Elimination of systemic risk in financial networks by means of a systemic risk transaction tax

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by  Sebastian Poledna

Elimination of systemic risk in financial networks by means of a systemic risk
transaction tax
Sebastian Poledna1 and Stefan Thurner1,2,3∗
1Section for Science of Complex Systems; Medical University of Vienna; Spitalgasse 23; A-1090; Austria
2Santa Fe Institute; 1399 Hyde Park Road; Santa Fe; NM 87501; USA
3IIASA, Schlossplatz 1, A-2361 Laxenburg; Austria
Financial marketsareexposedtosystemicrisk(SR),theriskthatamajor fraction ofthesystem
ceases to function and collapses. Since recently it is possible to quantify SR in terms of underlying
financialnetworkswherenodesrepresentfinancialinstitutions,andlinkscapturethesizeandmatu-
rityofassets(loans),liabilities,andotherobligationssuchasderivatives. Weshowthatitispossible
toquantifytheshareofSRthatindividualliabilitiesinafinancialnetworkcontributetotheoverall
SR.Weuseempiricaldataofnation-wideinterbankliabilitiestoshowthatafewliabilitiescarrythe
majorfractionoftheoverallSR.Weproposeataxonindividualtransactionsthatisproportionalto
theircontribution to overall SR.Ifa transaction does not increase SRit is tax free. With an agent
basedmodel(CRISISmacro-financialmodel)wedemonstratethattheproposedSystemicRiskTax
4
(SRT) leads to a self-organized re-structuring of financial networks that are practically free of SR.
1
ABMpredictionsagreeremarkablywellwiththeempiricaldataandcanbeusedtounderstandthe
0
relation of credit risk and SR.
2
Keywords: systemicrisk,DebtRank, agentbasedmodel,self-organizedcriticality,multiplexnetwork
b
e
F
INTRODUCTION financial regulation is known as macroprudential regula-

0 tion, and is currently put in place around the globe [13–
1
15]. TheBasleIIIframeworkrecognizessystemicallyim-
Failure to manage systemic risk (SR) has been proven
portantfinancialinstitutions (SIFI) andrecommendsin-
] to be extremely costly for society. The financial crisis of
M creasedcapitalrequirementsforthem,thesocalled“SIFI
2007-2008anditsconsequencesdemonstratedtheimpor-
surcharges”[16,17]. BasleIIIfurtherintroducescounter-
R tance to reduce it. The threat of collapse of large parts
cyclical buffers that allows regulators to increase capital
. of the financial system forced national governments to
n requirements during periods of high credit growth.
bail out hundreds of banks [1]. As a result one observed
i
f fallingglobalstockandrealestatemarkets[2–4],asevere Nomatterhowwellintendedthesedevelopmentsmight
-
q and global credit crunch [5], skyrocketingand prolonged be, they miss the central point about the nature of SR,
[ unemployment rates [6–8], and several Western govern- and might not be suitable to improve stability of the fi-

2 ments at the verge of bankruptcy [6]. Bank bailouts nancialsysteminasustainableway. SRistightlyrelated
v caused dangerously high levels of sovereign debt around to the network structureof financialassets andliabilities
6 the world, and it becomes necessary to find alternatives in a financial system. Management of SR is essentially
2 to finance bailouts. The International Monetary Fund a matter of re-structuring financial networks such that
0
proposed a tax on banks, called the “financial stability the probability of cascading failure is reduced, or ideally
8
. contribution” (FSC) that can be seen as a contribution eliminated.
