submitted, 1–41

Financial Network Systemic Risk Contributions∗
NIKOLAUS HAUTSCH1 , JULIA SCHAUMBURG2 and MELANIESCHIENLE3
1

University of Vienna; 2 VU University Amsterdam; 3 Leibniz University Hannover

Abstract. We propose the realized systemic risk beta as a measure of financial companies’ contribution to systemic risk, given network interdependence between firms’ tail risk exposures. Conditionalon statistically pre-identified network spillover effects and market and balance sheet information, we
define the realized systemic risk beta as the total time-varying marginal effect of a firm’s Value-at-risk(VaR) on the system’s VaR. Statistical inference reveals a multitude of relevant risk spillover channels
and determines companies’ systemic importance in the U.S. financial system. Our approach can beused to monitor companies’ systemic importance, enabling transparent macroprudential supervision.
JEL Classification: G01, G18, G32, G38, C21, C51, C63

1. Introduction
The financial crisis of 2007-2009 has shown that cross-sectional dependencies between assets andcredit exposure can cause risks of individual banks to cascade, ultimately substantially threatening
the stability of the entire financial system.1 Under certain economic conditions, company-specificrisk cannot be appropriately assessed in isolation without accounting for potential risk spillover effects from other firms. Indeed, it is not merely the size and idiosyncratic risk of a firm but also its
interconnectedness with other firms that determines its systemic relevance. The latter is a firm’s potential to increase the risk of failure of the entire system – which we denote as systemic risk.2 There∗

We thank Thierry Foucault und two anonymous referees, as well as Tobias Adrian, Frank Betz,
Christian Brownlees, Markus Brunnermeier, Jon Danielsson, Robert Engle, Tony Hall, Simone Manganelli, Robin Lumsdaine, Tuomas Peltonen as well as participants of the annual meeting of theSociety for Financial Econometrics (SoFiE) in Chicago, the 2011 annual European Meeting of the
Econometric Society in Oslo, the 2011 Humboldt-Copenhagen Conference in Copenhagen, the 2012
Financial Econometrics Conference in Toulouse and the European Central Bank high-level conference on “Financial Stability: Methodological Advances and Policy Issues”, Frankfurt, June 2012.
Research support by the Deutsche Forschungsgemeinschaft via the Collaborative Research Center 649 “Economic Risk” is gratefully acknowledged. Hautsch acknowledges research support by
the Wiener Wissenschafts-, Forschungs- und Technologiefonds (WWTF). J. Schaumburg thanks theEuropean Union Seventh Framework Programme (FP7-SSH/2007-2013, grant agreement 320270 SYRTO) for financial support.
1
For a thorough description of the financial crisis, see, e.g., Brunnermeier (2009).
2
Bernanke (2009) and Rajan (2009) stress the danger induced by institutions that are “too interconnected to fail” or ”too systemic to fail”, in contrast with firms that are simply “too big too fail”.

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HAUTSCH, SCHAUMBURG and SCHIENLE

is a broad consensus that any prudential regulatory policy should account for the consequences of
network interdependencies in the financial system. In practice, however, any attempt at transparent
implementation of such a policy must fail, as long as suitable empirical measures of firms’ individual risk, risk spillovers and systemic relevance are not available. In particular, how to quantify
individual risk exposure and systemic risk contributions in an appropriate but parsimonious and empirically tractable way, given the prevailing underlying network structure, remains an open question.
Moreover, there is need for empirically feasible measures that rely only on available data of publicly
disclosed balance sheets and market information but still account for the complexity of the financial
system.
A general empirical assessment of systemic relevance cannot build on the vast theoretical literature on financial network models and financial contagion, as such studies typically require detailed
information on intra-bank asset and liability exposures (see, e.g., Allen and Gale, 2000; Freixas et al.,
2000; Leitner, 2005). Such data are generally not publicly disclosed, and even supervisory authorities
can only collect partial information on inter-bank linkages. Available empirical studies linked to thisliterature can therefore only partially contribute to a full picture of companies’ systemic relevance,as these studies focus on particular parts of specific markets at particular times under particular financial conditions (see, e.g., Upper and Worms, 2004; Furfine, 2003, for Germany and the U.S.,
respectively).3 Furthermore, assessing risk interconnections on the basis of multivariate failure probability distributions has proven to be statistically complex in the absence of restrictive assumptions(see, e.g., Boss et al., 2004, or Zhou, 2009, and references therein). Finally, for banking regulators, it
is often unclear how complex structures eventually translate into dynamic and predictable measuresof systemic relevance.
The objective of this paper is to develop an applicable measure of a firm’s systemic relevance,
explicitly accounting for the company’s interconnectedness within the financial sector. We assesscompanies’ risk of financial distress on the basis of share price information, publicly accessible market data and balance sheet data. Our measure quantifies the risk of distress of individual companies
and of the entire system, using tails of the corresponding asset return distributions. Consequently, itbuilds on extreme conditional quantiles and thus the concept of conditional Value-at-Risk (VaR), a
popular and widely accepted measure of tail risk.4 For each firm, we identify its so-called relevant(tail) risk drivers as the set of macroeconomic fundamentals, firm-specific characteristics and risk
spillovers from other institutions driving the company’s VaR. Such a conditional VaR specification
yields a reliable measure of a firm’s idiosyncratic risk in the presence of network effects. Moreover,detecting which firms an institution is connected with and measuring the strengths of these connections enables us to construct a tail risk network for the financial system. A company’s contribution
to systemic risk is then defined as the effect of an increase in its individual tail risk on the VaR of thefinancial system.
The underlying statistical setting is a two-stage quantile regression approach: In the first step,firm-specific VaRs are estimated as functions of firm characteristics, macroeconomic state variables
and tail risk spillovers of other banks captured as loss exceedances. The major challenge is to shrink
the high-dimensional set of possible cross-linkages between all firms to a feasible number of relevant
3

See also Cocco et al. (2009) on parts of the financial sector in Portugal, Elsinger et al. (2006) for
Austria and Degryse and Nguyen (2007) for Belgium. A rare exception is the unique data set for
India with full information on the intra-banking market studied in Iyer and Peydrió (2011).
4
In principle, our methodology could also be adapted to other tail risk measures such as, e.g., expected shortfall. Such a setting, however, would involve additional estimation steps and complications, probably inducing an overall loss of accuracy in our results, given the limited amount ofavailable data.

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

3

risk connections. We address this issue statistically as a model selection problem in individual institution’s VaR specifications, a problem that we solve in the first step. Specifically, we use a novel Least
Absolute Shrinkage and Selection Operator (LASSO) technique (see Belloni and Chernozhukov,
2011), which allows for identification of the relevant tail risk drivers for each company in a datadriven way. The resulting risk interconnections are represented in a network graph, as illustrated,e.g., in Figure 1 for the system of the 57 largest U.S. financial companies. In the second step, toFig. 1. Risk network of the U.S. financial system schematically highlighting key companies
in the system in 2000-2008. Details on all firms in the system that appear as unlabeled shaded
nodes will be provided later in the paper. Depositories are marked in red, broker dealers ingreen, insurance companies in black, and other firms in blue. An arrow pointing from firm j
to firm i reflects the impact of extreme returns of j on the VaR of i (V aRi ), a connection that
is identified as relevant through the statistical selection techniques presented in the remainder of the paper. VaRs are measured in terms of 5%-quantiles of the return distribution. The
effect of j on i is measured in terms of the impact of an increase of the return X j on V aRi ,given that X i is below its 10% quantile, i.e., i’s so-called loss exceedance. The size of therespective increase in V aRj , given a 1% increase in the loss exceedance of i, is reflected in
the thickness of the respective arrowhead, whereby we distinguish between three categories:
thin arrowheads indicate an increase of up to 0.4, medium sized arrowheads indicate an increase of 0.4-0.8, and thick arrowheads indicate an increase greater than 0.8. The thicknessof the line of an arrow reflects these same categories. If an arrow points in both directions,the thickness of the line corresponds to the larger of the two effects. The graph is constructed
so that the total length of all arrows in the system is minimized. Accordingly, more highlyinterconnected firms are located in the center.
measure a firm’s systemic impact, we individually estimate the VaR of a value-weighted index of
the financial sector as a function of the firm’s estimated VaR while controlling for the pre-identified

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HAUTSCH, SCHAUMBURG and SCHIENLE

1Bank of America

3

AXP

5

JP Morgan

15

Charles Schwab

16

Citigroup

2.0
1.5

1

3
4
5

●
●
●

● 17

0.5

1.0

2

Morgan Stanley

21

0.0

realized systemic risk beta

2.5

3.0

company-specific risk drivers and the macroeconomic state variables. We derive standard errors that
explicitly account for estimation errors that arise in the first estimation step. Additionally, we utilize
bootstrap methods needed for accurate parameter tests in finite samples.
We determine a company as systemically relevant if the marginal effect of the firm’s VaR on the
VaR of the system is statistically significant and nonnegative. In analogy to an (inverted) asset pricing
relationship in quantiles, we call this marginal effect systemic risk beta. It is modeled as a functionof firm-specific characteristics, such as leverage, maturity mismatch and size, while controlling for
macroeconomic conditions and the firm’s network position. Thus, a firm’s marginal systemic impact
can change due to varying market or balance sheet conditions, although its individual risk level might
be identical at different points in time. The total increase in the system VaR due to a change in a firmspecific VaR is obtained as the product of the firm’s systemic risk beta and its VaR. The latter, calledthe ”realized” systemic risk beta, rises with increases in the firm’s VaR. We use it to compare thelevels of systemic importance of different companies and thus rank them across the system.

03/2007

06/2008

Fig. 2. Systemic importance of five exemplary firms in the U.S. financial system at two
points in time before and at the height of the financial crisis, 2008. Systemic relevance isdetermined by the statistical significance and positivity of ”systemic risk betas” quantifying
the marginal increase of the VaR of the system, given an increase in a bank’s VaR, while
controlling for the bank’s (pre-identified) risk drivers. All VaRs are computed at the 5% level
and are by definition positive. We depict the degree of systemic relevance by the size of therespective “realized” version of the systemic risk beta, i.e., the product of the risk beta andthe corresponding VaR of a company, representing the company’s total effect on systemicrisk. Connecting lines are added to graphically highlight changes between the two points intime but do not represent actual evolutionary paths. The size of each element in the graphreflects the size of the VaR of the respective company at each of the two points in time. We
use the following scale: the element is k times the standard size with k = 1 for V aR ≤ 0.05,
k = 1.5 for V aR ∈ (0.05, 0.1], k = 2 for V aR ∈ (0.1, 0.15], k = 3 for V aR ∈ (0.2, 0.25]
and k = 5.5 for V aR ∈ (0.65, 0.7]. Attached numbers inside the figure mark the position of
the respective company in an overall ranking of the 57 largest U.S. financial companies foreach of the two time points.

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

5

Our empirical results reveal a high degree of tail risk interconnectedness among U.S. financial
institutions, network effects that are dominant drivers of firms’ individual risk. Detected spillover
channels can be largely attributed to direct credit or liquidity exposure, although in some cases, they
may also result from common factors, e.g., factors specific to the sector or the business model, which
are not covered by our firm- specific control variables. Generally, these links contain fundamental
information for supervisory authorities but also for company risk managers. Based on the topologyof the systemic risk network, we categorize firms into three broad groups, according to their typeand extent of connectedness with other companies: main risk transmitters, risk recipients and companies that both receive and transmit tail risk. From a supervisory point of view, the second group
has the least systemic impact. Monitoring this group, however, may nevertheless convey important
information on hidden risks and possible threats induced by a high degree of interconnectedness. The
highest attention of supervisory authorities should be directed toward firms that mainly act as risk
drivers or are highly interconnected risk transmitters within the system. These are firms, labeled “toointerconnected to fail”, in the center of the network, but also risk producers at the network peripherythat are linked to only a few heavily connected risk transmitters.
While the systemic risk network yields qualitative information regarding risk channels and theroles of companies within the financial system, estimates of systemic risk betas allow us to quantify
the systemic relevance of individual firms and thus complement the full picture. Ranking companies
based on (realized) systemic risk betas shows that large depositories are particularly risky. After controlling for relevant network effects, these firms have overall the strongest impact on systemic risk
and should be regulated accordingly. Time series patterns of (realized) systemic risk betas indicatethat most companies’ systemic risk contributions sharply increased during the 2007/08 financial crisis, effects that were particularly pronounced for firms that experienced financial distress during thecrisis and are (ex post) identified as clearly systemically risky under our approach. Figure 2 illustrates
the paths of their marginal systemic contributions, as reflected in their systemic risk betas and their
exposures to idiosyncratic tail risk, as quantified by their VaRs. A pre-crisis case study confirms thevalidity of our methodology, as firms such as, e.g., Lehman Brothers are ex-ante identified as highly
systemically relevant. It is well-known that the subsequent failure of this firm indeed had a huge
impact on the stability of the entire financial system. Similarly, the extensive bail-outs of American
International Group (AIG), Freddie Mac and Fannie Mae can be justified, given their high systemicrisk betas and high interconnectedness as of the end of 2007.
The remainder of the paper is structured as follows. Section 2. describes the paper’s links withrelated literature and presents the underlying data. In Section 3., we present the model and the procedure used to estimate individual companies’ VaRs, which are the basis for determining the systemic
tail-risk network structure. The notion of a realized systemic risk beta is formally introduced in
Section 4., and realized systemic risk betas are identified for each firm in an individually tailoredparsimonious partial equilibrium setting. This section also presents the corresponding estimation
procedure and valid inference for a two-step quantile regression setting. Our empirical results arepresented in the form of systemic risk rankings. In Section 5., we validate our model and results. In
particular, in a case study that uses only pre-crisis data, we illustrate that realized systemic risk betas
are effective in predicting the distress and systemic relevance of five large financial institutions thatwere affected by the financial crisis. Section 6. concludes the paper.

