What Is The Systemic Risk Exposure of Financial Institutions? John Sedunov∗ The Ohio State University September, 2011

Abstract I compare the performance of three measures of institution-level systemic risk exposure — Exposure CoVaR (Adrian and Brunnermeier, 2010), Systemic Expected Shortfall (Acharya, et al., 2010), and Granger Causality (Billio, et al., 2010). I modify Exposure CoVaR to allow for forecasting, and estimate the ability of each measure to forecast the performance of financial institutions during systemic crisis periods in 1998 (LTCM) and 2008 (Lehman Brothers). I find that Exposure CoVaR forecasts the within-crisis performance of financial institutions, and provides useful forecasts of future systemic risk exposures. Systemic Expected Shortfall and Granger Causality do not forecast the performance of financial institutions reliably during crises.

∗

I thank my dissertation committee, Isil Erel, Bernadette Minton, and Ren´e Stulz (advisor) for their guidance and discussions. Further, I thank Tobias Adrian for his help with the CoVaR measure and seminar participants at The Ohio State University for helpful comments and feedback. Address correspondence to John Sedunov, Fisher College of Business, The Ohio State University, 740 Fisher Hall, 2100 Neil Avenue, Columbus, Ohio, 43210; or e-mail: sedunov [email protected]

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1

Introduction

Events beginning in September 2008, including the collapse of Lehman Brothers and the rescue of AIG, showed the effects that a systemic crisis can have on the economy.1 The distress and even failure of some key institutions during that time prevented the financial system from functioning normally and led to further distress of financial institutions. Because regulators, investors, and executives had a limited understanding of the exposure of individual institutions to systemic risk, it was difficult for them to effectively manage institutions during the crisis. Thus, going forward, it is important to have an effective measure of the systemic risk exposure of financial institutions. A systemic risk exposure measure is a forecast of the performance of a financial institution conditional on a crisis. Therefore, such a measure makes it possible to assess which institutions will be seriously endangered if a crisis were to occur. Further, a knowledge of which institutions have higher systemic risk exposures relative to their peers will allow researchers to investigate what determines each institution’s level of systemic risk exposure. Thus far, there is no systematic analysis of the performance of systemic risk exposure measures. This paper analyzes the existing measures of institution-level systemic risk exposure in terms of their ability to forecast the within-crisis performance of financial institutions. For this analysis, I consider two crisis periods: the LTCM crisis of 1998 and the Lehman Brothers crisis of 2008. Because each measure was developed in response to the 2008 crisis, estimates using data from the 1998 crisis can serve as out-of-sample tests of each measure’s forecasting ability. For these two periods, I especially focus on the worst weeks of the crises. The three measures of institution-level systemic risk exposure I investigate are Exposure CoVaR (Adrian and Brunnermeier, 2010), Systemic Expected Shortfall (SES, Acharya, et al., 2010), and Granger Causality (Billio, et al., 2010).2 Exposure CoVaR uses quantile regressions to esti1 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); Gray, Merton, and Bodie (2008); Adams, Fuss, and Gropp (2010);

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mate the sensitivity of the value-at-risk (VaR) of an institution’s assets to fluctuations in the VaR of the total assets of the financial system. VaR is defined as the loss that will not be exceeded at some specified confidence level (Hull, 2009). SES uses an expected shortfall methodology to estimate the sensitivity of an institution’s stock returns to overall stock market returns. Expected shortfall is defined as the expected loss an institution faces conditional on being in the tail of its distribution of returns (Hull, 2009). Granger Causality quantifies the number of other institutions to which a single institution is connected. While SES and Exposure CoVaR directly examine institution-level systemic risk exposure, Granger Causality may be interpreted as a systemic risk contribution measure or as a systemic risk exposure measure, since interconnectivity can be related to either systemic risk exposure or contribution. Systemic risk contribution measures estimate the sensitivity of the financial system to a systemic event in a single institution. The CoVaR model in Adrian and Brunnermeier (2010) is estimated unconditionally using all the available data from 1986 to 2010. This is in contrast to the other measures, which use only a portion of the data available at a given time. I therefore modify the CoVaR model of Adrian and Brunnermeier (2010) so that the measure at any point in time is estimated using only past data. Through most of the paper I focus on estimations of CoVaR where I use two years of past data, but I also discuss alternative implementations. My modification makes it possible for an institution’s systemic risk exposure to change over time. I call the modified measure Adapted Exposure CoVaR when it is estimated using two years of data. Moreover, the Exposure CoVaR methodology examines the change in the risk exposure of an institution given a systemic crisis. Thus, it is not clear that a measure such as this will forecast the performance of a financial institution. Therefore, to estimate systemic risk exposure throughout the paper, I focus on a coefficient used within the CoVaR methodology. This coefficient, Adapted Exposure CoVaR beta, estimates the sensitivity of the market value of assets of an institution to changes in the market value of the assets of the Kritzman, Li, Page, and Rigobon (2010); and Giglio (2010). In general, these papers propose models which estimate the probability of a crisis throughout the entire system based on individual bank data.

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financial system. I show that, among these measures, the CoVaR methodology of Adrian and Brunnermeier (2010) is the measure which best predicts the within-crisis performance of financial institutions over multiple crisis periods. Using a sample of the 25 largest banks, insurers, and brokers I demonstrate that a one standard deviation increase in systemic risk exposure led to a decrease of 1.79% and 1.34% in the market value of the assets of a given financial institution during the worst week of the LTCM and Lehman Brothers crises, respectively. This represents a decrease of 63.48% and 30.45% beyond mean asset returns during each week. Neither SES nor Granger Causality forecast the performance of financial institutions reliably during the worst weeks of these systemic crises. I also examine the time-series properties of the measures of systemic risk exposure by estimating the ability of each measure to forecast future risk exposures. Such predictive power would ensure that at the onset of a crisis, the set of “systemically important” institutions is not different from the group designated as such prior to the crisis. I find that Adapted Exposure CoVaR beta is superior to other measures along this criterion. My regressions show that pre-crisis exposure in terms of Adapted Exposure CoVaR beta is positively related to within-crisis exposure levels, implying that institutions which are systemically risky prior to a crisis remain risky during the crisis. I do not find similar forecasting power for the SES or Granger Causality measures. I further find that estimating systemic risk exposures using different time-series of available data leads to different levels of estimated exposure for the same institution. Specifically, measures calculated using the entire set of available data prior to a crisis are not successful in forecasting the within-crisis performance of financial institutions, while measures calculated using data available in the two year window before a crisis begins are successful in forecasting the within-crisis performance of financial institutions. This shows that systemic risk exposure changes over time within institutions, and that the modification to Exposure CoVaR that I propose is essential if it is to be used as a forecasting tool. This paper also examines how the systemic risk exposure measures perform in terms of fore3

casting stock returns during a crisis period. The market value of assets is an important measure, as it addresses the concern of institution solvency during crisis periods. However, stock returns are also integral to the viability of institutions, and they are used to calculate both MES and Granger Causality. I find that both Adapted Exposure CoVaR beta and MES forecast stock returns during the Lehman Brothers crisis period, but do not forecast stock returns during the LTCM crisis period. Granger Causality fails to forecast stock returns during both periods. Because these variables fail the out of sample forecasting test, they should not be used as forecasting tools in terms of stock returns. Given that Adapted Exposure CoVaR beta is the measure which is best suited for predicting the performance of financial institutions in terms of asset returns, I examine its properties in more detail. First, I find that Adapted Exposure CoVaR beta is successful in forecasting the withincrisis performance of financial institutions at a maximum of one year prior to the onset of a crisis period. Further, this measure is capable of forecasting an institution’s returns over periods longer than just the worst one week period of a crisis. I find that Adapted Exposure CoVaR beta has forecasting ability over cumulative return windows spanning as long as five weeks around the worst week of a crisis. I also show that Adapted Exposure CoVaR beta does not fluctuate simply due to the onset of a crisis, whereas other risk exposure variables tend to increase during a crisis period. This is because Adapted Exposure CoVaR beta is reflecting only an institution’s level of systemic risk exposure, rather than changes in the characteristics of an institution brought about by a systemic crisis. Finally, I examine the performance of Adapted Exposure CoVaR beta during a period of dramatic stock losses which is not systemic in nature. If Adapted Exposure CoVaR beta captures only the systemic component of an institution’s risk exposure, it should not forecast negative returns during a period such as this. Indeed, I find that following the Dot-Com Bubble, Adapted Exposure CoVaR beta does not forecast the performance of financial institutions. In addition to literature on systemic risk exposure, this paper also ties in with the literature on systemic risk contribution. Models of systemic risk contribution include: Tarashev, Borio, and 4

Tsatsaronis (2009); Chan-Lau (2010); Gray and Jobst (2010); Allen, Bali, and Tang (2010); and Adrian and Brunnermeier (2010). Systemic risk exposure and systemic risk contribution can be linked, as institutions which initially do not cause a crisis but have both high exposure and high contribution measures may add additional stress to the financial system in the event of a crisis. The remainder of the paper proceeds as follows. Section two describes the characteristics of a systemic risk exposure measure. Section three presents the measures of systemic risk I compare in this paper, and provides a 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.

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Characteristics of a Systemic Risk Exposure Measure

A measure of systemic risk exposure should have three characteristics. I present each characteristic below. I later investigate the performance of Systemic Expected Shortfall, Granger Causality, and Adapted Exposure CoVaR in terms of each characteristic.

2.1

Performance Predictability

A measure of institution-level systemic risk exposure is a forecast of 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 when estimated well before a crisis period because it will allow for regulators, institution executives, and investors to understand the impact that a systemic crisis would have on an institution well before its onset. 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 or stock returns. Empirically, I focus on lags as short as one week prior to a crisis and as long as four quarters prior 5

to a crisis.

2.2

Exposure Forecasting

A second characteristic of a measure of systemic risk exposure is its ability to forecast future systemic risk exposure. This is a useful feature for a measure of systemic risk exposure as it will allow the measure to assess which institutions are systemically risky prior to a crisis period. This feature may further provide evidence that a measure is not a proxy for other characteristics of financial institutions. Exposure forecasting may be particularly useful in a practical sense, as, for example, the Dodd-Frank Wall Street Reform and Consumer Protection Act requires the designation of a list of “systemically important” institutions. I empirically investigate whether a measure provides a forecast of future exposures by examining the relation between the current measure of systemic risk and its lagged values. If a measure can forecast future exposures, one would expect a positive coefficient estimate for the lagged exposure measure.

