Week 5

Journal of Banking and Finance 71 (2016) 183–205

Contents lists available at ScienceDirect

Journal of Banking and Finance

journal homepage: www.elsevier.com/locate/jbankfin

Derivatives usage, securitization, and the crash sensitivity of bank

stocks �

Rouven Trapp a , Gregor N.F. Weiß b , ∗

a Technische Universität Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany b Universität Leipzig, Grimmaische Str. 12, D-04109 Leipzig, Germany

a r t i c l e i n f o

Article history:

Received 9 July 2015

Accepted 4 July 2016

Available online 9 July 2016

JEL Classification:

G32

M40

G01

Keywords:

Financial crisis

Equity tail risk

Derivatives

Securitization

Risk disclosure

a b s t r a c t

We show that the information on derivatives usage and securitization activities of U.S. banks as disclosed

in their pre-crisis 10-K filings explains extreme equity returns of banks during the financial crisis. Stocks

of banks that had previously disclosed a more extensive use of financial derivatives and loan securitiza-

tion were more likely to experience extreme losses. Our findings are consistent with investors viewing

banks that used derivatives for non-hedging purposes as highly vulnerable to the crisis. Moreover, banks

which had significant securitization activities and were thus potentially exposed to under-capitalized risks

from conduits possess a higher vulnerability of their equity to market downturns.

© 2016 Elsevier B.V. All rights reserved.

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. Introduction

Many commentators of the recent financial crisis have stressed

he notion that the panic of 20 07–20 08 was set in motion by a

un on the sale and repurchase market (see, e.g., Gorton and Met-

ick, 2012 ). In particular, high uncertainty about the solvency and

he involvement and risk exposure of banks in the market for se-

uritized loans sparked a “run on repo” that ultimately caused the

nterbank lending market to freeze (see Kwan, 2009 ) and subse-

uently the temporary insolvency of the U.S. banking system. Ad-

itionally, ex-post analyses of the crisis have concluded that inade-

uate risk management at many banks contributed to the severity

� Former title: Disclosed derivatives usage, securitization, and the systemic equity

isk of banks. We received very useful comments from Carol Alexander (the editor),

wo anonymous referees, Itay Goldstein, Scott Hendry, Dilip Madan, Seung Jung Lee,

lfred Lehar, Babak Lotfaliei, Jens Müller, Bettina Schiller, Lakshmanan Shivakumar,

oenke Sievers, André Uhde, Thomas Werner, and participants of the 2014 North-

rn Finance Association Annual Conference and the TAF research seminar at the

niversity of Paderborn. We are grateful to Judith Lameyer, Janina Mühlnickel, Sara

chmidt, and Christin Schumacher for their outstanding research assistance. Support

y the Collaborative Research Centers “Statistical Modeling of Nonlinear Dynamic

rocesses” (SFB 823, project A7) and “Economic Risk” (SFB 649) of the German Re-

earch Foundation (DFG) is gratefully acknowledged. ∗ Corresponding author.

E-mail addresses: rouven.trapp@tu-dortmund.de (R. Trapp), weiss@uni-

eipzig.de , weiss@wifa.uni-leipzig.de (G.N.F. Weiß).

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ttp://dx.doi.org/10.1016/j.jbankfin.2016.07.001

378-4266/© 2016 Elsevier B.V. All rights reserved.

f the crisis. 1 Yet, the majority of both theoretical and empirical

nalyses on the financial crisis and systemic risk in banking have

olely concentrated on the role of banks’ business models (see

runnermeier et al., 2012 ), their funding fragility and leverage (see

drian and Shin, 2010; Brunnermeier and Pedersen, 2009 ) as well

s their risk culture and corporate governance (see Fahlenbrach

nd Stulz, 2011; Aebi et al., 2012; Fahlenbrach et al., 2012 ). In this

aper, we investigate whether bank transparency concerning the

anks’ securitization activities and risk management can explain

xtreme stock returns of U.S. banks during the financial crisis. 2

ore precisely, we show that information on the securitization ac-

ivities and risk management of U.S. banks as disclosed in their

re-crisis 10-K filings explains the sensitivity of their equity prices

o market downturns during the crisis. Banks with a more elab-

rate use of financial derivatives and which securitized loans had

ignificantly higher Marginal Expected Shortfall (MES) and �CoVaR

stimates in 20 07–20 09. Analyzing the former (counterintuitive)

esult in more detail, we find the use of financial derivatives to

ave a particularly detrimental effect on banks’ equity returns in

1 For example, the Financial Crisis Inquiry Commission concluded in January 2011

hat “[...] dramatic failures of corporate governance and risk management at many

ystemically important financial institutions were a key cause of this crisis.” 2 Note that we consider banks’ current rather than expected returns during the

nancial crisis.

184 R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205

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case the bank employs derivatives primarily for non-hedging pur-

poses.

There now exists a wide consensus among financial economists

that the reluctance of banks to lend in the interbank market as

well as the credit crunch that ensued were at least in part due to

the opacity of banks and the uncertainty of investors about banks’

default risk (see Heider et al., 2010; Pritsker, 2010; Flannery et al.,

2013 ). In fact, the importance of financial reporting transparency

for market discipline and financial stability had been previously

underlined well before the start of the crisis in scientific stud-

ies (see, e.g., Flannery and Thakor, 2006 ) and by regulators (see

Basel Committee on Banking Supervision, 1998; 2001; Corporation,

2002 ). 3 The empirical evidence on the relation between account-

ing transparency and financial stability, however, is mixed at best.

For example, Barth et al. (2004) find no evidence for a decreas-

ing effect of higher bank transparency on the likelihood of a fi-

nancial crisis at the country-level. In contrast, Nier (2005) shows

that extreme negative stock returns become less likely with greater

transparency. 4 Although overall accounting transparency is gener-

ally associated with less firm risk of banks, the opposite is true for

unfavorable disclosures like, e.g., reports on a bank’s risk exposure.

Kothari et al. (2009) find that negative disclosures from firm and

press sources increase a company’s cost of capital and stock return

volatility. Closely related to their finding, Liu et al. (2004) and Lim

and Tan (2007) find banks’ trading Value-at-Risks (VaR) to have

predictive power for the banks’ total risk and future stock return

volatility. Investors in bank equities thus appear to act on disclosed

information on the market risk exposure of banks. Following this

line of argumentation, banks with a higher level of risk exposure

before the financial crisis could have suffered to a greater extent

from losses in stock prices than banks that had less risk exposure.

Moreover, publicly available information not only on the risk

exposure but also on a bank’s securitization activities could be pos-

itively related to large losses in the bank’s equity. As Acharya et al.

(2013) empirically show, many banks set up asset-backed commer-

cial paper conduits prior to the financial crisis to exploit regulatory

arbitrage thereby effectively securitizing assets without transfer-

ring the risks to other investors. Consequently, bank stocks could

also have experienced extreme negative returns during the crisis

because of available information on the banks’ securitization ac-

tivities that possibly made them retain under-capitalized risks on

their balance sheets. This conjecture mirrors previous research in-

dicating that securitizations impact investors’ risk assessments (see

Niu and Richardson, 2006; Barth et al., 2012; Dou et al., 2014 ).

Finally, a bank’s exposure and contribution to market-wide

shocks in equity prices could also have been caused by the banks’

extensive use of derivatives for hedging and non-hedging purposes.

While the trading volume of derivatives has increased consider-

ably during the last three decades, the empirical evidence on the

effects of derivatives usage on the performance and risk of firms

is ambiguous. 5 For instance, several studies have found the intu-

itive result that firms predominantly employ derivatives to hedge

rather than increase firm risk (see, e.g., Tufano, 1996; Guay, 1999;

Allayannis and Weston, 2001; Graham and Rogers, 2002 ). Recently,

Bartram et al. (2011) and Pérez-González and Yun (2013) found

empirical evidence that the use of financial derivatives significantly

3 The importance of transparency in financial reports is also discussed, e.g., in

Bushman and Smith (2001) who review the role of publicly reported financial ac-

counting information in the governance processes of corporations, and Hutton et al.

(2009) who show that opaque firms are more prone to stock price crashes. 4 As Nier and Baumann (2005) show, higher transparency is also associated with

more bank capital and thus higher financial stability. 5 Theoretically, hedging should not add value to a firm in case of perfect capital

markets following the famous reasoning of Modigliani and Miller (1958) . However,

market frictions could reverse this result as shown, e.g., by Smith and Stulz (1985) ,

Froot et al. (1993) , and Leland (1998) .

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educes both total firm risk and systematic risk as well as increases

rm value, respectively. Yet at the same time, several studies have

lso stressed the finding that derivatives usage does not signifi-

antly lower firm risk even if it is used for hedging purposes. 6

or example, Guay (1999) finds that systematic firm risk is unaf-

ected by the use of derivatives. Underlining this result, Hentschel

nd Kothari (2001) find that derivatives usage is not significantly

elated to a firm’s stock return volatility. In addition, the results

y Guay and Kothari (2003) and Jin and Jorion (2006) further

how that firm market values are relatively unaffected by hedging.

urning to the literature on banks’ derivatives usage, the study of

enkatachalam (1996) supports the finding that banks reduce their

isk exposure through hedging. 7 However, the study’s results also

how that only 47% of banks seem to use derivatives for hedging

urposes. Building on the idea that banks could use derivatives for

on-hedging purposes, many authors have argued that derivatives

sage could (1) tempt bank managers to engage in excessive risk-

aking (see, e.g., Franke and Krahnen, 2006 ) and (2) lead to a desta-

ilizing concentration of risks (see, e.g., Stulz, 2004; Rajan, 2005 ). 8

iven the divergent views in both the accounting and finance lit-

rature, the question of the effects of derivatives usage on a bank’s

rm risk especially during times of crisis is ultimately an empirical

ne.

We find strong evidence that both the exposure and the con-

ribution of U.S. banks’ equity to crashes of the financial sector

uring the financial crisis was significantly driven by the banks’

se of financial derivatives. More precisely, U.S. banks that used

ore financial derivatives in general and interest rates derivatives

n particular had economically significantly higher MES and lower

CoVaR estimates. Additionally, banks which disclosed informa-

ion on their securitization of loans also had a significantly higher

xposure (but not a higher contribution) to equity market crashes

uring the crisis. Furthermore, our regression results support the

ypothesis that the crash sensitivity of U.S. bank stocks critically

epended on the banks’ derivatives usage and securitization ac-

ivities before the crisis. In particular, banks that used derivatives

or non-hedging purposes have a systematically higher equity tail

isk than other banks that either used less derivatives or that used

erivatives for hedging. Our key results are robust to the addi-

ional inclusion of various idiosyncratic control variables proxying

or the banks’ business model, regulatory capital, funding fragility

nd size. Also, the relation between the derivatives usage and se-

uritization of banks and the crash sensitivity of the banks’ eq-

ity cannot simply be explained by the fact that larger (and thus

ystemically more important) banks employ a more elaborate risk

anagement. However, our analysis should not be mistaken for

simple analysis of the causes of the financial crisis. Rather, our

nalysis is concerned with the way stock market investors reacted

o publicly available information on a bank’s potential vulnerability

uring the crisis.

Our study is related to several papers in the literature. For in-

tance, Brunnermeier et al. (2012) employ the same measures of

bank’s equity tail risk as we do arguing that both the MES and

CoVaR do not only measure the crash sensitivity of bank stocks

ut also the banks’ exposure and contribution to systemic risk, re-

pectively. Their empirical findings show that higher non-interest

6 Perhaps most famously, Berkshire Hathaway CEO Warren Buffett referred to

derivatives as “financial weapons of mass destruction” in 2003. 7 In a related study, Purnanandam (2007) finds empirical evidence that deriva-

ives enable banks to maintain smooth operating policies in the event of external

acroeconomic shocks. Consequently, users of financial derivatives (in contrast to

on-users) do not have to bear the costs of offering new terms to their relationship

borrowers or depositors. 8 Further evidence on the detrimental side-effects of (especially credit) deriva-

ives usage on financial stability is provided by Instefjord (2005) , Dewally and Shao

(2013) , and Nijskens and Wagner (2011) .

R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205 185

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10 For example, we check whether the stock prices of our sample drop at least

once below a minimum price of $1 during the time period of July 2007 to Decem-

ber 2008 and whether monthly stock returns exist in our sample that are above

300% and which are reversed in the following month. 11 Alternatives to the equity-based systemic risk measures comprise, e.g., the CDS

spread-based measures of Oh and Patton (2013) . However, measuring systemic risk

via CDS spreads requires the availability of liquid CDS on the bank names in ques-

tion. 12 Acharya et al. (2010) propose to define a market crash by a market index being

in its lower 5% tail. We follow their definition and estimate the MES accordingly

ncome increases a bank’s contribution to systemic risk as prox-

ed by its �CoVaR. In a similar study, Anginer et al. (2014a) come

o the conclusion that deposit insurance had both a beneficial ef-

ect on banks’ equity tail risk during crises as well as an adverse

ffect caused by increased risk-taking by bank managers. The eq-

ity tail risk of banks has also been studied by Anginer et al.

2014b) and Weiß et al. (2014) in the context of bank consolida-

ion. However, none of these studies looks at the role of derivatives

sage or risk disclosure during the financial crisis. Our paper is

lso related to the studies by Venkatachalam (1996) , Guay (1999) ,

urnanandam (2007) , and Bartram et al. (2011) in which the ef-

ects of using financial derivatives on idiosyncratic and systematic

isk are analyzed. In contrast, our paper is concerned with the ef-

ects of derivatives and risk disclosure on extreme stock returns of

anks. Next, our paper is related to the work of Mayordomo et al.

2014) on the nexus between banks’ derivatives holdings and sys-

emic risk. In contrast to their paper, however, we explicitly focus

n the purpose of the banks’ usage of derivatives and its effect on

xtreme stock returns. Finally, our choice of dependent variables is

elated to the study of DeFond et al. (2014) who analyze the im-

act of mandatory IFRS adoption on firm-level crash risk which is

roxied by the frequency of extreme negative stock returns. 9 They

nd that crash risk decreases among industrial firms and increases

mong financial firms after the IFRS mandate.

The paper proceeds as follows. In Section 2 , we describe our

ata and discuss both our dependent and independent variables

f interest. In Section 3 , we document our main finding that the

quity tail risk of U.S. banks during the financial crisis was driven

y information on the banks’ use of derivatives and securitization

s disclosed in their pre-crisis 10-K filings. Section 4 concludes.

. Data and methodology

The following section outlines the construction of our sample as

ell as data sources, defines the main dependent and independent

ariables used in the statistical analysis, and presents the empirical

trategy for our cross-sectional regressions.

.1. Sample construction and data sources

For the construction of our sample, we follow Fahlenbrach and

tulz (2011) and Fahlenbrach et al. (2012) and first select all banks

ith SIC codes between 60 0 0 and 630 0 listed in Thomson Reuters

inancial Datastream . We then exclude all firms that are not in the

raditional banking industry, i.e., we concentrate on banks whose

espective two-digit SIC code equals 60 (depository banks), 61,

r 62 (non-depository banks). To rule out a possible survivorship

ias, we select all banks from both the active and dead-firm lists

n Datastream . While financial accounting data is retrieved from

homson Reuters Worldscope , we manually collect information on

bank’s derivatives usage and securitization activities as well as

isk management from the banks’ respective 10-K filings with the

EC. 10-K filings are retrieved from the Morningstar Document Re-

earch database. We then content-analyze by hand the U.S. banks’

0-K filings from the fiscal year 2006 for two reasons. First, we

re interested in testing the predictive power of a bank’s pre-crisis

isk management for forecasting its extreme stock returns during

he crisis. Second, using explanatory variables from 2006 mitigates

therwise possible concerns of biased regression results due to

ndogeneity. Our initial sample comprises 1,087 U.S. banks, from

hich we first exclude banks for which Morningstar does not pro-

ide the 10-K filings from 2006 (159 firms). We also exclude banks

9 Other related studies in the literature by Beisland and Frestad (2013) and Chen

t al. (2014) examine the effects of corporate governance and fair-value accounting

ule changes on derivatives usage.