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HAUTSCH, SCHAUMBURG and SCHIENLE

2. Literature and data
2.1 RELATION TO THE RECENT EMPIRICAL LITERATURE
Our paper relates to several strands of recent empirical literature on systemic risk contributions.
Building on the concept of VaR, Adrian and Brunnermeier (2011) were the first to model systemicrisk contributions based on balance sheet characteristics. They introduce the so-called CoVaR as afirm’s (conditional) VaR, given that some other firm’s stock return takes a certain benchmark value(e.g., the individual VaR). There are, however, substantial conceptional differences between their approach and ours: The realized systemic risk beta in our approach is the direct marginal effect of anindividual VaR on the VaR of the system. Conversely, CoVaR builds on the marginal effect of the return and is only evaluated at the value of the (pre-estimated) VaR. As returns are below their VaR(q)(1 − q)% of the time5 , the estimated marginal systemic importance of CoVaR tends to systematicallyoverrate firms with lower average returns for identical risk levels. Furthermore, CoVaR can by definition only vary over time through the channel of individual VaRs. Due to multicollinearity, however,it cannot be modeled in terms of firm-specific variables. Thus, changes in firms’ systemic relevanceonly result from variations in underlying macroeconomic factors, while variations in firms’ leverageand interdependence with other institutions have no direct effect. Under our approach, by contrast,
we identify network spillovers as crucial elements in measuring individual risk and in unbiased estimation of systemic relevance. This is illustrated in a robustness study in Subsection 3.3.1. Moreover,the proposed realized systemic risk beta captures variations in firms’ marginal systemic importancedriven by changes in firm-specific characteristics.
Our work also complements papers, such as Acharya et al. (2010), Brownlees and Engle (2012)
and Acharya et al. (2012), that measure a company’s systemic relevance in terms of the size of potential bail-out costs. Such approaches cannot detect spillover effects driven by the topology of therisk network and may tend to under-estimate the systemic importance of highly interconnected companies. While Brownlees and Engle (2012) study an individual firm’s conditionally expected asset
return given distress of the system, we investigate the reverse relation and measure the effect on thesystem given a firm is in financial trouble. Taking complementary perspectives, the two approaches
measure different dimensions of systemic risk. However, as our model is based on economic statevariables and loss exceedances, it automatically adjusts and prevails in distress scenarios under external shocks. This is a clear advantage of our approach compared with pure time series approaches(cp. e.g., White et al., 2010; Brownlees and Engle, 2012). As illustrated in the validity case study
in Section 5.2, the estimated systemic risk betas indicate an increase in systemic relevance of somecompanies earlier than in competing settings.
Our work also augments research of Billio et al. (2012), who present a collection of different systemic risk measures. These measures mainly build on regressions of (conditional) means of returns.
However, assessing and predicting systemic and firm-specific risk requires regression in the (left)
tails of asset return distributions rather than the center. Hence, our approach focuses on extreme
quantiles and thus substantially differs from a correlation type analysis, as in Billio et al. (2012).
Moreover, in contrast to our approach, the latter authors’ determination of causality is based only
on pairwise relations. Such a setting, however, produces misleading results in a high-dimensional
interconnected system, as it is impossible to identify whether one firm drives another or if both are
driven by a third company. Our results are also complementary to network analysis based on volatility spillovers in vector autoregressive systems, for example, Diebold and Yilmaz (2012) and Diebold
and Yilmaz (2013).
5

The VaR(q) is defined as the negative q-conditional return quantile.

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

7

Finally, we contribute to macroeconomic approaches that take a more aggregated view, e.g., theliterature on systemic risk indicators (e.g., Segoviano and Goodhart, 2009; Giesecke and Kim, 2011)or papers on early warning signals (e.g., Schwaab et al., 2011; Koopman et al., 2011).

2.2 DATA
Our analysis focuses on publicly traded U.S. financial institutions. The list of included companies
in Table 1 in the Appendix comprises depositories, broker dealers, insurance companies and otherfirms.6 To assess a firm’s systemic relevance, we use publicly accessible market and balance sheet
data. The forward-looking nature and real-time availability of equity market data serves well in providing an immediate and transparent measure of systemic risk. The advantage of timeliness is evident, even if new financial regulations compel institutions to reveal information on mutual credit
linkages and leverage to supervisory authorities. Currently, however, data on connections between
firms’ assets and obligations is largely proprietary and far from comprehensive, even for supervisors.
Daily equity prices are obtained from Datastream and are converted to weekly log returns. To
account for the general state of the economy, we use weekly observations of seven lagged macroeconomic variables, M t−1 , as suggested and used by Adrian and Brunnermeier (2011) (abbreviations
used in the remainder of the paper are given in brackets): the implied volatility index, VIX, as computed by the Chicago Board Options Exchange (vix), a short term ”liquidity spread”, computed as
the difference of the 3-month collateral repo rate (available on Bloomberg) and the 3-month Treasury
bill rate from the Federal Reserve Bank of New York (repo), the change in the 3-month Treasury billrate (yield3m) and the change in the slope of the yield curve, corresponding to the spread between
the 10-year and 3-month Treasury bill rate (term). Additionally, we utilize changes in credit spreads
between BAA rated bonds and the Treasury bill rate (both at 10 year maturity) (credit), the weekly
equity market return from CRSP (marketret) and the one-year cumulative real estate sector return,
computed as the value-weighted average of real estate companies, available in the CRSP data base
(housing).7 Analyzing the time series properties of the variables reveals that, with the exceptions ofvix and housing, they are stationary. Applying the Engle and Granger (1987) two-step procedure,
however, we find evidence of cointegration between the two variables, which implies that their joint
explanation in the model is stationary and that inference thus remains valid (see Pagan and Wickens,
1989). Therefore, to maintain the comparability of our results with those in the literature, we use thetwo regressors in levels.
To capture characteristics of individual institutions that predict a bank’s propensity to become
financially distressed, C it−1 , we follow Adrian and Brunnermeier (2011) and use (i) leverage, calculated as the value of total assets divided by total equity (in book values) (LEV), (ii) maturity
mismatch, measuring short-term refinancing risk, calculated as short term debt net of cash divided
by total liabilities (MMM), (iii) market-to-book value, defined as the ratio of the market value to thebook value of total equity (BM), (iv) market capitalization, defined as the logarithm of market valued
total assets (SIZE) and (v) equity return volatility, computed from daily equity return data (VOL).

6

Companies are classified into these groups according to their two-digit SIC codes, following thecategorization in Adrian and Brunnermeier (2011), Appendix C.
7
We found that this set of aggregate financial market variables provides sufficient explanatory powerthat is not further increased by additional controls such as, e.g., Fama-French type factors (see Subsection 3.3.1 for details).

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HAUTSCH, SCHAUMBURG and SCHIENLE

The system return is chosen as the return on the financial sector index provided by Datastream. It is
computed as the value-weighted average of prices of 190 U.S. financial institutions.8
As balance sheets are available only on a quarterly basis, we interpolate the quarterly data todaily level, using cubic splines, and then aggregate them back to calendar weeks.9 We focus on 57
financial institutions that existed throughout the period from the beginning of 2000 to the end of
2008, resulting in 467 weekly observations of individual returns. This criterion excludes companies
that defaulted during the financial crisis. The latter are analyzed separately in a shorter sample casestudy.

3. A tail risk network
3.1 DETERMINING DRIVERS OF FIRM-SPECIFIC TAIL RISK
We measure the tail risk of a company with asset return Xti at time t as its conditional Value-at-Risk(i)i(VaR), V aRq,t, given a set of company-specific tail risk drivers Wt :
(i)

(i)

i
Pr(−Xti ≥ V aRq,t|Wt ) = Pr(Xti ≤ Qiq,t |Wt ) = q

(1)

(i)

i
i
with V aRq,t= V aRq,t(Wt ) = −Qiq,t denoting the (negative) conditional q-quantile of Xti .10
The relevant i-specific tail risk drivers are determined out of a large set of potential regressors Wt
containing lagged macroeconomic state variables Mt−1 , lagged firm-specific characteristics Cit−1 ,ji
the i-specific lagged return Xt−1
and influences of companies other than i, E−it = (Et )j6=i . We
capture these network dependencies in terms of so-called loss exceedances, defined (for firm j)
as Etj = Xtj 1(Xtj ≤ Q̂j0.1 ), where Q̂0.1 is the unconditional 10% sample quantile of X j . Hence,company j only affects the VaR of company i if the former is in distress.
We model the conditional VaR of firm i at time t = 1, . . . , T as a linear function of the i-specific(i)
tail risk drivers Wt ,0

V aRqi = W(i) ξiq .

(2)This relation could be estimated using a corresponding linear model in the corresponding return
quantile(i) 0

Xti = −Wt ξiq + εit ,(i)with Qq (εit |Wt ) = 0(3)

if we knew the i-relevant risk drivers W(i) selected from W. Then the estimates ξbiq of ξiq could beobtained from the standard linear quantile regression (Koenker and Bassett, 1978) by minimizing
T

1 X
(i) 0
ρq Xti + Wt ξiq
T





(4)

t=1

8

See Adrian and Brunnermeier (2011), Appendix C, who explicitly show that this variable induces
no inherent endogeneity in the model.
9
For in-sample estimation, this interpolation step captures changes in balance sheet characteristics
in a smoother way than the use of plain data. For forecasting purposes, however, interpolation is notpossible. See Hautsch et al. (2014) for details.
10
Defining VaR as the negative p-quantile ensures that the VaR is positive and is interpreted as aloss position.

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FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

with loss function ρq (u) = u(q − I(u < 0)), where the indicator I(·) is 1 for u < 0 and zero otherwise, and
0 i

i

(i)
V[
aRq,t = Wt b
ξq .

(5)

The relevant risk drivers W(i) for firm i, however, are unknown and must be determined from W in
advance. Appropriate model selection techniques are not straightforward in the given setting, as testsof the individual significance of single variables do not account for the (possibly high) collinearity between the covariates. Similarly, sequences of joint significance tests have too many possible
variations to be easily checked in cases of more than 60 variables. Therefore, we choose the relevant covariates in a data-driven way by employing a statistical shrinkage technique known as theleast absolute shrinkage and selection operator (LASSO). LASSO methods are standard for highdimensional conditional mean regression problems (see Tibshirani, 1996) and have recently been
adapted to quantile regression by Belloni and Chernozhukov (2011). Accordingly, we run an l1 penalized quantile regression and calculate, for a fixed individual penalty parameter λi ,i1eξq = argminξi

T

T
X

p
ρq

Xti + W0t ξi



+λ

t=1

i

K

q(1 − q) X
σ̂k |ξki | ,
T

(6)

k=1

with the set of potentially relevant regressors Wt = (Wt,k )K
k=1 , which are demeaned, componentPT
2
wise variation σ̂k2 = T1
(W
)
,
and
the
loss
functionρq as in (4). The key idea is to selectt,kt=1
relevant regressors according to the absolute values of their estimated marginal effects (scaled by the
regressor’s variation) in the penalized VaR regression (6). Regressors are eliminated if their shrunkenicoefficients are sufficiently close to zero. Here, all firms in W with absolute marginal effects |e
ξ | below a threshold τ = 0.0001 are excluded, and only the K(i) remaining relevant regressors W(i) areretained. Hence, LASSO de-selects regressors that contribute only small amounts of variation. Dueito the additional penalty term in (6), all coefficients e
ξq are generally downwardly biased in finite
samples. Therefore, we re-estimate the unrestricted model (4) only with the selected relevant regressors W(i) , yielding the final estimates ξbiq . This post-LASSO step produces finite sample estimates of
the coefficients ξiq , estimates that are superior to the original LASSO estimates or plain quantile regression results without penalization, which suffer from overidentification problems (see the original
paper by Belloni and Chernozhukov, 2011 for the consistency proof of the post LASSO step).
The selection of relevant risk drivers via LASSO crucially depends on the choice of the companyspecific penalty parameter λi . The larger is the chosen value of λi , the more regressors are eliminated.
Conversely, in case of λi = 0, we are back in the standard quantile regression setting (4) without any
de-selection. For each institution, we determine the appropriate penalty level λi in a completely
data-driven way by using the supremum norm of a rescaled gradient of the sample criterion function,
evaluated at the true parameter value, as in Belloni and Chernozhukov (2011)11 . Consequently, thenumber and set of relevant risk drivers are determined only from the data, without any restrictive
pre-assumptions. For further details on this empirical procedure, see (A5) in the Appendix.
Evaluating the goodness of fit of the resulting conditional VaR specifications requires quantifying
how well the model captures the specific percentile of the return distribution and how well the model
predicts the size and frequency of losses. With respect to the latter issue, it is not sufficient to use
a simple quantile-based modification of the conventional R2 statistic. We therefore consider a VaR
specification as inadequate if it either fails to produce the correct empirical level of VaR exceedancesor the sequence of exceedances is not independently and identically distributed. This ensures that VaR
11

See Step 1 for (A5) in the Appendix for the scaling and the exact formula.

