Does Prudential Regulation Contribute to Effective Measurement and Management of Interest Rate Risk? Evidence from Italian Banks

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Does Prudential Regulation Contribute to Effective Measurement and

Management of Interest Rate Risk? Evidence from Italian Banks

Article in Journal of Financial Stability · May 2017

DOI: 10.1016/j.jfs.2017.05.004 CITATION 1 READS 52 4 authors:

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Rosa Cocozza

University of Naples Federico II

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Domenico Curcio

University of Naples Federico II

11 PUBLICATIONS 54 CITATIONS SEE PROFILE Igor Gianfrancesco Extrabanca 8 PUBLICATIONS 15 CITATIONS SEE PROFILE

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ContentslistsavailableatScienceDirect

Journal

of

Financial

Stability

journalhomepage:www.elsevier.com/locate/jfstabil

Does

prudential

regulation

contribute

to

effective

measurement

and

management

of

interest

rate

risk?

Evidence

from

Italian

banks

夽

Rosaria

Cerrone

a

_,

_Rosa

_Cocozza

b

_,

_Domenico

_Curcio

b,∗

_,

_Igor

_{Gianfrancesco}

c

a_Department_of_Business_Studies,_Management_and_Innovation_Systems,_University_of_Salerno,_Via_Giovanni_Paolo_II,_132,_Fisciano,_SA,_84084,_Italy b_Department_of_Economics,_Management_and_{Institutions,}_University_of_Naples_“Federico_II”,_Via_Cinthia,_Complesso_Monte_S._Angelo,_Napoli,_NA_80126,

Italy

c_Risk_Management_Department,_Extrabanca,_Via_Pergolesi_2/A,_Milano,_MI_20124,_Italy

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received9October2016

Receivedinrevisedform5March2017 Accepted2May2017

Availableonline6May2017 JELcodes: G21 G28 G32 Keywords: Bankregulation Interestraterisk MonteCarlosimulations Historicalsimulations Backtesting

a

b

s

t

r

a

c

t

Thispapercontributestopriorliteratureandtothecurrentdebateconcerningrecentrevisionsofthe

regulatoryapproachtomeasuringbankexposuretointerestrateriskinthebankingbookbyfocusing

onassessmentoftheappropriateamountofcapitalbanksshouldsetasideagainstthisspeciﬁcrisk.We

ﬁrstdiscusshowbanksmightdevelopinternalmeasurementsystemstomodelchangesininterestrates

andmeasuretheirexposuretointerestrateriskthataremorereﬁnedandeffectivethanareregulatory

methodologies.Wethendevelopabacktestingframeworktotesttheconsistencyofmethodologyresults

withactualbankriskexposure.UsingarepresentativesampleofItalianbanksbetween2006and2013,

ourempiricalanalysissupportstheneedtoimprovethestandardizedshockcurrentlyenforcedbythe

BaselCommitteeonBankingSupervision.Italsoprovidesusefulinsightsforproperlymeasuringthe

amountofcapitaltocoverinterestrateriskthatissufﬁcienttoensurebothﬁnancialsystemfunctioning

andbankingstability.

license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Internationalbankingauthoritieshaverecentlydeveloped mod-elsandissuedguidelinestoassessbanks’exposuretointerestrate riskinthebankingbook(IRRBB), becauseofitspeculiarnature andsystemicrelevance.Followingthesavingsandloancrisisof the1980s and‘90s, theU.S.Federal ReserveBank (FED) devel-opedtheeconomicvaluemodel,whichmeasuresIRRBBthrough changesinabank’seconomicvalueofequity(EVE)viaa duration-basedestimateofinterestratesensitivity (Houptand Embersit, 1991;SierraandYeager,2004;Sierra,2009;WrightandHoupt, 1996Sierra,2009;WrightandHoupt,1996).Subsequently,in2004, theBaselCommitteeonBankingSupervision(BCBS)adoptedan accounting-baseddurationmodelthatestimatesIRRBBby

apply-夽 Thisresearchdidnotreceiveanyspeciﬁcgrantfromfundingagenciesinthe public,commercial,ornot-for-proﬁtsectors.

∗ Correspondingauthor.

E-mailaddresses:rocerro@unisa.it(R.Cerrone),rosa.cocozza@unina.it (R.Cocozza),domenico.curcio@unina.it(D.Curcio),gianfrancescoi@extrabanca.eu (I.Gianfrancesco).

ingastandardizedshockininterestrates.Thestandardizedshock isalternativelygivenbya±200bpparallelshiftintheyieldcurve ﬁxedforallmaturities(theparallelshiftsmethod),orbythe1st and99thpercentileofobservedinterestratechanges,usinga one-yearholdingperiodandaminimumﬁveyearsofobservations(the percentilesmethod).Thesescenariosofchangesininterestrates allowcalculationofarisk indicator,whichisgiven bytheratio ofthechangeinabank’sEVEtoitsregulatorycapitalandwhose alertthresholdissetequalto20percent.Throughoutthepaper, wetermtheparallelshiftsandpercentilesmethodsas“regulatory methodologies.”

ThedrawbacksoftheBCBSframeworkhavebeenpointedout notonlybyacademicresearch,bymainlytestingitsunderlying assumptions (Abdymomunovand Gerlach,2014;Cocozza etal., 2015;Entropetal.,2008;Entropetal.,2009;FioriandIannotti, 2007),butalsobytheﬁnancialauthorities(BCBS,2009).InMay 2015,theEuropeanBanking Authority (EBA,2015)publisheda technicaldocumenttoreviseandsupplementtheguidelines pro-posedbytheCommitteeofEuropeanBankingSupervisors(CEBS, 2006).Recently,BCBS(2016)issuednewstandardstorevisethe principlesfor IRRBB management and supervision setin 2004.

http://dx.doi.org/10.1016/j.jfs.2017.05.004

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Thesestandardsareintendedtocomeintoforcein2018andshould provide more extensive guidanceon crucial areas, such asthe developmentofinterestrateshockscenariosandanupdated stan-dardizedframework.

Within their internal capital adequacy assessment process (BCBS, 2006;CEBS, 2006), banksusetoset asideagainstIRRBB an amount of internal capital corresponding to the numerator of the previously mentioned risk indicator, i.e., the change in banks’EVE due toan interest rateshock.Therefore, inaccurate estimates of IRRBB would lead banks to reserve anamount of internalcapitalthatmighteitherunderestimateoroverestimate abank’sactualriskiness,withpotentiallynegativeconsequences inbothcases:underestimationmightjeopardizebankingstability, whereasoverestimationmightchargebankshigheropportunity costsandeventuallyreducetheircreditsupplytotheeconomy.1

Apropermeasurementofbankriskexposureisrelevantfromthe perspectiveofsupervisoryauthoritiessince,basedontheresults ofthisassessment,theiractionsmayhaveahugeimpactonbank activity.2 _Furthermore,_inaccurate_estimates_of_IRRBB_would_also

provide poorindications for banks’ assetand liability manage-ment(ALM)strategies:underestimationmightdrivemanagersto takeexcessiverisk,whereasoverestimationmightpreventbanks fromimplementingproﬁtableALMstrategies.Overall,theoutput oftheriskmodelsembeddedwithintheBaselregulationscould haveatremendousimpactontherealeconomyand,therefore,itis importanttounderstandtowhatextentbothbanksandﬁnancial authoritiescanrelyonthemandwhentheiruseisnotadvisable (seeDanielssonetal.,2016forageneralframeworktoquantify modelrisk).

Basedontheseissuesandthecurrentlow-interest-rate environ-ment,modelinginterestratechangesandmeasuringtheirimpact onthebankingsectorarestilltimelyandkeyresearchareas.Recent papershaveinvestigatedhowbanksmanagedtheirinterestrate riskduringthecrisisyears,whenunconventionalmonetary pol-icydecisionsdroveinterestratestounprecedentedlowlevels3,4

(Espositoetal.,2015;Chaudron,2016;Memmeletal.,2016).Our contributiontopriorliteratureandtothecurrentdebate concern-ingrecentrevisionstotheIRRBBregulatorytreatmentistwofold andcentersonanassessmentoftheappropriateamountofthe internalcapitalthatbanksshouldsetasideagainstthisspeciﬁcrisk. First, consistentwith important regulatoryconstraints com-monlyappliedtoquantifyIRRBB-relatedinternalcapital,weshow howbanksmightadoptsimulationtechniquestomodelchanges in interest rates in a more reﬁned and effectiveway than the regulatorystandardizedshock.Simulationtechniqueshavebeen extensivelyexaminedbypriorliteraturetoestimatemarketrisk

1_The_risk_indicator_also_provides_useful_information_with_regard_to_the

equilib-riumofbanks’assetsandliabilitiesstructuresintermsoftheirrespectivematurities andrepricingdates.Fromthisperspective,itcomplementsthenetstablefunding ratiosetbytheBCBStomeasureandmanagebanks’exposuretoliquidityrisk(for ananalysisoftheimpactofthenetstablefundingratioonﬁnancialstabilitysee Ashrafetal.,2016).

2_Kupiec_et_al.₍₂₀₁₆₎_have_recently_highlighted_the_importance_of_bank

examina-tionbysupervisoryauthoritieswithregardtoU.S.creditinstitutions.Theirevidence suggeststhatthebanksupervisionprocesssuccessfullyconstrainsthelending activ-itiesofbanksoperatinginanunsafeandunsoundmanner.