1
of the financial sector to the public costs of the finan- Credit risk is the risk that a borrower will default on
0
4 cial crisis, and to create reserves for future crises. Bank a given debt by failing to make the full pre-specified re-
1 taxes have been implemented in many countries around payments. It is usually seen as a risk that emerges be-
: the world, such as the “Financial Crisis Responsibility tween two counterparties once they engagein a financial
v
i Fee” in the US. The European Commission proposed an transaction. The lender is the sole bearer of credit risk,
X EU-wide bank tax under the “Single Resolution Mecha- andfiguresthe likelihoodoffailedrepaymentsintoarisk
r nism”. Inadditionto banktaxesafinancialtransactions premium. Lendersusuallychargehigherinterestratesto
a
tax (FTT) is considered by many countries. FTT is not borrowersthataremorelikelytodefault(risk-basedpric-
ataxonfinancialinstitutionsperse,butalevyplacedon ing). Credit risk is relatively well understood, and can
specifictypesoffinancialtransactions. Itsmainpurpose, be mitigated through a number methods and techniques
besides generating revenue for governments, is to curb [18]. The Basle accords provide an extensive framework
volatility of financial markets [9, 10]. Empirical studies dealing foremost with the mitigation of credit risk [19–
are generallyinconclusive, anda causalrelationbetween 21].
volatility and FTTs remains ambiguous [11, 12]. In re- Whentwocounterpartiesarepartofafinancialsystem,
sponse to the financial crisis of 2007-2008 a consensus forexampleasnodesinafinancialnetwork,thesituation
for the need of new financial regulation emerged. New changes, and their transaction may affect the financial
financial regulation should be designed to mitigate the systemasawhole. Thelenderno moreis the solebearer
riskof the financialsystemasa whole. This approachto ofcreditrisk,nordoescreditriskdependonthefinancial
2
conditionsoftheborroweralone. Theimpactofadefault mized. Sinceeverytransactioninafinancialnetworkhas
of the borrower is no longer limited to the lender, but it an impact on the overall SR of a system, we suggest a
may affect the other creditors of the lender (who also transactiontaxonalltransactionsbetweenanytwomar-
lendtothesameborrower)aswellastheircreditors,and ketparticipantsthatincreasetheSRoftheentiresystem.
so on. Similarly, the lender is not only vulnerable to The size of the tax is proportional to the SR contribu-
a default of the borrower but also to defaults from all tion of the particular transaction. Market participants
debtors of that borrower as well as their debtors, etc. looking for credit will try to avoid this tax by looking
In financial networks credit risk loses the local character for credit opportunities that do not increase SR and are
between two counterparties, and becomes systemic. thus tax free. As a consequence the network arranges
SR is the risk that the financial system as a whole or toward a topology that, in combination with the finan-
a large fraction of it can no longer perform its function cialconditionsofindividualinstitutions,willleadtoade
as a credit provider and collapses. SR is a result of the facto elimination of SR, meaning that cascading failures
networknatureof financialtransactionsandliabilities in can no longer occur. In the spirit of risk-based pricing
the financial system. It unfolds as secondary cascades of as it is used for credit risk, here we propose a systemic
credit defaults, triggered by credit defaults between in- risk premium. It was shownin [39] that SR can be dras-
dividual counterparties. These cascades can potentially tically reduced by reducing borrowing from systemically
wipe out the financial system by a de-leveragingcascade risky nodes. This is achieved by distributing SR evenly
[22–29]. Itisobviousthatlendershaveastrongincentive overthenetworkandbypreventingtheemergenceofsys-
to mitigate credit risk. In the case of SR the situation is temically super-risky nodes. The mechanism works in a
less clear,since the loss-bearerswillin generalnotbe di- self-organized way: risky nodes reduce their SR because
rectlyinvolvedinthosetransactionsthattriggersystemic they are blocked from lending, non-risky nodes become
damage. It is not obvious which players in the financial moresystemicallyriskythroughtheirlending. ASRpre-
systemhaveatrue interestto mitigate SR.Management miumencouragesborrowerstoborrowfromsaferlenders
of SR is foremost in the public interest. (since the borrower pays the tax). Further, lenders have
ItisimportanttonotethatSRspreadsbylending. Ifa an incentive to become systemically safe so that no (or
systemicallyrisky node lends to asystemically non-risky only little) SRT is added to their loan offers, and they
one, the later inherits SR from the risky node, since if can offer competitive rates. Since mitigation of SR is
the non-risky borrowershould (for whatever reason)not foremost in the public interest we propose to charge a
repay the loan, the risky node would trigger systemic systemic risk tax as a margin on every financial transac-
damage. InthissenseSRspreadsfromtheriskythrough tion that increases global SR.