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HAUTSCH, SCHAUMBURG and SCHIENLE

violations today do not contain information about VaR violations in the future and that both occur
according to the same distribution. This can be formally tested using a likelihood ratio (LR) versionof the dynamic quantile (DQ) test developed in Engle and Manganelli (2004) which is described indetail in (A7) in the Appendix. Berkowitz et al. (2011) show that this LR test has superior size andpower properties compared with competing conditional VaR backtesting methods, which dominate
plain unconditional level tests (as e.g. Kupiec (1995)).
Using the LASSO selection procedure described above, we estimate VaR specifications for
q = 0.05 for all individual companies.12 Table 2 provides exemplary V aRi (post-)LASSO regression results for firms in four industry sectors: depositories, insurance companies, broker dealers andothers. We find that the dominant drivers of company-specific VaRs are loss exceedances of otherfirms. In their presence, macroeconomic variables and firm-specific characteristics often do not haveany statistically significant influence and are not selected by the LASSO procedure. In Table 2, forinstance, VaR specifications for Goldman Sachs (GS), Morgan Stanley (MS), JP Morgan (JPM) and
AIG exclusively contain loss exceedances of other firms. The importance of cross-firm effects asdrivers of individual tail risk is confirmed by a joint significance test of the individually selected
loss exceedances E−it and the superiority of resulting VaR forecasts. The latter aspect is analyzed in
Subsection 3.3.
As a result of our estimation procedure, we not only detect “relevant” risk connections but can
assign directions thereof. Selecting E j as a relevant risk driver of V aRi implies a directed link fromj to i. If, in addition, E i significantly affects V aRj , we observe a bi-directional relation, which is,
however, not symmetric13 . Note that our analysis, thus, is not affected by simultaneity biases. For
instance, a highly negative return of company j increases the conditional loss quantile and thus the
VaR of firm i. The latter, however, does not necessarily imply a higher (realized) loss exceedanceof i, as the relationship between a specific conditional quantile and the conditional distribution of
exceedances (for a fixed threshold) is generally unknown. Even if quantiles and exceedances are
positively related, an increase in V aRi may only induce an increase in the expected loss exceedance,
not necessarily in the realized loss exceedance. Consequently, the potential effect of a simultaneity
bias (if it exists at all) is expected to be much weaker than in classical mean regressions and thus canbe safely ignored. We consider it an advantage of our approach that it addresses network dependencies in a parsimonious way, avoiding infeasible treatment of an explicit large system of conditional
quantiles.14
There may be several economic reasons for linkages between two companies – reasons, however, that cannot be empirically identified from publicly disclosed market data.15 By including firmspecific characteristics and macroeconomic state variables in our model, we do, however, preventthat determined identified risk connections result from common (risk) factors. Hence, we rule out thepossibility that tail dependencies are driven, for instance, by periods of high volatility, the flattening
12

Due to the limited number of observations, we refrain from considering more extreme probabilities.
13
For the significance of effects, see Subsection 3.3.1
14
Statistically, it is an open question how to generally handle such a system of conditional quantiles.
In contrast to relations in (conditional) means, it is unclear how marginal q-quantiles constitute thecorresponding quantile in the joint distribution under appropriate independence assumptions. Only inlags, restricted to very small dimensions and under strong assumptions, have solutions been obtained
via CaViAR type structures (see White et al., 2010).
15
Note that a valid empirical classification into different types of linkages would require comprehensive data on the credit and liquidity exposures of firms. Such information, however, is largely not
publicly available.

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

11

of yield curves or declining overall credit quality. Accordingly, the identified risk connections arelikely to be attributable to remaining factors, such as credit or liquidity exposure, business model
commonalities or sector-specific risk factors. In this sense, connections between close competitors
such as Goldman Sachs and Morgan Stanley or the influence of the mortgage company Freddie Mac(FRE) on AIG confirm market evidence.
3.2 NETWORK MODEL AND STRUCTURE
We construct a tail risk network of the system, using individually selected loss exceedances.16 Taking
all firms as nodes in such a network, there is an influence of firm j on firm i, if E j is LASSO-selectedin (6) as a relevant driver of V aRqi . Let E j be the k-th component of W(i) . Then the correspondingicoefficient ξq,kin ξiq marks the impact of firm j on firm i in the network. If E j is not selected as arelevant risk driver of firm i, there is no network arrow from firm j to firm i.
An overview of the identified tail risk connections between all companies (based on VaR specifications with q = 0.05) is provided in Table 3.17 The number of risk connections substantially varies
over the cross-section of companies. To effectively illustrate identified risk connections and directions, we graphically depict the resulting network of companies in Figure 6. The layout of the network is chosen so that the sum of cross-firm distances is minimized. Consequently, the most highly
connected firms are located in the center.
The resulting network topology allows us to distinguish between three major categories of firms:
The first group contains companies with only a few incoming arrows but many outgoing ones; hence,such firms mainly act as risk drivers within the system. These are institutions whose failure may
affect many others, while they themselves would be relatively unaffected by the distress of others.
Such firms should be closely monitored by supervisory authorities, as the failure of such a bank could
have widespread consequences. An example of such a bank is State Street Corporation (STT), oneof the top ten U.S. banks and a firm whose failure would affect financial services companies suchas American Express and Northern Trust (NTRS), Bank of New York Mellon and Morgan Stanley.
Another example is the financial services firm SEI Investments, which has links to various large
institutions such as Bank of America, American Express, Morgan Stanley and the online broker TD
Ameritrade (AMTD).
The second group contains companies that mainly act as risk takers. These companies are notnecessarily systemically risky, but they may suffer severely from the distress of others and should
account for such spillover effects in their internal risk management. According to Table 3 and Figure
6, such firms are primarily insurance companies.
The third group is the largest category. It consists of companies that serve as both risk recipientsand risk transmitters that amplify tail risk spillovers by further disseminating risk into new channels. Due to their role as risk distributors, such companies are key systemic players and should besupervised accordingly. Examples of strongly connected companies in this category are Goldman
Sachs, Citigroup, Morgan Stanley, AON Corporation (AON), Bank of America, American Express
16

In the Bayesian network literature, a network that builds on direct one-step influences constitutes
a so-called Markov blanket, which is assumed to contain all relevant information needed to predict a
node’s role in the network (see Friedman et al., 1997).
17
More extreme probabilities are theoretically feasible but require a larger number of observations
for sufficient statistical precision. We also used alternative thresholds for loss exceedances but foundthat the 10% (unconditional) quantile optimally balances the trade-off between sufficient numbers ofnonzero observations in E−it and sufficiently many extreme losses.

12

HAUTSCH, SCHAUMBURG and SCHIENLE

and Freddie Mac. The latter was particularly affected by the 2008 credit crunch in the mortgage sector. Details on the specific roles of Citigroup and Morgan Stanley within the system are highlighted in
Figure 7. Examples of firms with risk connections with only a few other institutions are Fannie Mae
and AIG. Fannie Mae exhibits significant bilateral risk connections with its main competitor Freddie
Mac. AIG holds significant positions in mortgage backed securities and thus is closely connected toboth Fannie Mae and Freddie Mac. Although the numbers of their relevant risk connections within
the network are limited, such firms can nevertheless critically impact the overall system. In the 2008
financial crisis, the dependence between Freddie Mac and Fannie Mae and their interactions with
AIG had severe systemic consequences.
Figure 8 indicates that it is not sufficient to focus exclusively on sector-specific subnetworks,
as interconnectedness of institutions is widespread between industry sectors. We observe that tailrisks of depositories, insurance companies and other firms are relatively evenly distributed among
all industry groups. Depositories are the most strongly connected industry sector and exhibit theirstrongest connections among themselves. This contrasts with the other industries, where cross-firmconnections within groups are less intense. In addition, broker dealers differ from other industry
categories in that they display a much more concentrated risk outflow.
3.3 ROBUSTNESS

3.3.1 Network model validity
The validity of the network identified is confirmed by four analyses: First, the significance of network effects in the individual VaR specifications are formally tested using a joint significance test of
the individually selected loss exceedances E−it in (2). We conduct this analysis based on a quantile
regression version of the F -test for joint linear hypotheses developed by Koenker and Bassett (1982).
Our results show that the selected tail risk spillovers are highly significant in all but a few cases. See
Table 3 for an overview of all cross-effects. Detailed test results are available from the authors uponrequest.
Second, the importance of including other companies’ loss exceedances as risk drivers for company
i is further supported by comparing the (in-sample) forecast performance of our specifications withcorresponding models of V aRi , using macroeconomic variables only (as in Adrian and Brunnermeier (2011)). According to the employed backtests, specifications allowing for cross-firm dependencies have strong predictive ability and are significantly superior to models that ignore network
linkages. Figure 3 shows the distributions of the backtesting p-values implied by both models. Hence,
inter-company linkages add crucial explanatory power in VaR specifications.
Third, network effects remain important when we alter the set of economic state variables M
by adding asset pricing factors such as the three Fama-French factors and the momentum factor of
Carhart (1997).18 We find that in the presence of network exceedances, these factors are de-selected
in all cases by the LASSO method and thus have no additional explanatory power. Hence, tails ofasset returns are driven by factors other than the equity risk premium (associated with conditional
means of returns).
Finally, our results show that the most significant information about cross-company dependencies
in tail risk is primarily contained in contemporaneous loss exceedances E−it . In contrast, alternative
VaR specifications that utilize contemporaneous returns Xt−j or lagged loss exceedances E−i
t−1 yield
18

The
data
are
downloadedfromthewebsiteofKennethhttp://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

French

at

13

0.6
0.4
0.0

0.2

P−Values

0.8

1.0

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

Makro model

LASSO modelFig. 3. Boxplots of backtesting p-values indicating the in-sample model fit (i.e., testing thenull hypothesis of formal statistical adequacy) of VaR specifications including macroeconomic regressors only (left) and VaR specifications resulting from the LASSO selection procedure (6) (right).
significantly inferior backtest performance, with the regressors mostly found to be insignificant injoint F-tests.19

3.3.2 Accuracy of the LASSO selection step
The firm-specific LASSO penalty parameter λi is a crucial coefficient under our approach, as it determines the denseness of the risk network and influences the selection of control variables whenestimating systemic risk betas in Section 4.. It is chosen in a data-driven way, optimizing a backtest
criterion (see Sections 3.1 and 6.). To validate this model selection step and to assess whether theprocedure prevents overfitting, we analyze the consequences of increasing the LASSO penalty parameter. Note that higher values of λi lead to the selection of smaller models. If our procedure had
a tendency to overfit the tails, the overall goodness of fit would increase for higher values of λi . We
check for this by increasing all penalty parameters by 10% and 20%.20 We show that, based on backtest performance, overall goodness of fit deteriorates substantially. This is demonstrated by the threeboxplots and illustrations of individual p-values in Figure 12. For higher values of λi , the p-values
decrease, and thus statistical support for the null hypothesis of a good model fit declines. Likewise,
joint significance tests do not support the exclusion of additional regressors due to higher penalties.
In particular, newly de-selected regressors are mostly significant (jointly with the selected ones). Thisfinding is confirmed by the Bayesian Information Criterion (BIC) for quantile models proposed by
Lee et al. (2013). As shown in Figure 12, the BIC is increasing, indicating a less favorable model
when the penalty parameter is increased. These evaluations support our choice of penalization andindicate that there is no evidence of a tendency to overfit the tails.

19

The corresponding results are available upon request and are omitted here for brevity.
Increasing the penalties beyond 20% is not advisable because, for some VaRs, no regressors are
selected anymore.
20

14

HAUTSCH, SCHAUMBURG and SCHIENLE

3.3.3 Network characteristics

1.8

In addition to providing a graphical illustration, standard network characteristics provide a morecomprehensive picture of the interconnectedness and the role of each network node in the system.
In Figure 4, we depict firms’ pagerank coefficient (see Brin and Page (1998)), a measure that does
not simply count links but empirically weights their importance in an iterative scheme.21 Confirming
the visual impression based on Figure 6, the most connected firms are Lincoln National Corporation,
AON, Bank of America, TD Ameritrade and Morgan Stanley. The graph also illustrates our abovefinding that depositories tend to have somewhat stronger network effects than other industry groups.
Insurance companies divide into a group of highly connected firms, such as Lincoln National Corp.,
AON and MBI, and a group of less connected companies, such as AIG, Humana Incorp. , Unum
Group (UNM) and Cincinnati Financial Corp.

●

LNC

●

AON
●

●

1.5

●

BAC

●

MBI
●

Page Rank
1.2

●

AFL

TROW

●

●

●

STI

●

●

●

L

CMA HBAN
●

C

●

●

0.9
0.6

●

CINF
CI
●

SNV

●

●

BK

●

BEN

●

●

●

FITB

LM
●

SLM

SCHW
●
HCBK
●

PNC

●

AMTD
●

STT

●

LUK

NYB

ETFC
MI
●

WRB

●

CVH

UNP
●

FNM

0.3

●

FRE

JPM

PBCT
●

●

●

●

●

WFC

●

●

HIG
●
GS
●
HUM
UNM
●
●
HNT ● AIG
MMC

AXP
●

MTB
ZION
●

●

●

SEIC

BBT

RF

CB

ALL
●
PGR
●
CNA
●

EV

NTRS
●

●

●

MS

TMK

●

●

1.5

●

●

●

WFC
CB●
●

Page Rank
1.0

UNM

●

FRE

●

HIG

●

●

●

●

●

MI

FNM

0.0

●

JPM

AIG
MMC
●

NYB● STT

0.5

●

LM● C

PGR

PNC

SCHW

CINF

AXP

FITB
ZION
●

●
●
●

●

RF

BEN
●

●

BAC

MS

TMK

0.0

0.2

0.4

0.6

0.8
5HDOized 6\VWHPLF5LVNBeta

1.0

1.2

1.4

Fig. 4. The upper figure displays pagerank coefficients based on the estimated tail risk network, computed as in Berkhin (2005), with institutions ordered by sector. Below, pagerankcoefficients are plotted against realized systemic risk contributions measured as average realized systemic risk betas according to (8) for all companies classified as systemically relevant,according to Subsection 4.3, for the years 2000-2008. The regression line shows only a small
correlation between the pagerank coefficent and the realized systemic risk beta, a conclusion
supported by the R2 value of 0.0265. Colors and acronyms are as in Figure 1.

21

The idea is to assign to each node (i.e., company) a weight that is increasing in the number ofconnections with other nodes and the relative importance thereof. The more connected a firm is, thegreater is its importance and thus the greater is the importance of its neighbor. The computation of
the pagerank coefficient can be viewed as an eigenvalue problem that can be solved iteratively. For
more details, see Berkhin (2005).

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

15

The degree of firms’ interconnectedness and the specific topology of the network allow for theidentification of possible risk channels in the system. Pagerank coefficients, like other network metrics, however, can only be used to assess the local impact and centrality of firms in the network but
do not allow for a full quantitative assessment of the systemic relevance of a financial institution.
To address the latter issue, we propose the concept of (realized) systemic risk beta, presented in thefollowing section.