3_Cukierman₍₂₀₁₃₎_describes_the_changes_that_occurred_in_the_conduct_and

instru-mentsofmonetarypolicyusedbymajorcentralbankswhenthecrisishit.Healso discussestheconsequentnewtradeoffsandcontroversiesandspeculatesabout additionallikelyfuturechangesinmonetarypolicyandinstitutions.

4_The_extremely_low_level_of_interest_rates_has_raised_many_issues_in_terms_of

finan-cialintermediaries’profitabilityandoverallfinancialsystemstability.Accordingto Barneaetal.(2015),monetarypolicyandfinancialstabilitypolicyarehighly inter-related.Theyshowthatthemonetarypolicytransmissionmechanismdependson financialstabilitypolicytoolsaswellasonregulatoryandinstitutionalconstraints. Inparticular,theyfindpolicytradeoffsintryingtoaccomplishbothmonetaryand financialstabilitytargetsthatcentralbanksmusttakeintoaccount.

(Jorion, 2007) and suggested by regulators tomeasure interest rateriskwithinbanks’internalmeasurementsystems(BCBS,2004; BCBS,2016;ComptrolleroftheCurrencyAdministratorofNational Banks,2012).Intheabsenceofspeciﬁcpreviouscontributions,we discusstheapplicationofhistoricalandMonteCarlosimulation techniquestomodelchangesininterestratestomeasureabank’s exposuretoIRRBBinalow-interest-rateenvironmentand hence-forthtermthem“internalmethodologies.”

Second,wedevelopabacktestingframeworktotestthe consis-tencyofamethodology’sresultswithactualbankriskexposure under ordinary operating business conditions. Our backtesting frameworkdrawsontheforecastevaluationmethodsdeveloped byLopez(1999)totestVaRmodelsbasedonpotentiallosses result-ingfromtheunderestimationofmarketrisk.However,giventhe peculiaritiesofIRRBBmeasurementandmanagement,wefocusnot onlyonitsunderestimationbutalsoontheeffectsof overestima-tion.Wecomparethedifferentmethodologiesbyassessingtheir abilitytoavoidunnecessaryreductioninbanklendingactivityand associatedopportunitycostsshouldtheestimatedriskindicator overestimateactualriskexposure,andtoreducetheriskof under-miningbankingsectorstabilityshouldunderestimationoccur.

ThisresearchexaminesexposuretoIRRBBbycollecting pro-prietarybalancesheetinformationfromasample of130Italian commercialbanksovertheperiodfrom2006to2013.Analysisof theItalianbankingsystemisespeciallyinterestingbecauseItalian banksgenerallyactasqualitativeassettransformers,meaningthat IRRBBarisesfrombasicbankingbusiness.Becauseofthecrucial roleplayedbycommercialbanksinmodernﬁnancialsystems,our investigationisalsorelevantfromaglobalperspective.

Overall,ItalianbanksadequatelymanageIRRBBandtheirrisk indicatorsarewellbelowthealertlevelenforcedbytheregulator. In termsofthenatureoftheirriskexposure, oursample inter-mediariesappearexposedtobothraising(asset-sensitivebanks) and,morefrequently,decreasing(liability-sensitivebanks)interest rates.WefindthathistoricalandMonteCarlosimulations (inter-nalmethodologies)produceestimatesofinternalcapitalthatare morerobustfromaprudentialadequacyperspectivewithregard tothisspecificaspect,whencomparedwithregulatory method-ologies.Infact,theinternalmethodologiesavoidaspecificissue that we term“riskneutrality.”Based onthis misleadingresult, somebanksexperienceanincreaseintheirEVEwhenthe regu-latorystandardizedshockisapplied,whethertheshockbeupor down.Consistentwiththeoveralldecreasingtrendininterestrates observedduringthesampleperiod,liability-sensitivebanksuse derivativestooffsettheiron-balancesheetriskexposuretoIRRBB, whereasasset-sensitivebanksusetheiroff-balancesheetpositions toenhancethegainsassociatedwiththesamescenario.Onaverage, derivativeshavealsoallowedbankstoreducethedistancebetween theirestimatedandactualriskexposureandthusoptimizetheir amountofinternalcapitalagainstIRRBB.Furthermore,theinternal methodologies,andtheMonteCarlosimulationsinparticular, per-formbetterthantheregulatoryonesintermsoftheirconsistency withactualbankriskiness,measuredthroughtheexpostchanges ininterestratesthatactuallyoccurredaftertheestimationdate.

Ouranalysisimprovesuponthestandardizedshocktreatment adoptedinBCBS (2004)andprovidesnewinsightsforproperly measuringbankinternalcapitalagainstIRRBB.Themethodological frameworkweproposeisapplicabletopubliclyavailabledataand canbereplicatedbythoseoutsidebankinginstitutions.Such pub-liclyavailablemeasuresofIRRBBcanprovideacrucialcontribution tothefunctioningandstabilityoftheinternationalbankingsystem, thuscallingforgreaterattentionnotonlyfromregulators, super-visorsandtheoverallbankingindustry,butalsofromacademic researchers.

Therestofthepaperisorganizedasfollows.Inordertoposition thisresearchwithintheliterature,inSection2wediscussthree

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papersthatexaminebanks’exposuretoandmanagementof inter-estrateriskduringtheﬁnancialcrisisandmeasureIRRBBthrough theeconomicvalueapproachadoptedinthispaper.Section3 pro-videsanoverviewofthecurrentregulatoryIRRBBframeworkand discusses previousliterature testing therobustness of its main assumptions. In Section 4, we describe the two methodologies thatbanksmightinternallydeveloptomodelinterestratechanges basedonhistoricalandMonteCarlosimulationtechniques. Sec-tion5presentsabacktestingframeworktotesttheeffectivenessof bothinternalandregulatorymethodologies.Section6presentsthe resultsofourempiricalanalysis,inwhichwemeasuretheIRRBB ofasampleofItalianbanksbasedonbothregulatoryandinternal methodologiesandimplementourbacktestingprocedure.Section 7concludesthepaper.

2. Theexposureandmanagementofinterestraterisk

duringtheﬁnancialcrisis

AfterthecollapseofLehmanBrothersin2008,interest-raterisk managementbecamemoreimportantthaneverforbothEuropean andU.S.banks,asaresultofunprecedentedmonetarypolicy deci-sionstakenbyboththeEuropeanCentralBank(ECB)andtheU.S. FED.5_The_previously_unheard_of_reduction_in_ofﬁcial_policy_rates

andunconventionalmeasuresadoptedbythetwocentralbanks hadastrongimpactonthetermstructureofmarketinterestrates andreducedthemtoanextremelylowlevel.AsshownbyBorio etal.(2015)andBuschandMemmel(2015),currentlowinterest ratesandtheﬂatyieldcurvehavealsodrivendownbank prof-itability.Majorissues, therefore,especially forbanksupervisors andpolicymakers,arewhetherornotthecurrent low-interest-rateenvironmenthascreatedincentivestotakemorerisk,andhow banksmanagedtheirriskexposureunderextraordinaryﬁnancial andeconomicconditionsduringthecrisis.Recentliteraturehas investigatedtheexposuretoandmanagementofinterestraterisk duringthecrisisyears.Weexaminebelowthreepapersthatrefer totheItalian,GermanandDutchbankingsectors,respectively,all usinganeconomicvalueapproachtomeasureIRRBB.

Espositoetal.(2015)measuretheIRRBBexposureofasampleof 68Italianbanksovertheperiodrangingbetweenthesecondhalfof 2008andthefirsthalfof2012.Inparticular,theyassesshow inter-mediariesmanagedIRRBBeithermodifyingthedurationmismatch betweenon-balancesheetassetsandliabilities(on-balancesheet restructuring)orrelyingoninterestratederivatives(off-balance sheetadjustment).Overall,byadoptingthedurationgapapproach ofthesimplifiedmethodologyintroducedbyBankofItaly(2006), andbyusingauniquedatasetofsemi-annualobservations,they findthatItalian banks’exposurewaswellbelowthepreviously mentionedalertthreshold.Furthermore,theyobservethatbanks usedtheiron-balancesheetinterestrateriskandtheiroff-balance sheetexposuretooffseteachother,ratherthantopursueastrategy aimingtoenhancethepotentialgainsthatmighthaveoccurredin thecaseofariseininterestrates.

Memmeletal.(2016),examineasampleofGermanbanks dur-ingtheperiodfrom2005to2014,inordertostudytherelationship betweenbanks’expectedreturnsfromtermtransformation and theirexposuretothecorrespondinginterestraterisk.According tothis research, decreasinginterest rates not only drivedown bankprofitmarginsbut,ifthelow-interest-ratescenariopersists, bankmanagershavetheincentivetoactasiftheyareriskprone, whichisextremelydangerousfromafinancialstabilityperspective. Theauthorsfindthattherelationshipbetweeninterestraterisk andbankrisktakingis,asexpected,usuallypositive,butbecomes

5 _See_ECB₍₂₀₁₁₎_for_a_discussion_of_the_{effectiveness}_of_{unconventional}_monetary

policymeasuresadoptedbythetwocentralbanks.

weakerwhenabank’soperatingincomedecreases.Theythenshow thattherelationshipchangesitssignandbanksstarttoincrease theirexposuretointerestraterisk,eveniftheexpectedreturns fromtermtransformationdecrease,whenoperatingincomefalls belowacertainthreshold.