lending. We test the proposed SRT within the framework of
SR is predominantly a network property of liability the CRISIS macro-financial model1. In this ABM we
networks. Differentfinancialnetworktopologieswillhave run the financial system in three modes. The first re-
differentprobabilitiesforsystemiccollapse,giventhelink flects the situation today, where banks don’t care about
density and the financial conditions of nodes being the their systemic impact, and where interbank credits are
same. ThemanagementofSRbecomesatechnicalprob- tradedwithan“interbankofferrate”. Thisinterestrate
lem of managing the network topology of financial net- reflects only the creditworthinessof the borrowing coun-
works. The goal is to do this in a way that does neither terparty, and does not contain any information on SR.
reduce the credit provision capacity, nor the transaction The second mode introduces the SRT. In this mode the
volume of the financial system. Data on the topology of interestratereflectsboththecreditworthinessofthebor-
credit networks is available to many central banks. Sev- rowing counterparty and the SR change associated with
eralstudiesonhistoricaldatashowtypicalscale-freecon- each transaction. For comparison, in a third mode we
nectivity patternsinliability networks[30–35],including implement a transaction tax on all transactions (Tobin
overnight markets [36], and financial flows [37]. tax)thatdoesnothaveanynetworkre-structuringeffect.
As a network property, SR can be quantified by using
networkmetrics[38,39]. Inparticulararelativeriskmea-
sure (DebtRank) canbe assignedto all nodes in a finan- SYSTEMIC RISK TAX
cial network that specifies the fraction of SR they con-
tribute to the system (institution- or node-specific SR) The systemic risk tax (SRT) is a levy placed on a fi-
[39]. As shown later, it is natural to extend the notion nancial transaction to offset the SR increase associated
of node-specific SR to individual liabilities between two withthattransaction. WeshowthatSRofatransaction
counterparties (liability-specific SR), and to individual can be quantified by the so-called DebtRank that was
transactions (transaction-specific SR).
Thecentralideaofthispaperistointroduceanincen-
tive structure in form of a transaction tax that dynami-
cally structures liability networks such that SR is mini- 1 http://www.crisis-economics.eu
3
suggested originally as a recursive method to determine negative∆(−mn)ELsyst meansthatL increasestheto-
mn
thesystemicrelevanceofnodeswithinfinancialnetworks tal SR.
[38]. It is a quantity that measures the fraction of the Finally,themarginaleffectofasingleloan(oratrans-
total economic value in the network that is potentially action leading to that loan) can be calculated. The lia-
affected by the default and distress of a node or a set of bility network without a specific loan l is
ijk
nodes. For simplicity in the following let us think of the
nodes in financial networks as banks. By L we denote
the liability (exposure2) networkof agivenfiijnancialsys- Li(j−k) =Lij − δimδjnδkκlmnκ , (5)
tem at a given moment. Lij = klijk is the sum of all mX,n,κ
loans l that bank j currently extends to bank i. C is
ijk i
thecapitalofbanki. IfbankidePfaultsandcannotrepay where the sum over m and n runs over all B banks, and
its loans, bank j loses the loans L . If j has not enough κ runs over all transactions that exist between i and j.
ij
capital available to cover the loss, j also defaults. Given The marginal systemic effect of a single loan (transac-
L and C , the DebtRank R (L ,C ) of node (bank) i tion) ∆(−k)ELsyst, is obtained by substituting L(−mn)
ij i i ij i ij
can be computed, see SI. by L(−k) in Eq. (4).
ij
DebtRankhastheprecisemeaningofeconomicloss(in
Obviously, the marginal systemic effect of adding a
dollars)thatiscausedbythedistressordefaultofanode
loanto anexisting liability networkL leadsto L(+k) =
[38]. This precise meaning of the DebtRank allows us to ij ij
L + δ δ δ l , i.e. by changing the minus
define the expected systemic loss for the entire economy, ij m,n,κ im jn kκ mnκ
to plus signs in Eq. (5). In this way every existing loan
which is the size of a possible loss times the probability P
in the financial system as well as every hypothetical one
of that loss occurring. For a single node i it is
can be evaluated with respect to its marginal systemic
ELsyst =PdefV R , (1) effect.