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ith no stock price available in Datastream (79 firms) at the start

f our sample and those banks with incomplete accounting data

vailable in Worldscope (305 firms). Eventually, we exclude firms

ith U.S. OTC Bulletin Board and “Pink Sheet” listings (13 firms),

econdary listings and American Depositary Receipts (ADRs) (24

rms) as well as non-primary issues (35 firms). Given that these

ata screens lead to 615 exclusions, our final sample consists of

72 U.S. banks. The construction of our final sample and the quan-

itative impact of the different data screens on the sample size are

hown in Appendix IA.I. Statistics on the U.S. banking sector pro-

ided by the Federal Deposit Insurance Corporation (FDIC) reveal

hat the sum of total assets represented by our final sample covers

7.2% of the total sum of the FDIC insured banks’ total assets in

006. Moreover, the total market cap of our sample banks in 2006

as $1.529 trillion compared to a market cap of the Datastream US

inancials Index of $3.061 trillion (note that the Datastream US Fi-

ancials Index is not solely composed of banks but also includes in-

urers and other financial firms). Our final sample should thus be

epresentative of the complete U.S. banking sector. For increased

ransparency, the names of the banks in our final sample are listed

n Appendix IA.II.

In the final step of our data collection, we apply several screen-

ng procedures for the daily returns on the banks’ stock prices to

ontrol for known data errors in Datastream and to minimize dif-

erences between returns calculated from stock prices taken from

atastream and the Center for Research in Security Prices (CRSP)

atabases (see Ince and Porter, 2006 ). 10 We find no significant evi-

ence of such data errors and the additional data screens we apply

ead to no further exclusions of banks from our sample.

In the following subsections, we define and discuss our set of

ependent and explanatory variables. Definitions and data sources

or all our variables are summarized in Appendix A .

.2. Dependent variables: measures of equity tail risk

To measure the extent to which information on risk manage-

ent and securitization affects the equity tail risk of U.S. banks,

e use one metric for the exposure and one metric for the con-

ribution of a bank to crashes in the returns on a financial sector

ndex. As such, both measures can be viewed as measures of the

rash sensitivity of a bank’s stock.

As our first dependent variable, we employ the Marginal Ex-

ected Shortfall as proposed by Acharya et al. (2010) which cap-

ures the marginal exposure of an institution to a system-wide col-

apse. 11 The MES is defined as the negative mean net equity re-

urn of a bank conditional on the financial sector as a whole ex-

eriencing an extreme crash. 12 We then follow Beltratti and Stulz

2012) and Fahlenbrach et al. (2012) and define the crisis period as

he time period from 1st of July, 2007 to 31st of December, 2008

nd compute the MES for each sample bank for this period using

he Datastream US Financials Index (DS code FINANUS) as a proxy

or the U.S. financial sector. 13 , 14 To be precise, we construct our

sing the 5% threshold. 13 Note that the periods over which the dependent and independent variables are

easured do not overlap. 14 We also employed the S&P 500 as an alternative market index for comput-

ng the banks’ MES in our robustness checks. The (unreported) results yielded a

186 R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205

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dependent variable by taking the mean of the daily MES estimates

computed via the dynamic model specification of Brownlees and

Engle (2012) during the crisis period. 15

As our second dependent variable, we use the �CoVaR mea-

sure proposed by Adrian and Brunnermeier (2010) as a measure

of a financial institution’s marginal contribution to the extreme re-

turns on a financial sector index. They define a bank’s CoVaR as

the Value-at-Risk of the financial system conditional on an insti-

tution being under distress. 16 The systemic risk contribution of a

bank is then proxied by the difference (referred to as �CoVaR) be-

tween CoVaR conditional on the institution being under distress

and the CoVaR in the median state of the institution. Just like the

MES, CoVaR and �CoVaR are based on the left tail of the joint

distribution of the returns on a sector index and an individual in-

stitution’s stock, and measure the externalities a bank causes on

the financial system in case of default. In our analysis, we employ

the conditional, time-varying version of the �CoVaR and estimate

it using a set of state variables that capture the evolution of tail

risk dependence over time. 17

Throughout our paper, we consider the MES and �CoVaR to be

measures of a bank’s equity tail risk rather than systemic risk (as

it is done, e.g., by Brunnermeier et al., 2012; Fahlenbrach et al.,

2012; Hovakimian et al., 2012; Anginer et al., 2014a; 2014b; Weiß

et al., 2014 ). Although both Acharya et al. (2010) and Adrian and

Brunnermeier (2010) argue in their respective studies that both

measures capture the systemic risk that emanates from an individ-

ual financial institution to the stability of the financial sector, both

measures have been heavily criticized in the literature for being

based solely on stock market returns. 18 For example, Benoit et al.

(2013) compare several equity-based measures of systemic risk and

come to the conclusion that these measures fall short in capturing

the multiple facets of systemic risk. Acharya et al. (2012) argue in

a similar fashion and point out the fact that both the MES and

�CoVaR neglect the size and the leverage of financial institutions.

In this paper, we do not consider the MES and �CoVaR as prox-

ies for the systemic risk of banks but rather as measures of the

sensitivity of the banks’ equity to crashes of the financial sector. In

this way, we circumvent an otherwise possible overinterpretation

of both the MES and �CoVaR and focus on the dynamics between

individual bank stock and sector returns during the financial crisis.

In particular, our main research hypothesis is that extreme stock

returns of banks can in part be explained by mandated disclosed

information on derivatives usage and securitization in banks’ 10-K

filings. Nonetheless, we note that extreme bank stock returns (or

equity tail risk) should of course be seen as an important part of a

bank’ systemic risk as shown, e.g., in the Capital Shortfall model of

Acharya et al. (2012) .

correlation between the two indexes of 90.64%, thus a near perfect positive corre-

lation between the two different sets of MES estimates, and our regression results

remained qualitatively and quantitatively the same. 15 To compute daily MES estimates, we follow Brownlees and Engle (2012) and

employ the Threshold-ARCH (TARCH) (see Rabemananjara and Zakoïan, 1993 ) and

ynamic Conditional Correlation (DCC) (see Engle, 2002 ) specifications for all trad-

ing days within the crisis period. As we employ back-looking averages of daily in-

ample estimates from the TARCH/DCC model, the MES estimates should not suffer

from a look-ahead bias. 16 We define a financial institution to be in distress if its stock return is in the

lower 5%-tail 17 We follow Adrian and Brunnermeier (2010) and use the change in the three-

month Treasury bill rate, the difference between the ten-year Treasury Bond and

the three-month Treasury bill rate, the change in the credit spread between BAA-

rated bonds and the Treasury Bond, the MSCI World Index as a proxy for the market

return, the return on the Case-Shiller Home Price Index, and implied equity market

volatility from VIX as state variables in the estimation of the conditional �CoVaR.

Data on interest rates are retrieved from the U.S. Federal Reserve Board’s H.15. 18 See, e.g., Bisias et al. (2012) and Giglio et al. (2013) for two recent surveys of

systemic risk measures.

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.3. Main variables of interest: derivatives usage and risk

anagement disclosure

Employing the previously described measures, we investigate

f disclosures on derivatives usage and securitization activities in

0-K filings published prior to the financial crisis explain the U.S.

anks’ equity tail risk during the crisis. We operationalize our in-

ependent variables by using a set of five measures.

The first variable that reflects derivatives usage and risk man-

gement disclosure is the Derivatives intensity, defined as the

umber of the used types of financial derivatives as disclosed

n the bank’s 10-K filing. This proxy indicates the intensity with

hich firms employ financial derivatives. While banks in the

nited States are mandated by FAS 133 to disclose information on

heir derivatives positions, the amount of information disclosed by

anks on the notional and/or fair values of derivative positions is

uite heterogeneous across our sample banks. Consequently, we

ollow Bartram et al. (2011) and employ the absolute number of

ifferent derivative types used by a bank (instead of the sum of

otional values) as a proxy of the bank’s derivatives intensity. We

rgue that the sign of the coefficient is unrestricted in our regres-

ions. On the one hand, banks may reduce their risk exposure by

sing derivatives for hedging (see Venkatachalam, 1996 ), suggest-

ng a negative sign for the corresponding coefficient. On the other

and, more intensive usage of derivatives, as signaled by a higher

erivatives intensity, may indicate that banks take higher risks (see

ranke and Krahnen, 2006 ). This expectation implies an increasing

mpact on a bank’s equity tail risk.

Our second variable, interest rate derivatives, is a dummy vari-

ble equaling one if a bank uses interest rate derivatives, and zero

f no such statement is made. Guay (1999) finds a negative correla-

ion between the use of interest rate derivatives and firm risk, in-

icating that the sign of the coefficient may be negative. However,

urnanandam (2007) provides evidence that banks with higher

isk exposures manage their interest rate risk more aggressively.

herefore, interest rate derivatives usage may increase equity tail

isk.

The third variable refers to the use of foreign exchange deriva-

ives (see Guay, 1999; Graham and Rogers, 2002 ). Similarly to the

se of interest rate derivatives, we measure the use of foreign

xchange derivatives with a dummy variable that equals one for

anks disclosing the usage of foreign exchange derivatives and zero

or those banks that do not use such derivatives. As in the case of

he use of interest rate derivatives, we argue that using derivatives

elated to foreign exchange risks may reduce a bank’s total risk.

t the same time, using FX derivatives may increase counterparty

isk. Therefore, the sign of the coefficient cannot be unambiguously

redicted.

Our fourth variable captures securitization activities disclosed

n the banks’ 10-K filings. The dummy variable equals one if a

ank discloses the use of loan securitization and zero if such in-

ormation cannot be found. As securitization implies the transfer

f risks, we may predict that its use decreases extreme bank stock

eturns. However, Acharya et al. (2013) find that banks may use se-

uritization for regulatory arbitrage without transferring the risk to

utside investors. Therefore, we expect the sign of the coefficient

o be unrestricted in our regressions.

Finally, our fifth variable disclosed risk types refers to the num-

er of risk types a bank is exposed to as disclosed in its 10-K fil-

ngs. On the one hand, the (mandatory) disclosure of more risk

ypes may indicate more risk-taking by the bank, suggesting an

xpected increasing impact on bank stock returns during the cri-

is. On the other hand, more comprehensive disclosure could indi-

ate a more alert risk management, corresponding with a decreas-

ng impact on a bank’s equity tail risk. Thus, we predict the sign of

he coefficient to be unrestricted in our regressions.

R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205 187

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.4. Control variables

In our regression analyses, we also use a comprehensive set of

ontrol variables to avoid an otherwise potential omitted-variable

ias. As control variables, we use several proxies for the banks’

ize, profitability, business profile, capital structure and market val-

ation. In the following, we discuss each control variable in turn,

ocusing on the hypothesized effect on our two measures of banks’

xtreme stock returns.

As a first control variable, we employ the natural logarithm of

he banks’ total assets as a proxy for bank size. If a bank is deemed

oo big to fail, a bank might receive a subsidy from safety net poli-

ies thereby incentivizing bank managers to take on more risks

han socially optimal. Consequently, large banks should contribute

ignificantly more to extreme downturns of a financial sector in-

ex than smaller banks. At the same time, large banks should also

ave a higher exposure of their equity to adverse effects spilling

ver from the financial sector (see O’Hara and Shaw, 1990; Acharya

nd Yorulmazer, 2008; Anginer et al., 2014b ).

Next, we include the banks’ return on assets (ROA) as an ex-

lanatory variable. We expect ROA to have a decreasing effect on

he extreme stock returns of banks as higher profits can shield

anks from the adverse effects of a financial crisis. A similar ar-

ument applies to the banks’ Tier 1 capital which we use later on

n our robustness checks. Higher bank capital can serve as a cush-

on against external shocks to the financial system thereby stabi-

izing both individual banks and the financial system as a whole

see, e.g., Kashyap et al., 2008; Hart and Zingales, 2011; BIS, 2012 ).

he opposite argument applies to the banks’ leverage, which we

ompute using the definition of Acharya et al. (2010) who define a

ank’s leverage as the book value of assets minus the book value

f equity plus the market value of equity, divided by the market

alue of equity. The expected sign of the influence of leverage on

he banks’ MES and �CoVaR is not clear ex-ante. On the one hand,

igher leverage could exert a disciplining effect on bank managers

hus limiting the risk-taking of banks. On the other hand, higher

everage could also lead to a more pronounced vulnerability of a

ank during a financial crisis (see Adrian and Shin, 2010 ). For simi-

ar reasons, we also use a proxy for the banks’ debt maturity which

e estimate by taking the banks’ ratio of their total long-term debt

o total debt. We expect a less fragile funding structure of a bank

o decrease our measures of equity tail risk as it makes the banks’

ess vulnerable to sudden shortages in liquidity during a crisis (see

runnermeier and Pedersen, 2009 ).

We also use the banks’ non-interest income to total interest in-

ome ratio as a control variable. Brunnermeier et al. (2012) state

nd confirm the hypothesis that a focus on non-core activities out-

ide the traditional lending business increases a bank’s extreme

tock returns measured by their MES and �CoVaR. Conversely, a

igher loans to total assets ratio could indicate a business model

hat focuses on lending rather than more risky activities like, e.g.,

nvestment banking. Both our proxies for equity tail risk could

lso be dependent on the banks’ risk culture. Fahlenbrach et al.

2012) show in their study that banks sticked to their risk culture

ausing them to perform similarly during both the LTCM crisis of

998 and the recent financial crisis. To control for persistence in

he banks’ risk culture, we compute and use in our regressions the

anks’ buy-and-hold returns in 1998. In addition, we make use of

he banks’ market-to-book ratio in our cross-sectional regressions.

s pointed out by, e.g., Keeley (1990) , greater charter value could

ncentivize bank managers to keep their bank’s capital ratio and to

imit their risk-taking.

Additionally, we also use in our robustness checks a proxy for

he overall transparency and amount of information disclosed in

he banks’ 10-K filings. Pérignon and Smith (2010) propose in their

tudy on a sample of international banks a simple index of the

evel of VaR-disclosure. We compute a similar VaR-disclosure in-

ex by taking the sum of several dummy variables that take on

he value of one if a certain information on the bank’s VaR-model

s disclosed, and zero otherwise. The index constituents cover the

uestions whether a) the confidence level of the VaR is disclosed,

) whether the bank calculates a model with a confidence level of

7.5% or higher, c) discloses information on the estimation method,

) the holding period, e) the employed backtests, and f) the overall

iversification effect in the bank portfolio.

Finally, we employ two standard corporate governance control

ariables in our regressions. As pointed out by, e.g., Diamond and

ajan (2009) and Aebi et al. (2012) , poor governance at banks

ould have contributed to the severity of the financial crisis. Con-

equently, we use the size and independence of the banks’ boards

o proxy for the governance of insurers before the financial cri-

is. Board size is defined as the natural logarithm of the number

f directors on a bank’s board. We expect board size to be posi-

ively related to equity tail risk because larger boards have been

ound to destroy firm value and possibly capital buffers (see, e.g.,

ermack, 1996 ). To proxy for the independence of the board, we

se the percentage of independent outside directors on the board

f directors. Because outside directors should be more concerned

bout the sensitivity of the bank’s stock price to market shocks,

e expect the board’s independence to have a decreasing impact

n extreme bank stock returns.

.5. Empirical strategy

The focus of our empirical analysis is the explanation of the

ross-sectional variation in the equity tail risk of U.S. banks dur-

ng the financial crisis. We estimate cross-sectional regressions of

he banks’ MES and �CoVaR using ordinary least squares (OLS)

ith Newey and West (1987) heteroskedasticity and autocorrela-

ion consistent standard errors. Our baseline regression models are

iven by

ES i,crisis = β0 + β1 × deri v at i v es intensit y i,pre −crisis + β2 × securit izat ion i,pre −crisis + β3 × disclosed risk types + � × bank controls i,pre −crisis + ε i . (1)

nd

CoV aR i,crisis = β0 + β1 × deri v at i v es intensit y i,pre −crisis + β2 × securit izat ion i,pre −crisis + β3 × disclosed risk types + � × bank controls i,pre −crisis + ε i . (2)

Each explanatory variable (derivatives intensity, risk manage-

ent, and control variables) is constructed using data for the end

f fiscal year 2006. As we use lagged explanatory variables, we

itigate a potential endogeneity bias caused by reverse causality

etween risk disclosure and banks’ equity tail risk. Furthermore,

he definition of the crisis period and our empirical strategy of us-

ng explanatory variables from 2006 in regressions of dependent

ariables during the crisis parallel similar approaches used in the

elated studies by Fahlenbrach and Stulz (2011) , Beltratti and Stulz

2012) , and Fahlenbrach et al. (2012) .

