What Is The Systemic Risk Exposure of Financial
Institutions?
John Sedunov∗
The Ohio State University
July 20, 2011
Abstract
This paper proposes a new method for estimating the systemic risk exposure of a financial institution. I compare this measure, Adapted Exposure CoVaR, to two other measures of
institution level exposure: Systemic Expected Shortfall (Acharya, et al. (2010)) and Granger
Causality (Billio, et al. (2010)). I estimate tests during systemic crisis periods in 1998 (LTCM)
and 2008 (Lehman Brothers). I find that the Adapted CoVaR measure is successful in predicting within-crisis returns using pre-crisis data, while providing clear indications of the risk
exposure level of a firm before the onset of a crisis. Systemic Expected Shortfall and Granger
Causality do not provide consistent economic interpretations over different crisis periods.
∗
e-mail: sedunov 1@fisher.osu.edu
1
1
Introduction
Events beginning in September 2008, including the collapse of Lehman Brothers and the rescue of
AIG, displayed the effects that a systemic crisis can have on the economy1 . The failure or distress
of key institutions during this time led to failures throughout the financial system. Without an accurate understanding of the exposure of individual firms to systemic risk, regulators, investors, and
executives were unable to minimize the effects of this crisis. Since the crisis, measures quantifying
institution-level systemic risk exposure have been proposed. However, these measures are not able
to forecast an institution’s sensitivity to a crisis, nor are they able to predict future exposure to a
systemic crisis.
In this paper, I propose a new method of estimating firm level systemic risk exposure, Adapted
Exposure CoVaR, which modifies the CoVaR measure of Adrian and Brunnermeier (2010), and
compare it with existing measures of bank level systemic risk exposure. To understand how different measures perform prior to crisis periods as evaluators of systemic risk exposure, I examine
their ability to predict returns and future risk exposure during the Long-Term Capital Management (LTCM) systemic crisis of 1998 and the Lehman Brothers systemic crisis of 2008 based on
information available prior to their onset.
Several measures of systemic risk have been proposed. This paper concentrates specifically
on institution-level measures of systemic risk exposure2 . One subset of institution-level systemic
risk measures estimates the systemic risk contribution of an institution, which is defined as the
sensitivity of the financial system to a systemic event in a single institution. These models include:
Tarashev, Borio, and Tsatsaronis (2009); Chan-Lau (2010); Gray and Jobst (2010); Allen, Bali,
1
Acharya (2009) defines a financial crisis as systemic if “many banks fail together, or if one bank’s failure propagates as a contagion causing the failure of many banks.”
2
A group of measures focusing on system-wide systemic risk also exists. Though I do not explicitly focus on
this literature, the group includes: Lehar (2005), Bodie, Gray, and Merton (2008), Adams, Fuss, and Gropp (2010),
Kritzman, Li, Page, and Rigobon (2010), and Giglio (2010). In general, these papers propose measures of systemic
risk for the system as a whole, providing probabilities of a crisis throughout the entire system based on individual bank
data.
1
and Tang (2010); and Adrian and Brunnermeier’s (2010) Contribution CoVaR. This paper focuses
instead on the other subset of institution-level measures, which quantify an institution’s exposure
to systemic risk. Exposure measures estimate the sensitivity of an institution to a systemic crisis.
Specifically, three measures within the literature estimate this type of risk: Systemic Expected
Shortfall (SES), proposed by Acharya, et al. (2010); Exposure CoVaR, proposed by Adrian and
Brunnermeier (2010); and Granger causality, proposed by Billio, et al. (2010). While SES and
Exposure CoVaR explicitly examine firm level systemic risk exposure, the Granger Causality measure can be interpreted as either a contribution or exposure measure, as it estimates the level of
interconnectedness that an individual institution shares with the rest of the financial system. These
three measures are the benchmarks to which I compare my Adapted Exposure CoVaR measure.
In practice, regulators, investors, and financial institution executives all have an interest in the
systemic risk exposure of a given institution (De Bandt and Hartmann (2000)). First, regulators can
utilize systemic risk exposure measures to classify “systemically important” firms, as mandated,
for example, by the Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010. Specifically, Title VIII of the act gives the Federal Reserve an “enhanced role in the supervision of risk
management standards for systemically important financial market utilities...” A good measure
of systemic risk exposure allows regulators to clearly designate “systemically important” firms.
Further, investors will be able to utilize systemic risk measures to make investment decisions, as
systemic risk can pose a threat to financial markets. Based on an accurate measure, investors
can adjust portfolio holdings according to their risk preferences. Investors may also wish to hold
hedges against possible systemic events. Finally, systemic risk exposures are relevant to institutions themselves. It will be useful for executives and risk management officers to understand the
potential losses their institutions will face given a crisis. This is especially true given the level of
systemic risk that is contained in structured products utilized by banks (Coval, Jurek, and Stafford
(2009)). Like investors, executives may use these measures to determine a viable hedging strategy
to mitigate losses created by a crisis.
2
A measure of systemic risk must be forward-looking in terms of an institution’s sensitivity to
a crisis if it is to be implemented in future research or in practice. This sensitivity could in theory
be based on equity returns, changes in the market value of firm assets, or the market value of debt.
The market value of debt is difficult to accurately measure, making it impractical to base a measure
of systemic risk exposure on it. Thus, the measures considered below focus on equity returns or
on changes in asset market values.
I investigate first the ability of the Adapted Exposure CoVaR measure to predict within-crisis
change in institution assets using pre-crisis data. Using a sample of the 25 largest banks, insurers,
and brokers during both crisis periods, I find that Adapted Exposure CoVaR accurately predicts
within-crisis returns up to one year prior to a crisis period. Moreover, I show that for a one standard
deviation increase in systemic risk exposure measured by Adapted Exposure CoVaR, a firm should
expect a decline in the market value of assets of 1.34 - 1.79% per week during a crisis. The other
measures of systemic risk exposure do not provide reliable forecasting.
I also examine the predictive power of each measure in terms of forecasting future risk exposures. This predictive power would ensure that at the onset of a crisis, the set of “systemically
important” firms is not different from the group designated as such prior to the crisis. Again, I
find that the Adapted Exposure CoVaR measure is superior to other measures along this criterion.
My estimations show that pre-crisis exposure is positively related to within-crisis exposure levels,
implying that firms which are systemically risky prior to a crisis remain risky during the crisis.
This paper provides two main contributions to the literature on systemic risk. First, it proposes
a new approach to quantifying systemic risk exposure, Adapted Exposure CoVaR. This measure
is a modification to the Exposure CoVaR measure. As currently constructed, Exposure CoVaR
introduces a look-ahead bias, by including information that would not be available at the time of
measurement. While this provides a clear picture of the overall risk a firm may face over a long
period, and allows for an understanding of which firm policies are clearly tied to systemic risk
exposure, this construction does not allow for forecasting. Moreover, it can not be utilized directly,
3
which forces users to examine systemic risk through related accounting variables. Accounting
variables may be specifically linked to a single crisis, but not others. This may be misleading when
preparing for a future systemic event. Generally, it is difficult to estimate an exposure measure
since tail events are rare and difficult to predict. Further, most available measures appear to move
in reaction to a crisis, rather than provide predictive power prior to a crisis. Second, this paper tests
each of the three proposed measures of systemic risk exposure along several criteria. This provides
clear insight as to which measure is best suited to estimate systemic risk exposure going forward
both in practice and within the finance literature. Having an accurate measure of systemic risk that
is able to circumvent the above issues will allow research to progress towards understanding what
makes institutions exposed to systemic risk, if institutions choose to be exposed to systemic risk,
and what institutions can do to reduce systemic risk exposure.
The remainder of the paper proceeds as follows. Section two describes the characteristics
of a systemic risk exposure measure. Section three defines the measures of systemic risk I am
comparing in this paper, providing a brief review of each measure. Section four describes the
data, while section five presents a discussion of the results. Section six provides robustness tests.
Section seven concludes.
2
Characteristics of a Systemic Risk Exposure Measure
A measure of systemic risk exposure should bear certain characteristics. First, a measure should,
given pre-crisis data, successfully predict within-crisis performance. I concentrate on an institution’s change in the market value of assets as the key measure of performance. Second, it should
provide an accurate forecast of future exposures. That is, the set of institutions estimated as “highrisk” should not vary based on whether the economy is in a crisis or not. Finally, a measure should
not vary in its interpretation from crisis to crisis. I investigate the performance of Systemic Expected Shortfall, Granger Causality, and Adapted Exposure CoVaR in terms of each characteristic.
4
2.1
Performance Predictability
A strong measure of institution-level systemic risk exposure should forecast a financial institution’s
sensitivity to a crisis. At a minimum, this condition should be fulfilled immediately prior to the
onset of a crisis. However, it will be beneficial if a measure has forecasting ability over a longer
horizon prior to a crisis period because it will allow for regulators, institution executives, and
investors to understand the impact that a potential crisis would have on an institution well before
its onset, and how to act on this information.
In a systemic crisis period, institutions with high exposure to systemic risk should perform
more poorly than institutions with low exposure. Thus, conditional on a crisis period, a lagged
measure of systemic risk exposure should be negatively related to future asset returns. Empirically,
I focus on lags as short as one week prior to a crisis and as long as one year prior to a crisis.
2.2
Exposure Forecasting
A second characteristic of a good measure of systemic risk exposure is its ability to provide consistent forecasts of future systemic risk measures. That is, an institution classified as high risk prior to
a crisis should remain classified as a high-risk institution at the onset of the crisis. This is a useful
feature for a measure of systemic risk exposure as it will allow the measure to be consistent in how
it ranks firms over time. It may further provide evidence that a measure is not proxying for other
characteristics, but is providing an accurate estimate of the level of systemic risk each institution is
exposed to at a given time. Further, regulators may be interested in this feature as, for example, the
Dodd-Frank Wall Street Reform and Consumer Protection Act requires the designation of “systemically important” firms. If an exposure measure shows that a certain set of ten firms is high-risk
one year prior to a crisis period, but shows that a set of ten different firms are systemically risky
during a crisis, then it is difficult to designate institutions as “systemically important” based on that
measure.
5
I empirically investigate whether a measure provides an accurate forecast of future exposures
by examining the relation between the current measure of systemic risk and its lagged values. If
a measure has consistent forecast ability, one would expect a positive coefficient estimate for the
lagged exposure measure.
2.3
Performance Over Time
A third characteristic of a good systemic risk exposure measure is that it is functional across crises.
That is, a measure should be able to forecast within-crisis performance in any crisis period. Thus, it
is important that a measure of systemic risk exposure not be too closely tied to a specific systemic
event. This criterion can be evaluated by examining the performance of the systemic risk measures
in empirical tests conducted over different systemic crisis periods, and comparing their results. In
tests that follow, I examine two crisis periods: the LTCM crisis period of late 1998 and the collapse
of Lehman Brothers in late 2008. I infer that a measure is functional across multiple crisis periods
if it is a statistically significant predictor of institution performance for both crisis periods.