ByinvestigatinghowbankshavemanagedtheirIRRBBexposure underascenarioofdecreasinginterestratesandaﬂatteningyield curve,Chaudron(2016)detectstheinterest-rateriskpositionof42 Dutchbanks,representingroughly90percentoftheentirebalance sheetoftheDutchbankingsectorduringtheinvestigationperiod from2008untilthemiddleof2015.Theauthorinvestigateshow bankriskpositionchangesovertime,howmuchoftheirreturns onassetsandnetinterestmarginsdependonincomefrom matu-ritytransformationandwhichfactorsinﬂuencetheirinterest-rate riskposition.Interestrateriskismeasuredthroughthebasispoint value,whichisthechangein theeconomicvalueofequity due toa changeintheinterest ratebyone hundredthof apercent (0.01%).Dutchbanksshowrathersmallinterestrateriskpositions, areactiveinmaturitytransformationonlytoalimiteddegree,and donotmaintainaconstantinterestrateriskposition,butadjustit tochangesintheeconomicenvironment.Basedonapanelmodel estimation,interest-rateriskpositionsarenegativelyrelatedto on-balancesheetleverage,exhibitaU-shapedrelationwithsolvability, and, contrarytotheevidencereportedin otherstudies,do not varysystematicallywiththesizeofthebanks.Finally,banksthat receivedgovernmenthelpduringthecrisistookongreaterinterest raterisk.

3. Regulatorymethodologiestoestimateinterestraterisk

inthebankingsector:overviewandrelatedliterature

BasedonBCBS(2004),BankofItaly(2013)requiresbanksto allocateon-andoff-balancesheetaccountsintothefollowing14 timebandsofamaturityladder:i)demandandrevocable,ii)upto 1month,iii)1–3months,iv)3–6months,v)6–12months,vi)1–2 years,vii)2–3years,viii)3–4years,ix)4–5years,x)5–7years,xi) 7–10years,xii)10–15years,xiii)15–20years,xiv)morethan20 years.Overall,ﬂoatingrateassetsandliabilitiesareslottedintothe timebandsbasedontheirnextrepricingday,whereasﬁxed-rate accountsareassignedaccordingtotheirresidualmaturity.

Byassumingthat on-and off-balancesheetaccountshave a maturityexactlycoincidingwiththemidpointofeachtimebandito whichtheyareallotted,IRRBBismeasuredthroughpredetermined sensitivitycoefficients,i.e.,modifiedduration coefficients(MDi). Assets and liabilitiesare offset to calculate netpositions (NPi), whichareweightedbythecorrespondingMDiandtheassumed interestrateshock(r).Theresultingnetweightedpositionsare thensummedupacrossthedifferenttimebandstocalculatethe changeinabank’sEVE,whichisfinallydividedbythebank regula-torycapital(RC)toobtainariskindicator(RI),whosealertthreshold issetequalto20%: RI= 14

i=1 NPi·MDi·r RC ≤20% (1)

Undertheparallelshiftsmethod,risgivenbya±200bp paral-lelshiftintheyieldcurve.Accordingtothepercentilesmethod,the interestrateshockisbasedonthe1stand99thpercentilesofthe yearlyinterestratechange,obtainedbyusingtheoverlappingdata techniquewithaone-yearholdingperiodandaminimumﬁveyears ofobservations(BCBS,2004).Basedontheso-callednon-negativity constraint,negativeshocksininterestratescannotdrivetheterm structureoftheobservedinterestratesbelowthezerolevel.

WithintheBCBSframework,accounting-baseddataareusedto obtainthecashﬂowstructureofabank’son-andoff-balance

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posi-tions.Therefore,abank’sexposuretoIRRBBdepends,amongthe otherthings,onassumptionsconcerningthedistributionofasset andliabilitymaturitiesandrepricingdateswithinthetimebands ofthematurityladder.Byusingtime-seriesaccounting-baseddata, Entropet al. (2008) develop a model toestimate the distribu-tionofthematuritiesofabank’sassetsandliabilitieswithineach timeband.Theirestimatesaremoreinlinewiththoseinternally obtainedbybanks,andtheirmodelexplainsthecross-sectional variationinbankinterestrateriskbetterthantheBCBSapproach.

Asfarasinterestrateshocksandpredeterminedsensitivity coef-ficientsareconcerned,FioriandIannotti(2007)developaValue at Risk(VaR)methodology tomodel interest ratechanges that takesintoaccountbothasymmetryandkurtosisoftheinterest-rate distribution.Theirmethodology,basedonaprincipalcomponent MonteCarlosimulation,accountsnotonlyfortheconceptof dura-tionbutalsoforthat ofconvexity,andcalibratesthesensitivity coefficientsusingmarketdata.Byanalyzingthe18major large-andmedium-sizedItalianbanks,theyshowthattheirresultsare consistentwiththeriskexposureestimatedviathe±200bp par-allelshiftiftheregulatorysensitivitycoefficientsarecalibratedon thebasisofcurrentmarketdataattheevaluationdate.

BCBS(2004)andBankofItaly(2013)setspecificcriteriatoallot specificaccountswhoselegalmaturitydiffersfromthebehavioral one.Withregardtonon-maturitydeposits,Cocozzaetal.(2015) develop a methodology that considers their actual behavior in termsofbothpricesensitivitytochangesinmarketratesand vol-umestabilityovertime.Accordingtotheirresultsfromasampleof 30Italiancommercialbanks,theuseofdifferentallocationcriteria affectsnotonlythesizeoftheriskestimatebutalsothenatureof bankriskexposure.Allotmentcriteriamayalsodeterminethe so-calledriskinversionphenomenon,i.e.,banksformerlyexposedto anincreaseininterestratescanalsobecomeexposedtoareduction ininterestrates.Furthermore,theyshowthat,whenmarketrates arelow,somebanks,definedasrisk-neutralbanks,appearto expe-rienceanincreaseintheirequityeconomicvaluewhetherinterest ratesdecreaseorincreaseundertheparallelshiftsmethod.

AbdymomunovandGerlach (2014)showthat,when market rates are low, the methods used by banks and supervisors to assessinterestrateriskunderstressedconditionscanunderstate banks’exposureandproposeanewmethodforgenerating yield-curvescenarios.TheirevidencefromalargeU.S.bankshowsthat theirmodelgeneratesyield-curvescenarioswithawidervariety ofslopesandshapesthanalternativehistoricalandhypothetical scenario-generationmethods,includingtheregulatory methodolo-gies.

ByconsideringtheaggregatedGermanuniversalbanking sys-tem, Entrop et al. (2009) analyze how a bank’s risk exposure changesifsomemajorassumptions oftheregulatorymodelare modified.Inparticular,theyconsidertheallotmentofnon-maturity depositsintothetimebands,theallotmentofassetsand liabili-tieswithinthetimebands,thenumberandboundariesofthetime bands,theamortization rateofcustomerloans, and thespread betweenthecouponandthemarketinterestrateusedto calcu-latethemodifieddurationassociatedwitheachtimeband.They provethattheresultsoftheregulatoryframework significantly dependontheunderlyingassumptionsand mustbeconsidered withcautionforbothsupervisoryandrisk-managementpurposes, sincetheycannotbeassumedtobeabovethelevelofrealbank riskiness.

4. InternalmethodologiestoestimateIRRBB

Within their internal capital adequacy-assessment process, ItalianbanksmeasureIRRBB,underbothordinaryandstressed con-ditions,byapplyingdifferenttechniques,ceterisparibus,tomodel

interestratechanges.Therefore,inlinewithbankingpractice,here wetaketherestoftheregulatoryassumptionsasgivenandfocus onmodelinginterestratechanges,inordertoaddressthelimitsof theBCBS(2004)parallelshiftsandpercentilesmethods.In particu-lar,theparallelshiftsmethodissetregardlessofactualchanges in interestrates. In this respect,thetwo scenarios correspond-ingtothe1stand99thpercentilesofthepercentilesmethodare changesthatactuallyoccurred.Nevertheless,thesechangesmight haveoccurredondifferentdays.Forexample,the1stpercentile mightrefertoJanuary22nd,2008fortheinterestrateoftheﬁrst timeband,toDecember23rd,2010fortheinterestrateassociated withthesecondtimeband,etc.Therefore,aswithparallelshifts,the percentilesmethoddoesnotaccountforthecorrelationsactually observedamongtheannualchangesininterestrates.

In this section, we present two methods that banks can internallydevelopbymakinguseofhistoricalandMonteCarlo sim-ulationtechniques,respectively.Theshocksareappliedtoaterm structureofinterestrates(henceforth,ourkeyrates)whosenodes correspondtothemidpointsofthe14timebandsoftheregulatory maturityladder.

Thehistoricalsimulationmethodcanaccountforcorrelations amongtheannualchangesinkeyratesbecausetheriskindicatoris basedonscenariosofchangesininterestratesthatarerepresented bythejointannual changesin ourkey ratesthat haveactually occurredoverthepastﬁveyears.Thesescenariosarecalculated onagivendaythroughtheoverlappingtechnique,assuggested byBCBS(2004),andareappliedtothenetpositionstoobtainthe netweightedpositions.Wethensumthenetweightedpositions tocalculatethechangeinabank’sEVEanddividethissumbythe regulatorycapitaltoobtainanempiricaldistributionof therisk indicator.Thisdistributioniscutincorrespondencewiththe per-centileassociatedwiththedesiredconﬁdencelevel,whichisset equalto99%followingBCBS(2004).However,itispossiblethatthe non-negativityconstraintmightpreventthismethodfrom captur-ingthecorrelationswheninterestratesareverylow.