4. Quantifying systemic risk contributions
4.1 MEASURING AND ESTIMATING SYSTEMIC RISK BETASIn addition to valuable information on financial network structures, supervisory authorities seek an
accurate but parsimonious measure of an institution’s systemic impact. We quantify the latter as theeffect of a marginal change in the tail risk of firm i on the tail risk of the system, given the underlying
network structure of the financial system. Similarly to a firm’s tail risk, as measured in equation (1),ssystem tail risk is measured as the Value-at-Risk V aRp,tof the system return Xts , conditional oni
V aRq,tand other control variables. We then define the systemic risk beta as the marginal effect offirm i’s VaR on the system VaR given by
(i)

i
s
)
∂V aRp,t(Vt , V aRq,ts|i= βp,q,i∂V aRq,t(7)(i)

where Vt are firm-specific control variables.22 The systemic risk beta can be interpreted by analogy
with an inverse asset pricing relationship in quantiles, where bank i’s q-th return quantile drives thep-th quantile of the system, given network-specific effects and firm-specific and macroeconomic statevariables. We classify the systemic relevance of institutions according to the statistical significances|iof βp,q at a given level and magnitude of their total effects
s|i
s|i
β̄p,q
:= βp,q
V aRti ,(8)

which we refer to as the realized systemic risk contribution. In contrast to the marginal systemic risk
beta, the realized system risk beta captures the full partial effect of an increase in V aRi on V aRts
and is thus cross-sectionally comparable across banks.
s|i
Producing unbiased estimates of a firm’s marginal effect βp,q requires accounting for i-specificcontrol variables in (7). Consequently, for each company i, we estimate an individual quantile regression of V aRs of the form
(i) 0

s
s|i
i
V aRp,t= Vt γ sp + βp,q
V aRq,t
,
(i)

(9)

(−i)

where the vector of regressors Vt = (1, Mt−1 , VaRq,t ) includes a constant effect, lagged macroeconomic state variables and the VaRs of all companies that are identified as risk drivers for firm
i in Section 3.. The resulting specifications are parsimonious, as they contain the minimum set of(i)s|ivariables Vt that are necessary but sufficient to guarantee unbiased estimates of βp,q .23 Therefore,
22

We only study immediate effects of risk shocks of company i on the system and do not infer
further steps. The latter would require additional dynamic modeling, which is beyond the scope of
this analysis.
23
Controlling for the relevant VaRs of other companies precludes simultaneity issues related topotential effects of V aRs on V aRi . Therefore, any remaining “reverse causality” can only stem16

HAUTSCH, SCHAUMBURG and SCHIENLE

variables unrelated to V aRi do not affect firm i’s systemic risk contribution and can be omitted.24
We view this approach as a tractable alternative to a structural equilibrium model, which would require us to address involved specification issues. In addition, even if the latter model were correctly
specified, it would yield imprecise estimates due to the high dimensionality and interconnectednessof the financial system, given limited data availability.
Systemic risk betas in (9) are allowed to be time-varying, accounting for periods of turbulence inwhich not only banks’ risk exposures change, but also their marginal importance to the system mayvary. We model potential time variations of β s|i , using a linear model in lagged observable factors,
Zit−1 , that characterize a bank’s propensity to experience financial distress,
s|i

0

s|i

βp,q,t = β0,p,q + Zit−1 η s|i
p,q ,

(10)

s|i

where η p,q are parameters. Including Zi in lagged form renders systemic risk betas predictable,
which is important for forward-looking monitoring and supervision of the financial system. Imposs|i
ing linearity on βp,q,t in Zit−1 yields stable estimates, given that these factors are updated only quar25
terly.
s|i
The time-varying systemic risk betas βp,q,t are estimated using (9) and (10), with the (unknown)(−i)
VaR quantities V aRit and VaRq,t replaced by the corresponding (post-LASSO) pre-estimatesi(−i)

d q,t from (6).26 Hence,V[aRt and VaR
s|i

i

0

0

i

d
(i)
s
s
Xts = −β0,p,q V[
aRq,t − (V[aRq,t · Zit−1 ) η s|ip,q − V t γ p + εt ,
i

(11)

(i)

s|i
b t , Zit−1 ) = 0. As in Section 3., estimates of all components of βp,q,t
arewhere Qp (εst |V[
aRq,t , V
obtained via a quantile regression minimizing
T

1 X
(i) 0
ρp Xts + Bt ξs
T





(12)

t=1

0

(i)

(i) 0

in the unknown parameters ξs , with Bt ≡ (V aRti , V aRti · Zit−1 , Vt )0 . The resulting estimate ofs|ithe full time-varying marginal effect βbp,q in (10) is then given by
s|i

s|i

0

βbp,q,t = βb0,p,q + Zit−1 η
d
p,q

s|i

,

(13)

from i-specific risk drivers that are not part of our sample but are constituents of the financial system
portfolio. While this possibility cannot be completely neglected, given the composition of our sample,
the remaining companies tend to be relatively small and unimportant. It thus appears quite unlikelythat reverse causality may arise through this channel.
24
See Angrist et al. (2006) for a simple Frisch-Waugh-type argument in quantile regressions.
25
More flexible functional forms (see e.g. Fan et al., 2013) would substantially increase the computational burden and are not easily tractable, given the available data.
s|i
s|i
26
Note that a direct one-step estimation is not feasible, as the individual parameters β0,p,q and η p,q(i)

could not be identified without the additional identification condition Qq (εit |Wt ) = 0, implicitly
bringing back the first-step estimation and model selection step. Moreover, inserting the linear individual VaR (2) into the linear sytem VaR model (9) yields a full model of the system’s tail risk inobservable characteristics. Model selection based on such a full model, however, is infeasible because
correlation effects among the large number of regressors would produce unreliable results.

17

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

for given values Zit−1 . Constant systemic risk betas occur as a special case under the restrics|i
s|i
s|i
s|i
tion η p,q = 0, yielding βbp,q,t = βb0,p,q = βbp,q . An estimate of the realized beta (8) is obtained as
s|i

i

s|i

b̄
[
b
β
p,q,t := βp,q,t V aRt .
The fact that certain regressors are not observed but only pre-estimated has crucial consequences
for statistical inference. The quantile regression asymptotic standard errors obtained with commonlyused software packages based on Koenker and Bassett (1978) are generally too small, as they do notaccount for the pre-step. In contrast to mean regressions, such two-step results are non-standard ina quantile setting and are therefore provided in detail in (A3) in the Appendix. To the best of ourknowledge, these are new to the literature.
4.2 DETERMINING SYSTEMIC RELEVANCE
We determine a firm’s systemic relevance and the potential time variation thereof via formal statisticalsignificance tests. As quantile versions of asymptotic t- or F-tests are not valid in finite samples, andsimple direct bootstrap adaptations yield incorrect results for quantiles27 , we perform finite-samples|iinference for a linear hypothesis H on βp,q,t ∈ ξs based on the test statistic
ST =

min
s

T
X

T
X

(i) 0

ρp (Xts + Bt ξs ) − s minξ unrestrictedξ under H(i) 0ρp (Xts + Bt ξs ),

(14)

t=1

t=1
(i)

where Bt is as defined above, and ξs denotes the corresponding parameter vector.28 Note, however,that the asymptotic distribution of ST involves unknown terms, so that a bootstrap procedure isneeded. Conventional re-sampling techniques remain inconsistent for ST , due to the non-smoothobjective function of the quantile regression. However, we can construct an adjusted “wild-type”
bootstrap method that yields valid inference. This is described in detail in the Appendix above (A9)(compare Chen et al., 2008). For all tests below, we generally consider effects significant if p-values
are below 10%.
We define a company as systemically relevant if an increase in its potential loss position, given
economic state variables and i-specific risk inflows from other companies, entails significantly higher
potential systemic loss. This requires that its systemic risk beta is significant and non-negative.29
s|i
Accordingly, we test for the joint significance of all components of βt , using the hypothesis
s|i

s|i

s|i

s|i

s|i

s|i

H1 : β0 = ηM M M = ηSIZE = ηLEV = ηBM = ηV OL = 0.
27

Generally, asymptotic distributions often only provide a poor approximation of the true distribution of the (scaled) difference between the estimator and the true value when sample sizes are notsufficiently large. In the case of quantile regressions, this effect is even more pronounced, as valid
estimates of the asymptotic variance have poor non-parametric rates and thus require even larger
sample sizes to obtain the same precision.
28
This test is an adaptation to the quantile setting of a method proposed by Chen et al. (2008) for
median regressions.
29
Because we do not impose a priori non-negativity restrictions, systemic risk betas can become
negative at certain points in time. In a few cases, we can attribute these effects to sudden time variations in one of the (interpolated) company-specific characteristics Zit−1 , driving systemic risk betas
temporarily into the negative region. These effects might be reduced by linking β s|i in (10) to (local)
time averages of Zit−1 , which would stabilize systemic risk betas at the cost of a potentially substantial loss of information. We see this as an alternative approach. However, we do not pursue it in thepresent context.

18

HAUTSCH, SCHAUMBURG and SCHIENLE

Testing whether marginal effects on the system are indeed time-varying in firm-specific characteristics implies the joint hypothesis
s|i

s|i

s|i

s|i

s|i

H2 : ηM M M = ηSIZE = ηLEV = ηBM = ηV OL = 0.
s|i

If H2 is not rejected, we re-specify the systemic risk beta as a constant (βt = β s|i ), re-estimate themodel without interaction variables and test the hypothesis H3 : β s|i = 0.
4.3 EMPIRICAL RESULTS AND ROBUSTNESS OF SYSTEMIC RISK BETAS
We estimate systemic risk betas according to the approach described in 4.1, based on q = 0.0530 andusing all firm-specific characteristics as potential drivers of time-variation in systemic risk betas, i.e.,
Zit = Cit . As a consequence, systemic risk contributions of two companies with the same exposure
to macroeconomic risk factors and financial network spillovers may still differ due to their balance
sheet structures.31
Table 4 reports the p-values of the test described in Section 4.2, which is performed using thewild bootstrap procedure (illustrated above (A9) in the Appendix), based on 2, 000 re-samplings ofthe test statistic.32 We find that the majority of firms have a significant time-varying systemic risk
beta. Conversely, for approximately 25% of the firms, systemic risk betas are insignificant. Table 5ranks all systemically relevant companies for the period from 2000 to 2008, according to their average realized systemic risk contributions β̄ˆs|i . The systemically most risky companies are found to be
JP Morgan, American Express, Bank of America and Citigroup. According to our network analysis
above, these firms are strongly interconnected and thus should be closely monitored. Realized systemic risk betas, however, contain information on systemic relevance beyond a company’s network
interconnectedness. This is illustrated in Figure 4, which reveals only slightly positive dependencies
between pagerank coefficients and realized systemic risk betas. With an R2 of just 2%, this relationship, however, is not very strong. Hence, firms’ interconnectedness is not sufficient to assess theirsystemic relevance.
As a first rough validity benchmark of our assessment, we compare our results with the outcomesof the Supervisory Capital Assessment Program (SCAP), conducted by the Federal Reserve in thespring of 2009, just after the end of our sample period. While we rely exclusively on publicly available market data, the Fed could draw on extensive non-public confidential balance sheet informationthat reveals credit and other risk interconnection channels among the 19 largest U.S. bank holding companies.33 The financial institution with the most severe shortcomings with respect to capital
buffer, according to the SCAP, was Bank of America, which ranks among our most highly systemically relevant companies, leading the ranking in June 2008 (Table 6 b). In addition, we identify six
30

As we set p = q, we suppress the quantile index.
Note that we keep the set of regressors M parsimonious, as described in Section 2.2 and justified
in Subsection 3.3.1.
32
Because of multi-collinearity effects, the interpretation of individual coefficients η might be misleading. Therefore, we refrain from reporting corresponding estimates.
33
For details on SCAP, see Federal Reserve System (2009). To determine requested individual capital buffers under different market scenarios, the Fed’s measure of systemic relevance uses proprietary information regarding risk interconnections. According to Huang et al. (2010), the two network
based evaluations should be related, as companies with the highest detected systemic relevance in
2000-2008 should carry the highest shares of hypothetical loss insurance premia. Consequently, theyshould face the highest requested increases in individual capital buffers in 2009.

31

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

19

of eight banks in our database that, according to the SCAP results, were threatened by financial distress under more adverse market conditions.34 These results confirm the usefulness of our approachin detecting systemically risky companies and as a monitoring tool for supervisory agencies. For a
more detailed validity study, see the next section below. Additionally, statistical robustness checks ofan adapted realized systemic risk beta in a forecasting setting are provided in Hautsch et al. (2014).
To illustrate the time evolution of systemic risk betas, we show systemic risk rankings at two
selected points in time: Table 6a provides the systemic risk ranking for the last week of March 2007,
which was a relatively ”calm” time before the start of the financial crisis. Table 6b, on the other
hand, shows the ranking at the end of June 2008, shortly before the collapse of Lehman Brothers.
Comparing the pre-crisis and crisis rankings, we observe that systemic risk betas generally increased
during the crisis, a trend that is particularly pronounced for American Express, Bank of America, JP
Morgan, Regions Financial and State Street. Exceptions are Citigroup and Morgan Stanley.
During the crisis, we detect Bank of America (BAC) as systemically most relevant. Among all
systemically relevant companies, it is also the most interconnected firm, according to the pagerankcoefficient in Figure 4, mutually influencing and influenced by other companies in the center of the
network (see Table 3). Figure 9 shows that BAC’s systemic risk beta was relatively stable before
the financial crisis but fell significantly following implementation of the Federal Reserve’s rescue
packages. Its realized systemic risk contribution, however, strongly increased during the crisis, adevelopment that can mainly be attributed to network effects. 35 This is, for instance, in contrast to
AIG, where network effects entering through increases in other firms’ VaR’s play a secondary role
during the crisis period. AIG’s systemic relevance, however, rapidly declined from the beginningof 2008 until its government bailout (see Figure 9). Here, market data appear to have incorporated
bail-out information into the systemic risk beta well in advance, making both systemic risk betas andrealized betas appear to be forward-looking.36
s|i
By construction, realized systemic risk contributions vary over time through both βt and V aRti .
For selected companies, these effects are schematically depicted before and during the crisis in Figure
2 in the introduction. As for BAC, in many cases, as shown in Table 6, we observe increases ofrealized systemic risk contributions that are mainly due to rising individual VaRs, while companies’
marginal contributions to the system VaR generally remain unchanged (see, e.g., American Express).
In most of these cases, the strong increase in VaR can mainly be attributed to tail risk spillovers in
the network (see also Table 2).
In several cases, increasing individual VaRs coincide with rising systemic risk betas. The mostpronounced effect can be observed for Wells Fargo, which was not even identified as systemically
relevant in 2007 but subsequently experienced a dramatic increase in both its systemic risk beta andits idiosyncratic tail risk, rendering it highly systemically risky in 2008. Other examples include
State Street, Progressive Ohio and Marshall & Isley. Here, direct sources of increasing systemic
relevance can only be partially found in the network structure (see, e.g., State Street, which does
not face significant risk spillovers from other companies but has high systemic relevance). For twocentral nodes in the network, Citigroup and Morgan Stanley, however, declining systemic risk betas

34

We detect Citigroup, FifthThird Bancorp, Morgan Stanley, PNC, Regions Financial and Wells
Fargo as systemically relevant. Due to a lack of data, we cannot include in our analysis KeyCorp and
GMAC, which have also been found to be financially distressed in critical macroeconomic environments.
35
The detailed BAC results for the post-LASSO coefficients in Table 2 are omitted for the sake ofbrevity but are available upon request.
36
For details on the USD 150 billion rescue packages from the Federal Reserve, see Schich (2009).