3
Measures of Systemic Risk
I compare three methods of estimating systemic risk in terms of the characteristics described above:
Adapted Exposure CoVaR, Granger Causality estimates (Billio, et al., 2010), and Systemic Expected Shortfall (Acharya, et al., 2010). These are the only approaches to calculating institutionlevel systemic risk exposure in the literature thus far. As discussed in section one, several other
measures of systemic risk exist, however, they estimate the risk of a collapse of the entire system,
or the amount of systemic risk a firm contributes to the system, but not necessarily the risk faced
by single entities within the system. The measures compared here calculate the systemic risk an
institution is exposed to at a given point in time, but each measure approaches this estimation in a
different way. Below, I define each method and discuss how the respective measures describe the
6
systemic risk of an institution.
3.1
3.1.1
Adapted Exposure CoVaR
Definition of CoVaR
My measure, Adapted Exposure CoVaR, is based on Adrian and Brunnermeier (2010). They provide two key measures for determining the systemic risk of an institution. Each measure captures
a different aspect of institution systemic risk. Contribution CoVaR estimates the contribution to
the overall losses suffered by the financial system from an individual institution, given a crisis
event. Alternatively, Exposure CoVaR provides an estimate of the change in an institution’s VaR
given a systemic crisis. I focus specifically on adapting the Exposure CoVaR measure for use as a
forecasting variable.
The authors define Exposure CoVaR (specifically, ∆CoVaRqj|s ) as “institution j’s increase in
VaR in the case of a financial crisis.” Here, I denote the financial system as s. Formally, Exposure
CoVaR is given by the q-quantile of the conditional probability distribution:
s
Pr(X j ≤ CoVaRqj|C(X ) |C(X s )) = q
(3.1)
Where X j is the variable for which the value-at-risk of institution j is defined and C(X s ) is an
event within the system. The variable q denotes a probability level corresponding to the left tail of
the distribution of firm level asset returns. This value is typically set to 1%. Further, the system’s
contribution to j, which is in turn j’s exposure to the system, is given by:
j|X s =VaRiq
∆CoVaRqj|s = CoVaRq
− CoVaRqj|X =Median = q
s
s
(3.2)
Empirically, Adrian and Brunnermeier (2010) estimate exposure CoVaR on a weekly basis
using quantile regressions. First, the authors calculate the median and 1% states of the VaR of
7
industry assets. Then, denoting the weekly change in an institution’s market value of assets as
X j and a set of macroeconomic conditioning variables (including: VIX, liquidity spread3 , change
in the three-month Treasury bill rate, change in the slope of the yield curve4 , the change in the
credit spread5 , weekly equity market return, and the one year cumulative real estate sector return)
as Mt−1 , the authors estimate, using a 1% quantile regression:
X j = β j|s X s + γ j|s Mt−1 + α j|s
(3.3)
Finally, β j|s is used to calculate Exposure CoVaR:
∆CoVaRqj|s = β j|s (VaRts (q) − VaRts (50%))
3.1.2
(3.4)
Proposed Changes to Exposure CoVaR
As constructed, Exposure CoVaR is not suited for use as a forecasting tool for future crisis periods,
or for use as a tool to denote which institutions are most at risk at a specific point in time. Rather,
it is a useful tool to discern what firm-level variables are closely linked to systemic risk over a long
horizon. I propose two modifications to Exposure CoVaR which will adapt Exposure CoVaR for
forecasting uses. These modifications would allow regulators and executives to directly observe
and utilize the Exposure CoVaR measure of an institution, rather than regulate firms or make firm
based decisions on a set of variables which are historically linked to Exposure CoVaR, as Adrian
and Brunnermeier (2010) propose. This is important as variables which are linked to systemic risk
may not remain linked in the future, since systemic crises have varying outside causes. Therefore,
basing decisions on variables which are related only to recent crisis periods rather than an exposure
measure directly may lead to inaccurate designations of so-called systemically important firms.
The first modification that I propose relates to the estimation of β j|s As currently calculated,
3
The difference between the three-month repo rate and the three-month bill rate
Measured by the yield-spread between the 10-year Treasury rate and the three-month bill rate
5
Between BAA rated bonds and the Treasury rate
4
8
β j|s does not vary over time. Rather, all information over the entire sample period of 1986-2005 is
used to estimate it. Thus, for example, information from 2005 is used to calculate the Exposure
CoVaR levels in 1998. I propose allowing β j|s to vary over time, using data available only over the
two years prior to the quarter of estimation.6 In all estimations that follow, Exposure CoVaR will
be calculated using this modified process. This modification removes a look-ahead bias built in to
Exposure CoVaR which is created by using future data to calculate current CoVaR. Because of this
bias, Exposure CoVaR reflects the institution’s future sensitivity to changes in system performance,
which may differ from the information which is available at the time. Given that this information
is built in to the measure, Exposure CoVaR should have near perfect forecasting power. Despite
this change, however, the economic definition of Adapted Exposure CoVaR does not change from
its original meaning, as it measures the sensitivity of institution performance conditional on a
systemic event.
The second modification is to alter the way the market value of institution assets is calculated.
Adrian and Brunnermeier (2010) calculate the market value of assets as market equity multiplied
by book leverage. I propose calculating the market value of assets as institution (book assets
- book equity + market equity), a more standard definition. The difference between these two
approaches can be illustrated with a simple example. Given a distressed firm with market-valued
equity equaling 10% of book equity, book leverage of 10, and book equity of $40 Billion; its
assets would equal $400 Billion. The first approach values assets at $40 Billion, while the second
approach values assets at $364 Billion, which may be a more reasonable approximation. Further,
this provides a smoother time-series of asset market values, which will help eliminate large spikes
in the CoVaR measure over time.
6
Other lag lengths can be utilized, and produce similar results to those below.
9
3.1.3
Adapted Exposure CoVaR Beta (βtj|s )
Throughout estimations below, I use the adapted version of β j|s as the primary measure of exposure
from the CoVaR family. Adapted Exposure CoVaR in its entirety provides an estimate of the
effects of an institution’s exposure rather than the institution’s exposure by itself. This is because
Adapted Exposure CoVaR is the product of βtj|s and the difference between then median state and
1% worst state of the financial system’s assets at time t. This will yield a measure that will spike
during crisis periods due to the state of the economy. Rather, a measure of exposure should remain
relatively constant over time, and not necessarily reflective of the economy-wide state, but rather
the institution’s state at a given time.
3.2
Granger Causality
Billio et al. (2010) provides several unique measures for determining the overall systemic risk
faced by the financial system, including correlation, principal components analysis, Markov switching regimes, and Granger causality tests. These measures are constructed using monthly return
indexes of all banks, brokers, insurers, and hedge funds. In general, these measures do not address
how an individual institution contributes to overall risk or how systemic risk affects an institution
individually. The authors then adapt the Granger causality tests to be used for individual banks,
using them as a way to measure the inter-connectedness of each bank within the system.
Granger causality tests measure linear causality between two time series (Granger, 1969). Following Billio et al. (2010), linear inter-relationships can be represented as:
Xt =
m
X
a j Xt− j +
j=1
m
X
j=1
10
b j Yt− j + t
(3.5)
Yt =
m
X
c j Xt− j +
m
X
d j Yt− j + ηt
(3.6)
j=1
j=1
Within the context of this test, Y Granger causes X when b j is not equal to zero. Similarly,
when c j is not equal to zero, the test implies that X Granger causes Y. However, when both b j and
c j are not equal to zero, no information can be discerned from the test as to which variable causes
the other. Note that these tests address linear relations between institutions. Even if no relation is
found or it the tests are inconclusive, this does not preclude a non-linear relation.
To apply this test to the financial system, the authors use the time series of daily stock returns for
large institutions to determine which institutions Granger cause the returns of others. A significant
relation (in only one direction) from one institution to another implies that the institutions are interconnected. Higher levels of interconnectedness can imply that either an institution is exposed to
higher levels of systemic risk, since it is connected to more firms; or that a firm contributes more
to systemic risk levels, as it drives the performance of other firms.
The authors calculate this measure for several time periods: 1994-1998, 1996-2000, 20002004, 2002-2006, and 2004-2008. As a proxy for overall systemic risk, they calculate the number
of connections (i.e. a connection is defined in the above context as b j or c j being significantly different from zero, but not both at the same time) between banks as a proportion of all possible connections. In general, the system is at its highest inter-connectedness in the midst of financial crises.
The authors note that during the sample period, inter-connected peaks during the Asian/Russian
crisis of 1997-1998, the 2000-2001 tech bubble crisis, and during the subprime crisis of 2007-2009.
These results hold true for the entire system. However, the authors only provide estimates for the
system, and do not speak to the effectiveness of this measure on an institution-by-institution basis.
I adapt this measure by calculating the inter-connectedness of each of the top 25 banks, brokers,
and insurance companies on a quarterly basis during the period 1995-2009 using the previous three
years of returns, following the authors’ method. This allows observations to occur on a more
frequent basis for the connectedness measure and will allow me to compare it to other frequently
11
observed systemic risk measures. I calculate the number of institutions that a single firm Granger
causes at both a 1% and 10% level, again following the authors.
3.3
Systemic Expected Shortfall
Acharya et al. (2010) provides one measure for determining the systemic risk exposure of an
institution to overall systemic risk of the financial system. The systemic expected shortfall (SES)
of an institution describes its “propensity to be undercapitalized when the system as a whole is
undercapitalized.” Rather than measure SES directly, the authors theoretically derive its two key
components: Marginal Expected Shortfall (MES) and Leverage (LVG). These two components are
used throughout the paper to proxy for SES.
MES measures the average firm return on days when the market as a whole is in the tail of its
loss distribution. Here and throughout the remainder of this paper, MES is calculated at a 5% level
over the previous one year of return data:
b
MES 5%
=
1
# days
X
Rbt
(3.7)
t: system in 5% tail
Where Rbt represent the daily returns of the institution. Further, the authors estimate leverage using
the following standard approximation:
LVG =
3.4
book assets - book equity + market equity
market value of equity
(3.8)
Discussion
Each measure discussed above approaches the systemic risk of an institution in a different way.
Granger causality examines the connections an institution has with other institutions over time,
SES measures the sensitivity of an institution’s stock returns to the returns of the system, and
12
Adapted Exposure CoVaR measures the sensitivity of changes in firm assets to changes in systemwide assets.
Granger causality may not be an accurate measure of firm interconnections. Data presented
in section 4 shows that this measure spikes during crisis periods, specifically the subprime crisis
period. There is not an intuitive reason to expect that interconnections will spike simply because
of a crisis. Further, the SES method is similar to calculating Expected Shortfall. Correlation tables
presented below suggest that the SES measure is highly correlated with Beta. Despite the fact that
the SES measure provides information showing how individual institutions’ stock returns react to
those of the entire system, it seems that the measure does not provide much new information beyond what the CAPM Beta provides. Finally, the Adapted Exposure CoVaR measure uses quantile
regressions in its estimation process, estimating values at the 1% level, whereas other regression
methods concentrate on the mean. This allows the measure to view systemic risk in terms of the
left-tail of the distribution. In turn, this lets Adapted Exposure CoVaR address the fact that tail
events are rare, to an extent. Rather than simply project how institutions respond to system-wide
shifts, the measure specifically examines how institutions respond to system-wide shifts during tail
events. This provides specific insight for crisis periods.
