Using Market Information for Banking System
Risk Assessment
∗
Helmut Elsinger,
a
Alfred Lehar,
b
and Martin Summer
c
a
Department of Finance, University of Vienna
b
Haskayne School of Business, University of Calgary
c
Economic Studies Division, Oesterreichische Nationalbank
We propose a new method for the analysis of systemic sta-
bility of a banking system relying mostly on market data. We
model both asset correlations and interlinkages from interbank
borrowing so that our analysis gauges two major sources of sys-
temic risk: correlated exposures and mutual credit relations
that may cause domino effects of insolvencies. We apply our
method to a data set of the ten major UK banks and ana-
lyze insolvency risk over a one-year horizon. We also suggest
a stress-testing procedure by analyzing the conditional asset
return distribution that results from the hypothetical failure
of individual institutions in this system. Rather than looking
at individual bank defaults ceteris paribus, we take the change
in the asset return distribution and the resulting change in the
risk of all other banks into account. This takes previous stress
tests of interlinkages a substantial step further.
JEL Codes: G21, C15, C81, E44.
∗
Martin Summer thanks the Bank of England for its hospitality and support
during the work on this project. Helmut Elsinger and Alfred Lehar are grateful for
financial support from the Jubil¨aumsfonds der Oesterreichischen Nationalbank
under grant number 10972. We thank Nyeong Lee for valuable research assistance.
We thank Charles Goodhart, Mathias Drehmann, Miguel Segoviano, Glenn Hog-
garth, Alistair Cunningham, Garry Young, and Simon Wells as well as seminar
participants at the Bank of England, the London School of Economics, Imperial
College London, the European Central Bank, the University of Frankfurt, and
the University of Munich for helpful discussions and comments. The views ex-
pressed in this paper are entirely the views of the authors and do not necessarily
reflect the views of OeNB. Corresponding author: Summer: Otto-Wagner-Platz
3, A-1011 Wien, Austria; e-mail: martin.summer@oenb.co.at, Tel: +43-1-40420
7212, Fax: +43-1-40420 7299. Other author contact: Elsinger: Br¨unner Strasse
72, A-1210 Wien, Austria; e-mail: helmut.elsinger@univie.ac.at, Tel: +43-1-4277
38057, Fax: +43-1-4277 38054. Lehar: 2500 University Drive NW, Calgary, AB,
Canada T2N 1N4; e-mail: alehar@ucalgary.ca, Tel: +1-(403) 220 4567.
137
138 International Journal of Central Banking March 2006
1. Introduction
We suggest a new method for analyzing systemic financial stability of
banking systems relying on market data and nonproprietary account-
ing data. The central idea is to combine concepts from finance and
modern risk management with a network model of interbank loans
to analyze the probability of simultaneous failures of banks—often
referred to as systemic risk—and to develop a simple stress-testing
procedure. We apply our ideas to a data set describing the system of
the ten major UK banks and find that this system appears to be very
stable. In particular, the likelihood of domino effects of bank insol-
vencies is very low. We also gain three more general insights. First,
we see that for the analysis of systemic risk, defined as the proba-
bility assessment of joint default events, the analysis of both corre-
lations and interlinkages is important. An analysis based on single
institutions underestimates these events. Second, we see that stress
testing of interbank linkages based on idiosyncratic default events
only underestimates the impact of bank defaults on the rest of the
system by a considerable margin. Third, we see that a simultaneous
risk analysis of all major banks in a system can be done even when
access to large proprietary microdata sets about individual banks is
not available.
1.1 Related Research
In a series of recent papers analyzing interbank exposures such as
Humphrey (1986), Angelini, Maresca, and Russo (1996), Furfine
(2003), Wells (2004), Degryse and Nguyen (2004), VanLelyveld and
Liedorp (2004), Upper and Worms (2004), and Mistrulli (2005), it
has become common practice to investigate contagious defaults that
result from the hypothetical failure of some single institution. This
sort of analysis is able to capture the effect of idiosyncratic bank
failures (e.g., because of fraud). It emphasizes one source of systemic
risk, namely interbank linkages, and ignores the other, i.e., it is silent
on correlation between banks’ exposures. We believe that a mean-
ingful risk assessment is only possible by studying both aspects in
conjunction. Our paper builds on the model developed in Elsinger,
Lehar, and Summer (2004), which incorporates both sources of sys-
temic risk simultaneously. While in their model the distribution of
Vol. 2 No. 1 Using Market Information 139
bank asset returns is inferred from bank-specific data on market and
credit risk exposures derived from a combination of various propri-
etary data sets of the Austrian Central Bank (OeNB), in contrast, in
this paper the distribution of bank asset returns is inferred indirectly
from stock market return data. The method of indirectly inferring
bank asset return correlations from market data builds on the work
of Lehar (2005).