2.3

Performance Over Time

A third characteristic of a systemic risk exposure measure is that it is useful across crises. Systemic crises occur for different reasons. Thus, if a measure is too closely tied to the cause of a single crisis, it will fail to forecast the performance of financial institutions during other crisis periods. This criterion can be evaluated by examining the performance of the systemic risk measures in empirical tests conducted over different systemic crisis periods. In this case, the 1998 LTCM crisis period serves as an out of sample test, given that measures were developed in response to the 2008 subprime crisis. I infer that a measure is useful across multiple crisis periods if it is a statistically significant predictor of the performance of financial institutions for both crisis periods.

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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 (Billio, et al., 2010), and Systemic Expected Shortfall (Acharya, et al., 2010). These are three major approaches to quantifying institution-level systemic risk exposure in the literature. These measures all estimate 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 systemic risk exposure of an institution.

3.1 3.1.1

Adapted Exposure CoVaR Definition of CoVaR

Adapted Exposure CoVaR is based on Adrian and Brunnermeier (2010). The authors provide two key measures for determining the systemic risk of an institution. Each measure captures a different aspect of an institution’s systemic risk. Contribution CoVaR estimates the contribution of a single institution to the overall losses suffered by the financial system, given a crisis event. Exposure CoVaR provides an estimate of the change in an institution’s VaR given an industry-wide 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.” I denote the financial system as s. Formally, Exposure CoVaR is given by the qth -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, C(X s ) is a tail event

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s

within the system, and CoVaRqj|C(X ) is the VaR of an institution conditional on the state of the financial system3 . The variable q denotes a probability level corresponding to the left tail of the distribution of institution-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 s

s

(3.2)

Empirically, Adrian and Brunnermeier (2010) estimate exposure CoVaR on a weekly basis using quantile regressions (Koenker and Bassett, 1978), which estimate coefficients at the 1% quantile rather than at the mean. First, the authors calculate the week-to-week change in the market value of institution and industry assets. X j denotes the change in the assets of a financial institution and X s denotes the change in the assets of the system. Then, denoting a set of macroeconomic conditioning variables (including the VIX, liquidity spread4 , change in the three-month Treasury bill rate, change in the slope of the yield curve5 , change in the credit spread6 , weekly equity market return, and one year cumulative real estate sector return) as Mt−1 , the authors estimate:

X j = β j|s X s + γ j|s Mt−1 + α j|s

(3.3)

The generated coefficients are then used to estimate the VaR and CoVaR of the institution and the system at the median and q = 1% levels. Finally, β j|s is used to calculate Exposure CoVaR:

∆CoVaRqj|s = β j|s (VaRts (q) − VaRts (50%)) 3

(3.4)

The usual convention is to express VaR as a positive number even though it corresponds to a loss. Adrian and Brunnermeier (2010) do not follow that convention. Thus, their VaR estimates are negative. To avoid confusion, I follow their practice. 4 The difference between the three-month repo rate and the three-month bill rate. 5 Measured by the yield-spread between the ten-year Treasury rate and the three-month bill rate. 6 Between BAA rated bonds and the Treasury rate.

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3.1.2

Proposed Changes to Exposure CoVaR

As constructed, the estimation method of Exposure CoVaR incorporates all available past information. Thus, it is a useful tool to discern what institution-level variables are closely linked to systemic risk exposure over the full length of a sample period. However, it is not clear that the measure best-reflects the systemic risk exposure of an institution at a specific time since there is no reason for exposure to be constant over time for an institution. I thus propose two modifications to estimating Exposure CoVaR compared to the approach used by Adrian and Brunnermeier (2010). The first modification relates to the estimation of β j|s . As currently calculated β j|s does not vary over time. I allow β j|s to vary over time by using data available only over the two years prior to the quarter of estimation.7 In all regressions that follow, Exposure CoVaR will be calculated using this modified process. This modification thus allows institution-level exposures to change over time. This is a beneficial change, since the drivers of systemic risk exposure may change over time. Thus, rather than use institution-level variables to indirectly forecast systemic risk exposure, the Exposure CoVaR measure may be utilized directly to determine which institutions have the highest levels of systemic risk exposure at a specific time. Despite this change, however, the economic definition of Adapted Exposure CoVaR does not change from its original meaning, as it measures the sensitivity of the performance of financial institutions conditional on a systemic event. The second modification is to alter the way the market value of the assets of financial institutions 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 (book assets - book equity + market equity), which is a standard definition. The difference between these two approaches can be illustrated with a simple example. Given a distressed institution with marketvalued 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 7

Other short lags can be utilized, and produce similar results to those below.

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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 fluctuations in the CoVaR measure over time.

3.1.3

Adapted Exposure CoVaR Beta (βtj|s )

βtj|s estimates the exposure of the assets of an institution to a change in the assets of the financial system. Alternatively, Adapted Exposure CoVaR in its entirety provides an estimate of the change in an institution’s VaR given its level of exposure. This is because Adapted Exposure CoVaR is the product of βtj|s and the difference between the median state and 1% worst state of the financial system’s assets at time t. Thus, Adapted Exposure CoVaR is a measure that increases during crisis periods due to the state of the economy. Rather, a measure of exposure should remain reflective of the institution’s state at a given time, rather than reflective of the state of the financial system. Therefore, I use Adapted Exposure CoVaR beta (βtj|s ) throughout the paper as the primary estimate of systemic risk exposure from the CoVaR family. This measure specifically relates the sensitivity of an institution’s assets, rather than the institution’s VaR, to changes in the value of the assets of the financial system. Because of this, Adapted Exposure CoVaR beta can be thought of as a measure of the exposure of the value of an institution to a systemic crisis.

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 indices 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. However, the authors modify the Granger Causality measure so it may be utilized on an institution-level basis. The modified version of Granger Causality measures the 10

inter-connectedness of each bank within the financial system. Granger Causality tests measure linear causality between two time-series (Granger, 1969). Following Billio et al. (2010), linear inter-relationships are represented as:

Xt =

m X

a j Xt− j +

m X

b j Yt− j + t

(3.5)

d j Yt− j + ηt

(3.6)

j=1

j=1

Yt =

m X

c j Xt− j +

m X 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 the test is inconclusive, a non-linear relation may still exist. To apply this test to the financial system, the authors use the time-series of daily stock returns to determine which institutions Granger cause the returns of others. Higher levels of interconnectedness can imply that either an institution is exposed to higher levels of systemic risk, since it is connected to more institutions; or that an institution contributes more to systemic risk levels, as it drives the performance of other institutions. I utilize 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 1996-2008 using the previous three years of returns, following the authors’ method. I calculate the number of institutions that a single institution Granger causes at both a 1% and 10% level, again following the authors. This measure differs from Adapted Exposure CoVaR beta in that it examines institution-level connections rather than how one institution is influenced by the system as a whole.

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3.3

Systemic Expected Shortfall

Acharya et al. (2010) provides another measure for determining the systemic risk exposure of an institution. The Systemic Expected Shortfall (SES) of an institution describes its “propensity to be undercapitalized when the system as a whole is undercapitalized.” The authors theoretically derive the two key components of SES: Marginal Expected Shortfall (MES) and Leverage (LVG). These two components are used throughout the paper to proxy for SES. MES measures the average return of financial institutions on days when the market as a whole is in the tail of its return distribution. Here and throughout the remainder of this paper, MES is calculated at the 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 represents the daily returns of the institution. Further, the authors estimate leverage using the following approximation:

LVG =

book assets - book equity + market equity market value of equity

(3.8)

SES is different from Adapted Exposure CoVaR beta and Granger Causality in how it attempts to measure systemic risk. SES examines how an institution is affected by the entire market rather than how individual institutions affect each other, like Granger Causality does. Further, SES utilizes stock returns while Adapted Exposure CoVaR beta uses changes in the market value of an institution’s assets. Although both SES and Adapted Exposure CoVaR beta examine the impact that the system has on an institution, they do so in different ways. The MES component of SES follows a calculation method similar to that of expected shortfall. The modification MES makes to expected shortfall allows it to estimate how individual institutions’ stock returns react to those of the entire market. Because MES compares how an institution performs relative to the performance

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of the stock market, it may not provide insight beyond that provided by the CAPM beta. Finally, Adapted Exposure CoVaR beta uses quantile regressions in its estimation process, which estimates values at the 1% level, whereas other regression methods concentrate on the mean. This allows the measure to estimate systemic risk exposure in terms of the left-tail of the distribution. In turn, this lets Adapted Exposure CoVaR beta, to an extent, address the fact that tail events are rare. 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. MES also concentrates on the left tail of the return distribution, examining the 5% worst return days for the market. Granger Causality, however, does not focus on the left tail of the distribution, as no distinction regarding the severity of stock returns is made in its estimation process.

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Data

Accounting data and stock returns are collected from Compustat and CRSP, respectively. I collect VIX and LIBOR data from Bloomberg. Finally, Treasury rates and the Baa corporate bond rate are collected from the Federal Reserve. Accounting data are used in calculating the SES measure LVG, Adapted Exposure CoVaR, and control variables (namely institution size and weekly changes in asset market values). I also 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 over the previous 20 quarters.8 Then, the institutions are ranked using this size measure, and the largest 25 institutions in each category are kept for analysis.9 The moving average method prevents institutions from repeatedly transitioning in and out of the 8

Following Billio, et al. (2010), I define banks as institutions with SIC codes between 6000 and 6199, brokers as institutions with SIC codes between 6200 and 6299, and insurers as institutions with SIC codes between 6300 and 6499. 9 I have also examined the sample consisting of all financial institutions regardless of size. Results presented below hold for this larger sample.