4
Data
Accounting data are collected from Compustat, and stock return data are collected from CRSP.
I collect VIX and LIBOR data from Bloomberg, and I collect other interest rate data from the
Federal Reserve. Accounting data are used in calculating the SES measure measure LVG, as well
as to calculate control variables (namely firm size variables and weekly changes in asset market
values). Further, I use accounting data to construct my sample on a quarterly basis. Starting
with the first quarter of 1995, I calculate the moving average of assets for all banks, insurance
companies, and brokers for the previous 20 quarters. I use a moving average method in order to
13
maintain a smooth set of sample institutions, such that I can avoid having institutions move in and
out of the sample over time. Following this, the institutions are ranked, and the top 25 institutions
in each category are kept for analysis. My sample thus contains a total of 3,900 institution-year
observations over the time period of 1996-2008. In all, 156 different institutions comprise the
sample, of which 50 are banks, 50 are insurers, and 56 are brokers. Return data from CRSP are
used for the computation of all measures and control variables. Finally, VIX, LIBOR, and other
interest rate are used as conditioning variables in calculating Adapted Exposure CoVaR.
Systemic risk measures are generally computed at a quarterly level. This is because the MES
portion of the SES measure is not feasible at a shorter frequency than quarterly, as lower numbers of
observations will lead to insufficient observations to find a 5% threshold for bad returns, especially
at a weekly frequency. The Granger causality measure, again using daily returns, may not utilize
enough observations to calculate a feasible result within periods shorter than one quarter. The
Adapted Exposure CoVaR measure is calculated at a weekly level. This is feasible due to the fact
that this measure incorporates weekly macro level variables along with week-to-week changes in
market values of assets7 . One feature of this measure is that even though it is feasible to calculate
at a short-term level, it can be aggregated to longer time horizons simply by summing it.
The estimations below focus primarily on examining the how each measure interacts with the
change in market values of institution assets. The market value of assets is an important consideration for financial institutions, as if liabilities exceed assets, the institution will be insolvent. The
Adapted Exposure CoVaR measure is constructed using changes in the market values of institution assets, while SES and Granger measures are constructed using stock returns. It is helpful to
understand whether measures based on stock returns can provide any information about institution
assets.
Table 1 presents summary statistics describing the various systemic risk measures used in the
7
Not only do I include weekly changes in the market value of equity, but I also include weekly changes in book
assets and book equity by interpolating them over each quarter.
14
analysis below. Though values are calculated on a quarterly level, the average level throughout the
year is presented so as to give an idea of levels of systemic risk before and during a crisis. The
measures of systemic risk display a noticeable increase during crisis periods. For example, the
average 1% Adapted Exposure CoVaR increases from -10.08% before the 1998 financial crisis to
-26.34% during the crisis; while the measure increases from -11.91% prior to the 2008 financial
crisis to -24.23% during it. A similar pattern holds for MES, Value-at-Risk (VaR), and Expected
Shortfall (ES), as each variable indicates that institutions became riskier during the crisis periods.
A notable exception are the Granger Causality measures. Levels of Granger Causality, which
measures the level of interconnectedness within the financial system, remain relatively steady in
the 1996-98 period, despite experiencing a large shock during the 2007-08 crisis.
Furthermore, table 2, panel A presents the correlation coefficients between all measures of
systemic risk and all control variables used in the analysis during the entire sample period of 19952009. For the most part, different measures of systemic risk are uncorrelated. This is surprising, as
this indicates that each measure is quantifying something different, even though they are all aimed
at estimating the systemic risk exposure of the institution. This may be due to the construction of
MES. Note that MES has a large correlation with all of the control variables. This is to be expected,
as the calculation method for MES is similar to that of ES or VaR, with some slight modification.
Moreover, MES is a measure that relates an individual institution to the market, just like beta,
which leads to a high correlation between beta and MES. The high correlation between MES and
the control variables then indicates that MES may simply be a proxy for the overall riskiness of the
firm rather than a measure of only the systemic component of firm risk. Further, Granger Causality
may have low correlation with other systemic risk variables as is may be quantifying the wrong
connections between firms. The connections measured by Granger Causality could, for instance,
be unrelated to the systemic risk of firms, or may be an estimate of systemic risk contribution rather
than exposure.
I calculate separately correlations for only the time periods that pertain to crisis periods and
15
generally find the same patterns, with some exceptions. As to be expected, the control variables
are highly correlated with each other. This pattern holds true for both subsamples, with the exception of Beta, which during both periods displays noticeable differences from its overall sample
correlation with other controls. During the 1996-98 period, Beta is correlated much less with other
control variables relative to its correlation during the entire period, while during the 2006-08 period, its correlation is much higher. Due to the high correlations I will include only one of these
variables at a time in a given regression.
Additionally, I plot the time series of the systemic risk variables in figures 1 and 2. Figure 1
corresponds to the 1996-98 time period, while figure 2 corresponds to the 2006-08 time period.
Each graphic provides the time series of the average values of each variable over all 75 institutions
in the sample for each quarter. Panel A of both figures plots the average of the Granger Causality
measure over time. In the first quarter of 1996, at a significance level of α = 1%, the average
institution Granger caused the returns of 3.01 other firms. In general, throughout the 1997-98
crisis period, this value remains relatively stable, spiking only in the fourth quarter of 1998, where
the average institution granger caused the returns of 4.11 other firms. The crisis of 2007-08 shows
a different pattern. Between the second quarter of 2007 and the first quarter of 2008, the level of
Granger Causality gradually rose from 1.61 to 2.21, before spiking in the second quarter of 2008 to
4.57, and remaining at that level or higher through the remainder of the crisis. In the latter period,
these shifts signal an increase in systemic risk, while this measure does not seem to provide an
early warning of an increase in risk in the earlier crisis period.
Panel B displays the time-series plot of the average firm’s Marginal Expected Shortfall (MES)
during the two crisis periods. MES is one of two components of Systemic Expected Shortfall
(SES), along with leverage (LVG). I plot only MES as average LVG remains relatively stable
throughout the sample period relative to MES. During the crisis of 1997-98, MES experiences
two sharp declines. First, between the fourth quarter of 1997 and the first quarter of 1998, MES
declines from -1.7% to -2.4%; and between the third and fourth quarter of 1998, average MES
16
declines from -2.3% to -3.6%. During the 2007-08 crisis, a similar pattern emerges, as average
MES shows two major periods in decline. First, between the third quarter of 2007 and the first
quarter of 2008, MES shifts from -1.6% to -3.6%; and between the third and fourth quarters of
2008, average MES shifts from -4.11% to -6.5%. This signals an increase in systemic risk in both
crisis periods.
Finally, Panel C of both figures displays the time series of Adapted Exposure CoVaR. In both
crisis periods, the CoVaR measures display a sharp decrease (which represents an increase in system or institution VaR, respectively) in the midst of the crisis. Specifically, this overall increase in
systemic risk, as measured by CoVaR, turns up in the third quarter of 1998 - directly corresponding
to the Russian/LTCM crisis, where average 1% Adapted Exposure CoVaR shifted from -21.4% to
-31.2%. Moreover, a similar pattern takes hold during the 2008 subprime crisis. CoVaR begins
a noticable drop between the second and third quarters of 2007, as average 1% Exposure CoVaR
shifts from -11.4% to -18.44%. A further downward decline is observed during the 2008 calendar
year, as average 1% Adapted Exposure CoVaR shifts from -20.17% in the third quarter of 2008 to
its peak of -37.79% in the fourth quarter of 2008. This directly corresponds to the events of the
Lehman Brothers collapse in late 2008. In both crisis periods, the CoVaR measures seem to signal an increase in the magnitude of the change in institution assets brought on by the institution’s
exposure to systemic risk.
Figure 3 presents a time-series of the mean Adapted Exposure CoVaR measure plotted against
the mean Adapted Exposure CoVaR Beta (βtj|s ) between 1996 and 2009. βtj|s is the true measure of
exposure that comes from the Adapted Exposure CoVaR methodology. Because Adapted Exposure
CoVaR represents the change in institution value-at-risk given the current state of system assets,
it should be viewed as the result of an institution’s systemic risk exposure, rather than the actual
level of exposure an institution has to system-wide events. For this reason, the Adapted Exposure
CoVaR measure will tend to spike during crisis periods, even if the institution’s level of exposure
remains unchanged. Within this figure, note that the overall level of exposure (βi|t j ) does not include
17
the same within-crisis spikes that Adapted Exposure CoVaR does8 .
5
Results
5.1
Systemic Measures as Predictors of Firm Performance
I evaluate whether systemic risk exposure measures can describe how an institution is affected by a
crisis by regressing within-period changes in the market value of institution assets on the systemic
risk measures estimated immediately before the crisis begins. Based on the characteristics presented in section 2, a measure of systemic risk exposure should accurately predict the performance
of an institution during a crisis period using pre-crisis information. Further, these measures should
predict that high-risk firms should experience low within-crisis performance.
The systemic events I study take place over short periods of time. In both the 1998 and 2008
crisis periods, events creating large losses in value spanned the course of only a few weeks. Accordingly, I will use weekly asset value changes as the dependent variable for this set of tests. For
each crisis period, I examine the one week period in which the market was in its highest period of
distress. For the Russian/LTCM crisis period, I consider the week of August 24 - 28, 1998. During
this week, the market experienced a 4.43% decline. During the subprime crisis period, I examine
the week of October 6-10, 2008. The market, during this week, fell 24.16%. This corresponds to
the middle of the Lehman Brothers crisis period.
In estimations presented in tables 3 and 4, I estimate the following specification, which includes a set of controls that may be related to changes in institution asset value over time or to the
institution’s risk position:
Returni,t = α + γ(S ystemici,t−1 ) + β(Controlsi,t−1 ) + λ(Institutioni ) + (5.1)
β (Adrian and Brunnermeier, 2010) would be represented in this graph as a horizontal line with minimal changes
over time. Any change in the level of average β j|s would be due to a change in the sample selection rather than a change
in the population average, as this variable, on an institution level, does not change over time.
8 j|s
18
S ystemici,t−1 represents the vector of systemic risk terms, which includes Adapted Exposure CoVaR, MES, LVG, and Granger Causality; Controlsi,t−1 represents the vector of control variables,
which includes an institution’s CAPM Beta, volatility, expected shortfall (ES), and value-at-risk
(VaR), firm size measured by the natural logarithm of assets, and prior period changes in asset
values; finally, Institutioni represents a set of three dummy variables, each taking a value of one if
a given institution is a bank, broker, or insurer, respectively. Only the CoVaR measure is flexible
enough to be estimated at a weekly level. Thus, I am able to use the one-week lagged Adapted
Exposure CoVaR in these estimations. Other measures are lagged one quarter behind.