. Does banks’ derivatives usage increase equity tail risk?

This section provides descriptive statistics for our data sample

nd results from our univariate and multivariate analyses.

.1. Descriptive statistics

Sample summary statistics of our data are shown in Table 1 .

188 R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205

Table 1

Descriptive statistics.

Minimum Maximum 5% Quantile 95% Quantile Mean Median Standard

deviation

Panel A: Equity tail risk measures

- MES −0.1190 0.1728 −0.03060 0.0980 0.0336 0.0338 0.0419 - �CoVaR −0.0512 0.0160 −0.0419 0.0041 −0.0172 −0.0147 0.0159 Panel B: Risk management variables

- Derivatives intensity 0 16 0 3 0.62 0 1.51

- Interest rate derivatives 0 1 0 1 0.25 0 0.50

- FX derivatives 0 1 0 0 0.04 0 0.20

- Disclosed risk types 0 8 0 7 4.35 5 1.61

- Securitization 0 1 0 1 0.17 0 0.38

- VaR-disclosure index 0 5 0 0 0.09 0 0.52

Panel C: Control variables

- Total assets 0.04 1884.32 0.22 34.11 22.08 0.87 147.40

- Return on assets −0.54 6.3 0.57 2.11 1.34 1.33 0.58 - Loans 0.14 8.29 0.63 1.23 0.95 0.93 0.39

- Non-interest income −0.02 1.41 0.04 0.40 0.18 0.14 0.15 - Buy-and-hold returns 1998 −1.00 0.20 −0.56 −0.00 −0.25 −0.24 0.19 - Debt maturity 0 1 0 0.96 0.52 0.53 0.27

- Leverage 1.77 37.36 3.92 11.39 7.00 6.42 3.02

- Market-to-book ratio 0.06 0.93 0.17 0.51 0.31 0.30 0.10

- Tier 1 capital ( n = 472) 6.91 62.10 8.73 21.58 13.05 11.62 5.54 - Stock liquidity ( n = 408) −2.40 −0.00 −1.79 −0.00 −0.44 −0.13 0.63 - DtD ( n = 455) −501.50 23.68 −2.71 9.99 1.82 3.17 25.45 - Board size ( n = 28) 9 24 9.4 20.8 14.11 13 3.57 - Board independence ( n = 26) 29.33 88.26 39.32 87.71 76.30 77.49 11.62

The table presents summary statistics for the different dependent and independent variables used in the empirical study. The sample includes 477 U.S. banks for which stock

price (2007 to 2008) and accounting data (2006) were available in Thomson Reuters Financial Datastream and Thomson Worldscope , respectively, and for which 10-K filings

were available in the Morningstar Document Research database. The sample construction and used data filters are given in Appendix IA.I and the full list of sample banks is

presented in Appendix IA.II. All variables and data sources are defined in Appendix A . Total assets are given in $ billion. Accounting data are measured at the end of fiscal

year 2006 while the two systemic risk measures are estimated based on the time period 07/01/2007 to 12/31/2008.

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The mean and median MES of U.S. banks during the crisis are

3.36% and 3.38%, respectively, while the corresponding mean and

median estimates of �CoVaR are −1.72% and 1.47%, respectively. These results are similar to those reported, e.g., by Acharya et al.

(2010) and Brunnermeier et al. (2012) for the financial crisis. Es-

pecially the 95% (MES) and 5% quantiles underline that U.S. banks

did not only contribute significantly to the turmoil in the financial

sector, but their stocks also suffered to a large extent from shocks

to the sector index. The standard deviation of the MES is consider-

ably higher than the standard deviation of our �CoVaR estimates.

In addition, the difference between the minimum and maximum

estimates is significantly smaller for �CoVaR than for the MES.

These findings show that the stocks of U.S. banks reacted quite dif-

ferently to the shocks to the sector index. In contrast, the influence

of shocks from individual bank stocks on the sector index was less

pronounced with �CoVaR having less variation across our sample

banks.

The U.S. banks in our sample had a mean derivatives intensity

of 0.6264 with the median being zero. The majority of banks used

zero to three types of financial derivatives in 2006 as shown by the

5% and 95% quantiles. Almost one quarter (24.74%) of our sample

banks disclosed using financial derivatives to lower their interest

rate risk exposure. At the same time, only 4.2% mentioned in their

10-K filing that they were using derivatives to hedge against for-

eign exchange risks. U.S. banks also disclosed a considerable num-

ber of risk types in their 10-K filings. On average, a U.S. bank ex-

plicitly mentioned 4.348 different sources of risk it was exposed

to. The median number of disclosed risk types was 5. Finally, on

average, 16.98% of our U.S. sample banks disclosed using the secu-

ritization of loans to transfer credit risk to other market investors.

As presented in Panel C of Table 1 , our sample includes a di-

verse set of small and large banks. The mean and median total

assets of our sample banks were $22.08 billion and $0.87 billion,

respectively. In addition to a large number of smaller banks, our

ample also includes several very large banks with total assets of

p to $1.88 trillion in 2006. The banks’ mean (median) return on

ssets in 2006 was 1.34% (1.33%) with the vast majority of banks

eporting a positive pre-crisis return on their assets. U.S. banks had

mean loans-to-deposits ratio of 94.55% and a mean non-interest

ncome to total interest income ratio of 17.69%. In line with our

xpectation, banks experienced a detrimental stock performance

n 1998. The banks’ buy-and-hold returns for the year 1998 were

25.14% on average with the stocks of several banks losing almost

ll value. Moreover, 90% of our sample banks had a negative stock

erformance during the year of the LTCM crisis. Banks had an aver-

ge ratio of long-term debt to total debt of 52.33%, a mean leverage

f 7.0047, and a mean market-to-book ratio of 0.3111. Finally, U.S.

anks had 14.1071 board members, on average, with 76.3% of the

oard’s members being independent outside directors.

.2. Univariate analysis

We now test our major hypotheses on the correlation between

ublic information on risk management and the equity tail risk of

.S. banks during the crisis. As stated in the introduction, stock

arket investors could have acted on publicly available informa-

ion on the use of financial derivatives and loan securitization by

oth investing and divesting during the crisis. Table 2 provides

trong evidence for the latter.

Users of both interest rate and FX derivatives had statistically

ignificantly higher MES and �CoVaR estimates in the full sample

han non-users. These differences are also highly economically sig-

ificant as, e.g., users of interest rate derivatives lost 1.77% more on

heir stocks than non-users on those days during which the mar-

et plummeted. For users of FX derivatives, this difference is even

arger with derivatives users losing 7.34% on their stocks during

he worst days of the financial crisis with non-users losing only

.15%. Similar results can be seen from our estimates of the banks’

R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205 189

Table 2

Equity tail risk of derivatives users and non-users.

Panel A: Derivatives users and non-users in the full sample.

Interest rate derivatives FX derivatives Securitization

Users Non-users Difference Users Non-users Difference Users Non-users Difference

n 110 367 24 453 81 396

�CoVaR −0.0258 −0.0147 −0.0111 ∗∗∗ −0.0340 −0.0164 −0.0177 ∗∗∗ −0.0225 −0.0162 −0.0063 ∗∗∗ MES 0.0472 0.0295 0.0177 ∗∗∗ 0.0734 0.0315 0.0420 ∗∗∗ 0.0493 0.0304 0.0190 ∗∗∗

Panel B: Derivatives users and matched non-users.

Derivatives usage

Users Non-users Difference

n 114 114

�CoVaR −0.0255 −0.0219 −0.0036 ∗∗ MES 0.0473 0.0346 0.0127 ∗∗∗

The table presents comparisons of the equity tail risk of derivatives users and non-users. Panel A presents mean estimates of Marginal Expected Shortfall (MES) and �CoVaR

separately for banks that use interest rate derivatives, foreign exchange derivatives, and banks that securitize loans in comparison to non-users and non-securitizers using

the full sample. The statistical significance of the difference between the two sample means is tested using the nonparametric Wilcoxon rank-sum test. The full sample

includes 477 U.S. banks for which stock price (2008 to 2009) and accounting data (2006) were available in Thomson Reuters Financial Datastream and Thomson Worldscope ,

respectively, and for which 10-K filings were available in the Morningstar Document Research database. The sample construction and used data filters are given in Appendix

IA.I and the full list of sample banks is presented in Appendix IA.II. In Panel B, mean MES and �CoVaR estimates are presented for banks that use derivatives and matched

non-using banks. The matching of users to non-users of derivatives is done using the propensity score matching technique which is also used by Bartram et al. (2011) . In

a first step, the banks’ propensity to use derivatives is estimated based on their distance-to-default, firm size, leverage, and their quick ratio. In a second step, derivatives

users are matched to those banks that do not use derivatives, based on this propensity. The statistical significance of the difference between the two sample means is tested

againby the use of the nonparametric Wilcoxon rank-sum test. The sample includes 114 U.S. banks that used derivatives and matched non-users. ∗∗∗ , ∗∗ , ∗ denote significance at the 1%, 5% and 10% level, respectively.

Fig. 1. Banks’ exposure to equity tail risk and derivatives intensity. The figure shows a scatter plot of estimates of U.S. banks’ Marginal Expected Shortfall during the financial

crisis against the respective U.S. banks’ derivatives intensity (defined as the number of types of financial derivatives used by the bank). The MES estimates are computed

for the crisis period running from 07/01/2007 to 12/31/2008, while the values of the banks’ derivatives intensity are taken from the banks’ 10-K filings at the end of 2006.

Variable definitions and data sources are provided in Appendix A . The sample consists of 477 U.S. banks.

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CoVaR. Banks that hedged their interest rate risks using financial

erivatives in 2006 pulled down the U.S. financial sector by 2.58%

n equity returns during the crisis. In comparison, the US Finan-

ials Index from Datastream lost only 1.47% on those days on which

on-users of derivatives had their stock perform worst during the

risis. Further evidence on the increasing impact of a bank’s deriva-

ives intensity on our two measures of equity tail risk is presented

n Figs. 1 and 2 .

Both Figures show that, on average, banks that used more

nancial derivatives had both a higher exposure and contri-

ution to equity tail risk. Finally, our comparison of banks

hat did or did not securitize loans shows a similar picture.

anks that employed loan securitization as a risk transfer tool

ad both statistically and economically significantly worse mean

ES and �CoVaR estimates than banks that did not securitize

oans.

190 R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205

Fig. 2. Banks’ contribution to equity tail risk and derivatives intensity. The figure shows a scatter plot of estimates of U.S. banks’ �CoVaR during the financial crisis against

the respective U.S. banks’ derivatives intensity (defined as the number of types of financial derivatives used by the bank). The �CoVaR estimates are computed for the

crisis period running from 01/07/2007 to 12/31/2008, while the values of the banks’ derivatives intensity are taken from the banks’ 10-K filings at the end of 2006. Variable

definitions and data sources are provided in Appendix A . The sample consists of 477 U.S. banks.

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Although these first results show strong support for system-

atic differences between the equity tail risk of users and non-users

of derivatives, an important caveat applies to the interpretation of

these univariate results. As noted, e.g., by Jin and Jorion (2006) and

Bartram et al. (2011) , the differences in the banks’ extreme stock

returns that we find may be confounded by the endogeneity of

a bank’s decision to hedge. To account for endogeneity concerns,

we follow Bartram et al. (2011) and match users and non-users

of derivatives using propensity score matching. In a first step, the

banks’ propensity to use derivatives is estimated based on their

distance-to-default, firm size, leverage, and their quick ratio. In a

second step, derivatives users are matched to those banks that do

not use derivatives, based on this propensity. In Panel B of Table 2 ,

we compare mean MES and �CoVaR estimates for banks that use

derivatives and matched non-using banks. Again, we find deriva-

tives users to have significantly higher MES estimates and lower

�CoVaR estimates than matched non-users.

In Table 3 , we split our sample into banks in the bottom and

top quartile of MES estimates. U.S. banks in the top MES quartile

had the highest exposure to shocks to the financial sector while

banks in the bottom MES quartile, by construction, had the lowest

exposure to equity tail risk. In Table 4 , we repeat this quartile anal-

ysis for the estimates of the banks’ �CoVaR during the financial

crisis and compare the characteristics of the largest contributors

(bottom �CoVaR quartile) with those of the weakest contributors

(top �CoVaR quartile) to downturns of the financial sector index.

The results in Table 3 show that U.S. banks that had the largest

exposure to crashes of the financial sector also had significantly

lower �CoVaR estimates. Even more importantly, banks in the

top MES quartile used more derivatives, had a higher likelihood

of using interest rate and FX derivatives and were more likely to

engage in loan securitization. Interestingly, banks in the top and

bottom MES quartile differ from each other with respect to almost

all of our control variables as well. Banks that were the most

exposed to equity tail risk were significantly larger, relied more on

on-interest income, performed worse in 1998, had less leverage,

nd a higher market-to-book ratio. Table 4 presents similar results

or our analysis of the contribution to stock market downturns.

op contributing banks had a higher derivatives intensity, were

ore likely to use interest rate and FX derivatives and disclosed

ore types of risk exposure and a higher likelihood to securitize

oans. Again, we find U.S. banks in the bottom �CoVaR quartile to

e significantly larger, to have higher non-interest income to inter-

st income ratios, and to have less leverage. Overall, our results are

trongly supportive of the hypothesis that public information on

more extensive usage of financial derivatives and securitization

f some banks led to the extreme losses on these banks’ stocks at

he height of the financial crisis.

A problem with these results is, however, that the variables we

mploy in our quartile analysis are obviously correlated thus fur-

her necessitating a multivariate analysis of our main hypotheses.

n addition, to further mitigate concerns of endogeneity, we later

mploy lagged values of our explanatory variables in our multivari-

te analyses. Moreover, in Section IA.6 in the Internet Appendix,

e perform a set of simultaneous equations regressions to control

or the possibility that a bank’s equity tail risk and derivatives in-

ensity are jointly determined.

.3. Multivariate regressions

We now turn to our cross-sectional regressions of U.S. banks’

quity tail risk. Table 5 presents the results of our baseline regres-

ions of our sample banks’ MES on our main independent variables

nd several control variables.

Table 5 presents strong support for the hypothesis that stocks

f banks whose pre-crisis 10-K filings revealed them to be more

xposed to the crisis via their use of financial derivatives and loan

ecuritization had systematically higher extreme losses than less

xposed banks. Columns 1 to 5 report the results of regressions

n which we test the isolated impact of our risk management

R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205 191

Table 3

Summary statistics for banks in the first and fourth Marginal Expected Shortfall quartile.