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sample over time. My sample thus contains a total of 3,900 institution-quarter observations over the time period of 1996-2008. There are 156 different institutions in the sample, of which 50 are banks, 50 are insurers, and 56 are brokers. Return data from CRSP are used in the computation of all measures and control variables. Finally, VIX, LIBOR, and interest rate data are used as conditioning variables in estimating Adapted Exposure CoVaR. Systemic risk measures are generally computed at a quarterly level. The MES component of the SES measure is not feasible at a frequency shorter than quarterly, as fewer observations are insufficient to find a 5% threshold for low returns. The Granger Causality measure, which also uses daily returns, may be influenced by noise in the data if it is estimated over periods shorter than one quarter. The Adapted Exposure CoVaR measure is calculated at a weekly level. This is feasible due to the fact that the measure incorporates weekly macro level variables along with week-to-week changes in the market values of the assets of financial institutions.10 Adapted Exposure CoVaR can be aggregated to longer time horizons by summing its weekly values. Table 1 presents summary statistics describing the systemic risk exposure measures used in the analysis below. Some measures of systemic risk display a noticeable increase during years containing a crisis period. For example, the average Adapted Exposure CoVaR increases from -10.08% before the 1998 financial crisis to -26.34% during the crisis; and 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 the systemic risk exposure of financial institutions increased during the crisis periods. Alternatively, the average level of the Adapted Exposure CoVaR beta increases from 0.15 in 1996 to 0.24 in 1998, however, its average level decreases from 0.23 in 2006 to 0.16 in 2008. Further, levels of Granger Causality do not fluctuate much in the 1996-98 period, but experience a large shock during 2008. Average 10% Granger Causality increases from 7.81 in 2006 to 13.49 in 2008. 10

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. This methodology follows Adrian and Brunnermeier (2010).

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Table 2, panel A presents the correlation coefficients between all measures of systemic risk exposure and all control variables used in the analysis over the 1996-2008 period. For the most part, different measures of systemic risk exposure are uncorrelated. This is surprising, as it indicates that each measure is quantifying something different, even though each aims to estimate the systemic risk exposure of the institution. One reason for this difference may be due to each measure’s construction. First, note that MES has a high correlation with all of the control variables. This is to be expected, as the estimation method for MES is similar to that of ES or VaR, but with a slight modification. Moreover, MES is a measure that relates the stock returns of an individual institution to the stock returns of the market, like beta. The construction of MES thus leads to a high correlation between it and beta. The high correlation between MES and the control variables then indicates that MES may simply be a proxy for the overall riskiness of the institution rather than a measure of the systemic component of the risk exposure of financial institutions. Additionally, Granger Causality may have low correlation with other systemic risk exposure variables as it may be quantifying the wrong connections between institutions. The connections measured by Granger Causality could, for instance, be unrelated to the systemic risk exposure of financial institutions. For example, connections may be an estimate of systemic risk contribution rather than systemic risk exposure. I calculate separately correlations for only the time periods that pertain to crisis periods. As to be expected, correlation among the control variables remains high. This pattern holds true for variables in both subsamples, except beta. During the 1996-98 period, beta has a lower correlation with other control variables relative to its correlation during the entire 1996-2008 period. Further, during the 2006-08 period, beta’s correlation with other control variables is much higher relative to its correlation with control variables during the 1996-2008 period. Due to their generally high correlations with each other, I will include only one control variable in a given regression. Additionally, I plot the time-series of the quarterly sample average of systemic risk exposure variables in figures 1 and 2. Figure 1 corresponds to the 1996-98 time period, while figure 2 15

corresponds to the 2006-08 time period. Panel A of both figures displays the time-series of the Adapted Exposure CoVaR measure. In both time periods, Adapted Exposure CoVaR displays a sharp decrease (which represents an increase in institution VaR) near the onset of the systemic crisis. Specifically, this overall increase in systemic risk exposure appears in the third quarter of 1998 - directly corresponding to the Russian/LTCM crisis - where average Adapted Exposure CoVaR shifted from -21.43% to -31.15%. Moreover, during the 2006-08 period, Adapted Exposure CoVaR begins a noticeable decline between the second and third quarters of 2007, as its average value shifts from -11.40% to -18.44%. A further decline is observed during the 2008 calendar year, as average Adapted Exposure CoVaR shifts from -20.17% in the third quarter to its peak of -37.79% in the fourth quarter. The second shift directly corresponds to the events of the Lehman Brothers collapse in late 2008. In both crisis periods, the Adapted Exposure CoVaR measure signals an increase in the value-at-risk of financial institutions brought on by each institution’s exposure to systemic risk. In comparison, Adapted Exposure CoVaR beta does not move sharply prior to a crisis period. Panel B of both figures plots the quarterly average of the Granger Causality measure. In the first quarter of 1996, at a significance level of α = 1%, the average institution Granger caused the returns of 3.01 other institutions. Throughout 1997 and 1998, this value remains relatively stable, increasing only in the fourth quarter of 1998, where the average institution Granger caused the returns of 4.11 other institutions. A different pattern emerges during 2007 and 2008. Between the second quarter of 2007 and the first quarter of 2008, the average level of Granger Causality gradually rose from 1.61 to 2.21, before increasing in the second quarter of 2008 to 4.57, and remaining at that level or higher through the remainder of the crisis. In the 2006-08 period, these shifts in Granger Causality signal an increase in systemic risk exposure. The measure does not signal an increase in systemic risk exposure during the 1996-98 period. Finally, Panel C displays the quarterly average of MES during the two crisis periods. I do not plot the LVG component of SES as it remains stable throughout the sample period relative to 16

MES. During the 1997-98 period, MES sharply declines twice. First, between the third and fourth quarters of 1997, MES declines from -1.68% to -2.95%; and between the second and third quarters of 1998, average MES declines from -1.99% to -4.59%. During the 2007-08 period, average MES has one major decline. Between the second and third quarters of 2008, average MES declines from -3.29% to -11.28%. Because decreases in the value of MES represent increases in systemic risk exposure, these shifts signal an overall increase in systemic risk exposure during both crisis periods. 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 2008. βtj|s is the true measure of exposure that comes from the Adapted Exposure CoVaR methodology. Adapted Exposure CoVaR represents the change in an institution’s value-at-risk given a change in the assets of the financial system, whereas Adapted Exposure CoVaR beta estimates only the level of exposure the assets of an institution have to system-wide events. For this reason, the Adapted Exposure CoVaR measure will tend to peak during crisis periods, even if the institution’s level of exposure remains unchanged. Note that in this figure, the overall level of exposure (βi|t j ) does not display the same within-crisis peaks that Adapted Exposure CoVaR does. Table 3 presents a listing of the ten riskiest banks and insurers during the 2008 Lehman Brothers crisis period. I report the rankings in terms of each measure of systemic risk exposure. All values correspond to the week of October 6-10, 2008. The ranking of the riskiest financial institutions differs for each measure. The Marshall & Ilsley Corporation (M&I) is listed as the bank with the largest systemic risk exposure during this period, according to the Adapted Exposure CoVaR methodology. Its exposure is measured at βtj|s = 0.28. Alternatively, MES ranks the CIT Group (MES = 19.11%) and Granger Causality ranks U.S. Bancorp (Granger = 38) as the riskiest banks during this period. Moreover, the Adapted Exposure CoVaR methodology ranks Ambac and American International Group (βtj|s = 0.25 and βtj|s = 0.18, respectively) as the riskiest insurers during the October 6-10, 2008 period. The MES measure ranks Conseco (MES = -28.82%), and 17

Granger Causality ranks Hartford Financial (Granger = 34) as the riskiest insurers during the same period. The difference in the ranking of financial institutions provided by each measure is further evidence that each measure is quantifying systemic risk exposure in a different way.

5

Results

5.1

Systemic Risk Measures as Predictors of the Performance of Financial Institutions

I evaluate first whether systemic risk exposure measures can forecast how an institution will be affected by a crisis. For this set of tests, I regress within-period changes in the market value of the assets of financial institutions on each systemic risk measure. Each measure is estimated immediately before the crisis begins. Based on the characteristics presented in section 2, a measure of systemic risk exposure should forecast that high-risk institutions experience low within-crisis performance. The systemic events I study take place during 1998 and 2008. I use weekly changes in the market value of the assets of financial institutions as the dependent variable for this set of tests, as the value of assets is directly related to the solvency of an institution. For each crisis period, I examine the one week period in which the market was in its greatest period of distress. The 1998 crisis period corresponds to the Russian/LTCM crisis, where I consider the week of August 24 - 28, 1998. During this week, the stock market experienced a 4.43% decline. Further, this is the week immediately following the Russian Government’s default on domestic debt (Chiodo and Owyang, 2002). During the subprime crisis period of 2008, I examine the week of October 6-10, 2008. The market, during this week, fell 24.16%. This corresponds to the Lehman Brothers crisis period, and was reported as the worst week in 112 years for the Dow Jones Industrial Average (Paradis,

18

2008).11 In regressions presented in tables 3 and 4, I estimate the following specification: Returni,t = α + γ(S ystemici,t−1 ) + β(Controlsi,t−1 ) + λ(Institutioni ) + 

(5.1)

S ystemici,t−1 represents the vector of systemic risk terms, which includes Adapted Exposure CoVaR beta, MES, LVG, and Granger Causality; Controlsi,t−1 represents the vector of control variables, which includes an institution’s CAPM beta, volatility, 5% expected shortfall (ES), 5% valueat-risk (VaR), institution size measured by the natural logarithm of assets, and prior period changes in asset values12 ; 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 Adapted Exposure CoVaR beta can be estimated at a weekly level. Thus, I use the one-week lagged Adapted Exposure CoVaR beta in these regressions, while other measures are lagged one quarter behind. ES and VaR are two common risk management measures that I use as control variables to account for an institution’s overall level of risk exposure. Both variables are calculated in terms of stock returns. VaR is the loss that will not be exceeded at some specified confidence level, α (Hull, 2009). For all calculations, I set α at the 5% level. Thus, VaR is calculated as the fifth percentile of the daily return distribution for a given institution in a given quarter. Additionally, ES is the expected value of losses, conditional on the institution being in the tail of its return distribution (Hull, 2009). Thus, I estimate the ES of an institution by averaging all returns falling below the fifth percentile of its distribution of daily returns within a given quarter. The first set of results (table 4) presents tests pertaining specifically to the 1998 Russian/LTCM crisis period. Regressions (1) through (4) incorporate the systemic risk exposure measures of interest and basic controls to account for institution size and prior week returns as independent 11

During this week, the Federal Reserve also announced a $900 billion provision in short-term cash loans for banks, emergency lending of $1.30 trillion to non-financial companies, and reduced interest rates by 0.50%. Further, President George W. Bush considered allowing government ownership stakes in private banks. 12 Results are robust to the inclusion of asset returns lagged over longer periods.