TheMonteCarlosimulationmethodallowsustogenerate sce-nariosthat bothtakeintoaccountthecorrelationsbetweenthe annualchangesinourkeyratesandmeetthenon-negativity con-straint.Wecarryoutasmanysimulationsasarerequiredtoobtain thedesirednumberKofscenarios,whichwesetequalto10,000, andrejectthosesimulationsleadingthetermstructureofourkey ratesunderthezerolevelinoneormorenodes.Inthisway,we obtainadistributionoftherisk indicatorthatis cutatthe per-centilecorrespondingtoa99percentconﬁdencelevel.Speciﬁcally, wedevelopthemethodasfollows:

i) Select the joint probability density function that guaran-teesthebestapproximationoftheactualdistributionsofannual changesinthekeyrates.Theapplicationoftheoverlappingdata techniquesupportstheuseofanormaljointprobabilitydensity function,alreadyadoptedbyFioriandIannotti(2007).

ii) Estimate meansand variances ofthe distributions of the annual changes in the key rates and theirvariance-covariance matrix().Distributionsofannualchangesarenotadjustedon thebasisofthenon-negativityconstraintinordertoaccountfor actualcorrelationsamongtheannualchangesinkeyrates.

iii)Generatearandomnumberui(i=1,...14)rangingfrom0to 1ateachnodeofourkeyratestermstructure.

iv)Converteachuiintoavaluezi(i=1,...14)distributed accord-ingtoastandardnormal.Insymbols:

zi=F−1(ui) (2)

whereF−1istheinverseofthedistributionfunctionofthe proba-bilitydensityfunctionoftheannualchangesoftheithkeyrate.

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v)Usethealgorithm ofCholeskyinordertodecomposethe matrixintwomatricesQandQ’suchthat:

Q_·_Q ₌_˝ ₍₃₎

vi)Calculatethevectorx,whoseelementsarethejoint sim-ulated annual changes in the key rates through the following formula:

x=Q_·_z₊ ₍₄₎

wherezisthevectorofthevalues calculatedinstepiv)and␮isthe vectorofthe14meansofthedistributionsofthekeyratesannual changescalculatedinstepii).Eachvectorxrepresentsasimulated scenariothatwillbeusedtocalculatetheriskindicator.

vii)Repeatstepsiii)-vi)untilwereachanumberKofscenarios thatmeetthenon-negativityconstraint.

viii)ApplytheKsimulated scenarios tothenetpositionsto calculatethenetweightedpositions.For eachscenario,thenet weightedpositionsaresummedinordertocalculatethechange inabank’seconomicvalue,whichisﬁnallydividedbythe regula-torycapital.Theempiricaldistributionoftheriskindicatorisﬁnally cuttoidentifythe99thpercentile.

Fromamethodologicalperspective,itisinterestingtonotethat, undertheparallelshiftsandpercentilesmethods,theriskindicator isobtainedbyassumingthatallthekeyratesmovetogetherinthe samedirection.Underboththeinternalmethodologiespresented here,however,keyratesareallowedtomoveindifferentdirections andtheonlyrestrictionappliedtothechangesinthekeyratesis thenon-negativityconstraintsetbyBCBS.Weallowthekeyratesto changebecauseepisodesintherecentandmoredistantpast,such asthemeasuresofmonetarypolicythathavedrivenmarketrates toextremelylowlevelsandtheU.S.savingsandloancrisis,have shownthattheirtermstructurecanactuallyassumecharacteristics anddynamicswhich,exante,wouldhavebeenjudgedunrealistic.

5. Abacktestingframework

Based onthe related literature (for a review, see Campbell, 2006),mainlytwoapproacheshavebeenemployedtoimplement abacktesting procedure. Abacktestcouldbe basedeither ona hitfunction(see,forexample,thebacktestsdevelopedbyKupiec, 1995;Christoffersen,1998;ChristoffersenandPelletier,2004)or onalossfunction(Lopez,1999).Regardingtheformer, backtest-ingproceduresbasedonalossfunctionhavegreaterflexibility, sincethelossfunctioncanbetailoredtoaddressspecificconcerns, eveniftheincreasedflexibilitygeneratesasubstantialincreasein theinformationalburdenassociatedwithassessingtheaccuracy ofacertainmodelunderconsideration.Infact,inordertoassess whethertheaveragelossis“toolargerelativetowhatwouldbe expected,”itisnecessary tounderstandthestochasticbehavior ofthelossfunction.Therefore,backtestingproceduresbasedona lossfunctionapproachrequireanexplicitassumptionaboutthe distributionofprofitsandlosses.

Givenourobjectiveofcomparingtheperformanceofthe dif-ferentmethodologiesusedtomeasureIRRBB,however,wedecide toadoptaloss-function-basedapproach,sincepriorliterature rec-ognizesthatloss-function-basedbacktestsmaybeveryusefulfor determiningwhetheronemodelprovidesabetterriskassessment than a competing model. From this perspective, loss-function-based backtests may be more suited to discriminating among competingmodelsrather than judging theaccuracy ofa single model,whichisexactlytheaimofourbacktestingframework.

Tosetupourbacktestingframework,weadoptthelogic under-lyingtheforecastevaluationmethodsproposedbyLopez(1999), whichtestsVaRmodelsbyfocusingonthepotentiallosses

asso-ciatedwiththeunderestimationofmarketriskandgivestoeach Table

1 Key rate term structures. t (evaluation date) Demand and revocable Up to 1 month From 1 to 3 months From 3 to 6 months From 6 months to 1 year From 1 to 2 years From 2 to 3 years From 3 to 4 years From 4 to 5 years From 5 to 7 years From 7 to 10 years From 10 to 15 years From 15 to 20 years Over 20 years December 31st 2006 3.69% 3.62% 3.66% 3.79% 3.95% 4.10% 4.13% 4.13% 4.13% 4.14% 4.17% 4.24% 4.29% 4.31% December 31st 2007 3.92% 4.18% 4.49% 4.70% 4.73% 4.63% 4.54% 4.53% 4.54% 4.58% 4.67% 4.80% 4.89% 4.91% December 31st 2008 2.35% 2.45% 2.79% 2.93% 3.02% 2.72% 2.86% 3.04% 3.18% 3.36% 3.61% 3.85% 3.88% 3.76% December 31st 2009 0.41% 0.40% 0.56% 0.84% 1.13% 1.59% 2.06% 2.41% 2.68% 2.99% 3.43% 3.82% 4.02% 4.05% December 31st 2010 0.82% 0.65% 0.89% 1.10% 1.37% 1.45% 1.75% 2.08% 2.34% 2.70% 3.12% 3.50% 3.67% 3.68% December 31st 2011 0.63% 0.76% 1.18% 1.48% 1.79% 1.37% 1.35% 1.45% 1.63% 1.91% 2.24% 2.57% 2.68% 2.65% December 31st 2012 0.13% 0.09% 0.15% 0.25% 0.43% 0.35% 0.42% 0.54% 0.69% 0.95% 1.37% 1.83% 2.09% 2.20% December 31st 2013 0.45% 0.20% 0.26% 0.34% 0.48% 0.48% 0.66% 0.89% 1.13% 1.49% 1.95% 2.41% 2.65% 2.73% This table shows the term structure of the key rates referred to each time band of the regulatory maturity ladder observed at the end of the years included in the 2006–2008 period. We use data from Datastream, and, in particular, we use the EONIA (Euro Overnight Index Average) rate for the maturity corresponding to the demand and revocable time band, the Euribor rates for maturities shorter than 12 months, and interest rate swap (IRS) rates for maturities longer than, or equal to, 1 year. Key rates referred to maturities not included in the market term structure are calculated through linear interpolation.

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Table 2 Descriptive statistics of the annual changes in the key rates observed over the 2009–2013 period with December 31st, 2013 as the evaluation date. Demand and revocable Up to 1 month From 1 to 3 months From 3 to 6 months From 6 to 1 year From 1 to 2 years From 2 to 3 years From 3 to 4 years From 4 to 5 years From 5 to 7 years From 7 to 10 years From 10 to 15 years From 15 to 20 years Over 20 years Mean − 0.76 − 0.80 − 0.86 − 0.88 − 0.87 − 0.79 − 0.74 − 0.70 − 0.67 − 0.61 − 0.55 − 0.49 − 0.45 − 0.43 Std. Dev. 1.32 1.41 1.45 1.41 1.38 1.16 0.97 0.86 0.79 0.71 0.61 0.56 0.56 0.57 Max. 1.22 0.94 0.85 0.77 0.83 1.00 1.09 1.05 0.93 0.78 0.59 0.60 0.62 0.66 Min. − 4.27 − 4.67 − 4.67 − 4.54 − 4.34 − 3.89 − 3.41 − 2.94 − 2.60 − 2.14 − 1.69 − 1.76 − 1.86 − 1.91 Kurtosis 0.29 0.16 0.08 0.11 0.07 0.41 0.16 − 0.33 − 0.68 − 0.99 − 1.13 − 1.07 − 0.92 − 0.93 Asimmetry − 1.21 − 1.12 − 1.07 − 1.05 − 0.99 − 1.00 − 0.67 − 0.30 − 0.08 0.11 0.17 0.12 − 0.02 − 0.11 We use data from Datastream, and, in particular, we use the EONIA (Euro Overnight Index Average) rate for the maturity corresponding to the demand and revocable time band, the Euribor rates for maturities shorter than 12 months, and interest rate swap (IRS) rates for maturities longer than, or equal to, 1 year. Key rates referred to maturities not included in the market term structure are calculated through linear interpolation.

methodologyascorebasedonacertainlossfunction:Thelower thescore, thebetteris themethodology performance. Forecast evaluationmethodsareparticularlysuitableforbacktestingwith datasetsassmallasoursbecausetheydonotsufferfromthelow powerofastandardtestsincetheyarenotfrequency-based statis-ticaltests.Furthermore,asmentionedabove,forecastevaluation methodsallowustotailorthelossfunctiontothespeciﬁc objec-tivesofthebacktestinganalysis.Therefore,giventhepeculiarities ofIRRBB,weadaptLopez’s(1999)backtestingframeworkto speciﬁ-callyaccountforbothregulatorandindustryconcernsinestimating IRRBB,especiallyintermsofbankingstabilityandcreditsupplyto theeconomy.