20

HAUTSCH, SCHAUMBURG and SCHIENLE

overcompensate for increasing VaRs, resulting in overall declining systemic relevance. Similarly to
AIG, for these firms, network effects play a minor (direct) role.
The above results show that realized systemic risk contributions conveniently condense information on banks’ systemic importance, although the underlying forces driving variations in banks’systemic relevance can be quite different. Therefore, simultaneously analyzing and monitoring (i)network effects, (ii) sensitivity to micro- and macroeconomic conditions, and (iii) time-variations insystemic risk betas provides a complete picture of companies’ specific roles in the network and thusbuilds a solid basis for supervisory authorities to monitor systemic risk.

5. Model validation
5.1 A SIMPLISTIC BENCHMARKIn this subsection, we illustrate the advantage of our two-step quantile regression approach comparedwith a one-step estimation of a ’global’ model of the system VaR. Under the two-step approach, we
model the system VaR as a function of all companies’ loss exceedances and the set of macroeconomic
state variables37 , i.e.,(s) 0s
V aRp,t= α1s + Et
(s)

(s) 0

αs2 + Mt−1 αs3 ,

(15)

(s)

where Et and Mt−1 are sets of loss exceedances and macroeconomic indicators, respectively,
selected by the LASSO method. Positive values of the unkonwn quantile-specific coefficients(α1s , αs2 0 , αs3 0 )0 indicate the degree of systemic relevance of each firm. We use an adaptive version of
the LASSO procedure in (15), employing regressor-specific weights in the penalty.38 This makes theprocedure comparable to the use of firm-specific LASSO penalties in our two-step procedure.
Figure 11 summarizes how the group of systemically relevant companies identified by the simplistic benchmark estimation compares with that determined by the two-step approach reported inTable 5.39 First, there is considerable overlap of companies – mostly large depositories and insurancecompanies (group 1) – found to be systemically relevant under both methods. In particular, 17 of 21
loss exceedances are selected under both approaches. Four remaining firms are identified as relevant
only in the benchmark case (group 2). These firms are relatively small companies that appear to be“overweighted” under the simplistic approach. The fact that they have been selected may indicate
a spurious effect due to co-movements with others. The third group of companies comprises firms
37

LASSO selection in a global system VaR model, based on all institutions’ pre-estimated VaRs,
would yield imprecise results due to the vast amount of pre-estimated regressors and inherent
multicollinearity effects. We therefore do not include individual (pre-estimated) VaRs but loss exceedances.
38
The adaptive LASSO criterion thus minimizes√PTq(1−q)P65

ρq (Xts + α1 + E0t α2 + M0t−1 α3 ) + λ T
w σ̂ |αk |. The weights wk are
k=1 k kcomputed as inverses of the absolute values of coefficients from an unrestricted quantile regression, σ̂k is as in (6), and λ is determined as in Section A.2., where c is chosen via the in-sample VaR
backtest of Berkowitz et al. (2011) (see Section A.3.). For details on the adaptive LASSO, see Wu
and Liu (2009).
39
In the benchmark case, the change in the short-term interest rate (yield3m) was also used as aregressor, in addition to the selected exceedances. The detailed results with the coefficients obtained
are available from the authors upon request.
1
T

t=1

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

21

that are not identified as systemically relevant in the benchmark case but nevertheless have significant positive systemic risk betas. Almost all of these are deeply interconnected with other companies(see Table 3). 40 Hence, a one-step approach to determining the system VaR (15) may provide only
a rough tool that can be used to gain a first impression of systemically relevant firms in a moderately interconnected system. However, as this approach cannot capture network linkages, it tends tosystematically falsely reject systemic relevance of firms that gain importance mainly through theirpositions within the network. Conversely, it is likely to falsely attribute systemic relevance to firms
with insignificant marginal effects when controlling for the network.
5.2 CASE-STUDY: PRE-CRISIS PERIOD
The above study is based on data available over the entire period from the beginning of 2000 to
the end of 2008. Consequently, institutions that defaulted or were taken over by other firms are notincluded. Nevertheless, to validate our findings, we perform a case study by re-estimating the modelfor the time period of January 1, 2000, to June 30, 2007 and including the investment banks Lehman
Brothers and Merrill Lynch.
The use of a shorter estimation period (and thus less data) renders a sharp ranking of companies
less distinct and more difficult to interpret. Therefore, Table 7 categorizes firms into groups according
to quartiles of the distribution of realized systemic risk betas. The group of highest systemic importance consists of AIG, Lehman Brothers, Morgan Stanley, JP Morgan and Goldman Sachs, among
others. “Medium” systemic riskiness is observed for large depositories and investment banks, including Bank of America, Merrill Lynch, Citigroup and Regions Financial but also for the mortgage
company Freddie Mac.
In this case study, we focus particularly on four companies that were massively affected by thecrisis: Lehman Brothers became insolvent on September 15, 2008 and was subsequently liquidated.
Merrill Lynch announced a merger with Bank of America in September 2008, which was executedon January 1, 2009. Freddie Mac is closely connected to the second largest real estate financing
company Fannie Mae and was placed under conservatorship by the U.S. government during thefinancial crisis. Finally, we investigate the systemic riskiness of AIG, which faced major distressduring the crisis and whose bailout was very costly to tax payers. As shown in Table 7 (with thespecific companies marked in bold), all of these firms belong to the group of systemically relevant
firms with high or mid-sized average systemic risk betas.
Table 8 summarizes the results of the network analysis of these four companies, using pre-crisis
data only. We observe that most of these institutions were subject to loss spillovers from directcompetitors. Observe, e.g., the strong interconnectedness of AIG, the mutual link between Freddie
Mac and Fannie Mae and the dependencies between Lehman Brothers and both Morgan Stanley andGoldman Sachs.
Figure 10 shows the time evolution of the realized betas of the four companies under investigation.
The exemplary case of Merrill Lynch shows that, over a longer time horizon, the network based
idiosyncratic VaR gradually decreased, despite the firm’s increasing systemic importance, with its
realized risk beta rising by more than 100% between mid-2006 and mid-2007. Moreover, Figure 5
shows that the overall high systemic relevance of Lehmann and AIG can be attributed to very different
time evolutions of their realized systemic risk betas well in advance of the crisis. While the systemic
relevance of Lehman brothers grew almost monotonically towards the beginning of the crisis, therealized beta of AIG was already high around 2005. At this time, the company was already highly40

We categorize a company as deeply connected if it has six or more incoming and/or outgoing risk
links in Table 3.

22

HAUTSCH, SCHAUMBURG and SCHIENLE

0.014

Lehman Brothers
●

0.010

●
●

0.006

●

●

●

●

●
●

●

●

●

2005.5

2006.0●2004.02004.52005.02006.52007.0

AIG
●
●

0.009

●
●

0.005

0.007

●

●
●

●

●

●

●

●

2004.0●2004.52005.02005.5

2006.02006.52007.0Fig. 5. Time evolution of systemic importance in terms of quarterly realized systemic risk
betas in 2004-2007 for two companies, AIG and Lehman Brothers (LEH), that are among
the most systemically risky companies. We depict quarterly averages, reflecting quarterly
observations of balance sheet characteristics, smoothing the exceedance effects in the VaR’s.

leveraged and was even downgraded. If we compare our results to the findings presented in Table 4(page 45 in the Appendix) of Brownlees and Engle (2012), according to their SRISK measure, theyalso find systemic relevance of LEH, FRE and ML. In contrast to their results, however, our measureappears to incorporate important market information substantially more quickly, thus providing abetter forward-looking monitoring tool. Similarly, the high systemic relevance of JPM before thecrisis is detected by SRISK with a significant time delay.
Our findings clearly show that, in June 2007, all four companies were relevant to the stabilityof the U.S. financial system. They indicate that bailouts during the crisis were justified for Freddie
Mac (and the closely-tied Fannie Mae) and AIG. In addition, a failure of Merrill Lynch would have
had harsh systemic consequences that could be prevented by its merger with Bank of America in2008. Second, the increasing systemic importance of Lehman Brothers could have been monitored,
and thus, the impact of its bankruptcy could have been anticipated in some degree. The direct bidirectional linkage of Lehman Brothers to JP Morgan as well as the connections to Morgan Stanley
and Goldman Sachs, which in turn are deeply interconnected, indicate a high risk of contagion in theevent of Lehman’s failure. Furthermore, our estimates show that Lehman’s systemic risk contribution
is only slightly lower than that of AIG, while it is substantially higher than that of, e.g., Freddie Mac.
Given these results, bailing out the latter but not the former is not necessarily justifiable from asystemic risk management point of view.

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

23

6. Conclusion
The global financial crisis of 2007-2009 has demonstrated the need for an improved understanding ofsystemic risk. Particularly in situations of distress, it is the interconnectedness of financial companies
that plays a major role but challenges quantitative analysis and the construction of appropriate risk
measures.
In this paper, we propose a measure of firms’ systemic relevance that accounts for dependence
structures within the financial network, given market externalities. Our analysis allows us to statistically identify relevant channels of potential tail risk spillovers between firms, where such channels constitute the topology of the financial network. Based on these relevant company-specific risk
drivers, we measure a firm’s idiosyncratic tail risk by explicitly accounting for its interconnectedness
with other institutions. Our measure of a company’s systemic risk contribution quantifies the impact
on the risk of distress of the system as a whole induced by an increase in the risk of an individual company in a network setting. Both measures exclusively rely on publicly observable balance
sheet and market characteristics and can thus be used in prudent supervisory decisions in a stress test
scenario.
Our empirical results show the interconnectedness of the U.S. financial system and clearly markchannels of relevant potential risk spillovers. In particular, we classify companies into major risk
producers, transmitters or recipients within the system. Moreover, at any specific time, firms can beranked according to their estimated contribution to systemic risk, given their roles and positions in
the network. Monitoring companies’ systemic relevance over time thus allows us to detect those firmsthat are most central to the stability of the system. In a case study, we highlight that our approach
could have served as a solid basis for a sensible forward-looking monitoring tool before the start of
the financial crisis in 2007.
Our approach is readily extendable in several directions. In particular, although the financial system is dominated by the U.S, it truly is a global business with many firms operating internationally.
Detecting inter- and intra-country risk connections and measuring firms’ global systemic relevanceshould be straightforward under our proposed methodology. Moreover, whenever additional (firmspecific or market-wide) information becomes available, as, e.g., when new information is reported tocentral banks, it can be directly incorporated into our measurement procedure. The data-driven selection step of relevant risk drivers then determines whether and how such information would increase
the precision of results.

Appendix
ECONOMETRIC METHODOLOGY

Asymptotic results for two-step quantile estimation
Under the adaptive choice of the penalty
q parameter, as described in the text, the LASSO selection

method is consistent with rate OP ( K(i)log(max(K, T )) and with high probability the coeffiT
cients selected from W contain the true coefficients in finite samples. These results follow directlyfrom Belloni and Chernozhukov (2011). Furthermore, V aRi is consistently estimated, using thepost-LASSO method described in the text, which re-estimates the unrestricted model with W(i) . In24

HAUTSCH, SCHAUMBURG and SCHIENLE

particular, for all q ∈ I, with I ∈ (0, 1) compact,iξ̂q − ξiq ≤ OP (rK(i)
log(max(K, T ))),T(A1)

as, in our setting, it is safe to assume that the number of wrongly selected components of W is
stochastically bounded by the number K(i) of components of W contained in the true model ofV aRi (see equation (2.16) in Belloni and Chernozhukov (2011)). Slightly abusing notation, we
write YT ≤ OP (rT ), with YT either OP (rT ) or even oP (rT ) for any random sequence YT anddeterministic rT → 0. Note that, in general, for T → ∞, both K and K(i) might grow only very
slowlyqin T , such that they can be treated nearly as constants, implying the standard oracle bound)OP ( log(T) in (A1).
T
If the true model is selected, we find, for the asymptotic distribution of the individual VaR estimates for any q ∈ [0, 1],41

r 
1 i
T

ξ̂q − ξiq

0


→N

q(1 − q)0
E[W(i) W(i) ]−10, 2 −1g (G (q))


,

(A2)

where g(G−1 (q)) denotes the density of the corresponding error εi distribution at the qth quantile.
This result is standard (see Koenker and Bassett, 1978). For the second step estimates, we derive theasymptotic distribution analogously to the two-step median results in Powell (1983)

r

0
K(i)
s|i
s|i
s 0
s|i
s
(β̂0,p,q , η̂ s|ip,q , γ̂ p ) − (β0,p,q , η p,q , γp )
T




→N

0, Q−1 E





(A3)


p(1 − p)p(1 − p) s|i 0
s
ρ
(ε
)
−
β
ρp (εit ), ρvp (Zt−1 εit )pt
f 2 (F −1 (p))
g 2 (G−1 (p)) p,q


,

(A4)

where in the scalar factor, f (F −1 (p)) is the density of the corresponding error εs at the pth quantile,
s|i
s|i
s|i
the function ρvp of a vector applies ρp to each of its components, and βp,q = (β0,p,q , η p,q ). The0(i)0remaining main part Q in the variance is given by Q = H E[AA ]H with A = (W , vec(Zt−1 ·0W(i) ), VaR(−i) ). Denote by I and 0 identity and null matrices, respectively, and by 1 a vector ofones of appropriate dimension. Then,diag(ξiq,2 )0···0······0···0diag(ξiq,1 )···0······0··· 0H0 = 
00diag(vec(1dz · ξiq )) · · · 0 · · ·  ,I0···0······0··· 00···0···
Id(−i) ×d(−i)





(−i)

where dZ is the dimension of Z, which is 3 in our application, d(−i) is the dimension of VaRt , andcoefficients ξiq,2 are the components of ξiq for regressors that appear both in the first and second step.
Correspondingly, ξiq,1 are coefficients of regressors that appear only in the first step of the individual
VaR regression. Note that in the variance matrix, there is a distinction in γ for parts of V that are also(−i)
controls in V aRi and VaRt , which only appear in V aRs .