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variables. Regressions (5) through (9) include all measures together, and add a set of controls to account for different traditional measures of an institution’s risk exposure. Note, however, that MES is not included in regressions (6) - (9), as it is highly correlated with the control variables used in each regression. Each regression includes institution fixed effects which control for whether an institution is a bank, broker, or insurer. Adapted Exposure CoVaR beta is negatively related to future crisis returns, and is statistically significant at the 5% level in regressions (5) and (7), and at the 1% level in all other regressions. This result holds regardless of which control variables and other measures of systemic risk exposure are included in a regression.13 This relation implies that riskier institutions experience lower returns during the crisis period. Using the coefficient from regression (1), -0.06, a one standard deviation increase in the systemic risk exposure of an institution implies a 1.79% decrease in an institution’s asset returns during the following week. Economically, this is a large decrease in the performance of an institution for a shift in its systemic risk exposure. In my sample, the average decrease in an institution’s market value of assets is 2.82% during the worst week of the crisis. Thus, the shift related to a one standard deviation increase in systemic risk exposure corresponds to a 63.48% decrease in institution performance beyond the mean return. Moreover, the coefficient on Adapted Exposure CoVaR beta remains near -0.06 despite the addition of MES variables, Granger Causality, and control variables. Further, the R2 for each regression including Adapted Exposure CoVaR beta is nearly double that of regressions which do not include it. Regressions including this variable have a minimum R2 of 62.81%, whereas regressions which do not include it have a maximum R2 of 40.24%. This indicates that Adapted Exposure CoVaR beta is explaining a much larger portion of the performance of financial institutions than competing measures and control variables. Measures from the SES family do not perform as well as Adapted Exposure CoVaR beta. 13

Results in this paper are presented with robust standard errors; however, all results presented in this paper are robust to bootstrapped standard errors. This addresses concerns related to cross-correlation of error terms due to return co-movement during the crisis period.

20

Coefficients from regressions (2) and (3) indicate that neither MES nor LVG forecast negative returns for institutions with higher systemic risk exposures (note that the MES measure denotes riskier institutions by lower negative values). Regression (5) shows that MES reverses its sign when included with other variables, however it lacks statistical significance. LVG retains its sign through all regressions, but is only statistically significant in regression (3). Finally, aside from regression (4), each regression incorporating the Granger Causality measure shows that it is related positively to future returns, and thus that more systemic risk exposure implies higher crisis period returns. In all regressions, Granger Causality is not statistically different from zero. The second set of results (table 5) presents regressions corresponding to the 2008 Lehman Brothers crisis period. Each regression shares the same specification as regressions in table 4. This set of results again shows that Adapted Exposure CoVaR beta has a higher level of statistical significance than SES or Granger Causality in terms of forecasting the within-crisis performance of financial institutions. Adapted Exposure CoVaR beta is statistically significant at the 5% level, and implies that higher systemic risk exposure is associated with lower crisis period returns. This relation holds equally well if other systemic risk exposure measures or control variables are included in the regression. Given the results of regression (1), a one standard deviation increase in Adapted Exposure CoVaR beta corresponds to a decrease of 1.34% in asset returns during the crisis period. This once again represents an economically large decrease in the performance of financial institutions. The average institution’s assets decreased in value by 4.40% during this week, which means that the change in institution performance implied by a one standard deviation shift in Adapted Exposure CoVaR beta represents a 30.45% decrease in institution performance beyond the mean level. In this case, R2 ’s are not notably larger in regressions containing Adapted Exposure CoVaR beta. This is because coefficients on the MES variable predict higher returns for financial institutions with higher systemic risk exposures at a 10% significance level. Thus, the coefficients on MES and LVG are again opposite of what is expected during a crisis period. Finally, the Granger Causality measure predicts that highly connected institutions earn lower returns during the crisis 21

period; however these results are not statistically significant. Additionally, it would be helpful for a measure to forecast the within-crisis performance of financial institutions when estimated well before a crisis period occurs. I provide estimates similar to the above set of tests, which examine the predictive power of systemic risk exposure measures for institution-level asset returns six months prior to a crisis. In this case, I estimate the systemic risk measures at a quarterly level, lag them two quarters, and use them to forecast asset value changes during each crisis period. These estimates use the specification of equation (5.1). Tables 6 and 7 provide the results of these regressions. Table 6 presents results corresponding to the 1998 Russian/LTCM crisis period. Here, the sixmonth lagged Adapted Exposure CoVaR beta predicts that riskier institutions should experience lower returns during the crisis period. This measure is significant at a 1% level in regressions (5) and (6), and at a 5% level in all other regressions. Using Adapted Exposure CoVaR beta’s coefficient from regression (1), 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 forecasts lower returns for risky institutions at a 5% significance level, implying a decrease in within-crisis returns of 1.38% for a one standard deviation increase in systemic risk exposure. However, Adapted Exposure CoVaR beta has a higher level of statistical significance when incorporated together with MES in regression (5). Moreover, estimates including Adapted Exposure CoVaR beta yield a higher R2 than other regressions. The lowest R2 for a regression which includes Adapted Exposure CoVaR beta is 53.60% while the maximum R2 for a regression which does not include Adapted Exposure CoVaR beta is 40.25%. These facts suggest that Adapted Exposure CoVaR beta is the superior long-horizon forecaster of within-crisis returns. Finally, the Granger Causality measure forecasts higher returns for risky institutions; however, the measure is not statistically significant. Table 7 presents a set of results corresponding to the 2008 Lehman Brothers crisis period. The Adapted Exposure CoVaR beta, lagged six months, forecasts that riskier institutions will experience lower returns during the crisis period. This measure is significant at the 5% level in each 22

regression, except for regressions (5) and (9), where the measure is significant at the 10% level. In this case, a one standard deviation shift in systemic risk exposure predicts a 1.68% decrease in within-crisis returns. The MES measure in these regressions suggests that riskier institutions earn higher returns; however, its coefficients are not statistically significant. Finally, the Granger Causality measure also implies that high risk institutions will experience higher within-crisis returns, however, it is not statistically significant. Economically, these results may be a function of the construction of each variable. The SES measures do not forecast performance over multiple time periods. This may be a result of the variable being tied closely to the 2008 subprime crisis period. Moreover, 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. Thus, MES 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 Granger Causality is measuring only connections where two institutions are linked in one direction, then it may not be suitable for forecasting within-crisis performance. It may be more useful to estimate the number of other institutions which affect a single institution.

5.2

Systemic Risk Measures as Predictors of Stock Returns

Tables 8 and 9 present estimates which utilize institution stock returns during a crisis period as the dependent variable. These estimates use the specification of equation (5.1). This is an important test as the SES and Granger Causality measures are designed using stock returns, and it is useful to understand how each measure behaves in terms of predicting the within-crisis stock performance of institutions. Table 8 presents estimates for the 1998 crisis period. I find that although Adapted Exposure CoVaR beta and MES correctly associate higher risk with lower returns, both coefficients lack statistical significance. These estimates show that for a one standard deviation increase in risk 23

exposure measured by Adapted Exposure CoVaR beta, an institution’s within-crisis weekly stock returns decrease by 0.51%. Further, using the coefficient from regression (2), a one standard deviation increase in MES predicts a 1.99% decrease in weekly stock returns. The Granger Causality measure is not a statistically significant predictor of stock returns during the 1998 crisis period. Finally, the R2 ’s for regressions (1) and (2) do not have a large disparity between them, as their difference is 1.39%. The respective levels of the R2 ’s, 20.80% and 22.19%, are lower than the R2 ’s of regressions in which the market value of institution assets is the dependent variable. Measures thus do not explain the variation in stock returns as well as they explain the variation in asset returns. However, both Adapted Exposure CoVaR beta and MES are explaining a similar portion of the variation in stock returns during this crisis period. Table 9 presents regressions which examine the 2008 crisis period. Adapted Exposure CoVaR beta is statistically significant at the 10% level in regressions (7) - (9), which include other measures of systemic risk exposure and control variables. A one standard deviation increase in Adapted Exposure CoVaR beta forecasts a decrease of 2.04% in within-crisis weekly stock returns. Alternatively, MES is statistically significant in both regressions in which it is included. This is not surprising, as the SES measures were developed specifically in response to the 2008 crisis period. A one standard deviation increase in MES predicts a 4.17% decrease in within-crisis weekly stock returns. The R2 ’s during this period are again relatively close in value, as the difference between the R2 of regressions (1) and (2) is 6.26% (respectively, R2 ’s are 24.65% and 30.91%). Thus, even though MES was developed specifically for this crisis period, there is not necessarily a large difference in its ability to explain the variation in stock returns from that of Adapted Exposure CoVaR beta. Finally, the Granger Causality measure is not statistically significant in any regression. The measure again forecasts higher returns for riskier institutions. Because systemic risk measures were conceived in response to the 2008 crisis, the 1998 crisis period provides an out-of-sample test to discern the effectiveness of the measures. Ideally, a measure of systemic risk exposure should be capable of forecasting the within-crisis performance 24

of financial institutions regardless of the underlying cause of the crisis period. Neither SES nor Adapted Exposure CoVaR beta is able to forecast stock returns during the 1998 crisis period despite their ability to do so in the 2008 crisis period.

5.3

Systemic Risk Exposure Over Time

In this section, I evaluate how systemic risk evolves over time. First, I examine the ability of each of the measures of systemic risk exposure to forecast the future exposure of financial institutions. Second, I investigate whether systemic risk exposures change over time by estimating the forecasting power of Exposure CoVaR and MES when they are calculated using different sets of pre-crisis data. This test will also provide insight into the benefits of the modification to Exposure CoVaR that I propose.

5.3.1

Systemic Risk Measures as Predictors of Future Systemic Risk Exposures

For a systemic risk exposure measure to be useful, institutions which are estimated as high-risk prior to a crisis should also be at high risk during a crisis. I thus present regressions in tables 10 and 11 with the following specifications: S ystemici,t = α + γ(S ystemici,t−8 ) + β(Controlsi,t−8 ) + λ(Institutioni ) + 

(5.2)

In these regressions, the set of control variables includes beta, VaR, and institution size measured by the natural logarithm of assets. I lag estimates of systemic risk 8 quarters before the crisis period. Again, all variables are measured at the quarterly level. If systemic risk exposures are similar over time, then lagged measures should be positively related to current measures. I use pre-crisis exposure estimates to predict exposures during the fourth quarter of 1998 and the fourth quarter of 2008. Table 10 provides results of regressions corresponding specifically to the 1998 Russian/LTCM 25

crisis period. 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%. A one standard deviation shift in exposure implies an increase in crisis period Adapted Exposure CoVaR beta of 0.13. The lagged MES measure is not a statistically significant predictor of crisis level exposure. Further, the measure is sensitive to the addition of control variables, as its coefficient switches from positive in regression (2) to negative in regression (5). Finally, the Granger Causality measure predicts within-crisis exposures at the 5% level. A one standard-deviation shift in this measure is related to an increase of 5.95 institutions that a given institution is linked to during the crisis period. Table 11 provides results specifically linked to the 2008 subprime crisis. I estimate regressions during all quarters in the 2007-08 period and during only the fourth quarter of 2008, which corresponds directly to the Lehman Brothers crisis. Again, lagged Adapted Exposure CoVaR beta predicts levels of exposure for the entirety of the 2007-08 period at the 5% level, and for the 2008 Q4 period at the 10% level. During the fourth quarter of 2008, a one standard deviation shift in lagged Adapted Exposure CoVaR beta predicts an increase of 0.06 in crisis period exposure. The MES measure does not provide a statistically significant result during the fourth quarter of 2008. Finally, the Granger Causality measure predicts that institutions which are systemically risky prior to the crisis period will be less interconnected, and thus less risky, during the crisis period. Granger Causality is statistically significant during the fourth quarter of 2008 at the 1% level.