Foreachsamplebank,wecomparetheexanteriskindicators withameasureofactualbankriskexposure,termedtheexpostrisk indicator.TheexpostriskindicatorisobtainedbysettingrinEq. (1)equaltothejointannualchangesinthekeyratesthatactually occurredovertheone-yeartimehorizonfollowingtheevaluation datet.Foranyevaluationdatet,weassigntoeachmethodologym ascore,calculatedthroughascorefunction,Sm,t,takingasinputs theresultsofanaccuracyfunction,Ai,t,thatisappliedtoeachbank i(i=1,2,...N,withN=130)ateachevaluationdatet.Thegeneric scorefunction,foramethodologymandanevaluationdatet,is formalizedasfollows: Sm,t= N

i=1 Ai,t N∗ (5) where:

-Ai,tisdeﬁnedsuchthattheoutputsofthescorefunctioncannot takenegativevaluesandbettermethodologiesarecharacterized bylowerscores.

-N*_is_an_integer_whose_value_depends_on_the_{speciﬁcation}_of_the accuracyfunction.

Thegenericaccuracyfunctioncanbewrittenasfollows: Ai,t=

f

RI_i,tpost,RIante i,t

if RI_i,tpost>RIante i,t g

RIpost_i,t ,RIante

i,t

if RI_i,tpost≤RIante i,t

(6)

-where:RI_i,tanteandRI_i,tpostaretheexanteandexpostriskindicators, respectively.BothRI_i,tanteandRIpost_i,t refertothetermstructureofthe ithbank’snetpositionsobservedintheevaluationdatet. -fandgdeﬁnethevaluesoftheaccuracyfunctioniftheexpost

riskindicatorishigherorlowerthan(equalto)theexanteone. Thefirsttwospecificationsoftheaccuracyfunctionrefertothe caseofanunderestimationofactualriskexposure,whentheexpost riskindicatorishigherthan(equalto)theexanteone.Therefore, consistentlywithLopez(1999),thefirstandsecondspecifications bothsatisfythefollowingcondition:

f

RIpost_i,t ,RIante i,t

≥g

RIpost_i,t ,RIante i,t

(7) Inparticular,accordingtotheﬁrstspeciﬁcationshowninthe followingEq.(8),theaccuracyfunctionequals1iftheexpostis higherthantheexanteriskindicator,and0otherwise:

A_i,t=

1 if RI_i,tpost>RIante i,t 0 if RI_i,tpost≤RIante

i,t

(8) BysettingN*equalto1inthescorefunction(5),thefinalscore isthenumberoftimesinwhichanunderestimationoccurs,fora givenmethodologymatanevaluationdatet,andisdefinedasa fre-quencyscore.UnderthesecondspecificationofEq.(9),theaccuracy

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functionprovidesameasureoftheseverityoftheunderestimation errorsinceitequalsthedifferencebetweentheexpostandtheex anteriskindicators,iftheformerishigherthanthelatter,and0 otherwise.Thelargerthedifference,thegreateristhe underesti-mationofactualriskexposureandthegreateristhepotentialthreat tobankingstability.Insymbolswehave:

A_i,t=

RI_i,tpost−RIante i,t if RI

post i,t >RIantei,t 0 if RIpost_i,t ≤RIante

i,t

(9) Inthiscase,N∗inthescorefunction(6)issetequaltothenumber ofbanksforwhichRIpost_i,t >RIante_i,t andthescorefunctioncaptures theaveragemagnitudeofthemeasurementerrorforeach method-ologymonacertainevaluationdatet,providingwhatweterma severityscorefortheunderestimationcase.

ByremovingtheconstraintofEq.(7),thethirdspeciﬁcationof theaccuracyfunction,showninEq.(10),accountsforan overesti-mationofactualriskexposure.Inparticular,itequalstheabsolute valueofthedifferencebetweentheexpostandtheexanterisk indicators,whentheformerislowerthanthelatter,and0 other-wise.Thelargerthedifference,thegreateristhepotentialreduction ofthecreditsupplytotheeconomy,sincetheamountofinternal capitalthatabankunnecessarilysetsasideishigher.Insymbolswe have:

A_i,t=

0 if RIpost_i,t ≥RIante i,t |RIposti,t −RIi,tante|if RI

post i,t <RIantei,t

(10) Inthiscase,N∗inthescorefunction(5)isthenumberofbanks forwhichRI_i,tpost<RI_i,tanteandtheﬁnalscorecapturestheaverage differencebetweenthemforagivenmethodologymandan evalu-ationdatet,providingameasureoftheaverageerror,i.e.,aseverity scorefortheoverestimationcase.

Finally,weadoptafourthspeciﬁcationoftheaccuracyfunction, whichisgivenbythecombinationofthepreviousaccuracy func-tions(9)and(10),thusconsideringthedistancebetweentheex anteandtheexpostriskindicatorsinbothcasesofunderestimation andoverestimation.Insymbols:

A_i,t=

RI_i,tpost−RIante i,t if RI

post i,t >RIantei,t |RIposti,t −RIi,tante|if RI

post i,t <RIantei,t

(11) Inthiscase,N∗ofthescorefunction(5)isthetotalnumberof banksandthefinalscoreisameasureoftheoverallproximityof theexantetotheexpostriskindicator,andisdefinedsimplyas aproximityscore.Theaccuracyfunction(11)makesno distinc-tionbetweencasesofunderestimationandoverestimation.Inany event,inordertosetaspecificorderofpriority,Eq.(11)canbeeasily adjustedtotakethekeyissuesassociatedwithoverestimationand underestimationofIRRBBintoaccountbydifferentlyweightingthe twocases.

6. Empiricalevidence

6.1. Data

Weestimateoursamplebanks’riskindicatorsasofDecember 31st for each of the years included in the 2006–2013 period. December31stisalsothedateonwhichweestimateIRRBBand towhichbankspeciﬁcbalancesheetdatarefer.Inconsistencywith theprevioussection,theseevaluationdatesareindicatedwitht (t=December31st,2006,December31st,2007, ...December31st, 2013).KeyratesareobservedonDecember31stforeachoftheyears includedintheinvestigationperiod.Tobuildthetermstructureof thekeyrates,weusetheEONIA(EuroOvernightIndexAverage) rateforthenodecorrespondingtothedemandandrevocabletime

band,theEuriborrateformaturitiesshorterthan12months,and interestrateswap(IRS)ratesformaturitieslongerthan,orequal to,1year,inlinewithcurrentbankingpractices.

Thecharacteristicsanddynamicsofthekeyratetermstructure overtimehaveastrongimpactonbankriskexposure.Table1shows thatthetermstructureofourkeyratesbecomessteeperand expe-riencesadownwardshiftovertime,whichmakestheapplication ofthenon-negativityconstraintmorelikelytooccur.

Table 2 shows the main descriptive statistics of the key ratesannualchangesobservedoverthe2009–2013period,with December31st,2013asevaluationdatet.Asexpected,short-term aremorevolatilethanlong-termkeyrates.Furthermore,the neg-ativekurtosiscoefficientsconfirmthatthedistributionsofinterest ratechangesgeneratedthroughtheoverlappingtechniquedonot sufferfromthefattailissue.Theseresultsareconfirmedfortherest oftheevaluationdatesandareavailableuponrequest.

Weusebothregulatoryandinternalmethodologiestomeasure IRRBBof130Italiancommercial,savings,andcooperativebanks. Onaverage,oursampleincludesbothbankinggroupsand inde-pendentbanks.Table3showstheaveragevaluesofoursample banks’cashassetsandoff-balancesheetlongpositionsinPanelA andcashliabilitiesandoff-balancesheetshortpositionsinpanelB, respectively.Itisworthconsideringthattheoff-balancesheet posi-tionsincludehedgingderivatives,suchasinterestrateswaps,and theoptionalitiesembeddedinsomefinancialcontracts,namelythe floorsandcapsassociatedwithfloating-rateloans.

Averagecustomerloansrepresentapproximately75percentof totalon-andoff-balancesheetpositions;alargeproportionofthese loans,equalto65percentoftotalon-andoff-balancesheet posi-tions,are floating-rateloans andare slottedin short-termtime bandsbecause,following theregulatoryallotmentcriteria, they aretreatedasshort-termloans.Non-maturitydepositsrepresent around37percentoftotalon-andoff-balancesheetpositions, con-firmingtheirimportancefromarisk-managementstandpointand therelevanceoftheItalianbankmaturitytransformationfunction. Overall,debtsecuritiesconstituteabout33percentoftotalon-and off-balancesheetpositions.Specifically,securitieswithamaturity shorterthanoneyearrepresentalmost22percentoftotalon-and off-balancesheetpositionsandmainlyconsistoffloating-rate secu-rities.Overtheentireinvestigationperiod,bothlongandshort on-andoff-balancesheetpositionsaccountonaverageforlessthan10 percentofthetotal,beingequalto9.35percentand9.85percent, respectively.