i i i
The central idea of the SRT is to tax every transac-
with Pdef the probability ofdefault of node i, andV the
i tion between any two counterparties that increase SR in
combined economic value of all nodes. R measures the
i the system. The size of the tax is proportional to the
fraction of the total economic value that is potentially
increase of expected systemic loss that this transaction
affected by node i. Assuming that we have a number of
adds to the system per time unit. The SRT for transac-
B banks in the system, the total expect systemic loss is
tionl betweentwobanksiandj cannowbeexpressed
ijk
B B byappropriatediscountingofEq. (4)andtakingthelife-
ELsyst = ELsyst = PdefV R , (2) time T of the loan into account3,
i i i
i=1 i=1
X X
T
which has the precise meaning of the expected economic SRT(k) =ζmax 0, dtVv(t)×
loss within a given timespan (dollars per year). ij
" Z0
To calculate the contribution of an individual inter-
bank liability Lmn, to the expected systemic loss for the × pˆ(t) R (L(+k),C )−R (L ,C (.6)
i i ij i i ij i
whole economy (marginal systemic effect), we define a #
liability network without that specific liability L by Xi (cid:16) (cid:17)
mn
L(−mn) ≡L − δ δ L , (3) Here pˆi(t) is the default probabilitydensity4 ofnode iat
ij ij im jn mn timet,andv(t)thepresentvalueof$1receivedattimet.
m,n
X R is computed at t=0. ζ is a proportionality constant
i
whereδij isthe Kronekersymbol. The marginaleffectof that specifies how much of the expected systemic loss is
the particular Lmn on the expected systemic loss is taxed. ζ = 1 means that 100% of the expected systemic
loss will be charged. ζ < 1 means that only a fraction
B
∆(−mn)ELsyst = PdefV R (L(−mn),C )−R (L ,C ) ,of the true SR increase is passed on to the tax for the
i i ij i i ij i causing institution. Ideally, it is chosen such that the
Xi=1 (cid:16) (4) (cid:17) efficiency of the financial system is kept the same as in
where R (L(−mn),C ) is the DebtRank of the liability the untaxedworld. We showthatthis isindeedpossible.
i ij i
network without the specific exposure L . Clearly, a
mn
2 NotethattheentriesinLij aretheliabilitiesbankihastowards 3 Valuationisdonesimilartocreditriskmodelsasforexamplefor
bank j. We use the convention to write liabilities in the rows creditdefaultswaps[40–42]
(secondindex)ofL. Ifthematrixisreadcolumn-wise(transpose 4 The default probability density is defined as pˆi(t) =
ofL)wegettheassetsorloans,banksholdwitheachother. h(t)exp−R0τh(τ)dτ,whereh(t)isthehazardrate.
4
withdrawals).
loans
Banks We give a short description of the agents, for more
details on the agents and their interactions, see [44, 46]
Firms and SI6.
deposits Households. There are H households of which there
exist two types, firm owners,and workers. Eachof them
wages / dividends has a personal account A (t) at one of the B banks. j
j,b
deposits indexes the worker, b the bank. Household accounts are
randomly assigned to banks. Workers apply for jobs at
consumption
theF differentfirms. Ifhired,theyreceiveafixedincome
w per time step, and supply a fixed labor productivity
α. Firm owners receive their income through dividends
Households
fromtheir firm’sprofits. Ateverytimestepeveryhouse-
holdspendsafixedpercentagecofitscurrentaccounton
the goods market. They compare prices of goods from z
randomly chosen firms and buy the cheapest.