ES and VaR are two common risk management measures that I use as control variables within
my tests. Both variables are calculated in terms of stock returns. VaR is the minimum potential
loss for a firm over a given time period for a specified confidence level, α. I consider α to be 5%
for all calculations. VaR is then calculated as the 5th percentile of the daily return distribution for
a given firm in a given quarter. Additionally, ES is the expected value of losses, conditional on
the firm being in the tail of its return distribution. This measure is also evaluated at the α = 5%
confidence level. I estimate the ES of an institution by averaging all returns falling below the 5th
percentile of the distribution of daily returns within a given quarter.
The first set of results (table 3) presents tests pertaining specifically to the 1998 Russian/LTCM
crisis period. Estimations (1) through (4) incorporate only the systemic risk exposure measures
of interest along with basic controls to account for firm size and prior week returns. Estimations
(5) through (9) include all measures together, and add a set of controls to account for different
traditional measures of firm risk. Note, however, that MES is not included in estimations (6) (9), as it is highly correlated with the control variables used in the estimations. Each regression
includes institution type fixed effects.
The Adapted Exposure CoVaR Beta is negatively related to future crisis returns, and is statistically significant at the 1% level, even as control variables and other measures of systemic risk
exposure are added in regressions (5) through (9). This relation implies that riskier firms experi19
ence lower returns during the crisis period. Using the coefficient from regression (1), -0.0596, a
one standard deviation increase in overall firm systemic risk exposure implies a 1.79% decrease in
firm returns during the following week. Economically, this is a large decrease in firm performance
for a shift in the risk exposure of a firm. In my sample, the average change in an institution’s
market value of assets is 2.82%. Thus, the shift related to a one standard deviation increase in
systemic risk exposure corresponds to a 63% decrease in firm performance below the mean level.
Moreover, the coefficient on Adapted Exposure CoVaR Beta remains stable throughout all estimations as well, staying within a range of -0.0554 to -0.0596 despite the addition of MES variables,
Granger Causality, and each control variable. Further, the R2 term for each estimation including
Adapted Exposure CoVaR Beta is nearly double that of estimations that do not include it. Regressions including this variable have a minimum R2 of 0.628, where as estimations which do not
include it have a maximum R2 of 0.402. This indicates that Adapted Exposure CoVaR is explaining
a much larger portion of firm performance than competing measures and control variables.
Measures from the SES family do not fare as well. The economic interpretation of both variables does not reflect a high risk, low return trade-off during the crisis period. In each case, an
increase in these measures implies higher crisis period returns (note that the MES measure denotes
riskier firms by lower negative values). Further, neither MES nor LVG are statistically significant.
Finally, the Granger Causality measure also bears an economic interpretation which is the opposite
of what is expected. Recall that this measure estimates the interconnectivity of each institution by
calculating the number of other institutions that are linked to it. Higher values of this measure
imply that the institution is connected to more of its counterparts, and are thus more risky. Aside
from estimation (4), each estimation incorporating the Granger Causality measure shows that it is
related positively to future returns, and that more risk implies higher crisis period returns.
The second set of results (table 4) presents estimations corresponding to the 2008 subprime
crisis period. Each estimation shares the same specification as those in table 3. Again, this set of
results shows that Adapted Exposure CoVaR Beta is more economically consistent and statistically
20
significant than SES or Granger Causality. Adapted Exposure CoVaR Beta is statistically significant at a 5% level, and bears an economic interpretation consistent with a high risk, low crisis
period return trade-off in each estimation that it is contained in. This interpretation holds regardless of if other systemic risk exposure measures or control variables are included in the regression.
Given the results of estimation (1), a one standard deviation increase in Adapted Exposure CoVaR
Beta would correspond to a decrease of 1.34% in firm asset returns during the following week in
the crisis period. This once again represents an economically large decrease in firm performance.
Given that the average institution’s assets decreased in value by 4.4% during this week, the change
in firm performance implied by a one standard deviation shift in systemic risk exposure would represent a 30.5% decrease in firm performance below the mean level. In this case, R2 terms are not
significantly larger in regressions containing Adapted Exposure CoVaR compared to those which
do not. This is because coefficients on the SES variables predict higher returns for high risk firms
at a 10% significance level. However, the economic interpretations of these variables is again opposite of what is expected during a crisis period. Finally, the Granger Causality measure predicts
that highly connected firms receive lower returns during the crisis period, however these results are
not statistically significant.
In unreported estimations, I replace the market value of assets with stock returns to calculate the
forecasting power of systemic risk exposure measures for within-crisis stock returns. I estimate
each test in the same manner as the tests above are described, examining only one week during
the height of the systemic crisis periods. During the 1998 crisis period, I find that although the
Adapted Exposure CoVaR Beta correctly associates higher risk with lower returns, its coefficient
lacks statistical significance. This relation holds true for the MES measure, but not for the Granger
Causality measure. These estimations show that for a one standard deviation increase in risk
exposure measured by Adapted Exposure CoVaR Beta, an institution’s within-crisis weekly stock
returns decrease by 0.4%. All risk measures maintain the same economic interpretation during
the 2008 crisis period. However, both Adapted Exposure CoVaR Beta and MES are statistically
21
significant at the 5% and 1% levels respectively. This is not surprising, as the MES measure was
developed in response to the subprime crisis period. The Adapted Exposure CoVaR Beta predicts
a decrease in weekly stock returns of 2% for a one standard deviation shift in risk prior to the crisis
period.
Additionally, it would be helpful for a measure to accurately forecast within-crisis firm performance when lagged well before a crisis period occurs. I provide estimates similar to the above
set of tests in order to examine the predictive power of systemic risk exposure measures for future
institution-level asset returns over longer ranges. In this case, I estimate each systemic risk measure at a quarterly level, lag them two quarters, and use them to forecast asset value changes during
the crisis period weeks listed above. I again include the same set of controls for each estimation.
Tables 5 and 6 provide the results of these estimations.
Table 5 presents results corresponding to the 1998 Russian/LTCM crisis period. Here, the sixmonth lagged Adapted Exposure CoVaR Beta predicts that riskier firms should experience lower
returns during the crisis period. This measure is significant at a 1% level for most estimations. A
one standard deviation increase in pre-crisis exposure corresponds to a 1.12% decrease in future
weekly returns. Further, the MES measure, by itself, predicts lower returns for risky firms at a
1% significance level, predicting a decrease in within-crisis returns of 1.38% for a one standard
deviation increase in exposure. However, Adapted Exposure CoVaR Beta bears a higher significance level when incorporated together with MES in estimation (5). This suggests that Adapted
Exposure CoVaR is a superior long-horizon forecaster of within-crisis returns. Finally, the Granger
Causality measure predicts higher returns for risky firms, however, the measure is not statistically
significant.
Table 6 presents a set of results corresponding to the 2008 subprime crisis period, again focusing specifically on the period surrounding the collapse of Lehman Brothers. The Adapted Exposure
CoVaR Beta, lagged six months, predicts that riskier firms will experience lower returns during the
crisis period. This measure is significant at the 5% level in each estimation. In this case, a one stan22
dard deviation shift in risk exposure predicts a 1.68% decrease in within-crisis returns. The MES
measure in these estimations provides a high risk, high return trade-off interpretation; however,
these coefficients are not statistically significant. Finally, the Granger Causality measure implies
that high risk firms will experience higher within-crisis returns, which again is not consistent with
the within-crisis interpretation it should bear.
Economically, these results may be a function of the construction of each variable and their
interpretations. The SES measures do not accurately forecast over multiple time periods. This
may be a result of the variable being tied closely to the 2008 subprime crisis period. Table 2 shows
that MES is highly correlated with the CAPM Beta. This correlation is stronger in the 2008 crisis
period than it is during other time periods. The variable simply may be producing results similar
to what one would expect from the CAPM Beta during the latter period. Further, results for the
Granger Causality variable may be a result of the variable measuring the wrong connections. If
the variable is measuring only connections where two institutions are only linked in one direction,
then the measure may not be suitable for forecasting within-crisis performance. It may be more
useful to estimate the number of other firms which affect a single institution.
5.2
Systemic Risk Measures Over Time
A beneficial feature of a measure is that institutions which are at estimated as high-risk prior to a
crisis should be estimated as high-risk during a crisis. One practical application of this feature is
that it will allow for an accurate designation of “systemically important” institutions. Should firms
designated as such prior to a crisis period suddenly become low-risk during a crisis, the designation
has no meaning. Further, investors and executives may wish to understand if the relative risk level
of an institution will persist from a non-crisis period to a crisis period. To check this condition, I
estimate the following series of tests in tables 7 and 8:
S ystemici,t = α + γ(S ystemici,t−8 ) + β(Controlsi,t−8 ) + λ(Institutioni ) + 23
(5.2)
In these estimations, the set of control variables includes Beta, VaR, and firm size measured by
the natural logarithm of assets. I lag estimates of systemic risk measures 8 quarters (two years)
before the quarter of the crisis. Again, all variables are measured at the quarterly level. If systemic
risk measures are consistent through economic periods, then lagged measures should be positively
related to current measures. In both sets of results, I use pre-crisis measures to predict within-crisis
measures, where within-crisis measures are calculated for the fourth quarter of 1998 and the fourth
quarter of 2008.
Table 7 provides results of estimations corresponding specifically to the 1998 Russian/LTCM
crisis period. Specifically, this refers to the fourth quarter of 1998. This set of regressions shows
that two-year lagged estimates of Adapted Exposure CoVaR Beta predict within-crisis measures
of Adapted Exposure CoVaR Beta at a statistical significance level of 1%. For example, a one
standard deviation shift in exposure implies an increase in crisis period CoVaR Beta of 0.134.
The MES measure does not significantly predict crisis level exposure, and further does not have a
consistent economic interpretation once control variables are added to the estimations. Finally, the
Granger Causality measure does, at the 5% level predict crisis-level exposures. A one standarddeviation shift in this measure is related to an increase of 5.95 firms that a given firm is linked to
during the crisis period.
Table 8 provides results specifically linked to the 2008 subprime crisis, both during all quarters between 2007-08 and for only the fourth quarter of 2008, which corresponds to the Lehman
Brothers collapse. Again, lagged Adapted Exposure CoVaR Beta significantly predicts levels of
exposure both for the entirety of the 2007-08 period, and for the 2008 Q4 period. During 2008
Q4, a one standard deviation shift in lagged Adapted Exposure CoVaR Beta predicts an increase
of 0.059 in crisis period exposure. Again, the MES measure does not provide a statistically or economically significant interpretation. Finally, the Granger Causality measure consistently predicts
that institutions which are systemically risky prior to the crisis period will be less interconnected,
and thus less risky, during the crisis period, although its statistical significance fluctuates.
24
These results show that the Adapted Exposure CoVaR Beta measure may be a stable measure
over time. Exposures to systemic risk should not fluctuate due to the occurrence of a crisis itself.
The MES measure and Granger Causality both tend to spike during crisis periods. Given this, it
may be that the measures provide estimates of the effects of systemic risk exposure rather than the
exposure itself.