Oursamplemostlyincludesbanksactiveatprovincial, inter-provincial, and regional levels. Consistent with their limited geographical scopesof activity,Table4shows that theaverage totalassetsofoursampleintermediaries,calculatedovertheentire investigationperiod,amounttoalmostD2,378million,withaclear increasingtrendfromD1,661millionin2006toD2,909millionin 2013.Furthermore,itisinterestingtonotethat,onaverage,about 88percentoftheintermediariesthatweexamine(115banksoutof 130)havetotalassetslowerthanD3.5billion,whichisthe thresh-oldbelowwhichtheyareidentifiedbyprudentialsupervisionas so-called“minorintermediaries.”Intermsofregulatorycapital,we alsofindevidenceofagrowingpath,evenifataslowerpacerelative tototalassets,fromavalueofD179millionasofDecember2006 toapproximatelyD254millionattheendof2013.Finally,despite theiroverallsmallsize,ourbanksmakeheavyuseofderivatives; onaverage,overtheentiresampleperiod,almost87percent(114 banksoutof130)arederivativeusers.Nevertheless,mostlikely becauseoftheirlimitedsize,theirhedgingpracticesappeartobe relativelyhomogeneous,consistingmainlyinusinginterestrate swapsagainsttheriskassociatedwithissuedbondsand amortiz-inginterestrateswapsspecificallytohedgetheriskpotentially arisingfromfixed-ratemortgageloans.

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Table3

Cashassetsandliabilitiestermstructureandoff-balancesheetpositions.

PanelA:cashassetstermstructureandoff-balancesheetlongpositions

2006 2007 2008 2009 2010 2011 2012 2013 Avg.peryear

Debtsecuritieswithmaturity shorterthan1year

8.56% 8.28% 10.95% 11.45% 10.99% 10.48% 12.10% 14.81% 10.95%

Debtsecuritieswithmaturity between1yearand5years

3.32% 2.48% 1.23% 1.74% 1.67% 2.61% 5.55% 7.06% 3.21%

Debtsecuritieswithmaturity longerthan5years

1.24% 1.04% 0.60% 1.23% 1.46% 1.77% 3.32% 4.43% 1.89%

Loanswithmaturityshorter than1year

65.58% 70.76% 70.64% 66.93% 67.07% 63.47% 59.54% 56.17% 65.02%

Loanswithmaturitybetween 1yearand5years

6.15% 3.86% 4.15% 5.64% 4.93% 6.34% 5.61% 6.27% 5.37%

Loanswithmaturitylonger than5years

5.52% 3.66% 4.53% 5.76% 3.47% 4.20% 2.93% 2.92% 4.12%

Totalcashassets 90.37% 90.80% 92.10% 92.75% 89.59% 88.87% 89.05% 91.66% 90.65%

Off-balancesheetlong positions

9.63% 9.20% 7.90% 7.25% 10.41% 11.13% 10.95% 8.34% 9.35%

PanelB:cashliabilitiestermstructureandoff-balancesheetshortpositions

2006 2007 2008 2009 2010 2011 2012 2013 Avg.peryear

Non-maturitydeposits 38.38% 37.02% 37.18% 40.36% 38.84% 36.07% 32.12% 34.21% 36.77%

Othercurrentaccounts 8.70% 8.40% 7.77% 8.20% 8.97% 8.79% 9.84% 7.85% 8.56%

Termdepositsandotherfunds withmaturityshorterthan 1year

11.86% 9.92% 7.52% 4.99% 5.52% 8.61% 14.99% 18.45% 10.23%

Termdepositsandotherfunds withmaturitybetween1year and5years

1.93% 1.14% 0.43% 0.37% 0.34% 1.39% 1.65% 2.17% 1.18%

Termdepositsandotherfunds withmaturitylongerthan5 years

0.35% 0.20% 0.17% 0.17% 0.22% 0.18% 0.18% 0.19% 0.21%

Debtsecuritieswithmaturity shorterthan1year

20.47% 25.47% 29.74% 28.33% 21.69% 19.40% 15.17% 13.96% 21.78%

Debtsecuritieswithmaturity between1yearand5years

7.40% 7.64% 8.60% 9.46% 12.81% 13.39% 14.07% 12.96% 10.79%

Debtsecuritieswithmaturity longerthan5years

0.66% 0.53% 0.39% 0.45% 0.78% 0.76% 0.67% 0.72% 0.62%

Totalcashliabilities 89.76% 90.32% 91.81% 92.33% 89.18% 88.59% 88.69% 90.51% 90.15%

Off-balancesheetshort positions

10.24% 9.68% 8.19% 7.67% 10.82% 11.41% 11.31% 9.49% 9.85%

Thistableshowstheaveragevaluesofoursamplebanks’cashassetsandoff-balancesheetlongpositionsinPanelAandcashliabilitiesandoff-balancesheetshortpositions inPanelB,respectively.Dataaretakenfrombanks’balancesheets,andrefertoDecember31stofeachyearincludedinthe2006–2013period.Resultsareexpressedin percentageoftotalon-andoff-balancesheetpositions.

Table4

Samplebanks’sizeandderivativesusage.

2006 2007 2008 2009 2010 2011 2012 2013 Avg.peryear

Avg.totalassets(Dmillion) 1,660.98 1,999.51 2,044.52 2,209.73 2,505.39 2,704.34 2,994.21 2,908.90 2,378.45

Avg.regulatorycapital(D million)

179.03 195.12 218.82 234.42 247.18 262.35 266.62 254.23 232.22

%ofbankswithtotalassets ≤D3.5bn.

91.54% 90.00% 90.00% 87.69% 87.69% 87.69% 86.15% 86.15% 88.37%

%ofderivativeusersbanks 79.23% 84.62% 85.38% 85.38% 87.69% 91.54% 92.31% 93.08% 87.40%

Intheﬁrstandsecondrows,thistableshowstheaveragetotalassetsandregulatorycapitalofoursamplebanks,respectively(bothdenotedinmillioneuros).Inthethird andfourthrows,thetableshowsthepercentageofbankswithtotalassetslowerthanD3.5billionandthepercentageofbanksusingderivatives.DatarefertoDecember 31stofeachyearincludedinthe2006–2013periodandaretakenfrombanks’balancesheets.

6.2. Thenatureofbanks’interestrateriskexposure

Italiancommercialbankstypicallyfundlong-termassetswith short- and medium-term liabilities. Therefore, if interest rates moveup(down),theireconomicvalueshoulddecrease(increase) because,ceterisparibus,thereduction(increase)intheeconomic valueoftheirlong-termassetsshouldbelarger,inabsolutevalue, than the decrease observed for theirshort- and medium-term liabilities.AdoptingBCBS terminology, ifinterest rates increase (decrease),thesumofthepositivenetweightedpositionsishigher (lower) than the absolute value of the negative net weighted positions.Wedeﬁneintermediariescharacterizedbythistypeof exposureasasset-sensitivebanks.

Nevertheless,bankriskexposurederivesfromtheinteraction of:i)thetermstructureofthenetpositions,whichistheresultof banks’ALMandcommercialstrategies;ii)theregulatoryallotment criteria,and iii)theactuallyappliedscenarioofannualchanges inthekeyrates,whichdependsontheadoptedmethodologyand ontheapplicationofthenon-negativityconstraint.Therefore,we alsoﬁndbanksexposedtodecreasinginterestrates(alsotermed “liability-sensitive”)andrisk-neutralbanks,i.e.,thosethat expe-rience anincreasein theireconomic valuewhetherthecurrent standardizedshockisappliedupordown.

If interest rates decrease (increase), liability-sensitive banks experienceadecrease(growth)intheireconomicvaluebecause, ceteris paribus,theincrease (decrease)intheeconomicvalueof theirlong-termassetsislower,inabsolutevalue,thantheincrease

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(decrease)observedfortheirshort-andmedium-termliabilities. Shouldinterestratesdecrease(increase),thesumofthepositive netweightedpositionswouldbehigher(lower)thantheabsolute valueofthenegativenetweightedpositions.

Based onthecalculation mechanism of therisk indicator, a bankisriskneutralif,inthecase ofapositive(negative) inter-estrateshock,thedecrease(increase)initsassetseconomicvalue islower(higher),inabsolutevalue,thanthedecrease(increase)in itsliabilities,thusdetermininganoverallincreaseinEVE.Inother words,usingBCBSterminology,whetherinterestratesincreaseor decrease,thesumofthepositivenetweightedpositionsislower thanthatofthenegativenetweightedpositionstakeninabsolute value.

Table5showsthat,duringourinvestigationperiod,outof130 institutions,onaverage40banksperyearareasset-sensitiveunder theparallelshiftsmethodandthatnumberincreasesto42ifwe measureIRRBBthroughtheMonteCarlosimulations.Ifweusethe percentilesmethodandhistoricalsimulations,thenumberofbanks exposedtoanincreaseininterestratesisaround25and27, respec-tively.Asfarasexposuretodecreasinginterestratesisconcerned, theaveragenumberofbanksperyeargoesfromapproximately76 undertheparallelshiftsmethod,toaround103forhistorical sim-ulations.Roughly13and21banksperyeararerisk-neutralunder theparallelshiftsandpercentilesmethods,respectively;however, weﬁndnoinstanceofrisk-neutralityforeithertheMonteCarloor thehistoricalsimulations.