Firms. There are F firms producing perfectly sub-
stitutable goods. At every time step firms compute an
expecteddemandd (t),andanestimatedpricep (t)(sub-
i i
FIG. 1. Schematic overview of the model structure showing
script labels the firm), based on a rule that takes into
the three agent types (banks, firms, and households), and
account both excess demand/supply and the deviation
their interactions. Firms pay dividends to their owners, and
wages (financed through income and loans) to their workers. of the price pi(t−1) from the average price in the pre-
Households consume goods produced by the firms. House- vious time step [44]. Each firm computes the number
holdsandfirmsdepositmoneyinbanks,banksgrantloansto of required workers to supply the expected demand. If
thefirms. the wages for the respective workforce exceed the firm’s
current liquidity, it applies for a credit. Firms approach
n randomly chosenbanks and choosethe credit with the
THE MODEL TO TEST THE EFFECT OF SRT
most favorablerate. If this rate exceeds a threshold rate
rmax,thefirmonlyasksforφpercentoftheoriginallyde-
To test the economic and financial implications of the
siredloanvolume. Basedontheoutcomeofthiscreditre-
SRT we use the CRISIS macro-financial model5. This
quest,firmsre-evaluatetheneededworkforce,andhireor
is an economic simulator that combines a well-studied
fire the needed number of workers. Firms sell the goods
macroeconomic ABM [43–45] with an ABM of financial
on the consumption goods market. Firms go bankrupt
markets. We useaslightlymodifiedversionofthemodel
if they have negative liquidity after the goods market
in [44] that includes an interbank market, and that is a
closes. Each of the bankrupted firm’s debtors (banks)
closed economic systemthatallowsno in- or out-flowsof
incurs a capital loss in proportion to their investment
cash. For a comprehensive description of the model, see
in the company. Firm owners of bankrupted firms are
[44, 46], for the modifications, see SI.
personally liable, their account is divided by the debtors
pro rata. They immediately start a new company, with
initially zero equity. Their initial estimates for d (t) and
The agents i
p (t) equal the respective current averages in the popu-
i
lation.
The model features three types of agents: households,
Banks. There are B banks that offer firm loans at
banks,andfirms,asdepictedinFig. 1. Theyinteracton
rates that take into account the individual specificity of
four markets
banks (modeled by a uniformly distributed randomvari-
(i) Firms and banks interact on the credit market.
able),andthefirms’creditworthiness. Firmspayacredit
(ii)Banksinteractwithbanksontheinterbankmarket.
risk premium according to their creditworthiness that is
(iii) Households and firms interact on the job market.
modeled by a monotonically increasing function of their
(iv)Householdsandfirmsinteractontheconsumption
financial fragility [44]. Banks try to provide requested
goods market.
firm loans and grantthem if they have enough liquid re-
(v) Banks interact a second time on the interbank
sources. If they do not haveenough cash, they approach
market(incasetheyneedadditionalliquidityfordeposit
5 http://www.crisis-economics.eu 6 http://www.complex-systems.meduniwien.ac.at/people/sthurner/SI/S
5
otherbanksintheinterbankmarkettoobtaintheneeded
amount. If a bank does not have enough cash and can
not raise the full amount for the requested firm loan on
the IB market it does not pay out the loan. Interbank
and firms loans have the same duration. Additional re-
financing costs of banks remain with the firms. Each
time step firms and banks re-pay τ percent of their out-
standing debt (principal plus interest). If banks have
excess-liquidity they offer it on the interbank market for
anominalinterestrate. Theinterbankrelationnetworkis
modeled as a fully connected network and banks choose
the interbank offers with the most favorable rate. In-
terbank rates r offered by bank i to bank j take into
ij
account the specificity of bank i, and the creditworthi-
ness of bank j. If a firm goes bankrupt the respective
creditor bank writes off the respective outstanding loans
as defaulted credits. If the bank has not enough equity
capitaltocovertheselossesitdefaults. Followingabank (a)
default an iterative default-event unfolds for all IB cred-
itors. This may trigger a cascade of bank defaults. For
simplicity, we assume no recovery for IB loans. This as-
sumption is reasonable in practice for short term liquid-
ity [47]. A cascade of bankruptcies happens within one
time step. After the last bankruptcy is taken care of the
simulation is stopped.