Descriptive statistics of banks in the bottom quartile Descriptive statistics of banks in the top quartile Test for equality

of the distribution of MES of the distribution of MES of means

Mean 5% Quantile 95% Quantile St. dev. Mean 5% Quantile 95% Quantile St. dev. t -statistic p -Value

Panel A: Systemic risk measures

- MES −0.0165 −0.0745 0.0061 0.0262 0.0847 0.0597 0.1512 0.0267 −42.2585 0.00 ∗∗∗ - �CoVaR −0.0013 −0.0148 0.0096 0.0073 −0.0289 −0.0428 −0.0044 0.0122 41.1967 0.00 ∗∗∗ Panel B: Risk management variables

- Derivatives intensity 0.21 0.00 1.00 0.58 1.13 0.00 5.00 2.31 −17.52 0.00 ∗∗∗ - Interest rate derivatives 0.13 0.00 1.00 0.34 0.33 0.00 1.00 0.47 −6.15 0.00 ∗∗∗ - FX derivatives 0.00 0.00 0.00 0.00 0.14 0.00 1.00 0.35 4.43 0.00 ∗∗∗

- Securitization 0.14 0.00 1.00 0.35 0.32 0.00 1.00 0.47 −5.47 0.00 ∗∗∗ - Disclosed risk types 4.15 0.00 6.00 1.60 4.46 1.00 7.00 1.63 −2.11 0.14 - VaR-disclosure Index 0.01 0.00 0.00 0.09 0.20 0.00 1.05 0.88 −23.00 0.00 ∗∗∗ Panel C: Control variables

- Total assets 0.57 0.19 1.21 0.32 44.25 0.30 108.05 219.49 −1512.15 0.00 ∗∗∗ - Return on assets 1.17 0.36 1.77 0.42 1.48 0.74 2.13 0.61 −8.07 0.00 ∗∗∗ - Loans 0.91 0.65 1.20 0.18 0.93 0.61 1.19 0.18 −1.01 0.48 - Non-interest income 0.15 0.03 0.36 0.12 0.23 0.05 0.53 0.21 −6.95 0.00 ∗∗∗ - Buy-and-hold returns 1998 −0.20 −0.48 0.00 0.15 −0.27 −0.62 −0.07 0.16 4.63 0.01 ∗∗∗ - Leverage 7.81 4.50 11.57 2.63 6.29 3.81 10.93 2.37 6.33 0.00 ∗∗∗

- Market-to-book 0.27 0.15 0.45 0.09 0.33 0.21 0.49 0.09 −7.12 0.00 ∗∗∗ - Debt maturity 0.55 0.00 1.00 0.28 0.52 0.09 0.94 0.25 1.42 0.30

This table presents summary statistics comparing the characteristics of banks whose Marginal Expected Shortfall was in the bottom quartile with the characteristics of banks

whose Marginal Expected Shortfall was in the top quartile. The sample includes 477 U.S. banks for which stock price (2007 to 2008) and accounting data (2006) were

available in Thomson Reuters Financial Datastream and Thomson Worldscope , respectively, and for which 10-K filings were available in the Morningstar Document Research

database. The sample construction and used data filters are given in Appendix IA.I and the full list of sample banks is presented in Appendix IA.II. All variables and data

sources are defined in Appendix A . Total assets are given in $ billion. Accounting data are measured at the end of fiscal year 2006 while the two systemic risk measures are

estimated based on the time period 07/01/2007 to 12/31/2008. The tests of differences between banks in the top and bottom MES are performed using the nonparametric

Wilcoxon rank-sum test. ∗∗∗ , ∗∗ , ∗ denote significance at the 1%, 5% and 10% level, respectively.

Table 4

Summary statistics for banks in the fourth and first �CoVaR quartile.

Descriptive statistics of banks in the top quartile Descriptive statistics of banks in the bottom quartile Test for equality

of the distribution of �CoVaR of the distribution of �CoVaR of means

Mean 5% Quantile 95% Quantile St. dev. Mean 5% Quantile 95% Quantile St. dev. t -statistic p -Value

Panel A: Systemic risk measures

- MES −0.0017 −0.0690 0.0540 0.0400 0.0621 0.0347 0.0967 0.0216 32.3850 0.00 ∗∗∗ - �CoVaR 0.0017 −0.0033 0.0096 0.0039 −0.0386 −0.0463 −0.0335 0.0038 −116.2432 0.00 ∗∗∗ Panel B: Risk management variables

- Derivatives intensity 0.26 0.00 1.00 0.60 1.39 0.00 6.00 2.36 5.42 0.00 ∗∗∗

- Interest rate derivatives 0.15 0.00 1.00 0.36 0.43 0.00 1.00 0.50 6.24 0.00 ∗∗∗

- FX derivatives 0.01 0.00 0.00 0.09 0.15 0.00 1.00 0.36 4.33 0.00 ∗∗∗

- Securitization 0.12 0.00 1.00 0.32 0.25 0.00 1.00 0.43 3.36 0.01 ∗∗∗

- Disclosed risk types 4.07 0.00 6.00 1.81 4.73 3.00 7.00 1.33 5.48 0.00 ∗∗∗

- VaR-disclosure Index 0.03 0.00 0.00 0.02 0.29 0.00 2.05 0.97 3.00 0.00 ∗∗∗

Panel C: Control variables

- Total assets 1.06 0.13 1.32 5.51 75.79 1.20 232.37 278.07 2.94 0.00 ∗∗∗

- Return on assets 1.17 0.36 1.81 0.46 1.62 0.85 2.47 0.60 8.24 0.00 ∗∗∗

- Loans 0.90 0.59 1.25 0.19 1.01 0.61 1.26 0.70 1.75 0.10 ∗ - Non interest income 0.15 0.04 0.32 0.12 0.25 0.04 0.68 0.22 5.23 0.00 ∗∗∗

- Buy-and-hold returns 1998 −0.18 −0.40 0.00 0.13 −0.26 −0.60 0.00 0.17 4. −5.35 0.00 ∗∗∗ - Leverage 7.45 4.12 11.23 2.59 5.65 3.78 7.91 1.55 −12.75 0.00 ∗∗∗ - Market-to-book 0.28 0.15 0.45 0.09 0.38 0.26 0.59 0.11 10.68 0.00 ∗∗∗

- Debt maturity 0.58 0.00 1.00 0.26 0.48 0.08 0.81 0.24 −4.65 0.00 ∗∗∗

This table presents summary statistics comparing the characteristics of banks whose �CoVaR was in the top quartile with the characteristics of banks whose �CoVaR was

in the bottom quartile. The sample includes 477 U.S. banks for which stock price (2007 to 2008) and accounting data (2006) were available in Thomson Reuters Financial

Datastream and Thomson Worldscope , respectively, and for which 10-K filings were available in the Morningstar Document Research database. The sample construction and

used data filters are given in Appendix IA.I and the full list of sample banks is presented in Appendix IA.II. All variables and data sources are defined in Appendix A . Total

assets are given in $ billion. Accounting data are measured at the end of fiscal year 2006 while the two systemic risk measures are estimated based on the time period

07/01/2007 to 12/31/2008. The tests of differences between banks in the bottom and top �CoVaR quartiles are performed using the nonparametric Wilcoxon rank-sum test. ∗∗∗ , ∗∗ , ∗ denote significance at the 1%, 5% and 10% level, respectively.

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ariables on the banks’ MES. With the exception of the disclosed

umber of risk types to which a bank is exposed, all our vari-

bles on a bank’s derivatives usage and loan securitization enter

he regressions with a highly statistically significant positive sign.

n column 6, we estimate a regression in which we use both the

anks’ derivatives intensity, the dummy for the securitization of

oans, and the number of disclosed risk types. Again, the banks’

erivatives intensity and the dummy for loan securitization enter

egression of the banks’ MES during the crisis with highly statisti-

ally significant coefficients. Adding the bank-specific control vari-

bles to this model in regression (7) does not change our find-

ngs. Derivatives intensity and loan securitization remain powerful

192 R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205

Table 5

Baseline regressions of a bank’s exposure to equity tail risk during the financial crisis.

Dependent Variable (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

MES MES MES MES MES MES MES MES MES MES

Panel A: Risk management variables

Derivatives intensity 0.007 ∗∗∗ 0.007 ∗∗∗ 0.005 ∗∗∗ 0.005 ∗∗∗

(0.0 0 0) (0.0 0 0) (0.0 0 0) (0.002)

Interest rate derivatives 0.017 ∗∗∗ 0.011 ∗∗∗ 0.013 ∗∗∗

(0.0 0 0) (0.006) (0.0 0 0)

FX derivatives 0.039 ∗∗∗ 0.007 0.001 (0.0 0 0) (0.368) (0.936)

Securitization 0.019 ∗∗∗ 0.016 ∗∗∗ 0.012 ∗∗ 0.011 ∗∗ 0.014 ∗∗ 0.013 ∗∗

(0.001) (0.002) (0.022) (0.033) (0.019) (0.028)

Disclosed risk types 0.001 −0.001 −0.002 −0.001 −0.001 −0.001 (0.377) (0.452) (0.194) (0.254) (0.588) (0.686)

Panel B: Control variables

Total assets ( ×10 11 ) 1.996 ∗∗ 0.350 2.265 ∗∗ 0.138 (0.047) (0.685) (0.030) (0.824)

Return on assets 0.007 ∗ 0.006 −0.002 −0.004 (0.069) (0.109) (0.732) (0.517)

Loans −0.008 ∗∗ −0.006 ∗ −0.009 ∗∗ −0.007 ∗∗ (0.032) (0.062) (0.022) (0.049)

Non interest income 0.025 ∗∗ 0.027 ∗∗ 0.024 ∗∗ 0.027 ∗

(0.011) (0.019) (0.044) (0.054)

Buy-and-hold returns 1998 −0.019 −0.022 (0.171) (0.110)

Leverage −0.001 ∗ −0.001 ∗ −0.002 ∗∗ −0.002 ∗∗ (0.068) (0.083) (0.047) (0.042)

Market-to-book 0.047 ∗∗ 0.049 ∗∗ 0.073 ∗∗ 0.075 ∗∗

(0.024) (0.022) (0.014) (0.012)

Debt maturity −0.003 −0.003 0.004 0.005 (0.562) (0.577) (0.604) (0.522)

Intercept 0.029 ∗∗∗ 0.029 ∗∗∗ 0.032 ∗∗∗ 0.030 ∗∗∗ 0.029 ∗∗∗ 0.031 ∗∗∗ 0.024 ∗∗ 0.022 ∗∗ 0.026 ∗ 0.024 (0.0 0 0) (0.0 0 0) (0.0 0 0) (0.0 0 0) (0.0 0 0) (0.0 0 0) (0.018) (0.035) (0.085) (0.132)

R 2 0.063 0.043 0.035 0.029 0.002 0.084 0.128 0.125 0.183 0.189

Adj. R 2 0.061 0.041 0.033 0.027 0.0 0 0 0.078 0.109 0.103 0.150 0.154

Observations 477 477 477 477 477 477 463 463 286 286

This table shows results from cross-sectional regressions of the Marginal Expected Shortfall of U.S. banks on several variables related to the banks’ risk management and

various control variables. The dependent variable in each regression is the average of the daily Marginal Expected Shortfall estimates for the time period 07/01/2007 to

12/31/2008 computed using the dynamic model specification proposed by Brownlees and Engle (2012) . All explanatory variables are based on stock market or accounting

data for the year 2006. Models (1) through (5) only employ one risk management variable at a time. Regression model (6) uses all risk management variables in our sample

excluding the dummy variables on the use of interest rate and foreign exchange derivatives which are highly correlated with the derivatives intensity variable. In regression

(7), various bank-specific control variables are added to the regression on the risk management variables. Model (8) is equal to regression (7) but uses the dummy variables

on the use of interest rate and foreign exchange derivatives instead of the derivatives intensity. Regression specifications (9) and (10) equal models (7) and (8) with the

exception that we additionally employ the banks’ stock performance in 1998 as a further explanatory variable (due to data availability, these regressions are performed

on a sub-sample only). Variable definitions and data sources are provided in Appendix A . All models are estimated with OLS. The statistical significance of the estimated

coefficients is tested with Newey and West (1987) heteroskedasticity and autocorrelation consistent t -tests. Corresponding p-values are shown in parentheses. R 2 and Adj. R 2

are the estimated regression models’ R -squared and adjusted R-squared, respectively. ∗∗∗ denote coefficients that are significant at the 1% level. ∗∗ denote coefficients that are significant at the 5% level. ∗ denote coefficients that are significant at the 10% level.

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19 Note that the adjusted R 2 in our regressions is comparable to (and sometimes

higher than) those reported for U.S. banks buy-and-hold returns in the study of

Fahlenbrach et al. (2012) . 20 We also compute for each explanatory variable the regressions’ variance infla-

tion factor (VIF) defined as 1 / (1 − R 2 ) , where R 2 is the multiple R-squared from the regression of MES/ �CoVaR on the remaining independent variables. For all our

explanatory variables, the VIF is always below the value of 2, suggesting that mul-

ticollinearity does not significantly affect our results.

determinants of a bank’s exposure to equity tail risk. These effects

are also economically significant with a one standard deviation in-

crease in a bank’s derivatives intensity in 2006 being associated

with a 0.76% increase in MES (0.005 × 1.5138) during the crisis. Disclosing the securitization of loans led to a 1.2% higher MES of

U.S banks.

In regression (8), we substitute our proxy for the banks’ deriva-

tives intensity with our dummy variables for the use of inter-

est rate and FX derivatives. While the dummy for FX derivatives

does not enter the regression with a statistically significant sign,

the use of interest risk derivatives is both statistically and eco-

nomically significantly related to a bank’s exposure to a crash in

the financial sector. Usage of interest rate derivatives is associ-

ated with a 1.1% higher MES during the financial crisis. Loan se-

curitization remains both statistically and economically significant

in this regression as well (1.1% increase in MES for banks that

securitize). Note that, interestingly, the number of risk types a

bank is exposed to does not statistically significantly affect the

banks’ exposure to shocks in the stock market. In columns 9

and 10, where we include the banks’ buy-and-hold returns dur-

ng the LTCM crisis, we find statistically and economically similar

vidence. 19

In our most comprehensive regression specifications (7)–(10),

he control variables enter the regressions with the expected signs.

or example, a higher non-interest income to interest income ratio

s associated with a higher MES of banks. Conversely, banks that

ranted more loans in 2006 had lower MES estimates during the

risis. Also, larger banks exhibited higher losses on the worst days

f the crisis. However, the effect of bank size on MES is attenu-

ted in our regressions in which we employ our dummy variables

or the use of interest rate and FX derivatives. 20 Finally, as in our

R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205 193

Table 6

Baseline regressions of a bank’s contribution to equity tail risk during the financial crisis.