41

Required assumptions of Belloni and Chernozhukov (2011) and quantile analogies to Powell(1983) are fulfilled in our setting.

25

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

Choice of the company-specific LASSO penalty parameter λi
We determine λi in a data-driven way following a bootstrap type procedure, as suggested by Belloni
and Chernozhukov (2011):
Step 1 Take T iid draws from U[0, 1] independent of W1 , . . . , WT denoted as U1 , . . . , UT . Conditional on observations of W, calculate the corresponding value of the random variable,
T
1 X Wt,k (q − I(Ut ≤ q))p.
1≤k≤K Tσ̂k q(1 − q)t=1

Λi = T max

Step 2 Repeat step 1 for B=500 times, generating the empirical distribution of Λi , conditional on W
through Λi1 , . . . , ΛiB . For the confidence level α ≤ 1/K in the selection, set
λi = c · Q(Λi , 1 − α|Wt ),
i

(A5)
i

where Q(Λ , 1 − α|Wt ) denotes the (1 − α)-quantile of Λ , given Wt and where c ≤ 2 isa constant.
The choice of α is a trade-off between a high confidence level and a corresponding high regularization
bias from high penalty levels in (6). As in the simulation results in Belloni and Chernozhukov (2011),
we choose α = 0.1, which suffices to obtain optimal rates of the post-penalization estimators below.
Finally, the parameter c is selected in a data-dependent way, such that the in-sample predictive abilityof the resulting VaR specification is maximized. (Belloni and Chernozhukov, 2011 proceed in asimilar way). The latter is evaluated in terms of its best backtesting performance, according to theprocedure described in Subsection 6. below.

Backtest for the model fit for V aRi
As suggested by Berkowitz et al. (2011), for each institution i, we measure VaR exceedances asi
Iti ≡ I(Xti < −V aRq,t). If the chosen model is correct, then,E[Iti |Ωt ] = q ,(A6)

where Ωt is the information set up to t. The VaR is estimated correctly, if, independently for each dayof the covered period, the probability of exceeding the VaR is q. Similarly to Engle and Manganelli(2004); Kuester et al. (2006); Taylor (2008), we include a constant, three lagged values of It and thecurrent VaR estimate in the information set Ωt . Then condition (A6) can be checked by estimating alogistic regression model
Iti = α + A0t θ + Ut ,iiiiwith covariates At = (It−1, It−2, It−3, V[
aRt−1 )0 . Denote by I¯i the sample mean of the binary response Iti , and define Flog (·) as the cumulative distribution function of the logistic distribution. Then,
under the joint hypothesis

H0 : α = q and θ 1 = · · · θ 4 = 0,
the asymptotic distribution of the corresponding likelihood ratio test statistic isa

LR = −2(ln Lr − ln Lu ) ∼ χ25 .

Pn

(A7)

Here, ln Lu = t=1 [Iti ln Flog (α + A0t θ) + (1 − Iti ) ln (1 − Flog (α + A0t θ))] is the unrestricted
log likelihood function, which, under H0 simplifies to ln Lr = nI¯i ln(q) + n(1 − I¯i ) ln(1 − q).

26

HAUTSCH, SCHAUMBURG and SCHIENLE

Bootstrap procedure for the joint significance test
The asymptotic distribution of the test statistic introduced in Subsection 4.1,
ST = min
s

T
X

ξ ∈Ω0

ρp (Xts − B0t ξs ) − mint=1

ξs ∈RKBTX

ρp (Xts − B0t ξs ),

(A8)

t=1

involves the probability density function of the underlying error terms and is not feasible. Furthermore, bootstrapping ST would directly yield inconsistent results. Therefore, we re-sample from theadjusted statisticST∗ = min
s

ξ ∈Ω0

−

T
X

wt ρp (Xts − B0t ξs ) − min

t=1

T
X
t=1

s
wt ρp (Xts − B0t ξ̂c ) −ξs ∈RKB

T
X

TX

wt ρp (Xts − B0t ξs )

t=1

!
s
wt ρp (Xts − B0t ξ̂ )

,

(A9)

t=1

s

where ξ̂c denotes the constrained estimate of ξs , and {wt } is a sequence of standard exponentiallydistributed random variables, with both mean and variance equal to one. According to Chen et al.
(2008), the empirical distribution of ST∗ provides a good approximation of the distribution of ST .
Thus, if the test statistic ST exceeds some large quantile of the re-sampling distribution of ST∗ , thenull hypothesis is rejected.
The proposed testing method does not require re-sampling of observations but is entirely basedon the original sample. This provides significant gains in accuracy in the two-step regression setting
relative to standard pairwise bootstrap techniques. A pre-analysis shows that this wild bootstrap typeprocedure is valid in the presented form, as any serial dependence in the data is sufficiently capturedby the regressors in the reduced-form relation not requiring block-bootstrap techniques.42

42

Pairwise block-bootstrapping yields block lengths of one, according to the standard procedure of
Lahiri (2001). The results are available upon request.

27

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONSTABLES AND FIGURES
Table 1 Included financial institutions in alphabetical order within sectors
Depositories (21)
BB T Corp (BBT)Bank of New York Mellon (BK)Bank of America Corp (BAC)
Citigroup Inc (C)Comerica Inc (CMA)
Hudson City Bancorp Inc. (HCBK)
Huntington Bancshares Inc. (HBAN)
JP Morgan Chase & Co (JPM)
M & T Bank Corp. (MTB)
Marshall & Ilsley Corp (MI)NY Community Bankcorp (NYB)
Northern Trust Corp (NTRS)
Peoples United Financial Inc. (PBCT)PNC Financial Services Group (PNC)
Financial Corp New (RF)S L M Corp.
State Street Corp (STT)
Suntrust Banks Inc (STI)
Synovus Financial Corp (SNV)
Wells Fargo & Co (WFC)
Zions Bancorp (ZION)

Others (11)American Express Co (AXP)
Eaton Vance Corp (EV)Fed. Home Loan Mortg. Corp (FRE)Fed. National Mortgage Assn (FNM)
Fifth Third Bancorp (FITB)Franklin Resources Inc (BEN)
Legg Mason Inc (LM)
Leucadia National Corp (LUK)SEI Investments Company (SEIC)
TD Ameritrade Holding Corp (AMTD)
Union Pacific Corp (UNP)
Broker-Dealers (7)E Trade Financial Corp (ETFC)
Goldman Sachs Group Inc (GS)
Lehman Brothers (LEH)∗
Merrill Lynch (ML)∗Morgan Stanley Dean Witter & Co (MS)Schwab Charles Corp New (SCHW)
T Rowe Price Group Inc. (TROW)∗

included only in the case study

Insurance Comp. (20)
AFLAC Inc (AFL)
Allstate Corp (ALL)American International Group (AIG)
AON Corp (AON)
Berkley WR Corp (WRB)
CIGNA Corp (CI)C N A Financial Corp. (CNA)
Chubb Corp (CB)Cincinnati Financial Corp (CINF)
Coventry Health Care Inc (CVH)
Hartford Financial (HIG)
HEALTH NET INC (HNT)
Humana Inc (HUM)
Lincoln National Corp. (LNC)
Loews Corp (L)Marsh & McLennan Inc. (MMC)
MBIA Inc (MBI)
Progressive Corp Ohio (PGR)
Torchmark Corp (TMK)
Unum Group (UNM)

HAUTSCH, SCHAUMBURG and SCHIENLE

28(Intercept)
Ex.AIG
Ex.AON
Ex.BAC
Ex.EV
Ex.GS
Ex.HBAN
Ex.HCBK
Ex.MTB
Ex.SCHW
Ex.SEICEx.STT(Intercept)
Ex.C
Ex.JPM
Ex.LM
Ex.MS
Ex.SCHW-0.004-0.091-0.256-0.3070.032-0.042-0.307-0.244-0.1960.024
0.251-0.041-0.1060.445-0.604-0.158-0.634-0.273-0.452-0.269-0.381-0.229-0.174-0.046-0.239-0.014-0.215-0.403-0.282

Fannie Mae
0.003
0.231
0.121

Regions Financial
0.004
0.04
0.086
0.104
0.087
0.064
0.085
0.114
0.1
0.007
0.16

Morgan Stanley
0.003
0.026
0.145
0.145
0.134
0.121
0.136
0.28
0.193
0.116
0.154
0.176

Std. Error
Goldman Sachs
0.004
0.205
0.119
0.111
0.079
0.244

-17.075-0.981-8.298-1.072-2.274-2.998-2.95
0.37-0.661-3.598-2.137-1.9473.221
1.568-16.017-4.036
3.066-4.157-1.179-5.236-2.006-1.611-1.392-3.294-1.485-0.986-12.54-1.17-0.121-1.932-5.096-1.153t-ratio

0.000
0.327
0.000

0.284
0.023
0.003
0.003
0.712
0.509
0
0.033
0.052
0.001
0.118

0.000
0.000
0.002
0.000
0.239
0.000
0.045
0.108
0.165
0.001
0.138
0.325

0.000
0.243
0.904
0.054
0.000
0.249

p-value(Intercept)
Ex.BAC
Ex.BK
Ex.C
Ex.GS
Ex.PNC
Ex.SCHW(Intercept)
Ex.AFLEx.ALL
Ex.BBT
Ex.HIG
Ex.LNC
Ex.NTRS
Ex.SEIC
Ex.UNM
Ex.UNP
repo(Intercept)
Ex.FRE
Ex.MBI
Ex.RF
Ex.TMK-0.035-0.42-0.361-0.145-0.112-0.153-0.181
0.014-0.1060.073-0.351-0.3-0.040-0.229-0.237-0.380-0.253-0.274-0.410-0.019-0.332-0.256-0.296-0.0840.002-0.002-0.243-0.088-0.242
0.031

American Express
0.003
0.408
0.205
0.126
0.139
0.153
0.163
0.114
0.09
0.067
0.159
0.126

JP Morgan
0.003
0.133
0.129
0.22
0.154
0.077
0.118

Torchmark
0.003
0.169
0.207
0.223
0.175
0.135
0.115
0.12
0.179
0.242
0.017

-11.723-1.03-1.757-1.151-0.808-0.999-1.1120.122-1.186
1.09
-2.2
-2.39

-12.963-1.724-1.842-1.729-1.648-3.583-3.472-7.203-1.962-1.237-1.329-0.4830.018-0.015-2.023-0.489
-1
1.78

Value
Std. Error
t-ratio
American International Group-0.0430.003-14.026-0.2010.014-14.033-0.3360.138-2.423-0.4550.051-8.975-0.8130.721-1.127

0
0.303
0.08
0.25
0.42
0.318
0.267
0.903
0.236
0.276
0.028
0.017

0.000
0.085
0.066
0.084
0.199
0.000
0.001

0
0.05
0.217
0.184
0.63
0.986
0.988
0.044
0.625
0.318
0.076

0.000
0.000
0.016
0.000
0.260

p-value(Intercept)
Ex.AFLEx.BAC
Ex.BBT
Ex.BEN
Ex.CINF
Ex.EV
Ex.L
Ex.SEICEx.SLM
Ex.STT
Ex.TROW

Table 2 Exemplary post-LASSO quantile regressions for V aRi with q = 0.05. Regressors were selected by LASSO as outlined in Section 3.1.
Ex.j is the loss exceedance of company j, all other regressors are as in Section 2.2.