1.2 An Overview of the Model and Main Results
We reconstruct a time series for the market values of assets for ten
large publicly traded UK banks by viewing equity as a call option on
total assets. We analyze the covariance structure of asset returns and
simulate potential risk situations for the banking system as a whole
based on this analysis. The advantage of this approach to model
the uncertainty of bank asset returns lies in the fact that it does
not depend on proprietary data sources. Of course, this advantage
does not come without a price. While in highly developed financial
systems stock market data are likely to incorporate all relevant public
information on a bank’s risk exposure, the data do not necessarily
incorporate private information that is often contained in supervisory
bank microdata and loan registers. Private information is, however,
likely to be important for assessing the risks of a bank due to the
opaque nature of bank asset values. One way to see the approach to
bank asset risk modeling suggested in this paper is that it offers an
alternative approach when private information—as is very often the
case in practice—is not available.
Using a network model of the interbank market (following the
model of Elsinger, Lehar, and Summer 2004) we investigate default
probabilities and so-called domino effects. More significantly, we ana-
lyze the differences that arise in risk assessment when we take a naive
approach, neglecting correlations; when we analyze correlations but
ignore interlinkages; and finally, when we additionally take inter-
linkages into account. We then model the impact of various stress
scenarios for the banking system by using a method that preserves
the idea of previous papers examining scenarios where each bank in
the system fails one at a time. But in contrast to this literature, we
do so in a way that is consistent with the correlation structure of
asset returns. Put another way, rather than simply removing a bank
140 International Journal of Central Banking March 2006
from the system one at a time (leaving everything else equal) we
look at the conditional distribution of asset returns resulting from
the event that one bank fails.
The empirical analysis gives the following main insights. First,
the UK banking system appears to be very stable. In particular, the
likelihood of domino effects is very low. Second, the simultaneous
consideration of correlation and interlinkages does indeed make a
difference for the assessment of systemic financial stability. In par-
ticular, the probability of systemic events such as the joint breakdown
of major institutions is underestimated when correlations between
banks are ignored. We can also show that ignoring interlinkages leads
to an underestimation of joint default events. Third, the analysis un-
covers substantial differences between banks concerning their impact
on others in stress scenarios and clearly identifies institutions with a
high systemic impact.
Finally, we demonstrate the importance of the assumption about
the source of the shock when studying the consequences of a bank de-
fault. While the previous literature has studied idiosyncratic shocks,
only our model captures systematic shocks too. We suggest a hypo-
thetical decomposition into idiosyncratic and systematic sources of a
shock that may hit a bank. In this way we can investigate not only the
extreme cases studied in the existing literature but also intermediate
cases. By measuring the expected shortfall for all other banks in the
system conditional on the default of one bank, we demonstrate that
a systematic shock has a much higher impact on financial stability
than an idiosyncratic one. Basing a stress test entirely on idiosyn-
cratic shock scenarios may therefore considerably underestimate the
impact of the shock on the banking system as a whole. The impact
of a bank’s default on the banking system is much smaller if we as-
sume an idiosyncratic shock than if we assume that the bank defaults
following a macroeconomic shock.
2. A System Perspective on Risk Exposure for Banks
Our network model of interbank credits is a version of the model
of Eisenberg and Noe (2001). We refer the reader to this paper for
technical details. For our purpose of risk analysis, we extend their
model to include uncertainty. Consider a set N = {1, ..., N} of banks.
Each bank i ∈Nis characterized by a given value e
i
netofinterbank
Vol. 2 No. 1 Using Market Information 141
positions and its nominal liabilities l
ij
against other banks j ∈Nin
the system. The entire banking system is thus described by an N ×N
matrix L and a vector e ∈ R
N
. We denote this system by the pair
(L, e).
The total value of a bank is the value of e
i
plus the value of
all payments received from counterparties in the interbank market
minus the interbank liabilities. If for a given pair (L, e) the total value
of a bank becomes negative, the bank is insolvent. In this case we
assume that creditor banks are rationed proportionally. Denote by
d ∈ R
N
+
the vector of total obligations of banks toward the rest of the
system, i.e., d
i
=
j∈N
l
ij
. Define a new matrix Π ∈ [0, 1]
N ×N
which
is derived from L by normalizing the entries by total obligations.
π
ij
=
l
ij
d
i
if d
i
> 0
0 otherwise
(1)
We describe a banking system as a tuple (Π,e,d)forwhichwe
define a clearing payment vector p
∗
. The clearing payment vector has
to respect limited liability of banks and proportional sharing in case
of default. It denotes the total payments made by the banks under
the clearing mechanism. It is defined by
p
∗
i
=
d
i
if
N
j=1
π
ji
p
∗
j
+ e
i
≥ d
i
N
j=1
π
ji
p
∗
j
+ e
i
if d
i
>
N
j=1
π
ji
p
∗
j
+ e
i
≥ 0
0if
N
j=1
π
ji
p
∗
j
+ e
i
< 0
(2)
This can be written more compactly as
p
∗
=min
d, max
Π
p
∗
+ e, 0
, (3)
where the min and max operators denote the componentwise max-
imum and minimum. The clearing payment vector directly gives us
two important insights: for a given structure of liabilities and bank
values (Π,e,d) we can identify insolvent banks (p
∗
i
<d
i
) and derive
the recovery rate for each defaulting bank (
p
∗
i
d
i
).