Dependent variable (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

�CoVaR �CoVaR �CoVaR �CoVaR �CoVaR �CoVaR �CoVaR �CoVaR �CoVaR �CoVaR

Panel A: Risk management variables

Derivatives intensity −0.003 ∗∗∗ −0.003 ∗∗∗ −0.002 ∗∗∗ −0.001 ∗ (0.0 0 0) (0.0 0 0) (0.001) (0.054)

Interest rate derivatives −0.009 ∗∗∗ −0.005 ∗∗∗ −0.005 ∗∗∗ (0.0 0 0) (0.0 0 0) (0.001)

FX derivatives −0.018 ∗∗∗ −0.001 0.001 (0.0 0 0) (0.762) (0.776)

Securitization −0.006 ∗∗∗ −0.005 ∗∗∗ −0.002 −0.002 −0.002 −0.001 (0.001) (0.007) (0.278) (0.383) (0.475) (0.614)

Disclosed risk types −0.002 ∗∗∗ −0.001 ∗∗ 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 (0.0 0 0) (0.014) (0.628) (0.568) (0.512) (0.521)

Panel B: Control variables

Total assets 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0

(0.386) (0.535) (0.643) (0.533)

Return on assets −0.004 ∗∗ −0.003 ∗∗ 0.002 0.002 (0.025) (0.039) (0.476) (0.355)

Loans 0.004 ∗ 0.003 0.004 ∗∗ 0.003 ∗

(0.051) (0.103) (0.045) (0.090)

Non interest income −0.008 −0.008 −0.005 −0.006 (0.102) (0.106) (0.357) (0.320)

Buy-and-hold returns 1998 0.008 ∗ 0.009 ∗

(0.081) (0.056)

Leverage 0.001 ∗∗∗ 0.001 ∗∗∗ 0.002 ∗∗∗ 0.002 ∗∗∗

(0.004) (0.003) (0.0 0 0) (0.0 0 0)

Market-to-book −0.040 ∗∗∗ −0.040 ∗∗∗ −0.053 ∗∗∗ −0.051 ∗∗∗ (0.0 0 0) (0.0 0 0) (0.0 0 0) (0.0 0 0)

Debt maturity 0.006 ∗∗∗ 0.006 ∗∗∗ 0.004 0.003 (0.009) (0.010) (0.306) (0.351)

Intercept −0.015 ∗∗∗ −0.015 ∗∗∗ −0.017 ∗∗∗ −0.016 ∗∗∗ −0.010 ∗∗∗ −0.011 ∗∗∗ −0.008 ∗∗ −0.007 ∗ −0.017 ∗∗∗ −0.017 ∗∗∗ (0.0 0 0) (0.0 0 0) (0.0 0 0) (0.0 0 0) (0.0 0 0) (0.0 0 0) (0.044) (0.060) (0.003) (0.003)

R 2 0.087 0.079 0.050 0.022 0.030 0.108 0.251 0.256 0.261 0.278

Adj. R 2 0.085 0.077 0.048 0.020 0.028 0.102 0.234 0.238 0.231 0.247

Observations 477 477 477 477 477 477 463 463 286 286

This table shows results from cross-sectional regressions of the �CoVaR of U.S. banks on several variables related to the banks’ risk management and various control

variables. The dependent variable in each regression is the average of the daily conditional �CoVaR estimates for the time period 07/01/2007 to 12/31/2008 computed using

the original model specification of Adrian and Brunnermeier (2010) . All explanatory variables are based on stock market or accounting data for the year 2006. Models (1)

through (5) only employ one risk management variable at a time. Regression model (6) uses all risk management variables in our sample excluding the dummy variables on

the use of interest rate and foreign exchange derivatives which are highly correlated with the derivatives intensity variable. In regression (7), various bank-specific control

variables are added to the regression on the risk management variables. Model (8) is equal to regression (7) but uses the dummy variables on the use of interest rate and

foreign exchange derivatives instead of the derivatives intensity. Regression specifications (9) and (10) equal models (7) and (8) with the exception that we additionally

employ the banks’ stock performance in 1998 as a further explanatory variable (due to data availability, these regressions are performed on a sub-sample only). Variable

definitions and data sources are provided in Appendix A . All models are estimated with OLS. The statistical significance of the estimated coefficients is tested with Newey

and West (1987) heteroskedasticity and autocorrelation consistent t -tests. Corresponding p -Values are shown in parentheses. R 2 and Adj. R 2 are the estimated regression

models’ R -squared and adjusted R -squared, respectively. ∗∗∗ denote coefficients that are significant at the 1% level. ∗∗ denote coefficients that are significant at the 5% level. ∗ denote coefficients that are significant at the 10% level.

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nivariate analysis, results from our regression emphasize the dis-

iplining effect of leverage as the banks’ MES is found to be neg-

tively associated with leverage. Note that the adjusted R-squared

alues for the regressions in Table 5 (and also in further regres-

ions) for the most comprehensive model specifications are com-

arable to the ones found in related studies (see, e.g., Beltratti and

tulz, 2012; Anginer et al., 2014a;b ).

Our multivariate results on the determinants of U.S. banks’ MES

re consistent with the hypothesis that the use of derivatives and

oan securitization made some banks riskier than non-users which

n turn resulted in the extreme losses on the stocks of derivatives

sers during the crash of the financial sector. In the next part of

ur analysis, we test the hypothesis that extreme negative stock

eturns of individual banks with a supposedly higher pre-crisis risk

xposure led to extreme stock losses of the whole financial sector.

Table 6 presents the results of our regressions of U.S. banks’

CoVaR estimates during the crisis.

Regressions (1)–(5) in Table 6 employ each of our risk manage-

ent variables one at a time. Each variable enters its respective

egression with a highly statistically significant coefficient. In addi-

ion, and as expected, all coefficients carry a negative sign. Banks

hat used more financial derivatives contributed more strongly to

eclines in the stocks of the financial sector. So did banks which

ecuritized loans and which had a more pronounced risk expo-

ure in 2006. These results carry over to regression (6), in which

e employ our three main risk management variables simultane-

usly. However, both our dummy variables for securitization and

he number of risk types lose their statistical significance after the

ddition of our control variables. In regressions (7) and (8), we use

ur full sample and find a bank’s derivatives intensity and its use

f interest rate derivatives to be significantly correlated with its

ontribution to the extreme stock returns of banks. Both effects are

conomically significant, although the effects are less pronounced

han those from our regressions of the banks’ MES.

Among our control variables, leverage and debt maturity enter

egressions (7) and (8) with a highly statistically and economically

ignificant positive sign. Banks that had lower leverage but a more

ragile funding structure thus contributed more to losses on the fi-

ancial sector index. Conversely, lower market-to-book ratios and

eturn on assets were associated with higher returns on the sector

194 R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205

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index on those days an individual bank’s stock plummeted. Finally,

regressions (9) and (10) employ the subsample of U.S. banks for

which we have data on their stocks’ buy-and-hold returns in 1998.

The stock performance during the LTCM crisis significantly influ-

ences the contribution of banks to the performance of the finan-

cial sector index. Banks that performed poorly in 1998 contributed

more to losses of the sector index during the financial crisis. Our

main finding from these regressions, however, is that the sample

banks’ derivatives intensity and the propensity to use interest rate

derivatives are positively associated with the banks’ �CoVaR.

3.4. Additional analyses

This section provides results of further analyses on the relation

between risk management and the equity tail risk of U.S. banks

during the financial crisis.

3.4.1. Does derivatives usage increase banks’ equity tail risk if used

for hedging?

Up to this point in our analysis, our results indicate a neg-

ative perception of derivatives usage by stock market investors.

One possible explanation for this finding could be that a more

elaborate risk management of a bank is indicative of a signifi-

cantly higher risk exposure and higher default risk. On the other

hand, banks with low risk exposure from their business operations

could have experienced extreme negative stock returns if they had

used derivatives and loan securitization for speculation rather than

hedging.

The results from our analysis of interactions shown later in this

section provide first evidence for the latter conjecture. In models

(3) and (10) in Table 10 , we include an interaction term between a

bank’s derivatives intensity and the number of disclosed risk types.

While the interaction term is not statistically significant in the re-

gression of MES, it is highly statistically significant in the regres-

sion of a bank’s contribution to the banks’ tail risk. A bank that

reports the use of more derivatives contributes more to extreme

downturns in the financial sector index, but this effect is attenu-

ated if the bank also reports a higher actual risk exposure. This

first analysis thus supports the conjecture that the use of deriva-

tives for purposes other than hedging was negatively perceived by

stock market investors during the crisis.

The disclosed number of risk types of a bank is obviously only

a suboptimal proxy for a bank’s true risk exposure. Therefore,

we additionally estimate the banks’ distance-to-default (DtD) (see

Merton, 1974; Hillegeist et al., 2004; Campbell et al., 2008; Anginer

et al., 2014b ) during the year 2006 to proxy for the banks’ pre-

crisis default risk. Everything else equal, we would expect a bank’s

distance-to-default to be negatively correlated with the bank’s MES

and positively correlated with �CoVaR as a higher distance-to-

default (and thus a lower default probability) should be reflected

in a bank’s equity tail risk. Table 7 presents the results of regres-

sions in which we employ the banks’ DtD as a further explanatory

variable. 21

Regressions (1), (2), (4), and (5) in Table 7 confirm both our

previous findings as well as the conjecture that default risk is pos-

itively related to equity tail risk. 22 The higher a bank’s pre-crisis

21 We also estimate regressions in which we employ the banks’ distance-to-default

estimated using data from 2008 as an explanatory variable. The results from these

regressions are qualitatively and quantitatively similar to those reported in the pa-

per. 22 In Section IA.1 in the Internet Appendix, we additionally test the hypothesis

that a bank’s derivatives intensity and its use of loan securitization did not only

increase equity tail risk, but also the bank’s default probability during the financial

crisis. Complementing our findings on equity tail risk, in the regressions presented

in Table IA.III, we find a bank’s derivatives intensity and the dummy variable for

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istance-to-default is, the lower (higher) is its MES ( �CoVaR) dur-

ng the crisis. In columns 3 and 6, we interact the banks’ distances-

o-default with the banks’ derivatives intensity and our dummy for

oan securitization. In both regressions, the interaction term of the

istance-to-default with the derivatives intensity is statistically sig-

ificant at the 10% level. Furthermore, the sign on the coefficient

f the interaction terms in both regressions supports the hypothe-

is stated above. The positive relation between the derivatives in-

ensity and the equity tail risk of banks is amplified by decreases

n default risk (at least during the financial crisis). Our results are

hus again consistent with the notion of a risk-increasing effect of

erivatives if used for non-hedging purposes. Finally, the interac-

ion terms with loan securitization are not statistically significant

n our regressions.

To get an even better understanding of the relation between

erivatives usage and banks’ equity tail risk, we test the hypothesis

hat the risk-increasing effect of derivatives usage is indeed caused

y banks employing derivatives for non-hedging purposes. To this

nd, we extract the fair value gains and losses on derivatives and

elected balance sheet items (investment securities, net loans, de-

osits, and long term debt) from our sample banks’ 10-K filings in

006. We then follow Venkatachalam (1996) and consider a bank’s

otive for using derivatives to be risk reduction and hedging if

oth the fair value gains/losses on derivatives and balance sheet

tems are of different signs. Conversely, if both variables are of the

ame sign, we consider this to be an indication of risk-taking be-

ng the bank’s primary motive for using financial derivatives. From

his information, we construct a dummy variable that takes on the

alue of one if derivatives are used for taking on increased risks,

nd zero if derivatives are used for hedging. 23 This dummy vari-

ble is then used in additional regressions in which we interact

he risk-taking/hedging dummy with the banks’ derivatives inten-

ities. 24

The results of these regressions are shown in Table 8 .

The results from regressions (1), (2), (4), and (5) in

able 8 show that the use of the dummy variable for a non-

edging purpose of derivatives usage as an alternative to our main

xplanatory variable is in line with our predictions. Banks that use

erivatives for non-hedging purposes, on average, have statistically

nd economically higher MES and �CoVaR estimates during the

risis. In regressions (3) and (6), we interact the non-hedging pur-

ose dummy with a bank’s derivatives intensity to test the hypoth-

sis that a non-hedging purpose does indeed increase the effect of

erivatives usage on equity tail risk. For the banks’ MES, this hy-

othesis cannot be rejected based on the results from regression

3) in which the interaction term is positive and statistically signif-

cant at the 10% level. In regression (6) of the banks’ �CoVaR, the

nteraction term is not statistically significant. Finally, correspond-

ng regressions of the banks’ default risk turn out unsuccessful.

It should be noted that the approach of Venkatachalam

1996) of assessing the purpose of derivatives usage by analyzing

he correlation between the gains/losses on derivatives and bal-

nce sheet items at a single point in time to some extent ne-

lects the fact that hedging operates through time for a given bank

see Skinner, 1996 ). To attenuate this concern, in unreported ro-

ustness checks we repeat our previous analysis using the sum

ecuritization to be significantly negatively related to a bank’s distance-to-default

uring the crisis. 23 We find 50.77% of our sample banks to be using derivatives for non-hedging

urposes. Quite interestingly, this proportion does not seem to have changed signif-

cantly over time. Almost 20 years ago, Venkatachalam (1996) found a comparable

3% of banks to have used derivatives for increased risk-taking. 24 In an unreported robustness check, we also directly employ the ratio of the fair

alue gains/losses on derivatives and balance sheet items as a proxy for the degree

or which a bank is a net user of derivatives for hedging purposes. Our findings

emain unchanged.

R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205 195

Table 7

Regressions of a banks equity tail risk during the financial crisis – default risk.

Dependent variable (1) (2) (3) (4) (5) (6)

MES MES MES �CoVaR �CoVaR �CoVaR

Panel A: Risk management variables

Derivatives intensity 0.005 ∗∗∗ 0.005 ∗∗∗ −0.002 ∗∗∗ −0.002 ∗∗∗ (0.003) (0.004) (0.002) (0.003)

Interest rate derivatives 0.010 ∗∗∗ −0.005 ∗∗∗ (0.008) (0.0 0 0)

FX derivatives 0.007 −0.001 (0.563) (0.811)

DtD ( × 10 4 ) −1.947 ∗∗ −2.037 ∗∗ −7.898 ∗∗ 0.899 ∗∗∗ 0.923 ∗∗∗ 3.149 ∗∗ (0.020) (0.015) (0.023) (0.003) (0.002) (0.012)

Securitization 0.014 ∗∗∗ 0.013 ∗∗∗ 0.013 ∗∗ −0.002 −0.002 −0.002 (0.005) (0.007) (0.014) (0.206) (0.286) (0.365)

Disclosed risk types −0.002 −0.002 −0.002 0.0 0 0 0.0 0 0 0.0 0 0 (0.149) (0.194) (0.143) (0.709) (0.662) (0.752)

Panel B: Control variables

Total assets 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0

(0.333) (0.769) (0.698) (0.478) (0.466) (0.919)

ROA 0.006 0.005 0.005 −0.003 ∗ −0.003 ∗ −0.003 (0.239) (0.299) (0.358) (0.059) (0.088) (0.100)

Loans −0.006 −0.005 −0.006 0.003 0.002 0.003 (0.247) (0.366) (0.244) (0.105) (0.194) (0.112)

Non interest income 0.023 ∗ 0.023 0.021 −0.008 ∗ −0.008 −0.008 (0.093) (0.105) (0.120) (0.098) (0.104) (0.123)

Leverage −0.002 ∗∗∗ −0.002 ∗∗∗ −0.002 ∗∗ 0.001 ∗∗∗ 0.001 ∗∗∗ 0.001 ∗∗∗ (0.004) (0.004) (0.016) (0.0 0 0) (0.0 0 0) (0.0 0 0)

Market-to-book 0.030 0.031 0.036 −0.033 ∗∗∗ −0.032 ∗∗∗ −0.034 ∗∗∗ (0.202) (0.190) (0.134) (0.0 0 0) (0.0 0 0) (0.0 0 0)

Debt maturity −0.003 −0.003 −0.003 0.006 ∗∗ 0.006 ∗∗ 0.006 ∗∗ (0.655) (0.671) (0.614) (0.023) (0.026) (0.021)

Panel C: Interactions

DtD × Securitization 0.0 0 0 −0.0 0 0 (0.226) (0.103)

DtD × Derivatives intensity ( × 10 4 ) 2.176 ∗ −0.793 ∗ (0.071) (0.069)

R 2 0.140 0.138 0.147 0.267 0.273 0.272

Adj. R 2 0.119 0.115 0.122 0.248 0.253 0.251

Observations 452 452 452 452 452 452

This table shows results from cross-sectional regressions of the Marginal Expected Shortfall and �CoVaR of U.S. banks on the banks’ pre-crisis default risk measured by their

distances-to-default (see Merton, 1974; Hillegeist et al., 2004; Campbell et al., 2008; Anginer et al., 2014b , for details of the computation of the DtD) and several control

variables. The dependent variable in the first three regressions is the average of the daily Marginal Expected Shortfall estimates for the time period 07/01/2007 to 12/31/2008

computed using the dynamic model specification proposed by Brownlees and Engle (2012) . In regressions (4) and (6), the dependent variable is the average conditional

�CoVaR of the banks during the same period. Regressions (3) and (6) include interaction terms between the banks’ distances-to-default and the banks’ derivatives intensity

as well as the dummy variable for loan securitization. All explanatory variables are based on stock market or accounting data for the year 2006. Variable definitions and

data sources are provided in Appendix A . All models are estimated with OLS. The statistical significance of the estimated coefficients is tested with Newey and West (1987)

heteroskedasticity and autocorrelation consistent t -tests. Corresponding p -Values are shown in parentheses. R 2 and Adj. R 2 are the estimated regression models’ R -squared

and adjusted R -squared, respectively. ∗∗∗ denote coefficients that are significant at the 1% level. ∗∗ denote coefficients that are significant at the 5% level. ∗ denote coefficients that are significant at the 10% level.

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first quintile is omitted.

f the gains/losses on both derivatives and balance sheet positions

or fiscal years 20 04, 20 05, and 20 06. Our conclusions remain un-

hanged.

.4.2. Does more hedging lead to higher equity tail risk?