(Intercept)
Ex.AMTD
Ex.AON
Ex.BBT
Ex.FITB
Ex.HBAN
Ex.PBCT
Ex.STI
Ex.ZIONBM
VOL-0.049-0.227-1.007

Value(Intercept)
Ex.AIG
Ex.FRE

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

29

Table 3 Tail risk cross dependencies: For each company i, we list direct risk drivers and risk recipients within the network topology. The risk drivers are loss exceedances selected by the LASSO
technique (6) as “relevant” regressors for the V aRi model (q = 0.05) (’Influencing companies’).
Direct risk recipients (’Influenced companies’) are companies for which the loss exceedance of company i appears as relevant via LASSO in their corresponding V aRj .
Name
ETFC
GS
MS
SCHW
TROW
BAC
BBT
BK
C
CMA
HBAN
HCBK
JPM
MI
MTB
NTRS
NYB
PBCT
PNC
RF
SLM
SNV
STI
STT
WFC
ZION
AFL
AIG
ALL
AON
CB
CI
CINF
CNA
CVH
HIG
HNT
HUM
L
LNC
MBI
MMC
PGR
TMK
UNM
WRB
AMTD
AXP
BEN
EV
FITB
FNM
FRE
LM
LUK
SEIC
UNP

Influencing companies

Influenced companies
Broker Dealers
AMTD,GS,MS
AMTD,C
C,JPM,LM,MS,SCHW
BEN,C,ETFC,JPM,LM,MS,SCHW
AIG,AON,BAC,EV,GS,HBAN,HCBK,MTB,SCHW,SEIC,STT
AMTD,BAC,EV,GS,HUM,LNC,ETFC,SEIC
AMTD,GS,JPM,NTRS,TROW
AMTD,MS,GS,JPM
AMTD,BEN,EV,JPM,LUK,NTRS,SEIC,SNV
AON,MBI,MMC,AMTD,AXP,BEN,EV,NTRS,SCHW
Depositories
AON,AXP,C,HBAN,LM,MS,MTB,PBCT,PNC,SEIC,STI,WFC
AXP,BBT,C,CMA,HCBK,JPM,LM,MBI,MS,MTB,PNC,STI,WFC
BAC,FITB,MTB,NTRS,STI,TMK,UNP,WFC
AXP,BEN,CMA,FRE,MTB,RF,TMK,UNP,WFC,ZION
AXP,JPM,MTB,NTRS,SNV,STT,WFC
CMA,JPM,NTRS,SEIC,SNV
BAC,ETFC,FITB,GS,JPM,LNC,LUK,MBI,MTB
BAC,GS,JPM,LUK
AON,BAC,BBT,BK,HBAN,RF,SNV,WFC
AON,PNC,SNV,ZION
AON,LNC,RF,STI,ZION
AON,BAC,CMA,EV,LNC,MS,PBCT,RF,ZION
AON,BAC,MBI,MTB,NYB
MS,MTB
BAC,BK,C,GS,PNC,SCHW
BK,C,GS,SCHW,SEIC,TROW
MMC,TMK
HIG,MMCBAC,BBT,HCBK,NYB,SNV,ZION
AON,BAC,BBT,BK,HCBK,MS,SNV,WFC,ZION,C
BEN,BK,LUK,MMC,SEIC,STT,TROW
AFL,AMTD,BBT,BEN,BK,HIG,MMC,PGR,SCHW,TMK,TROW,LUK,STT
PBCT,WFC
MTB,SLM,WFC,HCBK,PBCT
HBAN,NYB
AON,BAC,CB,NYB,RF
BAC,CMA,STT,TMK,WFC,ZION
BAC,JPM,ZION
AMTD,AON,BBT,FITB,HBAN,PBCT,STI,ZION
AIG,AON,CMA,EV,FITB,HBAN,MBI,SNV,STI,ZION
AON,AXP,FRE,MBI,NYB
AON,AXP,BEN,EV,FITB,MBI
BK,CMA,FITB,MTB,RF,ZION
BEN,BK,CMA,FITB,MTB,TROW
AON,BAC,FITB,LNC,RF,WFC,ZION
AFL,AON,BAC,BBT,FITB,HBAN,RF,ZION,CINF,HUM,UNM,WFC
AXP,NTRS
AXP,BK,NTRS,PNC,MS
BAC,BBT,CB,LNC,MTB,NYB,STI
FITB,PNC,STI,AFL,BAC,BBT,BK,CMA,NYB
BBT,CMA,HBAN,MTB,PNC,RF,STI
AON,RF,FITB,HBAN,LNC,MTB,PNC,SNV,STI
Insurance Companies
ALL,AON,CNA,EV,NTRS,SEIC,STI,TMK,WFC
AXP,CB,EV,PGR,TMK,UNM
FRE,MBI,RF,TMK
FNM,MBI,MS
CB,CNA,L,LNC,TMK
AFL,PGR,TMK,UNM
CMA,HBAN,MBI,MTB,PBCT,RF,SLM,STI,TROW,ZION
AFL,BAC,BEN,CMA,EV,FITB,HBAN,HCBK,LM,MBI,MS,RF,SLM,STI
AFL,L,LNC,PBCT,PGR
ALL,CINF,EV,HIG,L,WFC,WRB
CNA,HNT,HUM,LNC
HNT,HUM,LNC
CB,MBI,STI
AXP,LM
EV,L,LNC,MBI
AFL,ALL,CI,L,LNC,MBI
HUM
SEIC
CB,L,LNC,MI,NTRS,TMK
HUM,LNC,TMK
CI,EV,HUM,LM,LNC,PGR
CI,HUM,LM
CI,HIG,HNT,MS,STI
CI,HNT
CB,CNA,LNC,TMK,UNP
ALL,AXP,CB,CNA,HIG,LNC,UNM,UNP
CI,CNA,EV,HBAN,HIG,L,MS,SEIC,TMK,ZION
ALL,C,CB,CNA,HBAN,HIG,HNT,L,SEIC,STI,TMK,UNM,WFC,CI
AIG,AON,BAC,BEN,CNA,FRE,RF,SLM,TROW
AIG,AON,BEN,C,CINF,HCBK,SLM,CNA,LM
MI,NTRS,PGR,SEIC,TROW,UNM
MI,NTRS,UNM
AFL,ALL,NTRS,WRB
MMC,CB,HNT,WRB
AFL,ALL,BBT,HIG,LNC,NTRS,SEIC,UNM,UNP
AFL,BBT,EV,L,LNC,MI,PNC,AIG,ALL,HIG
AFL,ALL,L,LNC,MMC,STI
TMK,MMC
BEN,CB,PGR
PGR
Others
ETFC,MS,NTRS,SCHW,SEIC,TROW
ETFC,RF,SCHW,TROW
AFL,BAC,BBT,BEN,CINF,EV,L,SEIC,SLM,STT,TROW
BAC,BEN,BK,EV,SLM,STT
AON,AXP,BBT,EV,GS,LM,MBI,NTRS,SLM,SNV,TROW
AXP,EV,LM,MBI,NTRS,TROW,WRB
AFL,AON,AXP,BEN,CB,HBAN,MS,RF,SEIC,SLM,TMK,TROW
AFL,AXP,BEN,CNA,FRE,HNT,LM,LNC,MS,TROW
AON,LUK,RF,SLM,SNV,STI,WFC,ZION
BBT,C,FRE,RF,SNV,STI
AIG,FREFRE
BBT,EV,FITB,FNM,LUK
AIG,MBI,SLM,FNM
AON,BAC,BEN,CINF,EV,GS,HNT,MBI
BAC,BEN,GS,HNT,LUK
C,LM,NTRSC,FITB,FRE,NTRS,TROW
BK,CVH,JPM,LNC,MS
AFL,AMTD,AXP,BAC,EV,LNC,MMC,MS,NTRS,TMK,TROW
BBT,L
BBT,TMK,L30

HAUTSCH, SCHAUMBURG and SCHIENLE

Table 4 Classification of companies with significant and/or time-varying systemic risk betas
according to p-values of the corresponding significance tests. In all cases, the test level is taken
as 10% and firms are in alphabetical order within each category. P-values pH1 for the test on
significance of systemic risk betas in the time period 2000-2008 are depicted in column one(see Hypothesis H1 in Section 4.3). If β̂ s|i is detected as being significant, a second test on
time-variation of β̂ s|i in firm-specific characteristics Zti is performed yielding p-values pH2(see Hypothesis H2 in Section 4.3). For firms with a significant but not a time-varying systemicrisk beta (lower panel on the left, marked with stars), we re-estimate the systemic risk beta
without time-varying interaction terms and test again for its significance. These results (pH3 )are included in parentheses in the second column (see Hypothesis H3 in Section 4.3).
Companies with significant β s|i
Name
pH1
AMERICAN EXPRESS
0.001
AMERICAN INTL.GP.
0.002
BANK OF AMERICA
0.002
CHARLES SCHWAB
0.019
CHUBB
0.017
CIGNA
0.001
CINCINNATI FINL.
0.010
CITIGROUP
0.026
COMERICA
0.016
FANNIE MAE
0.001
FIFTH THIRD BANCORP
0.039
FRANKLIN RESOURCES
0.028
FREDDIE MAC
0.098
HARTFORD FINL.SVS.GP.
0.001
HUDSON CITY BANC.
0.043
HUNTINGTON BCSH.
0.010
LEGG MASON
0.026
LEUCADIA NATIONAL
0.041
LINCOLN NAT.
0.062
M & T BK.
0.033
MARSH & MCLENNAN
0.003
MARSHALL & ILSLEY
0.020
MORGAN STANLEY
0.041
PNC FINANCIAL SVS. GP
0.012
PROGRESSIVE OHIO
0.007
REGIONS FINANCIAL
0.034
STATE STREET
0.054
T ROWE PRICE GP.
0.090
TORCHMARK
0.002
UNION PACIFIC
0.040
UNUM GROUP
0.079
W R BERKLEY
0.007
WELLS FARGO & CO
0.015
ZIONS BANCORP.
0.095
AON*
0.063
E TRADE FINANCIAL*
0.072
JP MORGAN CHASE & CO.*
0.014
NY.CMTY.BANC.*
0.040
SEI INVESTMENTS*
0.014
TD AMERITRADE HOLDING*
0.049

pH2 (pH3 )
0.006
0.000
0.001
0.013
0.015
0.013
0.004
0.066
0.020
0.000
0.021
0.030
0.092
0.001
0.035
0.011
0.060
0.016
0.026
0.021
0.002
0.019
0.095
0.012
0.003
0.029
0.049
0.076
0.001
0.035
0.097
0.037
0.027
0.100
0.192 (0.135)
0.160 (0.233)
0.237 (0.047)
0.132 (0.088)
0.115 (0.025)
0.131 (0.188)

Companies with insignificant β s|i
Name
pH1
AFLAC
0.220
ALLSTATE
0.114
BANK OF NEW YORK MELLON
0.199
BB &T
0.120
CNA FINANCIAL
0.410
COVENTRY HEALTH CARE
0.257
EATON VANCE NV.
0.276
GOLDMAN SACHS GP.
0.667
HEALTH NET
0.371
HUMANA
0.189
LOEWS
0.276
MBIA
0.235
NORTHERN TRUST
0.305
PEOPLES UNITED FINANCIAL
0.105
SLM
0.391
SUNTRUST BANKS
0.213
SYNOVUS FINL.
0.289

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

31

Table 5 Ranking of companies according to average realized systemic risk betas over the years
2000-2008 Q3. Most systemic risk contributions are detected as time-varying in systemic risks|ib̄ are marked by ∗ . The underlying significance tests are perbetas - exceptions with constant β
avformed as described in Table 4. The third column lists relevant risk drivers for the corresponding
firm within the systemic tail risk network. They are determined through the LASSO selection
technique (6) as “relevant” loss exceedances to be included in the corresponding company’s
V aRi -regression.
Rank

Name

b̄s|i · 102βav

influencing companies

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

JP MORGAN CHASE & CO
AMERICAN EXPRESSBANK OF AMERICA
CITIGROUPLEGG MASONREGIONS FINANCIAL
MARSHALL & ILSLEYMARSH & MCLENNAN
MORGAN STANLEYAMERICAN INTL.GP.
PROGRESSIVE OHIOSTATE STREETZIONS BANCORP
FIFTH THIRD BANCORP
NY.CMTY.BANC.
PNC FINANCIAL SVS. GP
FANNIE MAE
FRANKLIN RESOURCESCHARLES SCHWABCHUBBWELLS FARGO & CO
FREDDIE MAC
HARTFORD FINL.SVS.GP.
CINCINNATI FINL.
TORCHMARKUNUM GROUP

1.41∗
1.22
1.01
0.87
0.83
0.72
0.65
0.63
0.62
0.61
0.58
0.55
0.51
0.49
0.49∗
0.47
0.45
0.34
0.33
0.30
0.28
0.19
0.19
0.16
0.12
0.04

BAC,BK,C,GS,PNC,SCHW
AFL,BAC,BBT,BEN,CINF,EV,L,SEIC,SLM,STT,TROW
AON,AXP,C,HBAN,LM,MS,MTB,PBCT,PNC,SEIC,STI,WFC
BAC,ETFC,FITB,GS,JPM,LNC,LUK,MBI,MTB
AON,BAC,BEN,CINF,EV,GS,HNT,MBI
AMTD,AON,BBT,FITB,HBAN,PBCT,STI,ZION„
MMC,TMKMI,NTRS,PGR,SEIC,TROW,UNM
AIG,AON,BAC,EV,GS,HBAN,HCBK,MTB,SCHW,SEIC,STT
FRE,MBI,RF,TMK
AFL,ALL,NTRS,WRB
AXP,NTRS
BBT,CMA,HBAN,MTB,PNC,RF,STI,
AON,LUK,RF,SLM,SNV,STI,WFC,ZION
PBCT,WFC
BAC,CMA,STT,TMK,WFC,ZION
AIG,FRE
AON,AXP,BBT,EV,GS,LM,MBI,NTRS,SLM,SNV,TROW
AMTD,GS,JPM,NTRS,TROW
AFL,L,LNC,PBCT,PGR
BAC,BBT,CB,LNC,MTB,NYB,STI
BBT,EV,FITB,FNM,LUK
CB,L,LNC,MI,NTRS,TMK
CB,MBI,STI
AFL,ALL,BBT,HIG,LNC,NTRS,SEIC,UNM,UNP,
AFL,ALL,L,LNC,MMC,STI32

HAUTSCH, SCHAUMBURG and SCHIENLE

Table 6 Rankings of relevant systemic risk contributions based on estimated realizeds|ib̄ at two specific points in time. In addition, estimated systemic
systemic risk betas βts|ib̄ . Most
risk betas and VaRs are listed, illustrating the different sources of variation in βtsystemic risk contributions are detected as being time-varying in systemic risk betas s|ib̄ are marked by ∗ . The underlying significance tests are perexceptions with constant βtformed as described in Table 4.
a) End of March 2007 (before the beginning of the financial crisis)
Rank

Name

b̄s|i · 102
β2007

β̂2007s|i[V
aR2007

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28

CITIGROUPAMERICAN EXPRESSBANK OF AMERICA
JP MORGAN CHASE & CO.
MORGAN STANLEYLEGG MASONMARSH & MCLENNANREGIONS FINANCIALPNC FINANCIAL SVS. GP
CHUBB
AMERICAN INTL.GP.
FRANKLIN RESOURCESSTATE STREETFIFTH THIRD BANCORPPROGRESSIVE OHIO
NY.CMTY.BANC.
MARSHALL & ILSLEYTORCHMARK
HARTFORD FINL.SVS.GP.
ZIONS BANCORP.
CHARLES SCHWABFREDDIE MAC
LEUCADIA NATIONALCINCINNATI FINL.
FANNIE MAE
UNUM GROUPT ROWE PRICE GP.
LINCOLN NAT.