5.3.2

Changes In Systemic Risk Exposure Over Time

Table 12 considers whether systemic risk exposure changes over time. What drives systemic risk exposure during one crisis period may not drive systemic risk exposure during another crisis period. If systemic risk exposures remain constant over time, then it is best to use the entire time-series of available data rather than limited samples of available data to calculate Exposure CoVaR or SES. Note that I refer here to Exposure CoVaR and not to Adapted Exposure CoVaR. The Exposure 26

CoVaR method utilizes all available past information, directly following Adrian and Brunnermeier (2010). These regressions also directly test the benefit of the modification to Exposure CoVaR that I propose. Panel A provides summary statistics for Exposure CoVaR beta and MES estimated with different estimation periods. For 1998, the average estimate of Exposure CoVaR beta using two years of past data is larger than the estimate which uses all past data, while in 2008 the average estimate using all past data is larger than the estimate which uses the previous two years of data. In both 1998 and 2008, MES estimates using one previous year of data estimate higher systemic risk exposure than estimates which use the entire time-series. For both SES and Exposure CoVaR beta, the difference between estimates using the different datasets calculated in 1998 is smaller than the difference between estimates calculated in 2008. If exposure to systemic risk is constant over time, then there would be no difference between estimates of each measure in a given quarter. Panel B shows estimates of regressions which use the measures calculated with the full timeseries of available data and lagged one quarter as predictors of the performance of financial institutions in terms of asset returns during the crisis periods. These regressions use the specification of equation (5.1). Regression (1) includes the Exposure CoVaR beta, institution size, lagged asset returns, and institution fixed effects as independent variables. In 1998, Exposure CoVaR beta is a significant predictor of the performance of financial institutions while in 2008 it is not. Further, regression (2) uses MES as the key independent variable. MES is a significant predictor of the performance of financial institutions in 1998 while it is not in 2008. Regression (3) includes both variables along with a set of control variables including institution size, lagged returns, Granger Causality, and institution fixed effects. Both MES and Exposure CoVaR beta are statistically significant predictors of the performance of financial institutions during 1998 while they are not statistically significant in 2008. Once again, Exposure CoVaR beta has a higher level of statistical significance than that of MES during the 1998 crisis period. Finally, regression (4) includes Exposure CoVaR beta, and adds value-at-risk to the set of control variables. Exposure CoVaR beta is 27

again a significant predictor of performance during 1998 but not during 2008. Results showing that measures are successful in predicting the 1998 crisis period performance of financial institutions may be due to the fact that the long series estimates are closer in value to short series estimates during the 1998 crisis relative to the same relation in the 2008 crisis period. These results further show that there is value in allowing the estimation window to be short in the calculation of systemic risk exposure variables. This is because systemic risk exposures change over time. Thus, the modification I propose is essential if Exposure CoVaR beta is to be used as a forecasting variable.

5.4

Discussion

It is beneficial if a measure of systemic risk exposure forecasts the performance of financial institutions over all crisis periods. If a measure is too heavily based on one crisis period, it will not be a reliable forecasting tool for future crisis periods. This is why the 1998 out of sample test is an important indicator of which measure is best suited for this purpose. The Adapted Exposure CoVaR beta measure fulfills this condition between the two most recent systemic crisis periods in the United States. The MES measure does not forecast asset returns during the 2008 crisis, and it does not meet the level of statistical significance of Adapted Exposure CoVaR beta during the 1998 crisis. Further, the Granger Causality measure is not a reliable forecasting tool during either crisis period. The above results, taken together, mean that Adapted Exposure CoVaR beta is the best measure for providing early warning signs of which institutions are most at risk should a crisis occur. Each alternative measure, while having strengths along some dimensions of the proposed criteria, does not perform as well across all tests and all crisis periods as Adapted Exposure CoVaR beta.

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6

Robustness

The above sections show that Adapted Exposure CoVaR beta is a suitable approach to estimating an institution’s systemic risk exposure. Regressions 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 the performance of financial institutions when lagged more than two quarters before a crisis. Also, it is helpful to understand if the measures can forecast the performance of financial institutions when cumulative return windows are extended beyond one week. Finally, I examine how measures perform during periods of dramatic stock losses which are not systemic in nature.

6.1 6.1.1

Using Longer Lags for Adapted Exposure CoVaR Beta Predicting Performance

It is helpful to understand first the amount of time prior to the onset of a crisis over which Adapted Exposure CoVaR beta can forecast the within-crisis performance of financial institutions. I show above that the measure is a reliable forecasting tool six months prior to a crisis; however the measure may be reliable well before then. Table 13 provides results of regressions which include the Adapted Exposure CoVaR beta measure from one quarter to one year prior to each crisis period as the key independent variable. These regressions use a similar format to equation (5.1). Regression (1) begins with no control variables added, while regression (2) adds the lagged asset returns and lagged institution size variables. Regression (3) adds to that the lagged MES, LVG, and Granger Causality measure as well as the set of institution fixed effects. Finally, regression (4) adds the institution’s VaR as a control variable. During the 1998 crisis, Adapted Exposure CoVaR beta is a reliable predictor of the performance of financial institutions at the 5% significance level or better up to one year prior to the onset of the crisis. This forecasting ability is robust to the inclusion of all control variables. The measure, 29

however, is a reliable predictor two quarters in advance of the 2008 crisis period. There is a noticeable decline in statistical significance between regressions (2) and (3), due to the inclusion of other measures of systemic risk exposure. Recall that these measures were developed particularly in response to the 2008 crisis. Thus, MES, LVG, and Granger Causality are explaining a portion of the performance of financial institutions, too. Without the other systemic risk exposure measures, however, Adapted Exposure CoVaR beta is a reliable predictor over the full one year horizon in 2008.

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 of a crisis. I now study lag lengths between two quarters and two years. I use the format of equation (5.2), and simply change the lag time of Adapted Exposure CoVaR beta on the right-hand side of the equation. Figures 4 and 5 both provide results of these tests for the 1998 and 2008 crisis periods, respectively. In both cases, as one approaches the crisis period, lagged estimates of Adapted Exposure CoVaR beta gain predictive power. For these figures, I consider the quarter prior to and following the crisis period for the Russian/LTCM crisis, which corresponds to 1998Q3 - 1999Q1. The quarters from 2007Q1 - 2008Q4 are considered for the 2008 crisis period.

6.2

Forecasting Over Long Return Windows

I also examine the cumulative return windows over which Adapted Exposure CoVaR beta is an effective predictor of returns during the crisis period. These regressions use the specification of equation (5.1). In this set of regressions, the key independent variable is the six month lagged Adapted Exposure CoVaR beta. Column (1) includes only the Adapted Exposure CoVaR beta on the right-hand side of the regression. Column (2) includes lagged institution size and lagged 30

changes in the market value of institution assets as control variables. Column (3) adds MES, LVG, and Granger Causality along with institution fixed effects, while column (4) adds the institution’s value-at-risk as a final control variable. Table 14 provides results of these tests. The first row of regressions for each crisis period examines the one week period of asset returns presented in all results above. Following this, regressions for the 1998 crisis include dependent variables ranging from two week cumulative returns to a maximum of five week cumulative returns. The longest window extends two weeks beyond the worst week of the crisis period (to Sept. 11, 1998) and two weeks before the worst week of the crisis period (to Aug. 10, 1998). With the exception of the final regression, which is the over the longest period, all regressions are robust to a longer cumulative return window. This longer window may be capturing returns which occurred before the onset of the crisis, as it includes the one week period prior to Russia’s default. Generally, as the window is expanded, the Adapted Exposure CoVaR beta loses some statistical significance. This pattern extends to the 2008 crisis period. Cumulative return windows for this crisis again cover periods between two and five weeks in length. With the exception of the four week period beginning with Sept. 15, 2008, results are robust to longer cumulative return windows and the addition of all control variables. Outside of a crisis period, it is not clear that high-systemic risk institutions should suffer lower returns relative to their counterparts.14 Thus, Adapted Exposure CoVaR beta may not have forecasting power for cumulative return windows which include non-crisis periods.

6.3

The Fluctuation of βtj|s During Crisis Periods

I estimate whether the βtj|s coefficient fluctuates during a crisis period. Where Adapted Exposure CoVaR estimates the magnitude of the changes in the VaR of an institution due to the institution’s 14

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 regressions show that highsystemic risk institutions do not have returns which are significantly different from low-systemic risk institutions during non-crisis periods.

31

exposure to systemic risk, βtj|s measures the actual exposure of the institution to systemic risk. Estimated exposure to systemic risk should not vary simply because the probability of a systemic crisis has increased. In other words, exposure should not vary based on macro-level conditions. Exposure may, however, vary on an institution-level due to the choices made by an institution as to its level of systemic risk exposure. Table 15 presents a set of results which examine whether βtj|s fluctuates given a macro-level increase in the probability of a systemic crisis. For the sample periods of 1998Q1 - 1998Q4 and 2008Q1 - 2008Q4, I estimate t-tests which evaluate whether the average βtj|s is statistically j|s different from the average βt−1 on a quarterly basis. In each case, I find that the average βtj|s does

not fluctuate from quarter to quarter on a system-wide basis. This is in sharp contrast to MES and Granger Causality (results reported in table 15 only include MES), which both display statistically significant changes from quarter-to-quarter during the crisis periods.