Our analysis so far has produced evidence that is equally con-

istent with banks that used more derivatives having higher eq-

ity tail risk and with banks that did not use financial derivatives

aving lower MES and �CoVaR estimates. Consequently, we cannot

ule out the possibility that our results are simply driven by mod-

rate returns on the stocks of non-hedging banks during times of

arket turmoil. We therefore investigate possible asymmetries in

he relation between a bank’s derivatives intensity and its equity

ail risk in the next part of our analysis. To this end, we divide

ur sample banks into quintiles based on their 2006 derivatives

ntensity. We then construct dummy variables for the membership

n each of the five quintiles with the first (fifth) quintile contain-

ng banks with the lowest (highest) pre-crisis derivatives intensity.

able 9 presents the results of regressions of MES and �CoVaR in

hich the banks’ derivatives intensity has been replaced with the

uintile indicators. 25

The results show that our findings are indeed driven by the

anks that had the highest pre-crisis derivatives intensity. While

embership in the second to fourth quintiles of derivatives inten-

ity is not statistically significantly related to MES or �CoVaR, the

ummy for membership in the fifth quintile enters all regressions

ith an economically and statistically significant sign. This effect

s not significantly affected in those regressions in which we con-

rol for differences in the banks’ Tier 1 capital. In the regressions

f the banks’ MES, our dummy variable for loan securitization re-

ains statistically and economically highly significant. In contrast,

he number of risk types disclosed in the banks’ 10-K filings enters

one of our regressions of MES and �CoVaR with a statistically

ignificant coefficient.

196 R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205

Table 8

Equity tail risk and the motives of derivatives usage.

Dependent variable (1) (2) (3) (4) (5) (6) (7) (8) (9)

MES MES MES �CoVaR �CoVaR �CoVaR DtD DtD DtD

Panel A: Risk management variables

Non-hedging purpose 0.014 ∗∗ 0.013 ∗∗ 0.010 −0.010 ∗∗∗ −0.009 ∗∗∗ −0.005 ∗ 0.195 0.846 2.240 (0.018) (0.025) (0.225) (0.0 0 0) (0.0 0 0) (0.087) (0.893) (0.632) (0.622)

Securitization 0.019 ∗∗∗ 0.012 ∗∗ −0.006 ∗∗∗ −0.002 −2.488 0.073 (0.001) (0.019) (0.001) (0.283) (0.332) (0.980)

Disclosed risk types 0.001 −0.002 −0.001 ∗∗∗ 0.0 0 0 −1.064 −0.859 (0.559) (0.178) (0.0 0 0) (0.603) (0.176) (0.214)

Derivatives intensity 0.001 −0.001 −0.141 (0.701) (0.413) (0.935)

Panel B: Control variables

Total assets 0.0 0 0 0.0 0 0 0.0 0 0

(0.205) (0.542) (0.120)

ROA 0.007 −0.004 ∗∗ 5.531 ∗ (0.111) (0.034) (0.053)

Loans to deposit −0.008 0.003 ∗ 6.781 ∗∗ (0.107) (0.062) (0.021)

NIItoII 0.025 ∗ −0.008 1.404 (0.063) (0.124) (0.856)

Leverage −0.001 ∗ 0.001 ∗∗∗ −4.108 ∗∗∗ (0.083) (0.004) (0.0 0 0)

Market-to-book 0.045 ∗∗ −0.040 ∗∗∗ −87.873 ∗∗∗ (0.041) (0.0 0 0) (0.0 0 0)

Debt maturity −0.003 0.006 ∗∗∗ 3.216 (0.616) (0.008) (0.409)

Panel C: Interaction

Hedging int. × Non-hedging purpose 0.006 ∗ −0.001 −1.956 (0.091) (0.423) (0.302)

R 2 0.013 0.042 0.134 0.042 0.085 0.256 0.0 0 0 0.006 0.287

Adj. R 2 0.011 0.035 0.111 0.040 0.080 0.236 −0.002 −0.001 0.268 Observations 477 477 463 477 477 463 455 455 452

This table shows results of cross-sectional regressions of the Marginal Expected Shortfall, �CoVaR, and distance-to-default (see Merton, 1974; Hillegeist et al., 2004; Campbell

et al., 2008; Anginer et al., 2014b , for details of the computation of the DtD) of U.S. banks on several variables related to the banks’ risk management, a dummy variable

for the banks’ motive for using derivatives, and various control variables. The dependent variable in the first three regressions is the average of the daily Marginal Expected

Shortfall estimates for the time period 07/01/2007 to 12/31/2008 computed using the dynamic model specification proposed by Brownlees and Engle (2012) . In regressions

(4) and (6), the dependent variable is the average conditional �CoVaR of the banks during the same period. Regressions (7) and (9) employ the banks’ distances-to-default

as the dependent variable. All explanatory variables are based on stock market or accounting data for the year 2006. Variable definitions and data sources are provided

in Appendix A . All models are estimated with OLS. The statistical significance of the estimated coefficients is tested with Newey and West (1987) heteroskedasticity and

autocorrelation consistent t -tests. Corresponding p -Values are shown in parentheses. R 2 and Adj. R 2 are the estimated regression models’ R-squared and adjusted R -squared,

respectively. ∗∗∗ denote coefficients that are significant at the 1% level. ∗∗ denote coefficients that are significant at the 5% level. ∗ denote coefficients that are significant at the 10% level.

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3.4.3. Is the relation between derivatives usage and banks’ extreme

stock returns exacerbated by bank size and mitigated by bank

capital?

In the next step of our analysis, we investigate whether the re-

lation between a bank’s derivatives intensity and its equity tail risk

during the financial crisis depends on a bank’s size and regula-

tory capital. Although we control for a bank’s size in our baseline

regressions, we nevertheless expect larger banks to use financial

derivatives more extensively than smaller banks. Also, we would

expect banks with more regulatory capital to have suffered less

during the crisis. In Table 10 , we undertake first tests of these hy-

potheses by running several cross-sectional regressions in which

we interact our main independent variables with size and bank

capital.

In columns 1 and 8 of Table 10 , we interact a bank’s derivatives

intensity with its size measured by its total assets. This test is un-

successful as the interaction terms in the regressions of both MES

and �CoVaR are statistically insignificant. In regression (2), we in-

teract the banks’ Tier 1 capital ratios with their derivatives inten-

sity. We find higher bank capital to have an attenuating effect on

the positive relation between a bank’s MES and its derivatives in-

tensity. Consequently, and in line with our expectation, stock mar-

ket investors view derivatives usage as less detrimental if the bank

s financially healthier (we do not find a comparable result in re-

ression (9) of the banks’ �CoVaR).

Regression specifications (4), (5), (11), and (12) show that bank

ize exacerbates to some extent the negative influence of the use

f interest rate derivatives on both the banks’ MES and �CoVaR.

he same result can be seen from regressions (6) and (13) which

how that bank size positively affects the relation between loan

ecuritization and equity tail risk. One explanation for this find-

ng could obviously be that larger banks possess a more elaborate

isk management than smaller banks. We address this concern in

ection 3.4.4 . Finally, higher Tier 1 capital is again associated with

less detrimental effect of securitization on banks’ extreme stock

eturns. Thus, both the exposure and contribution to equity tail

isk of a bank during the crisis were less pronounced in case the

ank held more capital.

.4.4. Is equity tail risk driven by the overall level of disclosure?

Although our results so far are strongly supportive of the hy-

othesis that banks that used more derivatives and securitized

oans (especially when reporting less risk exposure and less reg-

latory capital at the same time) experienced more extreme nega-

ive losses on their stocks than other banks, we cannot rule out the

ossibility that our results are driven by differences in the amount

R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205 197

Table 9

Regressions of a bank’s equity tail risk during the financial crisis – derivatives intensity quintiles.

Dependent variable (1) (2) (3) (4) (5) (6)

MES MES MES �CoVaR �CoVaR �CoVaR

Panel A: Risk management variables

Derivatives intensity 0.0 0 0 −0.001 −0.001 0.0 0 0 0.0 0 0 0.0 0 0 Quintile 2 (0.932) (0.886) (0.920) (0.981) (0.928) (0.971)

Derivatives intensity 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0

Quintile 3 (0.945) (0.937) (0.982) (0.932) (0.903) (0.961)

Derivatives intensity 0.002 0.002 0.001 −0.002 −0.002 −0.002 Quintile 4 (0.774) (0.767) (0.820) (0.304) (0.268) (0.329)

Derivatives intensity 0.016 ∗∗ 0.013 ∗∗ 0.015 ∗∗ −0.010 ∗∗∗ −0.009 ∗∗∗ −0.010 ∗∗∗ Quintile 5 (0.012) (0.031) (0.013) (0.0 0 0) (0.0 0 0) (0.0 0 0)

VaR-disclosure index −0.007 0.002 (0.247) (0.327)

Securitization 0.011 ∗∗ 0.010 ∗∗ 0.012 ∗∗ −0.002 −0.001 −0.002 (0.021) (0.042) (0.018) (0.323) (0.605) (0.298)

Disclosed risk types −0.001 −0.002 −0.002 0.0 0 0 0.0 0 0 0.0 0 0 (0.220) (0.179) (0.183) (0.792) (0.939) (0.865)

Panel B: Control variables

Total assets 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0

(0.752) (0.975) (0.306) (0.335) (0.925) (0.201)

Tier 1 capital ( × 10 4 ) −8.242 ∗∗ 4.238 ∗∗∗ (0.024) (0.003)

ROA 0.006 0.006 0.007 −0.003 ∗∗ −0.004 ∗∗ −0.003 ∗∗ (0.183) (0.165) (0.153) (0.038) (0.013) (0.028)

Loans −0.006 −0.009 ∗ −0.008 0.003 ∗∗ 0.005 ∗∗∗ 0.003 ∗∗∗ (0.223) (0.078) (0.144) (0.015) (0.0 0 0) (0.009)

Non interest income 0.028 ∗∗ 0.029 ∗∗ 0.036 ∗∗ −0.007 −0.008 −0.009 (0.039) (0.033) (0.018) (0.193) (0.164) (0.130)

Leverage −0.001 −0.001 0.001 ∗∗ 0.001 ∗∗ (0.109) (0.119) (0.017) (0.019)

Market-to-book 0.049 ∗∗ 0.073 ∗∗∗ 0.049 ∗∗ −0.038 ∗∗∗ −0.052 ∗∗∗ −0.038 ∗∗∗ (0.028) (0.002) (0.025) (0.0 0 0) (0.0 0 0) (0.0 0 0)

Debt maturity −0.004 −0.006 −0.004 0.007 ∗∗∗ 0.008 ∗∗∗ 0.007 ∗∗∗ (0.532) (0.400) (0.579) (0.001) (0.0 0 0) (0.001)

Intercept 0.022 ∗ 0.022 ∗∗ 0.021 ∗ −0.008 ∗∗ −0.007 ∗∗ −0.008 ∗ (0.052) (0.033) (0.058) (0.050) (0.038) (0.054)

R 2 0.128 0.131 0.130 0.278 0.281 0.279

Adj. R 2 0.102 0.106 0.103 0.257 0.260 0.257

Observations 463 462 463 463 462 463

This table shows results from cross-sectional regressions of the Marginal Expected Shortfall and �CoVaR of U.S. banks on dummy variables for membership in the second,

third, fourth and fifth quintile of derivatives intensity. The dependent variable in the first three regressions is the average of the daily Marginal Expected Shortfall estimates

for the time period 07/01/2007 to 12/31/2008 computed using the dynamic model specification proposed by Brownlees and Engle (2012) . In regressions (4) and (6), the

dependent variable is the average conditional �CoVaR of the banks during the same period. All explanatory variables are based on stock market or accounting data for the

year 2006. Variable definitions and data sources are provided in Appendix A . All models are estimated with OLS. The statistical significance of the estimated coefficients

is tested with Newey and West (1987) heteroskedasticity and autocorrelation consistent t -tests. Corresponding p -Values are shown in parentheses. R 2 and Adj. R 2 are the

estimated regression models’ R -squared and adjusted R-squared, respectively. ∗∗∗ denote coefficients that are significant at the 1% level. ∗∗ denote coefficients that are significant at the 5% level. ∗ denote coefficients that are significant at the 10% level.

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26 In essence, these regressions can be seen as placebo tests in which we expect

the VaR-disclosure index to be insignificant while our main explanatory variables

remain significant determinants of MES and �CoVaR.

f information disclosed by our sample banks. Especially, if larger

anks allocate more resources to foster investor relations and con-

equently disclose more information on their risk management on

op of the information mandated by regulators, our main findings

ould be due to spurious correlation rather than causation. To test

his conjecture, we run several additional regressions in which we

mploy the index proposed by Pérignon and Smith (2010) on the

evel of VaR-disclosure of our sample banks. This index captures

he level and quality of information disclosed by banks on their

se of Value-at-Risk in their risk management. In contrast to our

ain explanatory variables which also proxy (at least in part) for

bank’s risk-taking, however, the VaR-disclosure index only con-

eys information on the quality of a bank’s risk management (and

he bank’s transparency concerning its risk management). Even

ore importantly, in contrast to the mandatory information on a

ank’s derivative positions, VaR-based market risk disclosures are

ot mandatory but only encouraged by the SEC’s Financial Report-

ng Release Number (FRR) 48 and the Basel Accord. If our results

re indeed simply driven by differences in the amount of disclosed

nformation on a bank’s risk management, we would expect the

aR-disclosure index to capture this effect in our regressions. The

esults of these tests are presented in Table 11 . 26

The results of the regressions show a clear picture. As ex-

ected, more information on the use and estimation of VaR is as-

ociated with a lower MES and a higher �CoVaR. Despite this,

he VaR-disclosure index enters none of our regressions with a

tatistically significant coefficient. In contrast, our proxies for a

ank’s derivatives intensity, loan securitization, and use of interest

ate derivatives remain highly statistically and economically signif-

cant determinants of a bank’s equity tail risk during the financial

risis.

.5. Robustness

In this section, we perform various additional tests to check

he robustness of our main findings. We start by performing re-

198 R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205

Table 10

Regressions of a bank’s equity tail risk during the financial crisis – interactions.