Theapplicationofthenon-negativityconstraint,whichismore likelywheninterestratesarelow,isthemainfactorunderlying therisk-neutralityphenomenonforbothparallelshiftsand per-centilesmethods.Becauseofthenon-negativityconstraint,undera scenarioofdecreasinginterestrates,thereductioninabank’sEVE associatedwiththenegativenetpositionsofmedium-termtime bandsisnotsufﬁcienttooffsettheincreaseintheEVEattributable tothepositivenetpositionsoflong-termtime bands.6 _The

sig-nificantincreaseinthenumberofrisk-neutralbanksinthelast two years of oursample period,when interest rates are lower thanbefore,confirmsthisinterpretation.Nevertheless,underthe percentilesmethod,thefewcasesofriskneutralityobservedon December31stoftheyears2006–2008donotresultfrom appli-cationofthenon-negativityconstraint,whichdoesnotcomeinto play.Inthosecases,riskneutralitystemsfromthecombinedeffect ofpeculiarscenariosofchangesinthekeyrates,ontheonehand, andspecifictermstructuresofbanks’netpositionsacrossthetime bandsoftheregulatorymaturityladder,ontheotherhand.

Regardinghistorical andMonteCarlosimulations,wedo not observerisk-neutralitycases.Thesesimulationsmakeuseof mul-tiplescenarios,namelyaround1200scenariosfor thehistorical simulations,givenbythesumoftheapproximately240 scenar-iosperyearobservedoverthe5-yearperiodacrosswhich,based onthecurrentregulatoryframework,annualchangesinthekey rateshavetobemeasured, and10,000scenariosfor theMonte Carlosimulations.Withregard tothelatter,theprocessto gen-eratethe10,000scenariosofchangesinthekeyratesrequiresus toselectscenariosfromthosethatdonotdrivethekeyrateterm structurebelowzero,thusfulﬁllingthenon-negativityconstraint

6 _In_the_absence_of_the_{non-negativity}_constraint,_with_regard_to_the_parallel_shift,

byapplyinga−200bpparallelshock,abank,formerlyexposedtodecreasinginterest rates,wouldexperienceareductioninitseconomicvalueequal,inabsolutevalue,to theincreaseassociatedwitha+200bpparallelshock.Nevertheless,duetothe non-negativityconstraint,themagnitudeofthereductioninthebankeconomicvalue associatedwithnegativenetpositionswouldbelowerandnotenoughtooffsetthe increaseintheeconomicvaluegeneratedbythepositivenetpositions.Underthe percentilesmethod,wewouldnothaveasymmetricriskexposurebyapplyingthe 1stand99thpercentilesinabsenceofthenon-negativityconstraint,but,inessence, itsﬁnaleffectwouldbethesameasthatjustdescribedfortheparallelshiftsmethod.

byconstruction.Inthehistoricalsimulations,despiteapplication ofthenon-negativityconstraint,contrarytowhatoccurswiththe regulatorymethodologies,thekeyratesofthetermstructureare freetomoveindifferentdirectionswithinthesamescenario.The highnumberandthedifferentnature,intermsofsignand magni-tudeofinterestratechanges,ofthescenariosusedtogeneratethe distributionsoftheriskindicatorsminimizestheprobabilitythata bankwillberiskneutral.

6.3. Theon-andoff-balancesheetcomponentsofbankinterest rateriskexposure

Oursamplebankscarryoutahomogeneoushedgingactivity throughbasicinterestratederivatives,suchasinterestrateswaps. BasedontheapproachofEspositoetal.(2015),inordertodetect whetherandtowhatextentItalianbanksusederivativestomanage IRRBB,wehavedecomposedtheriskindicatorobtainedthrough Eq.(1) intotwo components,basedontheon-and off-balance sheetitems,respectively.However,itisimportanttopointoutthat, ashighlightedaboveinSection6.1,theoff-balancesheet compo-nentincludesnotonlyhedgingderivatives,butalsoﬂoorsandcaps embeddedinﬂoating-rateloans.

Basedonthecurrentregulatorytreatmentoftheseoff-balance sheetitems,theireffectonbankriskexposureisasfollows. Amor-tizinginterest rateswapstransform a fixed-rate mortgageinto a floating-ratemortgage.Therefore, ceteris paribus,theyreduce theaveragematurityofabank’sassetsandaccordinglydecrease (increase)theexposureofanoriginallyasset-sensitive (liability-sensitive)creditinstitution.Interestrateswapschangeafixed-rate issuedbondintoafloating-ratebondand,therefore,reducethe averagematurityofabank’sliabilities.Consequently,theydecrease (increase)theexposureofacreditinstitutionformerlyexposedto decreasing(increasing)interestrates.Finally,concerningthecaps andfloorsembeddedintofloating-ratemortgageloans,aportionof theseloans,basedontheoption’sdelta,becomesfixed-rateandan increaseintheaverageassetmaturityoccurs.Thus,ceterisparibus, theriskexposureofaformerlyasset-sensitive(liability-sensitive) bankincreases(decreases).

Foreach ofthefourmethodologiesdiscussedabove,Table6 shows our sample banks’ average overall risk exposure (see columnslabeled“Overall”),measuredthroughtheriskindicatorof Eq.(1),anditsbreakdownintheon-andoff-balancesheet com-ponents(see thecolumnslabeled“On” and“Off,”respectively). Overall,IRRBB is adequatelymanaged byItalian banks.Table6 showsthat the20 percentcriticalthresholdsetbytheBCBSis, onaverage,byfarhigherthanoursamplebanks’riskindicators.7

Theaverageriskindicatorcalculatedovertheentiresampleperiod forasset-sensitivebanksis10.37percentundertheparallelshifts method,versus6.87percentfortheMonteCarlosimulations,4.73 percentforthepercentilesmethodand5.98percentforthe histor-icalsimulations.Banksexposedtoincreasinginterestratesshow higherriskindicatorsundertheparallelshiftsmethodbecauseof theimpactofthe+200-bpshockonthenetpositionsoflong-term timebands.Thedistanceintermsofriskindicatorsamongthe dif-ferentmethodsshrinksforbanksexposedtodecreasinginterest rates,whoseaverageriskindicatorsgofrom5.32percentforthe MonteCarlosimulationsto7.54percentforthehistorical simula-tions.

Whenweconsiderthebreakdownoftheoverallriskexposure betweentheon-andoff-balancesheetcomponents,weﬁnd evi-denceofdifferentbehaviorbyoursamplebanks,dependingonthe

7_The_highest_single_value_(not_shown_in_the_Table)_is_15.20%,_which_is_observed

onDecember31st,2006fortheparallelshiftsmethodandreferstoasset-sensitive banks.Datareferringtoeachsingleyearareavailableuponrequest.

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Table5

Samplebanks’typesofinterestrateriskexposure:numberofbanksbymeasurementmethodology.

Parallelshiftsmethod Percentilesmethod Historicalsimulations MonteCarlosimulations

t(evaluationdate) A L RN A L RN A L A L December31st2006 47 83 0 41 87 2 40 90 40 90 December31st2007 32 98 0 23 105 2 25 105 23 107 December31st2008 23 107 0 15 107 8 20 110 23 107 December31st2009 31 94 5 18 111 1 17 113 43 87 December31st2010 21 105 4 11 119 0 10 120 20 110 December31st2011 38 78 14 27 96 7 18 112 35 95 December31st2012 60 20 50 32 20 78 43 87 73 57 December31st2013 71 25 34 36 27 67 42 88 77 53

Averagen.ofbanksperyear 40.38 76.25 13.38 25.38 84.00 20.63 26.88 103.13 41.75 88.25

Thistableshowsoursamplebanks’typeofriskexposurebasedonthemethodologyusedtomodelinterestrateshocks.Columns1–3refertotheparallelshiftsmethod, columns4–6tothepercentilesmethod,columns7–8tothehistoricalsimulationsandcolumns9–11totheMonteCarlosimulations.Foradescriptionoftheparallelshifts andpercentilesapproaches,seeSection3.ForadescriptionofthehistoricalandMonteCarlosimulationsapproaches,seeSection4.

Aindicatesbanksexposedtoincreasinginterestrates(asset-sensitivebanks),Lindicatesbanksexposedtodecreasinginterestrates(liability-sensitivebanks)andRNindicates risk-neutralcreditinstitutions.

InterestrateriskexposureiscalculatedaccordingtotheBankofItaly’sdurationgapapproachandisexpressedaspercentageofregulatorycapital,asshowninEq.(1). Non-maturitydepositshavebeenallottedwithin5yearsaccordingtothecriteriondeﬁnedinBankofItaly(2013)anddataaretakenfromDatastreamandbanks’balance sheets.

Table6

Samplebanks’averageriskindicators:breakdownbymeasurementmethodologyandtypeofinterestrateriskexposure.

Overall On Off Overall On Off Overall On Off Overall On Off

A 10.37% 6.82% 3.55% 4.73% 2.95% 1.78% 5.98% 4.66% 1.32% 6.87% 5.38% 1.49%

L 6.62% 7.93% −1.31% 7.11% 8.61% −1.51% 7.54% 8.93% −1.39% 5.32% 6.22% −0.91%

Thistableshowstheaverageriskindicatorsofoursamplebanksoverthe2006–2013period,basedonthemethodologyusedtomodelinterestrateshocks.

Columns1–3refertotheparallelshiftsmethod,columns4–6tothepercentilesmethod,columns7–9tothehistoricalsimulationsandcolumns10–12totheMonteCarlo simulations.Foradescriptionoftheparallelshiftsandpercentilesmethods,seeSection3.ForadescriptionofthehistoricalandMonteCarlosimulationapproaches,see Section4.