(b) (c)
Implementationof systemicrisk tax and “Tobin tax”
AsystemicriskpremiuminformoftheSRTisimposed
on all interbank transactions. The SRT is calculated ac-
cording to Eq. (6). Before entering a desired loan l ,
ijk
the credit seeking banks i can get quotes of the SRT(k) (d) (e)
ij
rates from the Central Bank, for various banks j. They
choose the IB offer from bank j with the smallest total
rate, which is composed of rtotal = r +SRT(k). All FIG. 2. Banking network. (a) Austrian IB network at the
ij ij ij endofthefirstquarterof 2006, (b)onlythe20 largest banks
other transactions are exempted from SRT. This makes
oftheAustrianIBnetwork,(c)bankingnetworkofthemodel
borrowing from banks with large systemic impact more
withouttax,(d)withFTT,and(e)withSRT.Nodesarecol-
expensive and does not affect lending activities of non- oredaccordingtotheirsystemicimpact Ri,from riskybanks
riskybanks. Incontrasttocurrentmarketpractice,with (red) to unrisky (green). The node size represents the capi-
the SRT banks do have a clear incentive to borrow from talization of the banks. Width of the links are the exposures
systemically non-risky banks. The SRT is collected in a of the banks in the IB network and the color is according to
thesource.
bailout fund.
For comparison we implement a financial transaction
tax (Tobin tax [10]) for interbank loans. We impose a RESULTS
constanttaxrateof0.2%ofthetransaction(thisisabout
5%oftheIBinterestrates)onallofferedinterbankrates. We implement the above model in Matlab code for
Other transactionsare not taxed. The FTT makeslend- B = 20 banks, F = 100 firms, and H = 1300 house-
ing less attractive for firms that borrowfrom banks that holds. The model is run in three modes, without any
need liquidity from the interbank market since refinanc- tax, with SRT, and with a Tobin-like financial trans-
ing costs remain with the firms. action tax. Results are averages over 10,000 indepen-
6
Ri00000.....156789 (a) systrelative EL [%]0000..01..01255 AUT NOTAXTOBIN SRT Ri00..168 (b) tsnoyobs ittnae xmtaixc risk tax tawehffliseteohc2tFo0iuvigtel.altyr2ag(rxebe,sd)t(.udccF)oeinwsgt.sirtpi2hbr(eucFat)TdesiThnmo,gowaossntfdtSohRf(eet)bshiytewupiSatrRhteivoS(enRrneoTtdifn.tdgThoeshtysems)tS,oeRdsmeeTe-l
0.4 0.4 ically risky nodes from lending. This can be seen from
0.3
0.2 0.2 the fact that there are only green links in Fig. 2(e). In
0.1 thesnapshotoftheAustrianIBnetworkandinthemodel
00 5 10i 15 20 00 5 10i 15 20 without the SRT numerous red links are clearly visible.
10−3 10−2 no tax In Fig. 3 (a) we show SR as measured by the DebtRank
tobin tax
∆ELsyst[%]1100−−54 ∆ELsyst[%]1100−−43 systemic risk tax Rcthoier.deIinnngdptaoorfttitochutealaltrhawisrsdeetsqsh)uoaowrftRtehrieofoAfru2ts0ht0er6i2a.0nBlbaaarnngkekssintagrbeasneockrtdsoe(rraeacdt-
ve10−6 ve byDebtRank,themostriskyistotheveryleft,thesafest
relati10−7 relati10−5 to the very right. The ABM results for Ri are presented
in Fig. 3 (b): without tax (red), with FTT (blue) and
(c) (d)
101−80−6 10−5 10−4 10−3 10−2 101−60 −4 10−3 10−2 10−1 with SRT (green). The shown distributions are averages
relativeloansize[%] relativeloansize[%]
over 10,000 independent simulation. Clearly, SRT dras-
tically reduces the SR contributions of individual banks.