1.78
1.35
1.16
1.05∗
1.01
0.98
0.83
0.78
0.77
0.74
0.61
0.60
0.51
0.50
0.42
0.41∗
0.40
0.39
0.38
0.26
0.25
0.23
0.19
0.13
0.09
0.23
0.06
0.04

0.263
0.387
0.304
0.265
0.146
0.205
0.222
0.202
0.248
0.240
0.143
0.143
0.114
0.104
0.092
0.090
0.088
0.173
0.099
0.115
0.042
0.057
0.057
0.026
0.019
0.045
0.014
0.010

0.068
0.035
0.038
0.040
0.069
0.048
0.037
0.038
0.031
0.031
0.043
0.042
0.045
0.048
0.046
0.045
0.045
0.023
0.039
0.054
0.060
0.041
0.033
0.050
0.049
0.051
0.043
0.036

i

b) End of June 2008 (during the financial crisis)
Rank

Name

b̄s|i · 102
β2008

β̂2008s|i[V
aR2008

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23

BANK OF AMERICAAMERICAN EXPRESSWELLS FARGO & CO
MARSHALL & ILSLEY
JP MORGAN CHASE & CO.
PROGRESSIVE OHIOLEGG MASONREGIONS FINANCIAL
MARSH & MCLENNANSTATE STREETNY.CMTY.BANC.
PNC FINANCIAL SVS. GP
CHUBB
TORCHMARKCHARLES SCHWABCITIGROUP
MORGAN STANLEYZIONS BANCORP.
UNUM GROUPUNION PACIFIC
HARTFORD FINL.SVS.GP.
FRANKLIN RESOURCES
T ROWE PRICE GP.

2.86
2.78
2.51
2.31
2.22∗
1.97
1.96
1.86
1.76
1.44
1.12∗
1.09
1.07
1.00
0.91
0.90
0.61
0.58
0.34
0.27
0.24
0.17
0.01

0.186
0.278
0.186
0.516
0.265
0.380
0.137
0.107
0.471
0.171
0.090
0.153
0.176
0.177
0.149
0.072
0.074
0.058
0.033
0.047
0.012
0.026
0.001

0.154
0.100
0.135
0.045
0.084
0.052
0.143
0.173
0.037
0.084
0.125
0.071
0.061
0.057
0.060
0.124
0.083
0.100
0.104
0.056
0.201
0.064
0.102

i

33

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

Table 7 Group ranking of systemic risk contributions for the pre-crisis period 2000 to
mid 2007. The upper part, group 1 (’high’), contains companies with significant averages|irealized systemic risk betas in the highest quartile: β̄ˆav · 100 ∈ [0.5, 1.3]. Group 2 referss|iˆ
to the third quartile (’medium’) with β̄av · 100 ∈ [0.03, 0.49] and Group 3 to realizeds|isystemic risk betas lower than the median value (’small’), for which β̄ˆav · 100 < 0.01.
Group 4 includes companies not determined to be systemically risky during the estimation period, i.e., those with insignificant systemic risk betas. Case study companies aremarked in bold.
Systemic risk contributions
Group 1 ’high’Group 2 ’medium’Group 3 ’low’
Group 4Companies
AIG, LEH, MS, JPM, GS,STT, CINF, LM, PBCTFRE, ML, BAC, C, RF, AXP, PNC,CNA, TROW, NTRSFNM, WFC, EV, TMK, BBT, AFL, HUM, MI, CMA, BK,
LNC, ALL, HNT, CB, CVH, SLM, ETFC
AMTD, AON, BEN, CI, FITB, HBAN, HCBK, HIG, L, LUK,MBI, MMC, MTB, NYB, PGR, SCHW, SEIC, SNV, STI, UNM,
UNP, WRB, ZION

Table 8 Summary of estimation and test results for the four case study companies: loss exceedances
influencing each company’s VaR, the most important other VaRs influenced, joint significance tests
s|i
on βt = 0 and estimated average systemic risk contributions as well as betas. Estimation period:
January 2000 to June 2007.
s|i

Name
FRE
ML
LEH
AIG

influenced by
AON, BBT, EV, FITB, FNM, HUM, MBI
AMTD, CB, CNA, HCBK, L, NYB, WRB
AMTD, AON, BEN, GS, JPM, LM, LUK, MI, MS
ALL, C, CB, CNA, ETFC, HIG, LEH, LNC, MBI,
MMC, SCHW, STT, TMK∗
time-varying betass|ib̄ · 100 average βbmainly influencing
overall sign. average βttBBT, FNM
0.048
0.38
0.092∗
C
0.051
0.03
0.030∗
AIG, AXP, ETFC, JPM
0.041
0.79
0.176∗
AFL, C, CNA, HIG,
0.026
0.73
0.210∗
HUM, MMC, UNM

HAUTSCH, SCHAUMBURG and SCHIENLE

34

MI

UNP

MMC

CVH

STT

PNC
BK

AMTD

CMA
LUK

BBT

Wells Fargo

JP Morgan

SEIC

L

ALL

AFL

SNV

MTB

CNA

BEN

AON

FITB

RF
Bank of America

EV

CB

HNT

Freddy Mac

STI

Morgan Stanley

ZION

HUM

LNC

American Express

Charles Schwab

TROW

TMK

NTRS

HIG
UNM

PGR

CI

AIG

Citigroup

HBAN

MBI

HCBK

SLM

PBCT

ETFC

NYB

Goldman Sachs

Fannie Mae

LM

CINF

WRB

Fig. 6. Full network graph for the system of the 57 largest financial companies in the U.S. For simplicity, arrows only mark risk spillover
effects without referring to their respective size. Otherwise, arrows and colors are as defined in Figure 1. A complete list of firms’ acronyms
is contained in Table 1. The graphical allocation is obtained via the Fruchtermann-Reingold algorithm used to minimize the total length of
all arrows.

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

35

Fig. 7. Full Network graphs of Citigroup (C) and Morgan Stanley (MS) highlighting risk
drivers and risk recipients directly connected to the respective companies with bold arrows,
according to the respective size of the effect. Arrows, colors and acronyms are as in Figure
6. For simplicity, all other links only indicate spillover effects without referring to size. The
list of firm acronyms is contained in Table 1.

HAUTSCH, SCHAUMBURG and SCHIENLE

36

GS

BBT
PBCT
BAC
RF
SLM
HBAN
CMA
NTRS
STI
MTB
SNV
ZION

TROW

HCBK

SCHW
MS
ETFC

C

HIG

C

STT

PNC BK WFC NYB

PNC BK WFC NYB

MI

MI

JPM
AXP

JPM AXP

BEN

AON

BEN

AON
CVH
MMCUNM AFL AIG TMK HUM HNT

STTCreated with NodeXL (http://nodexl.codeplex.com)

GS

BBT
PBCT
BAC
RF
SLM
HBAN
CMA
NTRS
STI
MTB
SNV
ZION
HCBK
TROW
SCHW
MS
ETFC

HIG

CVH
MMCUNM AFL AIG TMK HUM HNT

EV

CI

EV

CI

SEIC

AMTD

WRB
PGR
CB

ALL
CNA
L

FRE

FNM

LUK

UNP

FITB

LM

LNC
MBI
CINF

AMTD

LM

SEIC

L

GS

BBT
PBCT
BAC
RF
SLM
HBAN
CMA
NTRS
STI
MTB
SNV
ZION

ETFC

MS

SCHW

TROW

HCBK

NTRS

PBCT
BAC

GS

BBT

C

HIG

C

STT

PNC BK WFC NYB

MI

MI

JPM

JPM

AXP

AXP

BEN

BEN

AON
CVH
MMCUNM AFL AIG TMK HUM HNTPNC BK WFC NYB

AONCVH
MMCUNM AFL AIG TMK HUM HNT

STTCreated with NodeXL (http://nodexl.codeplex.com)

FRE

STI

RF
SLM
HBAN

WRB

MTB

CMA

PGR

ETFC

MS

SCHW

TROW

HCBK

ZION

SNV

CNA

ALL

CB

FNM

LUK

UNP

FITB

LNC
MBI
CINF

HIG

Created with NodeXL (http://nodexl.codeplex.com)

EV

CI

EV

CI

SEIC

AMTD

WRB

PGR

CB

ALL

CNA

L

FRE

FNM

LUK

UNP

FITB

LM

LNC

MBI

CINF

SEIC

AMTD

WRB

PGR

CB

ALL

CNA

L

FRE

FNM

LUK

UNP

FITB

LM

LNC

MBI

CINF

Fig. 8. Network graph arranged according to industry groups, highlighting the industry-specific risk spillovers from depositories (top left),insurance companies (top right), broker dealers (bottom left) and others (bottom right). Arrows mark risk spillovers effects without referringto their respective sizes. Otherwise, arrows and colors are as defined in Figure 1. A complete list of firms’ acronyms is contained in Table 1
in the Appendix.

37

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

AIG

BAC
Systemic risk beta

0.00

−0.10

0.10

beta.t0.20

beta.t
0.00
0.10

0.30

0.20

Systemic risk beta

2000

2002

2004
Time

2006

2008

2000

2002

2004

2006

2008

2006

2008

2006

2008

Time

VaR

0.05

0.1

VaR.t
0.3

VaR.t
0.15
0.25

0.5

0.35

VaR

2000

2002

2004
Time

2006

2008

2000

2002

2004
Time

Realized systemic risk beta

0

beta.t*VaR.t*100−3 −2 −1 0 1 2

beta.t*VaR.t*100
2
4
6

3

Realized systemic risk beta

2000

2002

2004
Time

2006

2008

2000

2002

2004
Time

Fig. 9. For each of the two institutions, American International Group (AIG) and Bank ofAmerica (BAC), the respective column comprises three time series panels, which depict,
i
s|i
aRt
from top to bottom, the time-varying systemic risk beta βbt , the time-varying VaR V[
s|ii

aRt of the firm.
and the realized systemic risk beta βbt V[
AIG: realized systemic risk beta

ML: realized systemic risk beta

●

●

●

0.005

0.005

0.008

●

●
●

●
●
●

●

●

●
●

●

●

●

●

2006Q1

2006Q2

2006Q3

2006Q4

2007Q1

FRE: realized systemic risk beta

−0.005●

2005Q4

●
●

0.004

●
●

●

2004.0 2004.5 2005.0 2005.5 2006.0 2006.5 2007.0

ML: VaR●●

2005Q4

2006Q1

2006Q2

2006Q3

2006Q4●

2007Q1●0.020−0.002●●

LEH: realized systemic risk beta●●

2006Q3

2006Q4

●

●

●
●

0.016

0.012

●
●
●

●

0.012

0.008

●

●

●
●

●

●

2005Q4

2006Q1

2006Q2

2007Q1●

2004.0 2004.5 2005.0 2005.5 2006.0 2006.5 2007.0

Fig. 10. Time evolution of systemic importance for all companies in the focus of the casestudy. The left column of the panel depicts quarterly averaged realized systemic risk betasof AIG, Freddie Mac (FRE) and Lehman Brothers (LEH) during the period immediately
preceding the crisis. The right column shows quarterly averaged realized systemic risk betasof Merrill Lynch (ML) for the longer time period from 2004 onward in comparison with its
VaR.

38

HAUTSCH, SCHAUMBURG and SCHIENLE

AXP, CB, CMA, FITB,
HBAN, HIG, MMC,
MS, TMK, UNM,
WFC, ZION

BAC, BEN, C, CINF,
FNM, JPM, LM, LNC,
LUK, MI, NYB,
PGR, RF, SCHW, SEIC,
STT, TROW

AIG, FRE, PNC

BBT,
ETFC,
EV,
PBCT

Fig. 11. The schematic figure depicts companies classified as systemically relevant, according to our two-step network technique, in comparison with a simplistic one-step model, withexceedances based on LASSO for (15). Companies in the dotted area are selected by the simplistic model as systemically relevant, while firms in the gray area have a significant systemic
impact in our network model, according to Table 4. Denote the overlay region as group 1,
which includes companies whose tail risks are determined as relevant to the system’s risk inboth settings. Group 2 comprises companies in the dotted but non-gray area selected only by
the simplistic model. Systemically relevant firms in the gray non-dotted region can be classified as either group 3, as they are deeply interconnected with other companies through morethan six links, according to Table 3 (upper larger only gray set in the figure), or as group 4,
with few but crucial risk links, according to Table 3 (lower only gray set in the figure withthree elements).

1.0

1.0

1.0

20% higher lambdas

0.8

0.8

0.8

●

0.9

1.0

●

lambda0.90

66
lambda

70

0.2

0.2

0.2

●

●

●

0.0

0.0

●

0.0

0.94

P−values

0.98

●

●

62

0.6

RF
0.70 0.72 0.74 0.76

GS●P−values

80

0.4

76

0.4

lambda72

P−values

68

0.6

●

76

0.4

72

P−values

68

0.6

●

64

P−values

10% higher lambdas

0.7

0.8

P−values

●

0.8

●

original lambdas

AXP

0.6

P−values

1.0

AFL

●

54 56 58 60 62 64
lambdaaverage BIC:
0.92331

average BIC:
0.94158

average BIC:
0.96259

Fig. 12. The left panel presents illustrative evolutionary paths of p-values from the V aRi
backtest described in Section 3.3.2 when individual-specific LASSO penalty parameters λi
are increased by 10% and 20%. The respective leftmost p-value corresponds to the original
choice. The right panel shows boxplots of all p-values obtained from backtesting all 57 VaRtime series. Higher p-values indicate better model fits. At the bottom of the right panel,
average values of an additional goodness-of-fit measure, the Bayesian Information Criterion(BIC) for quantiles, are reported. Lower values imply better model fits.

FINANCIAL NETWORK SYSTEMIC RISK CONTRIBUTIONS

39

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