Aindicatesbanksexposedtoincreasinginterestrates(asset-sensitivebanks)andLindicatesbanksexposedtodecreasinginterestrates(liability-sensitivebanks).Overall indicatestheoverallriskindicatorbasedonboththeon-andoff-balancesheetitems,Onindicatestheriskindicatorbasedontheonlyon-balancesheetitems,andOff indicatestheriskindicatorbasedontheonlyoff-balancesheetitems.Overallriskindicatorshavebeendecomposedintheon-andoff-balancesheetcomponentsfollowing Espositoetal.(2015).

natureoftheirriskexposure.Onaverage,fortheliability-sensitive banks,theon-andoff-balancesheetcomponentsshowapositive andanegativesign,respectively,whereas, thetwocomponents havethesamepositivesignfortheasset-sensitivebanks.Basedon theseresults,liability-sensitivebanksseemtousederivativesasa hedgingtooltooffseton-balancesheetinterestraterisk,whichis consistentwiththeoveralldecreasingtrendexperiencedby mar-ketinterestratesovertheinvestigationperiod.Ontheotherhand, asset-sensitivebanksseemtousetheiroff-balancesheetpositions toenhancethegainsassociatedwiththedecreasinginterest-rate trend.8

Thispreliminaryevidencedisregardsa substantial degreeof heterogeneity among intermediaries concerning their exposure toIRRBB. Therefore, in Table7 we splitour sample into three groups, according to the sign of their risk exposure over the entire2006–2013sampleperiod:i)banksthatwerealways asset-sensitive;ii)bankscontinuouslyexposed todecreasinginterest rates;iii)banksthatvariedthesignoftheirexposureatleastonce, alsotermed“otherbanks.”

Overall,Table7showsthatthevastmajorityofour130 sam-plebanksexperiencedachangeinthenatureoftheirinterestrate riskexposureatleastonceoverthetimehorizonweconsider.If

8_It_is_worth_underlining_that,_to_some_extent,_the_treatment_of_the_caps_and_ﬂoors

optionsembeddedintoﬂoating-rateloanscanhelpexplaintheevidence refer-ringtotheasset-sensitiveintermediaries,sinceitdeterminesgreatersensitivity toincreasinginterestrates.

IRRBBismeasuredthroughthehistoricalandMonteCarlo simula-tions,weobserveahighernumberofliability-sensitivebanks,i.e., 41fortheformerand20forthelatter,bothhigherthantheﬁgure observedfortheparallelshiftsandpercentilesmethods. Concern-ingthebreakdownoftheoverallriskexposureintotheon-and off-balancesheetcomponents,onaverage,theresultsreportedin Table7areconsistentwiththoseshowninTable6;theon-and off-balancesheetcomponentshavethesamepositivesignforthe asset-sensitivebanksandanoppositesignfortheintermediaries exposedtodecreasinginterestrates.

7. Backtestingresults

Table 8 shows theaverage resultsacrossthe wholesample period of our backtesting framework applied tothe regulatory andinternalmethodologies.PanelAreportstheaveragefrequency scoresbasedontheaccuracyfunction(8),whereasPanelsBand Cshowtheaverageseverityscoresinthecaseofunderestimation andoverestimationoftheactualexpostriskexposure,thatare cal-culatedthroughtheaccuracyfunctions(9)and(10),respectively. Finally,PanelDpresentstheaverageproximityscoresbasedon theaccuracyfunction(11).Theexanteriskexposureis alterna-tivelyassessedthroughtheparallelshiftsmethod(Columns2and 3),thepercentilesmethod(Columns4and5),thehistorical simula-tions(Columns6and7)andtheMonteCarlosimulations(Columns 8and9).Ineachpanel,ourresultsseparatelyrefertothewhole sampleandtothetwosub-groupsofasset-sensitiveand liability-sensitivebanks.Table8alsodistinguishesbetweenthescoresbased

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Table7

Samplebanks’averageriskindicators:breakdownbymethodologyandconstanttypeofinterestrateriskexposure.

N.ofbanks Overall On Off N.ofbanks Overall On Off N.ofbanks Overall On Off N.ofbanks Overall On Off

A* 6 13.22% 11.35% 1.87% 3 5.58% 5.47% 0.11% 2 5.97% 5.83% 0.14% 5 8.21% 7.00% 1.21%

L* 9 10.13% 10.83% −0.70% 9 11.05% 11.95% −0.90% 41 8.22% 9.48% −1.25% 20 6.18% 7.09% −0.91%

O 115 7.12% 6.78% 0.34% 118 5.77% 6.57% −0.80% 87 6.87% 7.61% −0.74% 105 5.62% 5.73% −0.10%

Thistableshowstheaverageriskindicatorsofoursamplebanksoverthe2006–2013period,basedonthemethodologyusedtomodelinterestrateshocks.

Columns2–4refertotheparallelshiftsmethod,columns6–8tothepercentilesmethod,columns10–12tothehistoricalsimulationsandcolumns14–16totheMonteCarlo simulations.Foradescriptionoftheparallelshiftsandpercentilesmethods,seeSection3.ForadescriptionofthehistoricalandMonteCarlosimulationapproaches,see Section4.

A*indicatesbanksexposedtoincreasinginterestrates(asset-sensitivebanks),overtheentiresampleperiod,L*indicatesbanksexposedtodecreasinginterestrates (liability-sensitivebanks)overtheentiresampleperiod,andOindicatesbankswhosenatureofinterestrateriskexposurechangedatleastonceoverthesampleperiod.

Overallindicatestheoverallriskindicatorbasedonboththeon-andoff-balancesheetitems,Onindicatestheriskindicatorbasedontheonlyon-balancesheetitems,andOff indicatestheriskindicatorbasedontheonlyoff-balancesheetitems.Overallriskindicatorshavebeendecomposedintheon-andoff-balancesheetcomponentsfollowing Espositoetal.(2015).

Table8

Backtestingresults.

PanelA:averagefrequencyscoresb

ParallelShifts Percentilesmethod Historicalsimulationsa _Monte_Carlo_simulationsa

Overall On Overall On Overall On Overall On

W 19.75 17.50 22.50 18.63 11.13 8.38 11.00 10.13

A 3.25 5.75 5.75 7.13 6.50 5.25 3.25 3.38

L 10.88 7.38 7.25 5.13 4.63 3.13 7.75 6.50

PanelB:averageseverityscoresintheunderestimationcasec

W 0.68% 0.76% 0.76% 0.83% 0.42% 0.50% 0.27% 0.23%

A 0.70% 0.89% 0.89% 0.82% 0.46% 0.38% 0.25% 0.29%

L 0.53% 0.59% 0.53% 0.64% 0.31% 0.34% 0.24% 0.19%

PanelC:averageseverityscoresintheoverestimationcased

W 6.60% 6.73% 4.72% 5.41% 5.22% 6.06% 3.67% 3.93%

A 9.73% 9.54% 3.82% 4.23% 4.78% 4.86% 5.47% 5.19%

L 4.34% 5.39% 4.81% 5.79% 5.34% 6.35% 3.06% 3.59%

PanelD:averageproximityscorese

W 6.02% 6.29% 4.62% 5.28% 5.17% 5.96% 3.55% 3.82%

A 9.08% 8.28% 4.07% 3.98% 4.65% 4.57% 5.28% 4.93%

L 4.19% 5.22% 4.74% 5.72% 5.27% 6.31% 3.01% 3.55%

Thistableshowstheaverageresultsoverthe2006–2013sampleperiodofourbacktestingprocedureappliedtothemethodologiesusedtomodelinterestrateshocks. Columns2–3refertotheparallelshiftsmethod,columns4–5tothepercentilesmethod,columns6–7tothehistoricalsimulationsandcolumns8–9totheMonteCarlo simulations.Foradescriptionoftheparallelshiftsandpercentilesmethods,seeSection3.ForadescriptionofthehistoricalandMonteCarlosimulationapproaches,see Section4.

Windicateswholesamplebanks,Aindicatesbanksexposedtoincreasinginterestrates(asset-sensitivebanks),andLindicatesbanksexposedtodecreasinginterestrates (liability-sensitivebanks).

Overallindicatestheoverallriskindicatorbasedonboththeon-andoff-balancesheetitems,Onindicatestheriskindicatorbasedontheonlyon-balancesheetitems,andOff indicatestheriskindicatorbasedontheonlyoff-balancesheetitems.Overallriskindicatorshavebeendecomposedintheon-andoff-balancesheetcomponentsfollowing Espositoetal.(2015).

a_The_score_is_calculated_by_comparing_the_99th_percentile_of_the_ex_ante_risk_indicator_distribution_with_the_ex_post_risk_indicator. b _Scores_are_calculated_by_applying_the_score_function₍₅₎_and_the_accuracy_function_(8).

c _Scores_are_calculated_by_applying_the_score_function₍₅₎_and_the_accuracy_function_(10). d _Scores_are_calculated_by_applying_the_score_function₍₅₎_and_the_accuracy_function_(11). e_Scores_are_calculated_by_applying_the_score_function₍₅₎_and_the_accuracy_function_(12).

onoverallriskexposureandthoseassociatedwithriskexposure basedononlytheon-balancesheetcomponents.Inthisway,we

cancapturetheeffectofderivativesonbankriskexposurewithin ourbacktestingframework.

Does Prudential Regulation Contribute to Effective Measurement and Management of Interest Rate Risk? Evidence from Italian Banks