5.3
Discussion
Shown in the results above, the Adapted Exposure CoVaR measure fulfills the major criterion of a
measure of systemic risk exposure, as it is able to predict within-crisis period returns both during
a crisis and prior to a crisis. Further, institutions that the measure estimates to be at high-risk prior
to a crisis are firms which are at high-risk during a crisis.
It is also beneficial if the interpretation and magnitude of results is similar from one crisis
to another. Thus far, this feature has not been discussed in terms of the results presented. The
Adapted Exposure CoVaR measure fulfills this condition between the two most recent systemic
crisis periods in the United States. Between crisis periods, the MES measure provides different
economic interpretations between both crisis periods, and in some cases within the same crisis period, depending on whether controls have been added to estimations. Further, the Granger Causality measure also shows signs of inconsistency between the two crisis periods, and sometimes is
inconsistent within a crisis period depending on the specification of the regression.
Combining the results together, the Adapted Exposure CoVaR measure is the best measure
for providing early warning signs for crisis periods and for within-crisis forecasting of institution
performance. Each other measure, while having strengths along some dimensions of the proposed
criteria, do not consistently perform as well as Adapted Exposure CoVaR.
25
6
Robustness
The above sections show that Adapted Exposure CoVaR is a suitable approach to estimating a
firm’s systemic risk exposure. Estimations described above examine only one week during each
crisis period and examine lag lengths only as long as six months. Accordingly, it will be beneficial to further examine the measure in terms of its ability to forecast over longer lag periods and
longer return windows. I provide the results of estimations which evaluate the maximum lag length
for which Adapted Exposure CoVaR remains a reliable predictor of an institution’s sensitivity to
crises and of an institution’s future exposures. Moreover, I show that the measure can forecast
sensitivities over multiple weeks.
6.1
6.1.1
Using Longer Lags for Adapted Exposure CoVaR
Predicting Performance
It is helpful to understand first the amount of time prior to the onset of a crisis that Adapted
Exposure CoVaR can accurately predict within-crisis performance. I show above that it is a reliable
forecasting tool six months prior to a crisis, however the measure may be reliable well before
then. Table 9 provides results of estimations which include the Adapted Exposure CoVaR Beta
measure from one quarter to one year prior to the crisis periods as the key dependent variable.
These estimations follow a similar format to equation (5.1). Estimation (1) begins with no control
variables added, while estimation (2) adds the lagged asset returns and lagged institution size
variables. Estimation (3) adds to that the lagged SES, LVG, and Granger measure as well as the
set of institution type fixed effects. Finally, estimation (4) adds the institution’s VaR as a control
variable.
During the 1998 crisis, Adapted Exposure CoVaR is a reliable predictor at the 5% significance
level or better up to one year prior to the onset of the crisis. Its functionality is robust to the
inclusion of all control variables. The measure, however, is a reliable predictor two quarters in
26
advance of the 2008 crisis period. There is a noticable decline in statisical significance between
estimations (2) and (3), due to the inclusion of institution type fixed effects. Without the fixed
effect variables, however, Adapted Exposure CoVaR is a reliable predictor for the full one year
horizon in 2008 as well. Although it may be helpful for a measure to have long-run predicatbility,
it is difficult to know exactly when a crisis will occur. This makes the one and two quarter lags
most important to those who would use this measure. If it is unknown as to when a crisis will
begin, regulators and executives can utilize this measure to make short-term predictions.
6.1.2
Predicting Exposures
A further set of robustness tests examines the predictability of future exposures. Above, I show
that quarterly Adapted Exposure CoVaR Beta is predictable up to two years in advance. I now
study lag lengths between two quarters and two years. I follow the format of equation (5.2), and
simply change the lag time of the measure of Adapted Exposure CoVaR on the right-hand side of
the equation.
Figures 4 and 5 both provide results of estimations of these tests for the 1998 and 2008 crisis
periods, respectively. In both cases, as one approaches the crisis period, the measures gain predictive power. For these figures, I consider the quarter prior to and following the crisis period for the
Russian/LTCM crisis, specifically 1998Q3 - 1999Q1, while the quarters from 2007Q1 - 2008Q4
are considered for the 2008 crisis period.
6.2
Predicting Over Long Return Windows
I also examine the window over which Adapted Exposure CoVaR is an effective predictor of returns
during the crisis period. These estimations follow the format of equation (5.1). However, in this
set of estimations, I focus only on the one quarter lagged Adapted Exposure CoVaR. I also add
control variables to each estimation as in the previous section.
27
In addition to examining the week of the height of each crisis period, I examine longer windows. Windows extend as far as five weeks in length. Table 11 provides results of these tests.
Results are generally not robust to the extension of the estimation window. However, this may
not have any implications for the measure itself. The results may simply be a product of a short
systemic crisis period. Outside of a crisis period, high-systemic risk firms may not suffer worse
returns relative to their counterparts9 . If this is the case, then outside of the crisis period, the measure should not yield significant results as to the performance of risky firms. The length of a crisis
will vary depending on the crisis period. Adapted Exposure CoVaR’s short-horizon predictability
of asset returns during the 1998 and 2008 crisis periods should not imply the same forecasting
window for all crisis periods.
6.3
The Consistency of βtj|s During Crisis Periods
I estimate the consistency of the βtj|s coefficient through crisis periods. Where Adapted Exposure
CoVaR estimates the magnitude of the changes in institution assets due to the institution’s exposure to systemic risk, βtj|s measures the actual exposure of the institution. Estimated exposure to
systemic risk should not vary simply because systemic risk has increased within the system. In
other words, exposure should not vary based on macro-level conditions. Exposure may, however,
vary on an institution-basis due to the choices made by the institution as to the level of exposure it
has.
Table 11 presents a set of results that examine whether βtj|s remains consistent despite an increase in systemic risk throughout the financial system. For the sample periods of 1998Q1 1998Q4 and 2008Q1 - 2008Q4, I estimate t-tests which evaluate whether the average βtj|s is statistically different from the average βtj|s
on a quarterly basis. In each case, I find that the average
1
9
In unreported results, I estimate the effect of systemic risk over the period 1999-2007, which corresponds to the
time between the systemic crises studied in this paper. The results of Fama-Macbeth estimations show that highsystemic risk firms do not have returns which are significantly different from low-systemic risk firms during non-crisis
periods.
28
β j|s remains consistent from quarter to quarter on a system-wide basis. This is in sharp contrast to
MES and Granger Causality (results reported in table 11 only include MES), which both display
significant changes from quarter-to-quarter during the crisis periods.
7
Conclusion
This paper provides three main contributions to the literature, proposing a new approach to estimating institution-level systemic risk exposure, Adapted Exposure CoVaR, which can be implemented
as a forecasting tool; testing this measure along with SES (Acharya, et al., 2010) and Granger
Causality (Billio, et al., 2010) along different dimensions of forecasting variables; and finally examining the bounds of the forecasting ability of Adapted Exposure CoVaR. I find that among the
three measures, the Adapted Exposure CoVaR measure performs the best. The primary criterion
I evaluate each measure on is the ability to forecast within-crisis performance prior to a crisis period, which lets the measure act as an indicator of systemic risk prior to a crisis period. I further
show that Adapted Exposure CoVaR has an interpretation that is similar throughout different crisis
periods, and is an accurate predictor of future risk exposures.
The major proposed change to Exposure CoVaR is the addition of a time-varying coefficient,
which does not incorporate forward looking information. Adrian and Brunnermeier’s approach
provides a snapshot of the firm’s systemic risk position, which provides an understanding of specifically which firm policies are tied to its systemic risk exposure over a long period. The approach
proposed here, alters CoVaR and allows it to change over time, considering information within
only the previous two years10 . This eliminates the look-ahead bias that is a part of the CoVaR measure, and Adapted Exposure CoVaR to be used directly as a forecasting tool to measure systemic
risk exposure, rather than to examine related firm policies.
The MES and LVG measures, along with the Granger Causality measure, are generally in10
The two year window may be altered to be shorter or to include the entire set of available information
29
consistent in their use as forecasting tools. These measures are often inconsistent in their interpretations from crisis to crisis, and frequently lack statistical significance. Further, the economic
interpretations of these variables vary between each test, as it appears that these measures have
different meanings during crisis periods and pre-crisis periods. At best, the effectiveness of each
measure is inconclusive.
Future research can focus on the drivers institution-level systemic risk by incorporating the
Adapted Exposure CoVaR measure as the primary estimate of institution-level systemic risk exposure. For example, merger activity, securitization activity, executive compensation, and liquidity
funding can all be drivers of systemic risk by leading to more interconnectedness in the financial
system or by leading institutions to take greater risk in various exotic securities. By exploring
these drivers, the reason for why some systemic risk measures perform differently in different time
periods can be examined. Finally, this work may lead to an ultimate goal of understanding why
firms decide to increase their exposure to systemic risk over time.
30
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32
33
Year
2006 Mean
Std. Dev.
2007 Mean
Std. Dev.
2008 Mean
Std. Dev.
Panel B: Subprime Crisis, 2006-2008
Year
1996 Mean
Std. Dev.
1997 Mean
Std. Dev.
1998 Mean
Std. Dev.
Adapted Exposure CoVaR
-.1191412
.16364
-.1506515
.1666067
-.2423113
.3475484
Adapted Exposure CoVaR
-.1008108
.1465407
-.2011936
.4406193
-.2634084
.3949794
Panel A: Pre-crisis and Russian Crisis of 1998 Q4
SES Family
LVG
MES
10.44934
-.0125143
6.71058
.0091428
10.68748
-.0286838
7.223385
.0163687
10.84056
-.0749532
7.368776
.0542315
SES Family
LVG
MES
11.86087
-.0174462
7.965255
.0103338
12.46703
-.0214265
9.166354
.0122856
12.24556
-.027339
9.841779
.0186348
10% Granger
7.813953
5.439847
10.03667
7.794732
13.49164
10.13147
10% Granger
11.55518
8.676095
10.66333
9.959953
11.93688
9.681563
Control Variables
Assets (Billions)
VaR
196.0
-.0186382
336.0
.0086383
234.0
-.0306426
402.0
.0192116
232.0
-.076774
437.0
.04776
Control Variables
Assets (Billions)
VaR
57.1
-.0225152
71.4
.0077097
65.8
-.0263114
82.6
.0079624
77.4
-.0365708
104.0
.0185756
ES
-.0259296
.0139165
-.0397134
.0255071
-.1039189
.0657753
ES
-.0299876
.0095843
-.0354645
.0119289
-.0472452
.0245932
Table 1: Summary Statistics
This table presents summary statistics for key variables used in the analysis below. I report summary statistics for the two time periods that correspond to
the crisis periods that are studied: the Russian crisis of the late 1998 and the Subprime crisis of late 2008. Exposure CoVaR corresponds to the Exposure
CoVaR of a firm at the 1% level, which measures the change in instution VaR given a system-wide crisis. This measure differs from Adrian and Brunnermeier’s (2010) Exposure CoVaR measure, as the coefficient on industry returns is allowed to change over time. MES corresponds to the Marginal Expected
Shortfall, which measures the average institution stock return during the worst 5% days of market returns, while LVG corresponds to institution leverage.
