





(XT )
(XT−1)
...
(Xd )





Y
=





(XT−1
) (XT−2
) · · · (XT−d
)
(XT−2
) (XT−3
) · · · (XT−1−d
)
...
...
...
...
(Xd−1
) (Xd−2
) · · · (X0
)





X



A1
...
Ad



B∗
+





( T
)
( T−1
)
...
( d
)





E
vec(Y) = vec(X B∗
) + vec(E)
= (I ⊗ X) vec(B∗
) + vec(E)
Y
Np×1
= Z
Np×q
β∗
q×1
+ vec(E)
Np×1
vec(E) ∼ N (0, Σ ⊗ I)
N = (T − d + 1), q = dp2
Assumption : At are sparse, d
t=1 At 0 ≤ k

Estimates
1-penalized least squares ( 1-LS)
argmin
β∈Rq
1
N
Y − Zβ 2
+ λN β 1
1-penalized log-likelihood ( 1-LL) (Lin and Michailidis, 2017)
argmin
β∈Rq
1
N
(Y − Zβ) Σ−1
⊗ I (Y − Zβ) + λN β 1

VAR in High Dimensions
Under the following regularity conditions
VAR process stable;
restricted eigenvalue (strong convexity) condition that regulates the behavior
of the minimum eigenvalue of X X/T over an appropriately defined cone for
the elements of Aj ’s along the directions of their sparse support;
deviation condition that regulates the behavior of X E ∞;
it is established (see Basu and Michailidis, 2015) that
d
h=1
Âh − Ah ≤ φ(At , Σ ) k (log dp2)/T .
Further, for Gaussian stable VAR models, the restricted eigenvalue and deviation
conditions are satisfied with high probability

Comments on the Consistency Results
Estimation error has two components:
1. φ(At , Σ ) large ⇔ the max eigenvalue M(fX ) of the spectral density of Xt is
large, the min eigenvalue m(fX ) of the spectral density of Xt is small
2. Recall that k log dp2/T: Estimation error for independent data
Estimation error same as i.i.d. data, modulo a price for temporal dependence

Extensions to the basic sparse VAR framework
Other penalties, such as group, sparse group, low rank plus sparse, etc. (Basu,
Shojaie, Michailidis, 2015; Melnyk, Banerjee, 2016; Basu, Li, Michailidis, 2018)
Lag selection through hierarchical VAR models (Nicholson, Matteson, Bien, 2017)
VAR models with local dependence constraints (Schweinberger, Babkin, Ensor,
2017)
VAR-X models with exogenous high-dimensional Z variables -
Xt = AXt−1 + BZt + Et (Lin, Michailidis, 2017)
Change point problems for VAR models (Saﬁkhani, Shojaie, 2017)
Joint estimation of related VAR models (Skripnikov, Michailidis, 2018)
VAR models for count data (Hall, Raskutti, Willett, 2016)
Finite sample bounds for non-stable VAR models with “heavy”-tailed errors
(low-dim regime though, see Faradonbeh, Tewari, Michailidis, 2018)

European Interbank Market and the eMID data set
Data cover the period 2006-2012
For the physical network, use all 212 banks in the data
For the correlation (Granger causal) network, use data for only the 54
publicly traded banks
In the analysis, the 54-bank physical subnetwork is then examined
The eMID interbank market covers about 20% of all transactions in the Eurozone
Analysis broken into the following three subperiods:
1. a pre-crisis period from January 2, 2006 until August 7, 2007 (when the ECB
noted worldwide liquidity shortages)
2. the ﬁrst crisis period (pre-Lehman) from August 8, 2007 until September 12,
2008
3. the second crisis period (post-Lehman) from September 16, 2008 through
April 1, 2009 (when the ECB announced the end of the recession)
4. the third (post-recession) crisis period, from April 2, 2009 through December
31, 2012.

Network Interconnectedness Measures
Both the physical and correlation networks were summarized through a number of
network statistics
1. degree
2. closeness (# of hops between nodes)
3. clustering coeﬃcient (proportion of triangular between banks)
4. eigenvalue centrality (captures hub character of nodes)
5. largest connected component (proportion of banks in the network reachable
by other banks)

Interconnectedness in the Physical Network

Inetrconnectedness in the Correlation Network

Economic Shocks and Network Connectivity
Premise: Markets react to announcements (Faust et al., 2007)
Goal: Aim to compare and contrast, we aim to compare and contrast how shocks
are reﬂected in the stock market and interbank market
Shocks of interest:
ECB interventions (reﬁnancing operations, and other non-conventional
monetary measures)
Announcements by ECB and other market regulators (used data from Rogers
et al., 2014)
Macroeconomic shocks (used data from Scotti, 2014)
Metholodogy: (follows Kilian and Vega, 2011)
Run regressions with the network connectivity measure as the outcome variable
and the shocks variables as the predictors

Summary of ﬁndings
Correlation and physical networks respond diﬀerently to monetary and
macroeconomic shocks
Early in the crisis central banks intervened heavily to promote funding and
market liquidity. Interconnectedness in physical networks adjusts strongly and
quickly to these central bank operations and announcements, revealing
important market characteristics related to interbank trading at short (daily)
horizons.
Conversely, interconnectedness in correlation networks changes little in
response to these events, presumably since these announcements and
interventions have little impact on the factors driving stock returns
In this light, monitoring the response of the interbank market to
announcements and interventions is more valuable to policy makers
interested in monitoring and enhancing interconnectedness among banks

Can Network Topology Characteristics Forecast Economic Activity Measures?
Test through regression models whether interconnectedness measures may serve
to forecast short-term (daily) economic conditions
Correlation and physical networks can identify (and forecast), at the daily
horizon, hard information like industrial production and retail sales
Complementarily, physical interbank trading networks serve to identify
weakening interconnectedness in the interbank system that may lead to
liquidity problems in the wholesale funding market

Concluding Remarks
Monitoring connectivity in ﬁnancial networks can be insightful to policy
makers in understanding systemic risk
However, a modeling framework is needed that delineates information
channels and transmission mechanisms of exogenous/endogenous shocks
Availability of data (with the exception of regulators) is a big challenge to
researchers
Reference: Brunetti, Harris, Mankad and Michailidis (2019), Interconnectedness in
the Interbank Market, Journal of Financial Economics, 133(2), 520-538

GDRR Opening Workshop - Network Connectivity and Implications for Systemic Risk - George Michailidis, August 6, 2019

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GDRR Opening Workshop - Network Connectivity and Implications for Systemic Risk - George Michailidis, August 6, 2019