6.4

Adapted Exposure CoVaR Beta During Periods of Dramatic Losses

To discern whether Adapted Exposure CoVaR beta is exclusively measuring the exposure of financial institutions to systemic risk or if it is also estimating exposure to non-systemic risk, I estimate a set of regressions examining its forecasting power during the end of the Dot-Com Bubble. Accordingly, if the measure is only estimating systemic risk exposure, it should not forecast negative performance during this period. The Dot-Com Bubble ended in March of 2000. Following this, the market suffered its worst week during April 7-11, 2000, when the NASDAQ lost over 27% of its value. Table 16 provides results of these regressions. Each regression uses the format of equation (5.1), as they include asset returns as the dependent variable, and a set of institution-level controls as independent variables. I do not include other measures of systemic risk exposure in these tests. For each regression, Adapted Exposure CoVaR beta is not statistically significant. Further, the measure implies that high-risk institutions earn lower returns. This relation holds for all regres32

sions, regardless of which control variable is included. This set of results implies that the measure is not estimating any risk beyond institution-level systemic risk exposure.

7

Conclusion

This paper tests the performance of three measures of systemic risk exposure - Exposure CoVaR (Adrian and Brunnermeier, 2010), SES (Acharya, et al., 2010), and Granger Causality (Billio, et al., 2010) - during two different systemic crisis periods. The primary criterion upon which I evaluate each measure is the ability to forecast the within-crisis performance of financial institutions during the worst weeks of the crises. Further, this paper proposes a modification to the CoVaR estimation methodology. The modified measure, Adapted Exposure CoVaR, incorporates only two years of past data in its estimation, while the model of Adrian and Brunnermeier (2010) incorporates all past data. This modification accounts for any change in the systemic risk exposure of an institution over time. I find that among the three measures, the Exposure CoVaR methodology best measures systemic risk exposure. Specifically, the Adapted Exposure CoVaR beta reliably forecasts the performance of financial institutions in different crisis periods, and is a predictor of future risk exposures, where Adapted Exposure CoVaR beta is a coefficient from the CoVaR methodology which relates the change in an institution’s assets to a change in the assets of the financial system. Moreover, this paper examines the bounds of the forecasting ability of Adapted Exposure CoVaR beta. I find that Adapted Exposure CoVaR beta can forecast the within crisis performance of financial institutions up to one year prior to the beginning of a crisis period, and that it can forecast the performance of financial institutions over the five week cumulative return windows surrounding the worst week of a crisis. I also examine the benefits of my proposed modification to Exposure CoVaR. I find that Exposure CoVaR provides a reliable forecast of institution performance when it includes only two years of past data in its estimation, but not when it includes all available past data. This shows that

33

systemic risk exposure changes over time within institutions. Thus, estimating Exposure CoVaR using only two years of past data is an essential modification if the measure is to be used to forecast the performance of financial institutions during future crisis periods. The MES and LVG measures, along with the Granger Causality measure, are not suited for use as forecasting variables. These measures lack statistical significance in empirical tests of their forecasting ability. Further, between each crisis period, these variables estimate different relations between systemic risk exposure and the performance of financial institutions. These measures may thus have different meanings during different crisis periods. Future research can focus on understanding the drivers of institution-level systemic risk by incorporating Adapted Exposure CoVaR beta 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 exposure by leading to more interconnectedness in the financial system or by leading institutions to take on greater positions in exotic securities. By exploring these drivers, the reason as to why some systemic risk exposure measures perform differently in different time periods can be examined. Finally, this work may lead to a better understanding of why institutions decide to increase their exposure to systemic risk over time.

34

References [1] Acharya, V. (2009): “A Theory of Systemic Risk and Design of Prudential Bank Regulation”, Journal of Financial Stability, 5, 224-255. [2] Acharya, V., L.H. Pedersen, T. Philippon, and M. Richardson (2010): “Measuring Systemic Risk”, Working Paper, New York University. [3] Adams, Z., R. Fuss, and R. Gropp (2010): “Modeling Spillover Effects Among Financial Institutions: A State-Dependent Sensitivity Value-at-Risk (SDSVaR) Approach”, Working Paper. [4] Adrian, T. and M. Brunnermeier (2010): “CoVaR”, Working Paper, Federal Reserve Bank of New York. [5] Allen, L., T.G. Bali, and Y. Tang (2010): “Does Systemic Risk in the Financial Sector Predict Future Economic Downturns?”, Working Paper. [6] Billio, M., M. Getmansky, A.W. Lo, and L. Pelizzon (2010): “Measuring Systemic Risk in the Finance and Insurance Sectors”, Working Paper. [7] Chiodo, A. and M.T. Owyang (2002): “A Case Study of a Currency Crisis: The Russian Default of 1998”, Federal Reserve Bank of St. Louis Review, November Issue, 7-18. [8] Chan-Lau, J. (2010): “Regulatory Capital Charges for Too-Connected-To-Fail Institutions: A Practical Proposal”, IMF Working Paper. [9] Giglio, S. (2010): “Credit Default Swap Spreads and Systemic Financial Risk”, Working Paper. [10] Granger, C.W.J. (1969): “Investigating Causal Relations by Econometric Models and CrossSpectral Methods”, Econometrica, 37(3), 424-438.

35

[11] Gray, D., A. Jobst (2010): “Systemic Contingent Claims Analysis (Systemic CCA) - Estimating Potential Losses and Implicit Government Guarantees to Banks”, IMF Working Paper (Washington: International Monetary Fund). [12] Gray, D., R. Merton, and Z. Bodie (2008): “New Framework for Measuring and Managing Macrofinancial Risk and Financial Stability”, Working Paper. [13] Hull, J.C. (2009): “Risk Management and Financial Institutions”, Prentice Hall. [14] Koenker, R. and G. Bassett (1978): “Regression Quantiles”, Econometrica, 46(1), 33-50. [15] Kritzman, M., Y. Li, S. Page, and R. Rigobon (2010): “Principal Components as a Measure of Systemic Risk”, Working Paper. [16] Lehar, A. (2005): “Measuring Systemic Risk: A Risk Management Approach”, Journal of Banking and Finance, 29, 2577-2603. [17] Paradis, T. (2008): “Wall Street Ends Mixed After 8 Days of Losses; Dow Swings Over 1,000 Pts. to End Lower”, Associated Press, October 10, 2008. [18] Tarashev, N., C. Borio, and K. Tsatsaronis (2009): “The Systemic Importance of Financial Institutions”, BIS Quarterly Review, September, 75-87. [19] United States. Cong. House. Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010. 111th Cong., 2010

36

37

Adapted Exposure CoVaR -.1008108 .1465407 -.2011936 .4406193 -.2634084 .3949794

Year 2006 Mean Std. Dev. 2007 Mean Std. Dev. 2008 Mean Std. Dev.

Adapted Exposure CoVaR -.1191412 .16364 -.1506515 .1666067 -.2423113 .3475484

Panel B: Subprime Crisis, 2006-2008

Year 1996 Mean Std. Dev. 1997 Mean Std. Dev. 1998 Mean Std. Dev.

Panel A: Pre-crisis and Russian/LTCM Crisis of 1998 Q4

Exposure CoVaR Beta .2301 .3135 .2051 .2300 .1676 .2157

Exposure CoVaR Beta .1552 .2221 .2093 .3797 .2447 .3574

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

This table presents summary statistics for key variables used in the analysis below. I report summary statistics for the two crisis periods that are studied: the Russian/LTCM crisis of the late 1998 and the Lehman Brothers crisis of late 2008. Adapted Exposure CoVaR corresponds to the Adapted Exposure CoVaR of a institution 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 system returns is allowed to change over time. Exposure CoVaR Beta refers to the βtj|s coefficient that comes from the the Adapted Exposure CoVaR methodology. This coefficient measures the sensitivity of the assets of a financial institution to the assets of the financial system. 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.

Table 1: Summary Statistics

38

Panel B: 1996-1998

Panel A: 1996-2008

Variables Adapted Exposure CoVaR Beta LVG MES Granger VaR ES Volatility Beta

Variables Adapted Exposure CoVaR Beta LVG MES Granger VaR ES Vol. Beta

Adapted Exposure CoVaR Beta 1.000 0.284 0.056 -0.145 0.090 0.081 -0.071 0.027

Adapted Exposure CoVaR Beta 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 0.077 0.086 -0.124 0.047

1.000 -0.150 0.071 -0.164 -0.120 0.147 0.261

1.000 -0.010 0.626 0.658 -0.518 -0.576

Granger

SES Family LVG MES

1.000 -0.080 0.721 0.735 -0.654 -0.684

Granger

SES Family LVG MES

1.000 0.927 -0.852 -0.273

VaR

1.000 0.939 -0.890 -0.526

VaR

1.000 0.539

1.000 -0.882 -0.271

1.000 0.279

Control Variables ES Volatility

1.000 -0.910 -0.518

Control Variables ES Vol.

1.000

Beta

1.000

Beta

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 1996-2008, the Russian/LTCM crisis period of 1996-98, and the Subprime crisis period of 2006-08. Adapted Exposure CoVaR Beta refers to the βtj|s coefficient that comes from the the Adapted Exposure CoVaR methodology. This coefficient measures the sensitivity of the assets of a financial institution to the assets of the financial system. 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.

Table 2: Correlation Matrix of Systemic Risk Measures

39

Panel C: 2006-2008

Variables Adapted Exposure CoVaR Beta LVG MES Granger VaR ES Vol. Beta

Adapted Exposure CoVaR Beta 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

40

Bank CIT Group Keycorp Citigroup, Inc. Sovereign Bancorp SLM Corp. Marshall & Ilsley Corp. Huntington Bancshares Bank of America Comerica, Inc. Suntrust Banks Insurer Conseco, Inc. Phoenix Companies Protective Life Corp. Lincoln National Corp. Prudential Financial Unumprovident Corp. Principal Financial Group American International Group, Inc. Hartford Financial AFLAC, Inc.

CoVaR βtj|s 0.286 0.177 0.176 0.165 0.165 0.160 0.152 0.137 0.123 0.119 CoVaR βtj|s 0.250 0.180 0.150 0.132 0.131 0.125 0.123 0.098 0.093 0.086

Bank Marshall & Ilsley Corp. Capital One Financial Corp. Northern Trust Corp. Bank of New York, Inc. Citigroup, Inc. Wells Fargo & Co. PNC Financial Services Group, Inc. American Express Co. J.P. Morgan Chase & Co. U.S. Bancorp

Insurer Ambac Financial Group, Inc. American International Group, Inc. Chubb Corp. CNA Financial Corp. Aetna, Inc. Allstate Corp. MBIA, Inc. Unumprovident Corp. AFLAC Inc. American Financial Group, Inc.