10% Granger corresponds to the number of other institutions’ returns that are granger caused by a given institution at the 10% level. Assets corresponds to
the book value of the institution’s assets, measured in billions of dollars. VaR represents the institution’s value at risk, measured in terms of stock returns at
the 5% level. ES represents the institution’s expected shortfall, measured in terms of stock returns at the 5% level. All variables are measured at a quarterly
frequency and averaged over the year.
34
Panel B: 1998 Q4
Panel A: 1995-2009
Variables
Exposure CoVaR
LVG
MES
Granger
VaR
ES
Vol.
Beta
Variables
Exposure CoVaR
LVG
MES
Granger
VaR
ES
Vol.
Beta
Adapted Exposure CoVaR
1.000
0.280
0.031
-0.161
0.068
0.059
-0.055
0.051
Adapted Exposure CoVaR
1.000
0.346
0.100
-0.010
0.126
0.101
-0.102
-0.078
1.000
-0.051
-0.053
0.038
0.057
1.000
-0.086
0.066
-0.086
-0.058
0.076
0.142
1.000
0.074
0.084
-0.118
0.054
1.000
-0.149
0.063
-0.165
-0.121
0.149
0.262
1.000
-0.012
0.629
0.662
-0.524
-0.583
Granger
SES Family
LVG
MES
1.000
-0.080
0.721
0.735
-0.654
-0.684
Granger
SES Family
LVG
MES
1.000
0.928
-0.853
-0.284
VaR
1.000
0.939
-0.890
-0.526
VaR
1.000
0.539
1.000
-0.883
-0.284
1.000
0.293
Control Variables
ES
Vol.
1.000
-0.910
-0.518
Control Variables
ES
Vol.
1.000
Beta
1.000
Beta
Table 2: Correlation Matrix of Systemic Risk Measures
This table presents the correlation coefficients between each set of systemic risk measures and control variables used in regressions. I report these tables for the entire sample period of 1995-2009, the Asian/Russian crisis period of 1996-98, and the Subprime crisis period of 2006-08. 1% Exp. CoVaR
corresponds to the Exposure CoVaR of a firm at the 1% level. This measures the change in instution VaR given a system-wide crisis. MES corresponds to
the Marginal Expected Shortfall, which measures the average institution stock return during the worst 5% days of market returns, while LVG corresponds to
institution leverage. Granger corresponds to the number of other institutions’ returns that are granger caused by a given institution at the 10% level. Control
variables include institution CAPM Beta and Stock Return Volatility. Expected Shortfall (ES) is a control which measures the average of all returns in the
left tail (5%) of an institution’s return distribution. Value-at-Risk (VaR) is a control which measures an institution’s stock returns at the 5% level of its return
distribution. All variables are measured at a quarterly frequency.
35
Panel C: 2006-2008
Variables
Exposure CoVaR
LVG
MES
Granger
VaR
ES
Vol.
Beta
Adapted Exposure CoVaR
1.000
0.379
0.173
-0.024
0.186
0.154
-0.183
-0.247
1.000
-0.350
-0.342
0.338
0.256
1.000
-0.109
0.109
-0.109
-0.082
0.080
0.172
1.000
-0.297
0.857
0.873
-0.874
-0.766
Granger
SES Family
LVG
MES
1.000
0.956
-0.950
-0.771
VaR
1.000
-0.967
-0.764
1.000
0.793
Control Variables
ES
Vol.
1.000
Beta
36
-0.0146
(-0.30)
75
0.628
Constant
-0.103
(-1.38)
75
0.317
0.00339
(1.13)
0.144
(0.41)
-0.136
(-0.46)
(2)
t statistics in parentheses
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Observations
R2
0.000460
(0.25)
0.399∗
(1.84)
(1)
-0.0596∗∗∗
(-2.73)
ln(Assets)t−1
Asset Returnt−1
ESt−1
VaRt−1
Volatilityt−1
Betat−1
Grangert−1
LVGt−1
MESt−1
CoVaR Betat−1
-0.0254
(-0.30)
75
0.402
-0.000331
(-0.09)
0.0463
(0.13)
0.00108∗
(1.73)
(3)
-0.106
(-1.42)
75
0.315
0.00361
(1.25)
0.164
(0.48)
-0.000000859
(-0.00)
(4)
0.00541
(0.10)
75
0.643
-0.000667
(-0.30)
0.373
(1.41)
0.000124
(0.79)
0.000422
(1.05)
0.0964
(0.40)
(5)
-0.0561∗∗
(-2.61)
-0.0284
(-0.50)
75
0.683
0.00130
(0.54)
0.455∗∗
(2.02)
-0.0162∗∗
(-2.17)
0.000129
(0.86)
0.000424
(1.00)
(6)
-0.0554∗∗∗
(-3.08)
0.0108
(0.19)
75
0.642
-0.000949
(-0.42)
0.355
(1.42)
-0.0363
(-0.16)
0.000113
(0.73)
0.000456
(1.11)
(7)
-0.0556∗∗
(-2.53)
0.0297
(0.49)
75
0.649
-0.00145
(-0.59)
0.384
(1.51)
0.322
(0.71)
0.000133
(0.82)
0.000536
(1.17)
(8)
-0.0579∗∗∗
(-2.87)
0.0216
(0.38)
75
0.645
-0.00127
(-0.54)
0.356
(1.44)
0.127
(0.56)
0.000122
(0.77)
0.000500
(1.15)
(9)
-0.0567∗∗∗
(-2.70)
This table presents results of regressions which use systemic risk measures to predict future returns during the 1998 Russian/LTCM crisis period. Specifically, this table examines the week
j|s
of August 24-28, 1998. Return data is calculated as the week-over-week change in the market value of assets. CoVaR Beta is the institution’s Adapted Exposure CoVaR Beta, βt , measured
on a weekly basis. This measures the sensitivity of the market value of the institution’s assets to a shift from the median state of the financial system to its 1% worst state. MES measures the
average return of the institution during the 5% worst days of market returns, while Granger Causality measures the level of interconnectedness between one institution and all others. Both MES
and Granger are measured at a quarterly level. Included as controls are one-week lagged asset returns; and one-quarter lagged assets, beta, volatility, Value-at-Risk, and Expected Shortfall measures.
Table 3: Predicting Returns During the LTCM crisis - One Week Prior
37
0.00833∗∗
(2.53)
-0.246∗∗∗
(-3.01)
70
0.586
0.00781∗∗∗
(2.94)
-0.210∗∗∗
(-3.11)
70
0.628
ln(Assets)t−1
Constant
t statistics in parentheses
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Observations
R2
0.948∗∗∗
(4.31)
-0.103∗
(-1.83)
(2)
0.879∗∗∗
(4.05)
(1)
-0.0721∗∗∗
(-2.68)
Asset Returnt−1
ESt−1
VaRt−1
Volatilityt−1
Betat−1
Grangert−1
LVGt−1
MESt−1
CoVaR Betat−1
-0.0889
(-1.02)
70
0.636
0.00163
(0.46)
0.894∗∗∗
(4.12)
0.00245∗∗∗
(3.55)
(3)
-0.252∗∗∗
(-3.10)
70
0.576
0.00898∗∗∗
(2.78)
0.897∗∗∗
(4.04)
0.000111
(0.32)
(4)
-0.0932
(-1.11)
70
0.670
0.00207
(0.59)
0.928∗∗∗
(3.80)
-0.000180
(-0.59)
0.00181∗∗∗
(2.76)
-0.0926∗
(-1.67)
(5)
-0.0577∗∗
(-2.15)
-0.0962
(-1.14)
70
0.671
0.00199
(0.57)
0.908∗∗∗
(3.86)
0.00574
(1.56)
-0.000138
(-0.47)
0.00178∗∗
(2.63)
(6)
-0.0588∗∗
(-2.17)
-0.103
(-1.23)
70
0.675
0.00221
(0.64)
0.908∗∗∗
(3.88)
0.230∗∗
(2.52)
-0.000201
(-0.68)
0.00179∗∗∗
(2.77)
(7)
-0.0563∗∗
(-2.07)
-0.0929
(-1.11)
70
0.668
0.00211
(0.60)
0.900∗∗∗
(3.80)
-0.0967∗
(-1.70)
-0.000154
(-0.51)
0.00182∗∗∗
(2.73)
(8)
-0.0546∗
(-1.97)
-0.0947
(-1.14)
70
0.675
0.00204
(0.59)
0.927∗∗∗
(3.89)
-0.0988∗∗∗
(-2.69)
-0.000217
(-0.73)
0.00180∗∗∗
(2.85)
(9)
-0.0564∗∗
(-2.10)
This table presents results of regressions which use systemic risk measures to predict future returns during the 2008 Subprime Crisis, specifically surrounding the events of the week of
j|s
October 6-10, 2008. Return data is calculated as the week-over-week change in the market value of assets. CoVaR Beta is the institution’s Adapted Exposure CoVaR Beta, βt , measured on a
weekly basis. This measures the sensitivity of the market value of the institution’s assets to a shift from the median state of the financial system to its 1% worst state. MES measures the average
return of the institution during the 5% worst days of market returns, while Granger Causality measures the level of interconnectedness between one institution and all others. Both MES and
Granger are measured at a quarterly level. Included as controls are one-week lagged asset returns; and one-quarter lagged assets, beta, volatility, Value-at-Risk, and Expected Shortfall measures.
Table 4: Predicting Returns During the Lehman Bros. Crisis - One Week Prior
38
0.00188
(0.81)
-0.0530
(-0.89)
75
0.536
ln(Assets)t−2
Constant
0.0203
(0.67)
-0.000697
(-0.20)
-0.0195
(-0.24)
75
0.403
0.00568∗∗
(2.56)
-0.146∗∗∗
(-2.65)
75
0.397
0.00119∗
(1.86)
(3)
0.0157
(0.43)
0.893∗∗
(2.49)
(2)
t statistics in parentheses
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Observations
R2
-0.0220
(-0.66)
(1)
-0.0466∗∗
(-2.49)
Asset Returnst−2
ESt−2
VaRt−2
Volatilityt−2
Betat−2
Grangert−2
LVGt−2
MESt−2
CoVaR Betat−2
-0.109
(-1.54)
75
0.309
0.00368
(1.32)
0.0110
(0.32)
-0.0000258
(-0.13)
(4)
-0.0650
(-1.13)
75
0.636
0.00251
(1.03)
-0.0128
(-0.42)
0.0000686
(0.39)
0.000384
(0.85)
0.846∗∗
(2.64)
(5)
-0.0439∗∗∗
(-2.72)
-0.0936∗
(-1.80)
75
0.628
0.00397∗
(1.80)
-0.0136
(-0.48)
-0.0188∗∗∗
(-3.01)
0.000136
(0.74)
0.000442
(1.18)
(6)
-0.0393∗∗∗
(-2.70)
0.00521
(0.08)
75
0.565
-0.000826
(-0.30)
-0.00971
(-0.32)
-0.395
(-0.61)
0.0000896
(0.47)
0.000788
(1.59)
(7)
-0.0421∗∗
(-2.40)
0.00659
(0.10)
75
0.568
-0.000886
(-0.32)
-0.0116
(-0.38)
0.290
(0.72)
0.0000949
(0.49)
0.000820∗
(1.74)
(8)
-0.0421∗∗
(-2.43)
0.00434
(0.07)
75
0.565
-0.000839
(-0.31)
-0.00974
(-0.32)
0.178
(0.61)
0.0000881
(0.46)
0.000780∗
(1.67)
(9)
-0.0417∗∗
(-2.38)
This table presents results of regressions which use lagged systemic risk measures to predict returns during the 1998 Russian/LTCM crisis period. Return data is calculated as the week-overj|s
week change in the market value of assets. CoVaR Beta is the institution’s Adapted Exposure CoVaR Beta, βt , measured on a quarterly basis. This measures the sensitivity of the market value of
the institution’s assets to a shift from the median state of the financial system to its 1% worst state. MES measures the average return of the institution during the 5% worst days of market returns,
while Granger Causality measures the level of interconnectedness between one institution and all others. Included as controls are lagged asset returns, one-quarter lagged assets, beta, volatility,
Value-at-Risk, and Expected Shortfall measures. All independent variables are measured at the quarterly level.