FIG. 3. Expected systemic loss as measured by DebtRank, Thesituationwithouttax resemblesthe empiricaldistri-
ELsiyst ∝ Ri. (a) DebtRank, Ri of the 20 largest banks of bution(a). InFig. 3(c)themarginaleffectsonexpected
theAustrianbankingsectorattheendofthethirdquarterof systemic loss from Eq. (4) are presented for all individ-
2008. Banks are ordered by DebtRank,the most risky being ualIBliabilitiesLdata,asafunctionoftherelativesizeof
mn
totheveryleft. Inset: Expectedsystemicloss from allbanks
IB loans. Every data point represents a single interbank
for the Austrian-IB data and the three model modes. Here
liabilityLdata frombankmton. IBloansarethemselves
the SR measure is the size of a possible loss for the entire mn
power-law distributed (not shown), which is known em-
economy times the probability of that loss occurring as de-
fined in 4. (b) Model results for Ri: without tax (red), with pirically [34]. The loan size captures the credit risk for
FTT (blue), and with SRT (green). Clearly, SRT drastically lenders,whereas∆(−mn)ELsyst istheSRcontributionof
reduces the SR contributions of individual banks. The sit- the liability. Figure 3 (d) shows the marginal effects for
uation without tax resembles the empirical distribution. (c) the ABM simulations for the three modes. It is clearly
Marginal effects on expected systemic loss ∆(−mn)ELsyst of
visiblethatSRTreducestheSRcontributionofliabilities
individualIBliabilitiesLmnvs. therelativesizeofIBloansin by about an order of magnitude (log scale!), but leaves
double logarithmic scale. Every data point represents an in-
terbank liability Ldata. Theloan size capturesthecredit risk contract sizes practically unchanged.
mn
for lenders, whereas ∆(−mn)ELsyst is the SR of the liability. The effects of the SRT and the FTT on total losses to
(d) Marginal effects for the simulations in the three modes. banksL(seeDataandMethodsfordefinition)thatoccur
SRTreduces SRbut leaves contract sizes unchanged. asaconsequenceofbankdefaultsareshowninFig. 4(a).
Clearly,the mode without tax (red) produces fat tails in
the loss distributions of the banking sector. The Tobin
dent, identicalsimulations across500time steps. We set
tax slightlyreduces losses(almostnotvisible). The SRT
Pdef =0.01, V = B B L , and ζ =0.02. For dif-
i i=1 j=1 ij gets completely rid of big losses in the system (green).
ferent tax rates for the Tobin-like financial transaction
P P The remaining losses are from firm defaults. This elimi-
tax and an alternative mode in which the SRT is set to
nation of losses on the IB market is due to the fact that
the true increase in SR associated with the transaction
under the SRT the possibility for cascading defaults is
(ζ =1), see SI.
largely reduced. This is seen in Fig. 4 (b), where the
We compare model results to historical, anonymized,
distributions of cascade sizes L (see Data and Methods
and linearly transformed interbank liability data pro-
for definition) for the three modes are compared. While
vided by the Austrian Central Bank (OeNB), see Data
the untaxedmode producesconsiderablecascadesizesof
andMethods. Thedatadoesnotcontaincreditratingsof
up to 20 banks, the maximum cascade sizes under the
banks. Thereforewe assumePdef =0.0257 for allbanks.
i SRT is about 10. The Tobin tax basically follows the
In Fig. 2(a) we show a snapshot of a the Austrian IB
untaxed case. As mentioned above the IB loan sizes are
network at the end of the first quarter of 2006. Clearly,
practically unchanged under the SRT. This is also true
for the total transaction volume V (see Data and Meth-
ods for definition) in the IB market, as is seen in Fig.
4 (c), where the distributions of transaction volumes at
7 ThiscorrespondsapproximatelytoStandard&Poor’sOne-Year
timestep100areshown. Obviously,thesituationforthe
Global Corporate Default Rates for Rating Categories A+, A,
and BBB+ in 2008 [48]. Representative Austrian banks are in SRT (green) is very similar to the untaxed case (red),
theRatingCategories A+,AandA-. whereas the transaction volume is drastically reduced in
7
0.18 systemiclosses. Thisforcesfinancialinstitutionstoavoid
no tax
0.16 tobin tax systemicallyriskytransactionsandtolookforsaverones
systemic risk tax
0.14 onthemarket. Effectivelythisleadstoare-configuration
y0.12 of financial networks.