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

MES -28.82% -24.97% -24.51% -21.92% -18.73% -18.13% -17.66% -15.97% -15.17% -13.21%

MES -19.11% -18.67% -17.91% -17.29% -16.48% -15.16% -14.29% -14.04% -13.30% -12.98%

Insurer Hartford Financial American International Group, Inc. Loews Corp. MBIA, Inc. Protective Life Corp. Conseco, Inc. Phoenix Companies Anthem, Inc. CNA Financial Corp. Lincoln National Corp.

Bank U.S. Bancorp SLM Corp. Sovereign Bancorp BB&T Corp. PNC Financial Services Group, Inc. Wells Fargo & Co. Bank of America J.P. Morgan Chase & Co. Regions Financial Corp. Huntington Bancshares

Granger 34 30 29 25 19 19 16 13 13 12

Granger 38 36 32 32 31 30 23 23 22 14

This table presents the ten banks and insurers with the highest exposure to systemic risk during the 2008 Lehman Brothers crisis. The systemic risk exposure of each institution is reported in terms of the βtj|s coefficient which comes from the Adapted Exposure CoVaR methodology, Marginal Expected Shortfall (MES), and Granger Causality. Granger Causality connections are measured at the 10% significance level. The exposures reported are estimated as of the week of October 6-10, 2008.

Table 3: Riskiest Institutions During the Lehman Brothers Crisis

41 -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 asset returns during the 1998 Russian/LTCM crisis period. Specifically, this table examines the j|s week 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 shifts in the market value of the assets of the financial system. 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. Fixed Effects which account for whether an institution is a bank, broker, or insurer are also included.

Table 4: Predicting Returns During the Russian/LTCM crisis - One Week Prior

42 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 asset returns during the 2008 Subprime Crisis, specifically surrounding the events of the week j|s of 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 shifts in the market value of the assets of the financial system. 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. Fixed Effects which account for whether an institution is a bank, broker, or insurer are also included.

Table 5: Predicting Returns During the Lehman Brothers Crisis - One Week Prior

43 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 asset returns during the 1998 Russian/LTCM crisis period. Return data is calculated as the j|s 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 shifts in the market value of the assets of the financial system. 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. Fixed Effects which account for whether an institution is a bank, broker, or insurer are also included. All independent variables are measured at the quarterly level.

Table 6: Predicting Returns During the Russian/LTCM crisis - Six Months Prior

44 -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 asset 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 shifts in the market value of the assets of the financial system. 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. Fixed Effects which account for whether an institution is a bank, broker, or insurer are also included. All independent variables are measured at the quarterly level.

Table 7: Predicting Returns During the Lehman Brothers Crisis - Six Months Prior

45

0.000576 (0.73)

0.000466 (0.50)

(9) -0.0142 (-0.41)

0.335 (1.55) 74 0.208

0.291 (1.49) 75 0.222

0.296 (1.55) 75 0.215

0.357∗ (1.90) 75 0.211

t statistics in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

Observations R2

Constant

-0.0152∗∗ (-2.07)

-0.0176∗∗ (-2.34)

0.299 (1.39) 74 0.231

-0.0146∗ (-1.76)

0.197 (0.86) 74 0.284

-0.00914 (-0.99)

0.350 (1.47) 74 0.216

-0.0176∗∗ (-2.03)

0.306 (1.21) 74 0.219

-0.0164∗ (-1.89)

0.352 (1.48) 74 0.216

-0.0176∗∗ (-2.06)

-0.0138∗ (-1.74)

-0.0187 (-0.26)

-0.621 (-0.52)

0.000534 (0.69)

0.000268 (0.33)

(8) -0.00926 (-0.24)

-0.0163∗ (-1.95)

-0.0300 (-0.43)

-0.0642 (-0.08)

0.000567 (0.70)

0.000462 (0.50)

(7) -0.0140 (-0.41)

ln(Assets)t−1

-0.0601 (-0.93)

-0.0557∗∗ (-2.31)

0.000565 (0.74)

0.000412 (0.40)

(6) -0.00927 (-0.33)

-0.0307 (-0.44)

-0.0651 (-1.13)

0.000669 (0.83)

0.000183 (0.18)

1.130 (1.46)

(5) -0.0195 (-0.63)

-0.0627 (-1.11)

-0.0392 (-0.60)

0.000541 (0.75)

(4)

-0.0286 (-0.47)

-0.0275 (-0.44)

0.000485 (0.57)

(3)

Returnst−1

1.003 (1.27)

(2)

0.0653 (0.12)

(1) -0.0169 (-0.58)

ESt−1

VaRt−1

Volatilityt−1

Betat−1

Grangert−1

LVGt−1

MESt−1

CoVaR Betat−1

This table presents results of regressions which use systemic risk measures to predict future stock returns during the 1998 Russian/LTCM crisis period. Return data is calculated as the j|s week-over-week change in the institution’s stock price. 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 shifts in the market value of the assets of the financial system. 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. Fixed Effects which account for whether an institution is a bank, broker, or insurer are also included.

Table 8: Predicting Stock Returns During the Russian/LTCM Crisis - One Quarter Prior

46 0.139 (0.66) 70 0.309

t statistics in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

Observations R2

0.283 (1.24) 70 0.246

-0.00835 (-0.96)

-0.0172∗∗ (-2.01)

ln(Assets)t−1 Constant

0.342∗∗∗ (3.71)

0.785∗∗∗ (2.71)

(2)

0.387∗∗∗ (4.13)

(1) -0.109 (-1.28)

Returnst−1

ESt−1

VaRt−1

Volatilityt−1

Betat−1

Grangert−1

LVGt−1

MESt−1

CoVaR Betat−1

0.0477 (0.12) 70 0.235

-0.00750 (-0.45)

0.361∗∗∗ (3.56)

-0.00227 (-0.60)

(3)

0.209 (0.87) 70 0.228

-0.0149 (-1.52)

0.377∗∗∗ (3.93)

0.0000740 (0.05)

(4)

0.0989 (0.26) 70 0.333

-0.00603 (-0.37)

0.347∗∗∗ (3.62)

0.00130 (1.01)

-0.00264 (-0.74)

0.752∗∗ (2.58)

(5) -0.115 (-1.43)

0.130 (0.35) 70 0.382

-0.00448 (-0.27)

0.336∗∗∗ (4.20)

-0.0590∗∗∗ (-3.76)

0.00115 (0.93)

-0.00221 (-0.63)

(6) -0.107 (-1.39)

0.170 (0.46) 70 0.387

-0.00652 (-0.40)

0.337∗∗∗ (4.04)

-1.981∗∗∗ (-4.45)

0.00164 (1.31)

-0.00266 (-0.74)

(7) -0.141∗ (-1.88)

0.0880 (0.23) 70 0.356

-0.00514 (-0.31)

0.322∗∗∗ (3.66)

1.117∗∗∗ (3.83)

0.00145 (1.05)

-0.00235 (-0.63)

(8) -0.137∗ (-1.72)

0.0985 (0.26) 70 0.351

-0.00545 (-0.33)

0.337∗∗∗ (3.68)

0.714∗∗∗ (3.88)

0.00151 (1.18)

-0.00289 (-0.79)

(9) -0.136∗ (-1.72)

This table presents results of regressions which use systemic risk measures to predict future stock 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 institution’s stock price. 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 shifts in the market value of the assets of the financial system. 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. Fixed Effects which account for whether an institution is a bank, broker, or insurer are also included.

Table 9: Predicting Stock Returns During the Lehman Brothers Crisis - One Quarter Prior

47 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)

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 j|s regression corresponds to the lagged independent systemic risk exposure 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 shifts in the market value of the assets of the financial system. 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. Fixed Effects which account for whether an institution is a bank, broker, or insurer are also included. All independent variables are measured at the quarterly level, and are lagged two years prior to the time period of interest.

Table 10: Predicting Within Crisis Exposures Using Pre-Crisis Levels: Russian/LTCM Crisis

48 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)

ln(Assets)t−8 -2.580 (-0.56) 580 0.014

0.549∗∗∗ (2.91) 1.390∗∗∗ (4.98) 580 0.340

-0.0500∗∗∗ (-4.85)

3.911 (1.65)

(4) 0.189∗∗ (2.34)

VaRt−8

-0.0131 (-0.11)

(3)

0.0489 (1.13)

-0.270 (-0.95)

2007-08 (2)

Betat−8

Grangert−8

MESt−8

CoVaR Betat−8

(1) 0.197∗∗ (2.30)

0.0228 (0.61) 580 0.048

3.017 (0.55) 580 0.024

0.409∗∗ (2.01)

10.89 (0.18)

-0.799∗∗ (-2.17) -0.00278∗∗ (-2.27)

-1.772 (-1.62)

-0.0354 (-0.29)

(6)

-0.0340∗∗∗ (-2.88)

-1.199∗∗∗ (-3.00)

2007-08 (5)

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)

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 risk exposure variable. CoVaR beta is the institution’s Adapted Exposure j|s CoVaR beta, βt , measured on a quarterly basis. This measures the sensitivity of the market value of the institution’s assets to shifts in the market value of the assets of the financial system. 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. Fixed Effects which account for whether an institution is a bank, broker, or insurer are also included. Included are both regressions which examine the entire period 2007-08 and regressions which examine only the fourth quarter of 2008.