Table 5: Predicting Returns During the LTCM crisis - Six Months Prior
39
-0.0299
(-0.27)
0.000509
(1.07)
(4)
0.0497
(0.40)
0.000354
(0.89)
0.00129
(1.27)
-0.0461
(-0.28)
(5)
-0.0814∗
(-1.95)
0.0504
(0.41)
0.0112∗
(1.69)
0.000346
(0.89)
0.000927
(0.93)
(6)
-0.0901∗∗
(-2.15)
0.0648
(0.52)
0.474
(1.29)
0.000312
(0.77)
0.000933
(0.92)
(7)
-0.0826∗∗
(-2.01)
0.0107∗∗∗
(3.83)
-0.295∗∗∗
(-4.20)
70
0.401
0.00754∗∗∗
(2.84)
-0.197∗∗∗
(-2.82)
70
0.512
ln(Assets)t−2
Constant
t statistics in parentheses
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Observations
R2
-0.0203
(-0.18)
0.0593
(0.51)
-0.145∗
(-1.71)
70
0.454
0.00401
(1.12)
-0.273∗∗∗
(-3.56)
70
0.410
0.00964∗∗∗
(3.05)
-0.0956
(-1.07)
70
0.541
0.00268
(0.72)
-0.110
(-1.24)
70
0.549
0.00282
(0.75)
-0.151
(-1.44)
70
0.547
0.00450
(1.08)
-0.133
(-1.30)
70
0.545
0.00391
(0.95)
0.0639
(0.51)
-0.206
(-1.04)
0.000342
(0.85)
0.00103
(1.00)
(8)
-0.0838∗∗
(-2.04)
0.000350
(0.88)
0.00111
(1.07)
(9)
-0.0820∗
(-1.99)
-0.126
(-1.19)
70
0.543
0.00374
(0.88)
0.0650
(0.50)
-0.0123
(-0.11)
0.00213∗∗
(2.29)
(3)
Asset Returnst−2
-0.0784
(-0.41)
(2)
-0.111
(-0.74)
(1)
-0.0895∗∗
(-2.24)
ESt−2
VaRt−2
Volatilityt−2
Betat−2
Grangert−2
LVGt−2
MESt−2
CoVaR Betat−2
This table presents results of regressions which use lagged systemic risk measures to predict returns during the 2008 Subprime crisis, specifically surrounding the events of the Lehman
j|s
Brothers collapse. Return data is calculated as the week-over-week change in the market value of assets. CoVaR Beta is the institution’s Adapted Exposure CoVaR Beta, βt , measured on
a quarterly basis. This measures the sensitivity of the market value of the institution’s assets to a shift from the median state of the financial system to its 1% worst state. MES measures
the average return of the institution during the 5% worst days of market returns, while Granger Causality measures the level of interconnectedness between one institution and all others. Included as controls are lagged asset returns, one-quarter lagged assets, beta, volatility, Value-at-Risk, and Expected Shortfall measures. All independent variables are measured at the quarterly level.
Table 6: Predicting Returns During the Lehman Bros. Crisis - Six Months Prior
40
0.00242
(0.11)
75
0.094
1.547∗
(1.97)
75
0.326
Constant
14.07
(1.46)
75
0.099
t statistics in parentheses
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Observations
R2
-0.00117
(-1.21)
-0.0603∗
(-1.87)
ln(Assets)t−8
-0.186
(-0.46)
(4)
0.819∗∗∗
(7.14)
1.681∗∗
(2.01)
75
0.336
-0.0616∗∗
(-2.14)
3.534
(0.88)
0.615∗∗
(2.47)
(3)
VaRt−8
0.300
(1.50)
(2)
-0.0260
(-0.35)
(1)
0.840∗∗∗
(6.84)
Betat−8
Grangert−8
MESt−8
CoVaR Betat−8
-0.0277
(-0.96)
75
0.173
0.000259
(0.20)
-0.267
(-1.27)
-0.0123∗
(-1.96)
-0.0308
(-0.15)
(5)
15.85
(1.40)
75
0.111
-0.360
(-0.73)
-40.81
(-0.40)
1.503
(0.77)
0.596∗∗
(2.60)
(6)
Table 7: Predicting Within Crisis Exposures Using Pre-Crisis Levels: LTCM Crisis
This table presents results of regressions which use lagged systemic risk measures to forecast systemic risk levels during the 1998 Russian/LTCM crisis. The dependent variable in each regression
j|s
corresponds to the lagged independent systemic variable. CoVaR Beta is the institution’s Adapted Exposure CoVaR Beta, βt , measured on a quarterly basis. This measures the sensitivity of the
market value of the institution’s assets to a shift from the median state of the financial system to its 1% worst state. MES measures the average return of the institution during the 5% worst days of
market returns, while Granger Causality measures the level of interconnectedness between one institution and all others. Included as controls are lagged asset returns, one-quarter lagged assets,
beta, volatility, Value-at-Risk, and Expected Shortfall measures. All independent variables are measured at the quarterly level, and are lagged two years prior to the time period of interest.
41
0.0142
(0.49)
580
0.013
1.255∗∗∗
(4.68)
580
0.331
Constant
t statistics in parentheses
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Observations
R2
-0.00287∗∗
(-2.60)
-0.0454∗∗∗
(-4.44)
-0.270
(-0.95)
2007-08
(2)
ln(Assets)t−8
VaRt−8
Betat−8
Grangert−8
MESt−8
CoVaR Betat−8
(1)
0.197∗∗
(2.30)
-2.580
(-0.56)
580
0.014
0.549∗∗∗
(2.91)
-0.0131
(-0.11)
(3)
1.390∗∗∗
(4.98)
580
0.340
-0.0500∗∗∗
(-4.85)
3.911
(1.65)
0.0489
(1.13)
(4)
0.189∗∗
(2.34)
0.0228
(0.61)
580
0.048
-0.00278∗∗
(-2.27)
-0.799∗∗
(-2.17)
-0.0340∗∗∗
(-2.88)
-1.199∗∗∗
(-3.00)
2007-08
(5)
3.017
(0.55)
580
0.024
0.409∗∗
(2.01)
10.89
(0.18)
-1.772
(-1.62)
-0.0354
(-0.29)
(6)
0.742∗
(1.94)
71
0.368
-0.0251∗
(-1.78)
8.603∗
(1.99)
0.109∗∗
(2.13)
(7)
0.213∗
(1.88)
0.109
(1.05)
71
0.111
-0.00920∗∗
(-2.49)
-0.790
(-0.97)
-0.0113
(-0.65)
0.749
(0.61)
4Q 2008
(8)
-47.58∗∗∗
(-2.74)
71
0.181
2.480∗∗∗
(3.66)
-81.41
(-0.43)
0.317
(0.13)
-0.755∗∗∗
(-2.80)
(9)
Table 8: Predicting Within Crisis Exposures Using Pre-Crisis Levels: Subprime Crisis
This table presents results of regressions which use lagged systemic risk measures to forecast systemic risk levels during the 2008 Subprime crisis, specifically surrounding the events of the
Lehman Brothers collapse. The dependent variable in each regression corresponds to the lagged independent systemic variable. CoVaR Beta is the institution’s Adapted Exposure CoVaR Beta,
j|s
βt , measured on a quarterly basis. This measures the sensitivity of the market value of the institution’s assets to a shift from the median state of the financial system to its 1% worst state. MES
measures the average return of the institution during the 5% worst days of market returns, while Granger Causality measures the level of interconnectedness between one institution and all others.
Included as controls are lagged asset returns, one-quarter lagged assets, beta, volatility, Value-at-Risk, and Expected Shortfall measures. All independent variables are measured at the quarterly
level, and are lagged two years prior to the time period of interest. Included are both regressions which examine the entire period 2007-08 and regressions which examine only the fourth quarter
of 2008.
Table 9: Return Predictability Over Long Horizons
This table presents results which display the ability of the Adapted Exposure CoVaR measure to predict returns over long horizons, ranging from
one week prior to a crisis to one year prior to a crisis period. Adapted Exposure CoVaR, along with each control, is lagged between one and four
quarters, and regressed on within crisis asset returns. The 1998 estimations correspond to the week of August 24-28, while the 2008 estimations
correspond to the week of October 6-10. Estimation (1) begins with no control variables. Estimation (2) adds quarterly lagged asset return and firm
size variables, while estimation (3) maintains these controls, and adds the quarterly lagged SES and Granger measures along with Institution Type
Fixed Effects. Finally, estimation (4) adds the quarterly lagged VaR measure to the above set of controls.
1998 Crisis
(1)
No Controls
-0.045∗∗
(-2.34)
(2)
Assets and Returns
-0.035∗
(-1.95)
(3)
Other Measures and Fixed Effects
-0.029∗
(-1.83)
(4)
VaR
-0.029∗
(-1.94)
2 Quarter Lag
-0.057∗∗∗
(-2.70)
-0.048∗∗
(-2.62)
-0.044∗∗∗
(-2.72)
-0.044∗∗∗
(-2.70)
3 Quarter Lag
-0.056∗∗
(-2.47)
-0.046∗∗
(-2.06)
-0.042∗∗
(-2.48)
-0.042∗∗
(-2.43)
4 Quarter Lag
-0.026∗∗
(-2.32)
-0.020∗∗
(-2.40)
-0.014∗∗
(-2.03)
-0.014∗
(-1.85)
1 Quarter Lag
-0.127∗∗∗
(-3.08)
-0.109∗∗∗
(-3.97)
-0.087∗∗∗
(-2.90)
-0.086∗∗∗
(-2.88)
2 Quarter Lag
-0.121∗∗∗
(-4.15)
-0.087∗∗
(-2.35)
-0.081∗
(-1.95)
-0.084∗
(-1.97)
3 Quarter Lag
-0.118∗∗∗
(-2.72)
-0.070∗
(-1.95)
-0.059
(-1.59)
-0.056
(-1.48))
4 Quarter Lag
-0.165∗∗∗
(-4.33)
-0.099∗∗∗
(-2.73)
-0.069
(-1.41)
-0.068
(-1.39)
1 Quarter Lag
2008 Crisis
t statistics in parentheses
∗
p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
42
Table 10: Return Predictability Over Longer Return Windows
This table presents results which display the ability of the Adapted Exposure CoVaR measure, lagged one quarter, to predict returns over longer
return windows than the one week windows estimated above. These windows vary depending on the crisis period. Adapted Exposure CoVaR, along
with each control, is lagged between one quarter prior to the estimation window, and regressed on within-window asset returns. The 1998 estimations are focused mainly on the week of August 24-28, while the 2008 estimations focus mainly on the week of October 6-10. Weeks surrounding
these key periods are examined as well. Estimation (1) begins with no control variables. Estimation (2) adds quarterly lagged asset return and firm
size variables, while estimation (3) maintains these controls, and adds the quarterly lagged SES and Granger measures along with Institution Type
Fixed Effects. Finally, estimation (4) adds the quarterly lagged VaR measure to the above set of controls.