Dependent variable (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

MES MES MES MES MES MES MES �CoVaR �CoVaR �CoVaR �CoVaR �CoVaR �CoVaR �CoVaR

Panel A: Risk management variables

Derivatives intensity 0.0 0 0 0.021 ∗∗∗ 0.009 0.004 ∗∗∗ 0.005 ∗∗∗ −0.004 −0.005 −0.008 ∗∗∗ −0.002 ∗∗ −0.002 ∗∗ (0.968) (0.002) (0.114) (0.003) (0.001) (0.355) (0.041) (0.0 0 0) (0.012) (0.012)

Interest rate derivatives −0.106 ∗∗∗ 0.010 ∗∗∗ 0.040 ∗∗∗ −0.005 ∗∗∗ (0.002) (0.007) (0.001) (0.0 0 0)

FX derivatives −0.001 0.108 0.002 −0.066 (0.922) (0.495) (0.719) (0.248)

Securitization 0.012 ∗∗ 0.009 ∗ 0.012 ∗∗ 0.008 ∗ 0.011 ∗∗ −0.140 ∗∗∗ 0.031 −0.002 −0.001 −0.002 0.0 0 0 −0.001 0.052 ∗∗∗ −0.013 ∗∗∗ (0.017) (0.058) (0.016) (0.089) (0.024) (0.001) (0.237) (0.263) (0.648) (0.355) (0.800) (0.409) (0.0 0 0) (0.010)

Discl. risks −0.002 −0.002 −0.001 −0.001 −0.001 −0.001 −0.002 0.0 0 0 0.0 0 0 −0.001 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 (0.213) (0.195) (0.275) (0.349) (0.260) (0.256) (0.166) (0.648) (0.717) (0.172) (0.438) (0.588) (0.513) (0.721)

Panel B: Control variables

Total assets ( × 10 11 ) 3.023 4.135 ∗∗ 1.293 1.827 1.885 4.072 ∗∗∗ 2.234 ∗∗ 0.214 1.026 −0.625 0.473 −1.340 1.277 ∗∗ 0.687 (0.259) (0.031) (0.524) (0.291) (0.514) (0.006) (0.018) (0.825) (0.140) (0.289) (0.446) (0.198) (0.049) (0.272)

Tier 1 capital ( × 10 4 ) −7.048 ∗ −6.308 ∗∗ 0.357 4.422 ∗∗∗ (0.053) (0.023) (0.001) (0.009)

Panel C: Interactions

Total assets × Hedging intens. 0.0 0 0 0.0 0 0 (0.614) (0.651)

Tier 1 capital × Hedging intens. −0.002 ∗∗ 0.0 0 0 (0.013) (0.151)

Discl. risks × Deriv. intens. −0.001 0.001 ∗∗∗ (0.500) (0.0 0 0)

Total assets × IR deriv. 0.008 ∗∗∗ −0.003 ∗∗∗ (0.001) (0.0 0 0)

Total assets × FX derivatives −0.006 0.004 (0.521) (0.256)

Total assets × Securit. 0.010 ∗∗∗ −0.004 ∗∗∗ (0.0 0 0) (0.0 0 0)

Tier 1 capital × Securit. −0.002 0.001 ∗∗ (0.454) (0.012)

R 2 0.129 0.144 0.129 0.147 0.125 0.160 0.137 0.251 0.259 0.267 0.278 0.258 0.276 0.266

Adj. R 2 0.108 0.123 0.108 0.125 0.102 0.140 0.115 0.233 0.241 0.249 0.258 0.238 0.259 0.248

Observations 463 462 463 463 463 463 462 463 462 463 463 463 463 462

This table shows results from cross-sectional regressions of the Marginal Expected Shortfall and �CoVaR of U.S. banks on several variables related to the banks’ risk man-

agement and various control variables together with interaction terms. The dependent variable in the first seven regressions is the average of the daily Marginal Expected

Shortfall estimates for the time period 07/01/2007 to 12/31/2008 computed using the dynamic model specification proposed by Brownlees and Engle (2012) . In regressions (8)

and (14), the dependent variable is the average conditional �CoVaR of the banks during the same period. Coefficients for the bank-specific control variables are not shown

for brevity. All explanatory variables are based on stock market or accounting data for the year 2006. Variable definitions and data sources are provided in Appendix A .

All models are estimated with OLS. The statistical significance of the estimated coefficients is tested with Newey and West (1987) heteroskedasticity and autocorrelation

consistent t -tests. Corresponding p -Values are shown in parentheses. R 2 and Adj. R 2 are the estimated regression models’ R -squared and adjusted R-squared, respectively. ∗∗∗ denote coefficients that are significant at the 1% level. ∗∗ denote coefficients that are significant at the 5% level. ∗ denote coefficients that are significant at the 10% level.

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27 See Mayordomo et al. (2014) for a similar approach to measure a bank’s deriva-

gressions using alternative estimation techniques to control for a

biasing influence of outliers on our results. For this, we reesti-

mate our main models from Tables 5 and 6 using median regres-

sions in which the sum of the absolute value of the regression’s

residuals are minimized. The results from our baseline OLS re-

gressions remain quantitatively and qualitatively the same. Addi-

tionally, we reestimate all our regressions using winsorized (1%

and 99% quantiles) explanatory variables as well as standard er-

rors clustered by derivatives intensity and total assets groups. To

further control for a confounding effect caused by different defi-

nitions of derivatives due to different auditors, and the geograph-

ical core/periphery structure of the U.S. banking sector, we rees-

timate our baseline regressions using auditor-fixed and state-fixed

effects. The results of all these robustness checks do not alter our

findings.

Next, it could be argued that our proxy of a bank’s derivatives

intensity does not take into account the actual size of a bank’s

derivatives position relative to the bank’s size. To address this con-

cern, we reestimate our regressions using the ratio of a bank’s to-

tal fair value of all asset and liability side derivatives holdings and

the bank’s total assets as an alternative proxy of the bank’s deriva-

ives intensity. 27 The results of this robustness check are presented

n Section IA.4 of the Internet Appendix. The results we get from

his robustness check are qualitatively and quantitatively similar to

hose reported in our main analysis.

Furthermore, we employ several additional explanatory vari-

bles in regressions of MES and �CoVaR. First, in Section IA.2 in

he Internet Appendix, we substitute our proxy for a bank’s lever-

ge for the bank’s Tier 1 capital ratio. In Section IA.3, we also es-

imate regressions in which we control for differences in the liq-

idity of the banks’ stocks. As investors prefer assets which are ei-

her liquid (see Amihud and Mendelson, 1986; Brennan and Sub-

ahmanyam, 1996 ) or are at least not exposed to systematic drops

n liquidity (see Acharya and Pedersen, 20 05; Sadka, 20 06 ), the dif-

erences in the banks’ equity tail risk could simply be due to dif-

erences in liquidity. The results of both robustness checks show

hat our main conclusions remain unchanged. Second, we estimate

egressions in which we use our two proxies for the corporate gov-

rnance of banks (board size and board independence). Although

tives intensity.

R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205 199

Table 11

Robustness check – VaR-disclosure index.

Dependent Variable (1) (2) (3) (4) (5) (6) (7) (8)

MES MES MES MES �CoVaR �CoVaR �CoVaR �CoVaR

Panel A: Risk management variables

VaR-disclosure index −0.005 −0.005 −0.009 −0.008 0.002 0.0 0 0 0.003 0.002 (0.363) (0.466) (0.142) (0.193) (0.399) (0.980) (0.244) (0.338)

Derivatives intensity 0.006 ∗∗∗ −0.002 ∗∗∗ (0.001) (0.001)

Interest rate derivatives 0.010 ∗∗∗ −0.005 ∗∗∗ (0.007) (0.0 0 0)

FX derivatives 0.010 −0.002 (0.4 4 4) (0.630)

Securitization 0.012 ∗∗ 0.012 ∗∗ −0.002 −0.002 (0.012) (0.019) (0.254) (0.356)

Disclosed risk types −0.002 −0.001 0.0 0 0 0.0 0 0 (0.152) (0.218) (0.721) (0.636)

Panel B: Control variables

Total assets 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0

(0.221) (0.404) (0.970) (0.329) (0.132) (0.508) (0.998) (0.280)

ROA 0.007 −0.002 0.008 ∗ 0.007 −0.004 ∗∗ 0.002 −0.004 ∗∗ −0.004 ∗∗ (0.122) (0.760) (0.094) (0.130) (0.022) (0.355) (0.019) (0.032)

Loans −0.007 −0.009 ∗ −0.009 ∗ −0.008 0.004 ∗ 0.004 ∗ 0.004 ∗∗ 0.003 ∗ (0.192) (0.087) (0.072) (0.131) (0.059) (0.056) (0.029) (0.068)

Non interest income 0.043 ∗∗∗ 0.044 ∗∗ 0.035 ∗∗ 0.035 ∗∗ −0.015 ∗∗∗ −0.010 −0.011 ∗∗ −0.011 ∗ (0.004) (0.012) (0.020) (0.028) (0.005) (0.151) (0.047) (0.063)

Buy-and-hold returns 1998 −0.025 ∗∗ 0.010 ∗∗ (0.045) (0.045)

Leverage −0.001 −0.002 ∗∗ −0.001 ∗ −0.001 0.001 ∗∗∗ 0.002 ∗∗∗ 0.001 ∗∗∗ 0.001 ∗∗∗ (0.183) (0.050) (0.099) (0.108) (0.009) (0.0 0 0) (0.004) (0.004)

Market-to-book 0.064 ∗∗∗ 0.100 ∗∗∗ 0.047 ∗∗ 0.049 ∗∗ −0.046 ∗∗∗ −0.060 ∗∗∗ −0.040 ∗∗∗ −0.040 ∗∗∗ (0.004) (0.001) (0.034) (0.027) (0.0 0 0) (0.0 0 0) (0.0 0 0) (0.0 0 0)

Debt maturity −0.004 0.004 −0.003 −0.003 0.006 ∗∗ 0.003 0.006 ∗∗ 0.006 ∗∗ (0.594) (0.619) (0.689) (0.680) (0.010) (0.329) (0.011) (0.011)

Intercept 0.011 0.013 0.023 ∗∗ 0.021 ∗∗ −0.006 ∗ −0.018 ∗∗∗ −0.008 ∗∗ −0.007 ∗ (0.258) (0.323) (0.031) (0.049) (0.079) (0.001) (0.048) (0.063)

R 2 0.097 0.143 0.133 0.128 0.230 0.247 0.253 0.257

Adj. R 2 0.082 0.115 0.111 0.105 0.216 0.222 0.235 0.237

Observations 463 286 463 463 463 286 463 463

This table shows results from robustness checks with cross-sectional regressions of the Marginal Expected Shortfall and �CoVaR of U.S. banks on several variables related

to the banks’ risk management and various control variables. The dependent variable in the first four regressions is the average of the daily Marginal Expected Shortfall

estimates for the time period 07/01/2007 to 12/31/2008 computed using the dynamic model specification proposed by Brownlees and Engle (2012) . In regressions (5) and

(8), the dependent variable is the average conditional �CoVaR of the banks during the same period. All explanatory variables are based on stock market or accounting

data for the year 2006. In contrast to our baseline regressions, we additionally employ the VaR-disclosure index in all regressions. Variable definitions and data sources are

provided in Appendix A . All models are estimated with OLS. The statistical significance of the estimated coefficients is tested with Newey and West (1987) heteroskedasticity

and autocorrelation consistent t -tests. Corresponding p -values are shown in parentheses. R 2 and Adj. R 2 are the estimated regression models’ R -squared and adjusted R-

squared, respectively. ∗∗∗ denote coefficients that are significant at the 1% level. ∗∗ denote coefficients that are significant at the 5% level. ∗ denote coefficients that are significant at the 10% level.

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f limited statistical value due to a small number of observations,

e do not find any evidence that the significant relation between

erivatives usage, securitization, and equity tail risk is attenuated

y the addition of these variables. Third, we address concerns that

ur regressions so far neglect the possibility that MES and �CoVaR

re indeed valid measures of systemic risk and thus influenced by

he banks’ interconnectedness with the rest of the banking sector.

n untabulated regressions, we employ the measure of a bank’s in-

erconnectedness proposed by Billio et al. (2012) based on a princi-

al component analysis of all banks’ stock returns as an additional

ontrol variable. Doing so does not change our conclusions.

We also reestimate our measures of equity tail risk using a dif-

erent index and different time periods. To be precise, we use the

&P 500 as a general market index instead of the Datastream US

inancials Index . For both indexes, we arrived at nearly identical re-

ults for the banks’ MES and �CoVaR. In another robustness check,

e reestimated the banks’ MES and �CoVaR using the time pe-

iod from 07/01/2007 to 06/30/2009 as the crisis period. Again, our

ain results remain unchanged.

In further robustness checks reported in Section IA.5 in the In-

ernet Appendix, we address concerns that our analysis of equity

ail risk is rather an analysis of the banks’ systematic risk. The re-

ults show that while MES and �CoVaR exhibit some correlation

ith the banks’ beta, the risk measures are far from being strongly

orrelated with each other. Consequently, the tail risk measures we

mploy do indeed capture a different facet of equity risk.

Finally, in Section IA.6 in the Internet Appendix, we perform a

et of simultaneous equations regressions to control for the possi-

ility that our measures of equity tail risk and default risk as well

s the banks’ derivatives intensity are jointly determined. The re-

ults of these robustness checks given in Table IA.VII clearly show

hat a bank’s derivatives intensity exerts a significant influence on

he bank’s MES, �CoVaR, and distance-to-default. We thus rule out

he possibility that our main findings are subject to reverse causal-

ty.

. Conclusion

In this paper, we find that the intensity with which U.S. banks

sed financial derivatives and their use of loan securitization as a

ool for transferring risks as disclosed in their 10-K filings before

he financial crisis explain the banks’ equity tail risk during the

200 R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205

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ningst

crisis. In particular, banks that used more derivatives and securi-

tized loans suffered greater losses on their stocks on those days

the market plummeted during the crisis. In addition, the market

suffered heavier losses in case the stocks of banks with a more

elaborate use of derivatives were in their lower left tail. These ef-

fects are economically large and cannot be attributed to larger (and

thus systemically more important) banks disclosing more informa-

tion on their risk management.

The results of our empirical work are consistent with the hy-

pothesis that derivatives usage for non-hedging purposes increases

an individual bank’s equity risk and potentially destabilizes the fi-

nancial sector. Banks that used derivatives and loan securitization

in their risk management had higher stock returns if they had a

higher actual risk exposure before the crisis. The same is true for

banks that had a higher default probability before the financial cri-

sis. In contrast, derivatives usage without need led to higher losses

on individual bank stocks and the sector index during the crisis.

Our paper fills an important gap in the empirical review of the

financial crisis. Our results show that banks did not exit indiscrim-

inate extreme losses on their stocks at the climax of the financial

crisis. If anything, extreme stock returns were driven by a ratio-

nal assessment of the banks’ pre-crisis default probability and ex-

posure to two major multipliers of the crisis: excessive usage of

derivatives and loan securitization.

Regarding disclosure on the usage of derivatives and securitiza-

tion, our findings appear particularly interesting in light of the ar-

guments by Barth and Landsman (2010) suggesting that disclosure

according to SFAS 133 and 140 respectively were too aggregated

and incomplete to indicate the risk inherent in these activities ad-

equately. In light of our findings that investor reaction reflected in-

formation on the usage of derivatives and loan securitization, our

study puts such concerns somewhat into perspective. Nevertheless,

our study cannot rule out that investor assessment could have dif-

fered if investors had more detailed information during the crisis.

Variable name Definition Data

Panel A: Systemic risk measures

MES Dynamic Marginal Expected Shortfall as

defined by Acharya et al. (2010) and

calculated following the procedure laid out

by Brownlees and Engle (2012) .

Data

� CoVaR Conditional � CoVaR as defined by Adrian and

Brunnermeier (2010) , measured as the

difference between the Value-at-Risk (VaR)

of a country-specific financial sector index

conditional on the distress of a particular

bank and the VaR of the sector index

conditional on the median state of the bank.

As state variables for the computation of

conditional � CoVaR, we employ the change

in the three-month Treasury bill rate, the

difference between the ten-year Treasury

Bond and the three-month Treasury bill rate,

the change in the credit spread between

BAA-rated bonds and the Treasury bill rate,

the return on the Case-Shiller Home Price

Index, and implied equity market volatility

from VIX.

Data

Ex

Bo

Panel B: Main variables of interest (derivatives usage and risk management disclosur

Derivatives intensity Proxy for the intensity with which firms

employ financial derivatives. The variable is

defined as the number of the used types of

financial derivatives as disclosed in the

bank’s 10-K filing (see Bartram et al., 2011 ,

for a similar definition).

Mor

bviously, this question remains unanswered empirically.

Although we find disclosed information on risk management to

e a powerful determinant of a bank’s extreme stock returns dur-

ng the crisis, our study should not be misunderstood as an inves-

igation into systemic risk or the causes of the crisis. Rather, our

esults explain how stock market investors reacted during the fi-

ancial crisis. In contrast, an analysis of systemic risk would ulti-

ately require private information on a bank’s funding structure,

ts interconnectedness, and detailed data on its derivatives usage.

owever, we do not consider this to be a weakness of our study

s we base all our findings on exactly the type of information that

as available to investors during the crisis: disclosed bank balance

heets and risk reports. Yet at the same time, if one assumes that

oth MES and �CoVaR as proxies of banks’ equity tail risk do in-

eed capture a significant portion of a bank’s exposure and contri-

ution to the fragility of the financial system (as it is done, e.g., by

runnermeier et al., 2012; Anginer et al., 2014b ), our results iden-

ify derivatives usage as a significant determinant of systemic risk

hat had previously been neglected in the empirical literature.

ppendix A. Variable definitions and data sources.