Table 11: Predicting Within Crisis Exposures Using Pre-Crisis Levels: Lehman Brothers Crisis

Table 12: Systemic Risk Exposures Over Time This table presents results which display the ability of Exposure CoVaR and MES to predict returns when estimated using all available data. Since Adapted Exposure CoVaR uses two years of past data in its calculation and MES uses one quarter of previous data in its calculation, this table presents a set of tests which examine the benefits of the modification I propose to Exposure CoVaR. Panel A provides summary statistics comparing the within-crisis mean and standard deviation of the measures when different sets of past data are used. Panel B provides regressions which use the format of equation (5.1). Regressions (1) and (2) include CoVaR beta and MES, respectively, with controls for institution size and lagged returns. Regression (3) includes both measures together along with LVG and Granger Causality measures. Regression (4) includes VaR as a control for institution-level risk exposure along with CoVaR beta. All regressions include institution fixed effects. Panel A: Summary Statistics 1998 Mean 0.196

1998 Std. Dev. 0.211

2008 Mean 0.245

2008 Std. Dev. 0.257

CoVaR Beta - Prev. Two Years MES - All Data

0.245 -0.019

0.299 0.006

0.161 -0.034

0.197 0.012

MES - Prev. Quarter

-0.046

0.019

-0.125

0.051

CoVaR Beta - All Data

Panel B: Systemic Risk Measures Using All Available Data as Forecasting Tools 1998 Crisis CoVaR Beta - All Data MES - All Data

CoVaR Beta - All Data MES - All Data

(1) -0.079∗∗∗ (-4.09)

(2) -

(3) -0.065∗∗∗ (-5.16)

3.012∗∗∗ 2.205∗∗∗ (2.94) (3.56) 2008 Crisis -0.007 (-0.20)

-0.024 (-0.81) -

-0.205 (-0.34)

49

0.056 (0.07)

(4) -0.073∗∗∗ (-3.78) -0.008 (-0.30) -

Table 13: Return Predictability Over Longer Horizons This table presents results which display the ability of Adapted Exposure CoVaR beta 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 beta, along with each control, is lagged between one and four quarters, and regressed on within crisis asset returns. The 1998 regressions correspond to the week of August 24-28, while the 2008 regressions correspond to the week of October 6-10. Regression (1) begins with no control variables. Regression (2) adds quarterly lagged asset return and institution size variables, while regression (3) maintains these controls, and adds the quarterly lagged SES and Granger measures along with Institution Fixed Effects. Finally, regression (4) adds the quarterly lagged VaR measure to the above set of controls.

1 Quarter Lag

(1) No Controls -0.045∗∗ (-2.34)

1998 Crisis (2) (3) Assets and Returns Other Measures -0.035∗ -0.029∗ (-1.95) (-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)

-0.014∗∗ (-2.03)

-0.014∗ (-1.85)

1 Quarter Lag

-0.127∗∗∗ (-3.08)

-0.020∗∗ (-2.40) 2008 Crisis -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)

t statistics in parentheses ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

50

Table 14: Return Predictability Over Longer Cumulative Return Windows This table presents results which display the ability of the Adapted Exposure CoVaR beta measure, lagged six months, 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 beta, along with each control, is lagged six months prior to the estimation window, and regressed on within-window cumulative asset returns. The 1998 regressions are focused mainly on the week of August 24-28, while the 2008 regressions focus mainly on the week of October 6-10. Weeks surrounding these key periods are examined as well. Regression (1) begins with no control variables. Regression (2) adds quarterly lagged asset return and institution size variables, while regression (3) maintains these controls, and adds the quarterly lagged SES and Granger measures along with Institution Fixed Effects. Finally, regression (4) adds the quarterly lagged VaR measure to the above set of controls.

(1) No Controls

(2) (3) Assets and Returns Other Measures 1998 Crisis -0.048∗∗∗ -0.044∗∗∗ (-2.62) (-2.72)

(4) VaR

Aug. 24-28, 1998

-0.057∗∗∗ (-2.70)

-0.043∗∗∗ (-2.70)

Aug. 24 - Sept. 4, 1998

-0.080∗∗ (-2.27)

-0.072∗∗ (-2.25)

-0.067∗∗ (-2.27)

-0.068∗∗ (-2.25)

Aug. 24 - Sept. 11, 1998

-0.073∗∗ (-2.07)

-0.062∗ (-1.90)

-0.060∗∗ (-2.02)

-0.059∗ (-1.94)

Aug. 17 - Sept. 11, 1998

-0.082∗∗ (-2.28)

-0.065∗ (-1.99)

-0.054∗ (-1.84)

-0.055∗ (-1.80)

Aug. 10 - Sept. 11, 1998

-0.078∗ (-1.98)

-0.043 (-1.28)

-0.043 (-1.28)

-0.081∗∗ (-1.95)

-0.083∗ (-1.97)

Oct. 6-10, 2008

-0.121∗∗∗ (-4.15)

-0.057 (-1.56) 2008 Crisis -0.087∗∗ (-2.35)

Sept. 29 - Oct. 10, 2008

-0.148∗∗∗ (-4.30)

-0.107∗∗ (-2.24)

-0.106∗∗ (-2.03)

-0.108∗∗ (-2.03)

Sept. 22 - Oct. 10, 2008

-0.163∗∗∗ (-4.13)

-0.113∗∗ (-2.10)

-0.119∗∗ (-2.13)

-0.120∗∗ (-2.12)

Sept. 15 - Oct. 10, 2008

-0.139∗∗∗ (-3.02)

-0.079 (-1.24)

-0.086 (-1.35)

-0.087 (-1.34)

Sept. 15 - Oct. 17, 2008

-0.185∗∗∗ (-3.99)

-0.123∗ (-1.93)

-0.129∗ (-1.95)

-0.128∗ (-1.92)

t statistics in parentheses ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

51

Table 15: The Fluctuation of Adapted Exposure CoVaR Beta j|s

This table presents results which test the fluctuations of the Adapted Exposure CoVaR beta (β j|s ) during crisis periods. βt is 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 not fluctuate from quarter-to-quarter as it is the institution’s exposure to systemic risk. Adapted Exposure CoVaR beta provides an estimate of the magnitude of the change in the VaR of an institution over a given time period due to that institution’s exposure, and thus will change over time due to macro-level conditions. Each quarter during the crisis periods, I j|s j|s conduct a t-test to determine whether 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

52

Table 16: Predicting Performance During Periods of Dramatic Stock Losses: The Dot-Com Bubble This table presents regressions which examine the ability of Adapted Exposure CoVaR beta to predict the performance of financial institutions during periods of dramatic stock losses which were not systemic. Return data is calculated as the week-over-week change in the market value of j|s 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 shifts in the market value of the assets of the financial system. Included as controls are one-week lagged asset returns; and one-quarter lagged assets, beta, volatility, value-at-risk, and expected shortfall measures. Fixed Effects which account for whether an institution is a bank, broker, or insurer are also included. For the Dot-Com Bubble, I use the week of Apr. 7, 2000 as the period of interest. During this period, the NASDAQ lost over 27% of its value.

CoVaR Betat−1

(1) -0.0162 (-1.25)

Betat−1

(2) -0.0168 (-1.32)

Dot-Com Bubble (3) (4) -0.0163 -0.0162 (-1.31) (-1.25)

(5) -0.0161 (-1.25)

-0.00605 (-1.52) -0.284∗∗ (-2.00)

Volatilityt−1 VaRt−1

0.0428 (0.56)

ESt−1

0.0683 (1.11) 0.263∗∗ (2.26)

0.262∗∗ (2.37)

0.249∗∗ (2.29)

0.261∗∗ (2.24)

0.248∗∗ (2.14)

ln(Assets)t−1

0.00176∗ (1.93)

0.00229∗∗∗ (2.67)

0.00176∗∗ (2.18)

0.00177∗ (1.95)

0.00174∗ (1.98)

Constant

-0.0439∗ (-1.82) 74 0.404

-0.0517∗∗ (-2.33) 74 0.423

-0.0345 (-1.56) 74 0.448

-0.0424∗ (-1.76) 74 0.406

-0.0399∗ (-1.74) 74 0.417

Asset Returnt−1

Observations R2

t statistics in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

53

Figure 1: Systemic Measures During the Russian/LTCM Crisis Period: 1996-1998 These figures present each of the three measures of systemic risk that I examine: Adapted Exposure CoVaR, Granger Causality, and SES, plotted as a time-series during the Russian/LTCM crisis. Adapted Exposure CoVaR calculates the percentage change in an institution’s Value-atRisk given 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. 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.

−.35

−.3

Adapted Exposure CoVaR −.25 −.2 −.15

−.1

Panel A: Adapted Exposure CoVaR

1996q1

1996q3

1997q1

1997q3 Quarter

54

1998q1

1998q3

0

5

10

15

Panel B: 1% and 10% Granger Causality Measures

1996q1

1996q3

1997q1

1997q3 Quarter

1% Granger

1998q1

1998q3

10% Granger

−.05

−.04

MES −.03

−.02

−.01

Panel C: MES Measure

1996q1

1996q3

1997q1

1997q3 Quarter

55

1998q1

1998q3

Figure 2: Systemic Measures During the Lehman Brothers Crisis Period: 2006-2008 These figures present each of the three measures of systemic risk that I examine: Adapted Exposure CoVaR, Granger Causality, and SES, plotted as a time-series during the Lehman Brothers crisis. 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. 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.

−.4

Adapted Exposure CoVaR −.3 −.2

−.1

Panel A: Adapted Exposure CoVaR

2006q1

2006q3

2007q1

2007q3 Quarter

56

2008q1

2008q3

0

5

10

15

Panel B: 1% and 10% Granger Causality Measures

2006q1

2006q3

2007q1

2007q3 Quarter

1% Granger

2008q1

2008q3

10% Granger

−.15

−.1

MES

−.05

0

Panel C: MES Measure

2006q1

2006q3

2007q1

2007q3 Quarter

57

2008q1

2008q3

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 2008. 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 institution. Adapted Exposure CoVaR beta is the coefficient from the 1% quantile regression that is estimated within the Adapted CoVaR methodology. This regression estimates the sensitivity of institution 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.

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Adapted Exposure CoVaR vs. CoVaR Beta, 1996-2008

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Figure 4: Forecasting Measures Over Longer Lags: 1998 Crisis These figures present results of regressions which utilize Adapted Exposure CoVaR beta as the dependent variable and lagged values of Adapted Exposure CoVaR beta for several quarterly lags as the independent variable. Regressions correspond to the the 1998 Russian/LTCM crisis period, which refers specifically to the fourth quarter of 1998, and its two surrounding quarters. Panel A provides coefficients, while Panel B provides t-statistics of the lagged Adapted Exposure CoVaR beta variable. Lags range from two quarters to eight quarters, which corresponds to a two-year window. Adapted Exposure CoVaR beta 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.

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Panel A: Coefficients

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Figure 5: Forecasting Measures Over Longer Lags: 2008 Crisis These figures present results of regressions which utilize Adapted Exposure CoVaR beta as the dependent variable and lagged values of Adapted Exposure CoVaR beta for several quarterly lags as the independent variable. Regressions correspond to the the 2008 Lehman Brothers crisis period, and include data from the first quarter of 2007 through the fourth quarter of 2008. Panel A provides coefficients, while Panel B provides t-statistics of the lagged Adapted Exposure CoVaR beta variable. Lags range from two quarters to eight quarters, which corresponds to a two-year window. Adapted Exposure CoVaR beta 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.

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