(1)
No Controls
(2)
Assets and Returns
(3)
Other Measures and Fixed Effects
1998 Crisis
-0.029∗
(-1.83)
(4)
VaR
Aug. 24-28, 1998
-0.045∗∗
(-2.34)
-0.035∗
(-1.95)
Aug. 24 - Sept. 4, 1998
-0.032∗
(-1.98)
-0.026∗
(-1.67)
-0.021
(-1.52)
-0.021
(-1.60)
Aug. 24 - Sept. 11, 1998
-0.20∗
(-1.82)
-0.016
(-1.48)
-0.012
(-1.28)
-0.013
(-1.35)
Aug. 17 - Sept. 11, 1998
-0.022∗
(-1.98)
-0.016
(-1.53)
-0.011
(-1.26)
-0.011
(-1.35)
Aug. 10 - Sept. 11, 1998
-0.015∗
(-1.67)
-0.010
(-1.16)
-0.006
(-0.84)
-0.006
(-0.92)
Oct. 6-10, 2008
-0.127∗∗∗
(-3.08)
-0.109∗∗∗
(-3.97)
-0.087∗∗∗
(-2.90)
-0.086∗∗∗
(-2.88)
Sept. 29 - Oct. 10, 2008
-0.062∗∗∗
(-3.05)
-0.045∗∗
(-2.22)
-0.030
(-1.41)
-0.029
(-1.44)
Sept. 22 - Oct. 10, 2008
-0.045∗∗∗
(-3.37)
-0.032∗∗
(-2.21)
-0.022
(-1.66)
-0.022∗
(-1.69)
Sept. 15 - Oct. 10, 2008
-0.024∗∗
(-2.03)
-0.011
(-0.83)
-0.003
(-0.24)
-0.010
(-0.52)
Sept. 15 - Oct. 17, 2008
-0.029∗∗∗
(-2.66)
-0.018
(-1.60)
-0.010
(-0.91)
-0.021
(-1.40)
-0.029∗
(-1.94)
2008 Crisis
t statistics in parentheses
∗
p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
43
Table 11: The Consistency of Adapted Exposure CoVaR Beta
j|s
This table presents results test the consistency of the Adapted Exposure CoVaR Beta (β j|s ) during crisis periods. βt estimated as the sensitivity
of an institution’s assets to changes in system-wide assets. It is the result of a quantile regression which is estimated at the 1% level and contains
several macro-level conditioning variables. This measure should remain consistent from quarter-to-quarter as it is the institution’s exposure to
systemic risk. Adapted Exposure CoVaR provides an estimate of the magnitude of the change in institution assets in a given time period due to that
institution’s exposure, and thus will not remain consistent over time. Each quarter during the crisis periods, I conduct a t-test to determine whether
j|s
j|s
βt is significantly different from βt−1 . I present results of t-tests to determine whether MES t is different from MES t−1 for comparison purposes.
j|s
βt
j|s
j|s
t-value: βt different from βt−1
MES t
t-value: MES t different from MES t−1
1998 Q1
1998 Q2
1998 Q3
1998 Q4
0.243
0.242
0.245
0.249
0.0126
-0.0478
-0.0632
0.4064
-0.015
-0.019
-0.046
-0.028
-7.5569∗∗∗
2.7318∗∗∗
10.7177∗∗∗
-6.0437∗∗∗
2008 Q1
2008 Q2
2008 Q3
2008 Q4
0.162
0.189
0.159
0.161
0.8776
-0.6889
0.7791
-0.0706
-0.042
-0.033
-0.113
-0.124
0.2101
-2.8038∗∗∗
7.6695∗∗∗
0.9146
44
Figure 1: Systemic Measures During the Asian/Russian Crisis Period: 1996-1998
These figures present each of the three measures of systemic risk that I examine: Granger Causality, SES, and Adapted Exposure CoVaR,
plotted as a time series during the Asian/Russian crisis. Granger Causality measures the causal relation between the returns of two institutions. One
institution is said to Granger Cause the returns of another if there is a significant (at the 1% or 10%) level relation between lagged returns of one
institution and current returns of the other, but not vice-versa. The average number of other institutions that a given institution granger-causes in
one quarter is plotted below. Systemic Expected Shortfall (SES) is proxied for below by the Marginal Expected Shortfall (MES) measure. Together
with Leverage (LVG), MES is considered to be a core component of calculating the expected SES of an institution for a given time period. MES
measures the average return of an institution during the worst 5% of return days for the overall market during the past calendar year. Average MES
by quarter is plotted below. Adapted Exposure CoVaR measures the sensitivity of an institution’s Value-at-Risk to a shift in the state of the financial
system from its median state to its 1% worst state. Average Adapted Exposure CoVaR measures by quarter are plotted below.
0
5
10
15
Panel A: 1% and 10% Granger Causality Measures
1996q1
1996q3
1997q1
1997q3
Quarter
1% Granger
45
1998q1
10% Granger
1998q3
−.035
−.03
MES
−.025
−.02
−.015
−.01
Panel B: MES Measure
1996q1
1996q3
1997q1
1997q3
Quarter
1998q1
1998q3
1996q3
1997q1
1997q3
Quarter
1998q1
1998q3
−.35
Time−Varying Exposure CoVaR)
−.3
−.25
−.2
−.15
−.1
Panel C: Adapted Exposure CoVaR
1996q1
46
Figure 2: Systemic Measures During the Subprime Crisis Period: 2006-2008
These figures present each of the three measures of systemic risk that I examine: Granger Causality, SES, and Adapted Exposure CoVaR,
plotted as a time series during the Subprime crisis. Granger Causality measures the causal relation between the returns of two institutions. One
institution is said to Granger Cause the returns of another if there is a significant (at the 1% or 10%) level relation between lagged returns of one
institution and current returns of the other, but not vice-versa. The average number of other institutions that a given institution granger-causes in
one quarter is plotted below. Systemic Expected Shortfall (SES) is proxied for below by the Marginal Expected Shortfall (MES) measure. Together
with Leverage (LVG), MES is considered to be a core component of calculating the expected SES of an institution for a given time period. MES
measures the average return of an institution during the worst 5% of return days for the overall market during the past calendar year. Average MES
by quarter is plotted below. Adapted Exposure CoVaR measures the sensitivity of an institution’s Value-at-Risk to a shift in the state of the financial
system from its median state to its 1% worst state. Average Adapted Exposure CoVaR measures by quarter are plotted below.
0
5
10
15
Panel A: 1% and 10% Granger Causality Measures
2006q1
2006q3
2007q1
2007q3
Quarter
1% Granger
47
2008q1
10% Granger
2008q3
−.06
−.04
MES
−.02
0
Panel B: MES Measure
2006q1
2006q3
2007q1
2007q3
Quarter
2008q1
2008q3
2006q3
2007q1
2007q3
Quarter
2008q1
2008q3
−.4
Time−Varying Exposure CoVaR)
−.3
−.2
−.1
Panel C: Adapted Exposure CoVaR
2006q1
48
Figure 3: Adapted Exposure CoVaR vs. Adapted Exposure CoVaR Beta
j|s
This figure presents the time series of Adapted Exposure CoVaR and Adapted Exposure CoVaR Beta (βt ) between 1996 and 2009. Adapted
Exposure CoVaR measures the change in institution VaR given a systemic event, and allows the beta coefficient to change over time, unlike the
Exposure CoVaR measure proposed by Adrian and Brunnermeier (2010). Adapted Exposure CoVaR is presented here as its absolute value, thus, a
higher value represents a riskier firm. Beta is the coefficient from the 1% quintile regression that is estimated within the Adapted CoVaR methodology. This regression estimates the sensitivity of firm assets to a change in system-wide assets by regressing the systems week-over-week change in
assets on an institution’s week-over-week change in assets. Data from only the previous two years is incorporated in the regression.
.1
.2
.3
.4
Adapted Exposure CoVaR vs. CoVaR Beta, 1996-2009
1995q1
2000q1
2005q1
2010q1
Quarter
Adapted Exposure CoVaR
49
mean_beta
Figure 4: Forecasting Measures Over Longer Lags: 1998 Crisis
These figures present results of estimations which regress Exposure CoVaR on lagged values of Exposure CoVaR for several quarterly lags.
Estimations correspond to the the 1998 Russian/LTCM crisis period, which refers specifically to the fourth quarter of 1998. Panel A provides
coefficients, while Panel B provides t-statistics of the lagged Exposure CoVaR variable. Lags range from two quarters to eight quarters, which
corresponds to a two-year window. Exposure CoVaR measures the change in the market value of an institution’s assets in response to a shift in
industry assets from the median state to the 1% worst state. Regressions include lagged returns, assets, and risk measures as controls.
0
.2
.4
.6
.8
Panel A: Coefficients
Lag 2
Lag 3
Lag 4
Lag 5
Lag 6
Lag7
Lag 8
Lag 2
Lag 3
Lag 4
Lag 5
Lag 6
Lag7
Lag 8
0
10
20
30
40
Panel B: T-Statistics
50
Figure 5: Forecasting Measures Over Longer Lags: 2008 Crisis
These figures present results of estimations which regress Exposure CoVaR on lagged values of Exposure CoVaR for several quarterly lags.
Estimations correspond to the the 2008 Subprime crisis period, and specifically refer to the Lehman Brothers collapse in the fourth quarter of 2008.
Panel A provides coefficients, while Panel B provides t-statistics of the lagged Exposure CoVaR variable. Lags range from two quarters to eight
quarters, which corresponds to a two-year window. Exposure CoVaR measures the change in the market value of an institution’s assets in response
to a shift in industry assets from the median state to the 1% worst state. Regressions include lagged returns, assets, and risk measures as controls.
0
.1
.2
.3
.4
.5
Panel A: Coefficients
Lag 2
Lag 3
Lag 4
Lag 5
Lag 6
Lag7
Lag 8
Lag 2
Lag 3
Lag 4
Lag 5
Lag 6
Lag7
Lag 8
0
2
4
6
8
10
Panel B: T-Statistics
51