c
en 0.1 We test the SRT within the framework of the CRISIS
u
eq0.08 macro-financial model. The model produces SR profiles
fr0.06 ofbanksthatarepracticallyidenticalwiththerealIBex-
posuredata. Evenonthelevelofindividualtransactions
0.04
the model is fully compatible with empirical data. The
0.02
(a)
SRT drastically reduces the probability for financial col-
0
0 t2o0t0al losse4s00tobank6s00(L) 800 lapseduetorestructuredliabilitynetworksthatminimize
the size of cascading failure. The tax is implemented in
0.45
no tax
a simple way: an agentwould like to make a transaction
0.4 tobin tax
systemic risk tax (with a given counterparty) and expresses this interest
0.35
by announcing it (and the envisioned counterparty) to
y 0.3
c the Central Bank. The later computes the SR increase
uen0.25 ofthetransaction,basedontheknowledgeofthepresent
eq 0.2 stateoftheentireasset-liabilitynetworkandthecapital-
r
f0.15 ization of its agents. The SR-increase is then multiplied
0.1 by the default probability of the agent, discounted, and
0.05 (b) presentedtothe agentasatax (SRT)for thatparticular
0 transaction. If the SR-increase is zero, there is no tax.
0 5 10 15 20
cascade sizes (C) The agent can now look for other counterparties to do
0.14 exactly the same transaction. If the new counterparty is
no tax
tobin tax systemically less risky, the tax will be lower. The agent
0.12
systemic risk tax
will therefore screen all possible counterparties and de-
0.1
cide on the one with the lowest tax. Once the agent
y
c
n0.08 decides to do the transaction, is is executed and the tax
e
u
q is payed to the CB or the government.
e0.06
fr We show explicitly that SR is to a large extend a NW
0.04 property. We show that the SRT is able to rearrange
0.02 financial liability networks without loss of credit volume
(c) in the financial markets. For the explicit demonstration
0
30 40 50 60 70 weimplementandtestaTobintaxwhichtaxesalltrans-
transaction volume IBmarket (V)
actions regardless of their SR contributions. The Tobin
tax does not restructure networks and only reduces SR
FIG. 4. Comparison of no transaction tax (red) on IB loans, because it also drastically reduces credit volume in the
withsystemicrisktax(green),andTobintax(blue). (a)Dis- system. This is damaging as it makes the system less
tribution of total losses to banks L, (b) distribution of cas- efficient; the loss of efficiency materializes as expensive
cade sizes C of defaulting banks,and (c) distribution of total credit for the real economy. We tested an alternative
transaction volumein theIBmarket V. 10,000 independent,
mode in which the SRT is set to the true increase in SR
identical simulations, each with 500 time steps, 20 banks.
associated with the transaction, and not only a fraction
(ζ = 1). This alternative leads to much more homo-
geneous SR-spreading across all agents, and makes the
the FTT scenario (blue), as expected.
system even safer, see Fig. 3(b) and SI.
The proposed SRT is a macroprudential regulation
aimed to reduce SR and the macroeconomic costs of
DISCUSSION
financial instability. In the classification of [49] credit
risk mitigation, including risk-based pricing, is a micro-
We extend the notion of SR to individual liabilities prudentialmeasure limiting distress of individual actors.
withinafinancialnetwork,andshowwithempiricaldata The SRT in this classification is a macroprudential ap-
ofnation-wideinterbankliabilitiesthatthisisindeedfea- proachthatreduces system-widedistress. Since SRT de-
sible. The notion of liability-specific SR allows us to pends both on the interbank liability network and the
quantify the SR that every financial transaction adds equity capital,SRT has pro-andcounter-cyclicaleffects.
to a financial network. We propose a tax on every SR- Thepro-cyclicalsidearisesthroughthefactthatSRTcan
increasing transaction proportional to the true expected bringsystemicallyriskybanksevenmoreunderstressby
8
reducing their possibilities for lending. However, the de- [1] http://www.economist.com/news/finance-and-economics/21583
pendence of SRT on the density of the liability network [2] http://www.economist.com/node/10134118.
has a strong counter-cyclicaleffect. It is easy to see that [3] http://research.stlouisfed.org/fred2/series/SPCS20RSA.
[4] http://research.stlouisfed.org/fred2/graph/?id=SP500.
the denser the IB network, the higher the SRT rate be-
[5] http://www.economist.com/node/9972489.
comes in general. The SRT rate increases with the de-
[6] http://epp.eurostat.ec.europa.eu/portal/page/portal/euroin
mand of interbank loans, and decreases by holding more
[7] http://data.bls.gov/timeseries/LNU04000000?years_option=al
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