The appendix presents data sources, definitions and expected

igns in our regression analyses for all dependent and indepen-

ent variables that are used in the empirical study. The expected

ign of each independent variable on the equity tail risk of a U.S.

ank is shown in the last column with a “+” indicating an ex-

ected increasing (and a “-” a decreasing) impact on equity tail

isk. The bank controls were taken from the Thomson Reuters Fi-

ancial Datastream and Thomson Worldscope databases and the

ariables on the banks’ derivatives usage and risk management

ctivities were extracted from the banks’ respective 10-K filings

etrieved from the Morningstar Document Research database.

e Hypotheses Expected sign

, own calc. –

, Chicago Board Options

e Market, Federal Reserve

H.15, S&P, own calc.

–

ar, 10-K filings. Hedging for risk management

purposes reduces total firm risk;

hedging could increase

counterparty risk; derivatives

usage could be indicative of

increased risk-taking. Smith and

Stulz (see 1985 ); Bartram et al.

(see 2011 ).

+ / −

R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205 201

( continued )

Variable name Definition Data source Hypotheses Expected sign

Interest rate derivatives Dummy variable that equals one for interest

rate derivative users and zero for non-users.

Morningstar, 10-K filings. Banks with higher probability of

financial distress manage their

interest rate risk more

aggressively; non-user banks

adopt conservative asset-liability

management policies (see Guay,

1999; Purnanandam, 2007 ).

+ / −

FX derivatives Dummy variable that equals one for users of

FX derivatives and zero for non-users.

Morningstar, 10-K filings. The use of FX derivatives for risk

management purposes reduces

total firm risk; use of FX

derivatives could increase

counterparty risk and be due to

non-hedging purposes (see

Graham and Rogers, 2002;

Rogers, 2002 ).

+ / −

Securitization Dummy variable that equals one if the bank

discloses the use of loan securization and

zero otherwise.

Morningstar, 10-K filings. Securitization should decrease

credit risk; banks could have

employed securitization for

regulatory arbitrage thereby

effectively securitizing loans

without transferring the risks to

other market participants (see

Acharya et al., 2013 ).

+ / −

Disclosed risk types Number of risk types a bank is exposed to as

disclosed in the 10-K filing.

Morningstar, 10-K filings. More disclosed risk types could

indicate more risk-taking by the

bank; more disclosure could also

indicate a more alert risk

management.

+ / −

VaR-disclosure index Index of the extent to which banks disclose

information on their employed Value-at-Risk

(VaR) models (see Pérignon and Smith, 2010 ,

for a similar index). The index is constructed

by taking the sum of several dummy

variables taking on the value of one if a

certain information on the bank’s VaR-model

is disclosed, and zero otherwise. The index

constituents cover the questions whether a)

the confidence level of the VaR is disclosed,

b) whether the bank calculates a model with

a confidence level of 97,5% or higher, c)

discloses information on the estimation

method, d) the holding period, e) the

employed backtests, and f) the overall

diversification effect in the bank portfolio.

Morningstar, 10-K filings. More voluntary disclosure on a

bank’s risk management

increases transparency and

decreases equity tail risk caused

by a panic-based contagion.

−

Panel C: Control variables

Total assets Natural logarithm of a bank’s total assets at

fiscal year end 2006.

Worldscope (WC02999). Larger banks could become

too-big-to-fail.

+

Return on assets A bank’s annual return on assets. Worldscope (WC08326). Higher profits shield banks from

adverse effects emanating from

the financial sector.

−

Tier 1 capital Tier 1 capital representing the primary capital

supporting the lending and deposit activities

of a bank.

Worldscope (WC18228). Higher regulatory bank capital acts

as a buffer against losses and

should stabilize both an

individual bank and the financial

sector.

−

Non-interest income Non-interest income divided by total interest

income.

Worldscope (WC01021 and

WC01016).

Higher values of non-interest

income relative to total interest

income could be indicative of a

business model that concentrates

more on non-deposit taking

activities (like, e.g., investment

banking) and thus more

risk-taking (see Brunnermeier

et al., 2012 ).

+

Loans Ratio of total loans to total assets. Worldscope (WC02271 and

WC02999).

A higher loans-to-assets ratio of a

bank could indicate a business

model that focuses on lending

rather than more risky activities.

−

Buy-and-hold returns

1998

Annual buy-and-hold stock returns in fiscal

year 1998.

Datastream, own calc. Subsequent to the “risk culture

hypothesis” of Fahlenbrach et al.

(2012) , a higher buy-and-hold

return during the LTCM crisis in

1998 together with persistence in

the bank’s risk culture, could

cause the bank to fare better

during subsequent crises.

−

( continued on next page )

202 R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205

( continued )

Variable name Definition Data source Hypotheses Expected sign

Leverage Book value of assets minus book value of

equity plus market value of equity, divided

by market value of equity (see Acharya et al.,

2010 ).

Worldscope (WC02999, WC03501,

WC08001), own calc.

Disciplining effect of leverage vs.

greater vulnerability during

financial crises (see Adrian and

Shin, 2010 ).

+ / −

Market-to-book Market value of common equity divided by

book value of common equity.

Worldscope (WC07210 and

WC03501).

Greater charter value incentivizes

bank managers to keep their

bank’s capital ratio and to limit

their risk-taking (see Keeley,

1990 ).

−

Debt maturity Total long-term debt (due in more than one

year) divided by total debt.

Worldscope (WC03251 and

WC03255).

A less fragile funding structure of a

bank makes it less vulnerable to

sudden shortages in liquidity

during a crisis (see Brunnermeier

and Pedersen, 2009 ).

−

Distance-to-default

(DtD)

A bank’s distance-to-default, defined as the

difference between the bank’s asset value

and the face value of its debt, scaled by the

standard deviation of the bank’s asset value

(see Merton, 1974 ). For its computation, we

follow the estimation methods laid out by

Hillegeist et al. (2004) and Campbell et al.

(2008) using Newton’s algorithm and the 1

year US treasury yield as the risk-free rate.

Datastream, Worldscope (WC05301,

WC03051, and WC03251), own

calc.

Higher distances-to-default imply

lower default probabilities of U.S.

banks and thus lower equity tail

risk.

−

Stock liquidity Amihud measure of an individual stock’s

illiquidity adjusted following the procedure

proposed by Karolyi et al. (2012) . The

adjusted Amihud measure is defined as

− ln (

1 + | R i,t | P i,t V O i,t

) where R i, t is the return, P i, t

is the price and VO i, t is the trading volume

of stock i on day t .

Datastream, own calc. More liquid stocks are more

susceptiple and contribute more

to downturns of a sector index.

+

Non-hedging purpose Dummy variable that takes on the value of one

if the fair value gains/losses on derivatives

and the fair value gains/losses on selected

balance sheet items (investment securities,

net loans, deposits, and long term debt) are

of the same sign, and zero otherwise.

Morningstar, 10-K filings, own calc. Derivatives usage for non-hedging

purpose increases equity tail risk

and default risk.

+

Board size Natural logarithm of the number of directors

on an insurer’s board.

ESG ASSET 4 (CGBSDP060) and

Morningstar (DEF 14A filings).

Larger boards destroy value and

capital buffers (see, e.g., Yermack,

1996 ).

+

Board independence Percentage of independent outside directors on

the board of directors.

ESG ASSET 4 (CGBSO07S) and

Morningstar (DEF 14A filings).

More independent board members

improve governance.

−

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Appendix B. Systemic risk measures

In this appendix, we shortly discuss the details of the estima-

tion of the measures of a bank’s equity tail risk used in our empir-

ical study.

Dynamic Marginal Expected Shortfall

As our first measure of a bank’s equity tail risk, we employ the

dynamic specification of the MES (see Acharya et al., 2010 ) pro-

posed by Brownlees and Engle (2012) . Therefore, let R j,t and R M,t

be the j th bank’s and the log return of the financial sector on day

t , respectively. The bivariate daily return process is then given by

R M,t = σM,t �1 M,t R j,t = σ j,t ρ j,t �2 M,t + σM,t

√ 1 − (ρ j,t ) 2 �2 j,t

(�1 M,t , � 2 j,t ) ∼ H,

where σ i,t is the conditional volatility of the sector return (i = m ) or bank j ’s return (i = j) , ρj,t is the conditional sector/bank correlation and (�1

M,t , �2

j,t ) are i.i.d. innovations with E (�

j i,t

) = 0 , ar(�

j i,t

) = 1 for n = { 1 , 2 } and i = { j, M} and zero covariance (al- though they are not necessarily independent of each other).

The one-period-ahead MES for a tail event S is denoted by

MES 1 j,t−1 = E t−1 (R j,t | R M,t < S)

= σ j,t E t−1 ( ρ j,t �

1 M,t +

√ 1 − (ρ j,t ) 2 �2 j,t | S/σM,t

) = σ j,t ρ j,t E t−1

( �1 M,t | S/σM,t

) + σ j,t

√ 1 − (ρ j,t ) 2 E t−1

( �2 j,t | S/σM,t

) .

urthermore, the conditional probability of the tail event is given

y

r 1 S,t (S) = P r t−1 (r M,t < S) = P r(�1 M,t < S/σM,t ) . Next, the multi-period-ahead MES is estimated by a simulation

rocedure to construct forecasts. First, K return paths of length h

or k = 1 , . . . , K are simulated on day t − 1

R k M,t+ δ−1

R k j,t+ δ−1

}h δ=1

.

urthermore, pseudo-innovations are drawn from the innovation

istribution H yielding

�1 ,k M,t+ δ−1 , �

2 M,t+ δ−1

)h δ=1 ∼ H.

o obtain the simulated return paths, the pseudo-innovations are

sed in the Dynamic Conditional Correlation (DCC) and GARCH

odels with the current levels of volatility and correlation as start-

ng conditions. The MES is then estimated as the Monte Carlo av-

rage of the simulated paths

R. Trapp, G.N.F. Weiß / Journal of Banking and Finance 71 (2016) 183–205 203

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A

ES h j,t−1 (S) =

∑ K k =1 R

k j,t : t + h −1 I{ R k M,t : t + h −1 < S} ∑ K

k =1 I{ R k M,t : t + h −1 < S} ,

here R k i,t : t + h −1 is the k

th simulated cumulative return of bank j or

f the sector from period t to period t + h − 1 , i.e.,

k j,t : t + h −1 = exp

{ h ∑

δ=1 r k

j,t : t + h −1

} − 1 .

inally, the multi-period probability of a tail event is given by

r 1 S,t (S) = P r t−1 (R k M,t : t + h −1 < S) = 1

K

K ∑ k =1

I{ R k M,t : t + h −1 < S} .

ollowing Brownlees and Engle (2012) , the 6-months period MES

s taken as the “long term” or “long run” MES of a bank.

CoVaR

The CoV aR j| i α of financial institution j (or the financial system) is

efined as its Value-at-Risk ( VaR ) given by P r(R i ≤ V aR i α ) = α con- itional on some (tail) event C (R i ) of institution i , where R i is the

eturn of institution i for which the V aR i α is defined. The CoV aR j| i α is

efined implicitly by the α-quantile of the conditional probability istribution:

r

( R j ≤ CoV aR j| C (R i ) α | C (R i )

) = α.

hen, the contribution of institution i to the VaR of institution j (or

he financial system) is given by

C oV aR j| C (R i ) α = C oV aR j| R i = V aR

i α

α − C oV aR j | R i = Med ian i

α .

o measure an individual bank’s contribution to the system’s tail

isk, j is simply set to be the financial sector. Hence, �CoV aR j| C (R i ) α

r simply �CoV aR i α denotes the difference between the financial

ystem’s VaR conditional on a particular financial institution i be-

ng in distress and the VaR of the financial system conditional on

he median state of institution i .

The unconditional CoVaR is then estimated by quantile regres-

ions. Let ˆ R system, j q be the predicted value of a quantile regression

f the financial sector on a particular institution or portfolio i for

he q th -quantile:

ˆ

system, j q = ˆ α j q + ˆ β j q ̂ R j q , here ˆ R

system, j q is the predicted value for a particular quantile con-

itional on institution j . The VaR of the financial system condi-

ional on R j , V aR system q | R j , is the predicted value of the quantile re-

ression of the system on institution j , ˆ R system, j q , since V aR

system q | R j

s the conditional quantile, i.e.,

aR system q | R j = ˆ R system, j q .

f R j = V aR i q , then the CoVaR measure conditioned on the event R j = V aR j q } is oV aR

system | R j = V aR j q q := V aR system q | V aR j q = ˆ α j q + ˆ β j q V aR j q

nd the �CoV aR j q is

CoV aR j q = V aR system | j q = ˆ β j q (V aR j q − V aR j 50% ) .

ow assume that the returns R i,t have the linear factor structure

j,t = φ0 + M t−1 φ1 + R i,t φ2 + (φ3 + M t−1 φ4 + R i,t φ5 ) �i t ith M t−1 as a vector of state variables. Furthermore, the i.i.d. er-

or term �t with zero mean and unit variance is independent of t−1 so that E [ �

j | M t−1 , R i,t ] = 0 . The returns are generated by

t

“location scale” process, therefore the conditional expected re-

urn E [ R j,t | M t−1 , R i,t ] = φ0 + M t−1 φ1 + R i,t φ2 and the conditional olatility V ar t−1 [ X

j t

| M t−1 , R i,t ] = φ3 + M t−1 φ4 + R i,t φ5 are depen- ent on the set of state variables M t−1 and on R i,t . The quantile egressions include estimates of the conditional mean and the con-

itional volatility for generating conditional quantiles. The model

s then estimated by this method for different percentiles. The cu-

ulative distribution function (cdf) of �j is given by F � j (� j ) and its

nverse cdf by F −1 � j

(q ) for percentile q with the conditional quantile

unction

−1 R j,t

(q | M t−1 , R i,t ) = αq + M t−1 γq + R i,t βq , here αq = φ0 + φ3 F −1 � j (q ) , γq = φ1 + φ4 F

−1 � j

(q ) and βq = φ2 + 5 F

−1 � j

(q ) for quantiles q ∈ (0, 1). We then have

aR j q = inf

V aR q { P r ( R t ≤ V aR q | M t−1 , R i,t ) ≥ q } = F −1 R j,t (q | M t−1 , R i,t )

nd by conditioning on X i t = V aR i q we get the CoVaR j| i q by

oV aR j| i q = inf

V aR q

{ P r

( R t ≤ V aR q | M t−1 , R i,t = V aR i q

) ≥ q

} = F −1

R j,t (q | M t−1 , V aR i q ) .

ere, the quantile function is estimated as the predicted value of he q -quantile regression of R i,t on M t−1 and R j,t by solving

min q ,βq ,γq

∑ t

{ q | R j,t − αq − M t−1 γq − R i,t βq | , if (R j,t − αq − M t−1 γq − R i,t βq ) ≥ 0 , (1 − q ) | R j,t − αq − M t−1 γq − R i,t βq | , if (R j,t − αq − M t−1 γq − R i,t βq ) < 0 .

In our empirical study, we employ the conditional version of

oVaR, i.e., the dynamic versions CoVaR t and VaR t of the static

ersions described above. We estimate the time variation of Co-

aR conditional on a vector of lagged state variables M t−1 . The tate variables can be interpreted as conditioning variables shift-

ng the conditional mean and the conditional volatility of the risk

easures. The previous quantile regression is now performed us-

ng weekly data with

R i,t = αi + γ i M t−1 + �i t , system,t = αsystem | i + βsystem | i R i,t + γ system | i M t−1 + �system | i . he predicted values of VaR and CoVaR are given by

V aR i t (q ) = ˆ αi + ˆ γ i M t−1 , oV aR i t (q ) = ˆ αsystem | i + ˆ βsystem | i V aR i t (q ) + ˆ γ system | i M t−1 . he predicted values from the regressions of R i,t and R system,t are

sed. In the end, �CoVaR i t for each institution is calculated by

CoV aR i t (q ) = CoV aR i t (q ) − CoV aR i t (50%) , = ˆ βsystem | i (V aR i t (q ) + V aR i t (50%)) .

he set of used state variables is mentioned in the main text.

upplementary material

Supplementary material associated with this article can be

ound, in the online version, at 10.1016/j.jbankfin.2016.07.001

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