BanksanalysisoffinancialdataAndreasP.Nawroth,JoachimPeinkeInstitutfu¨rPhysik,Carl-von-OssietzkyUniversita¨tOldenburg,D-26111Oldenburg,GermanyAvailableonline30MarchAbstractAstochasticanalysisoffinancialdataispresented.Inparticularweinvestigatehowthestatisticsoflogreturnschangewithdifferenttimedelayst.Thescale-dependentbehaviouroffinancialdatacanbedividedintotworegions.Thefirsttimerange,thesmall-timescaleregion(intherangeofseconds)seemstobecharacterisedbyuniversalfeatures.Thesecondtimerange,themedium-timescalerangefromseveralminutesupwardscanbecharacterisedbyacascadeprocess,whichisgivenbyastochasticMarkovprocessinthescaleτ.AcorrespondingFokker–Planckequationcanbeextractedfromgivendataandprovidesanon-equilibriumthermodynamicaldescriptionofthecomplexityoffinancialdata.Keywords:Banks;Financialmarkets;Stochasticprocesses;Fokker–Planckequation1.IntroductionFinancialstatementsforbankspresentadifferentanalyticalproblemthanmanufacturingandservicecompanies.Asaresult,analysisofabank’sfinancialstatementsrequiresadistinctapproachthatrecognizesabank’ssomewhatuniquerisks.Bankstakedepositsfromsavers,payinginterestonsomeoftheseaccounts.Theypassthesefundsontoborrowers,receivinginterestontheloans.Theirprofitsarederivedfromthespreadbetweentheratetheypayforfundsandtheratetheyreceivefromborrowers.Thisabilitytopooldepositsfrommanysourcesthatcanbelenttomanydifferentborrowerscreatestheflowoffundsinherentinthebankingsystem.Bymanagingthisflowoffunds,banksgenerateprofits,actingastheintermediaryofinterestpaidandinterestreceivedandtakingontherisksofofferingcredit.2.Small-scaleanalysisBankingisahighlyleveragedbusinessrequiringregulatorstodictateminimalcapitallevelstohelpensurethesolvencyofeachbankandthebankingsystem.IntheUS,abank’sprimaryregulatorcouldbetheFederalReserveBoard,theOfficeoftheComptrolleroftheCurrency,theOfficeofThriftSupervisionoranyoneof50stateregulatorybodies,dependingonthecharterofthebank.WithintheFederalReserveBoard,thereare12districtswith12differentregulatorystaffinggroups.Theseregulatorsfocusoncompliancewithcertainrequirements,restrictionsandguidelines,aimingtoupholdthesoundnessandintegrityofthebankingsystem.Asoneofthemosthighlyregulatedbankingindustriesintheworld,investorshavesomelevelofassuranceinthesoundnessofthebankingsystem.Asaresult,investorscanfocusmostoftheireffortsonhowabankwillperformindifferenteconomicenvironments.Belowisasampleincomestatementandbalancesheetforalargebank.Thefirstthingtonoticeisthatthelineitemsinthestatementsarenotthesameasyourtypicalmanufacturingorservicefirm.Instead,thereareentriesthatrepresentinterestearnedorexpensedaswellasdepositsandloans.Asfinancialintermediaries,banksassumetwoprimarytypesofriskastheymanagetheflowofmoneythroughtheirbusiness.Interestrateriskisthemanagementofthespreadbetweeninterestpaidondepositsandreceivedonloansovertime.Creditriskisthelikelihoodthataborrowerwilldefaultonitsloanorlease,causingthebanktoloseanypotentialinterestearnedaswellastheprincipalthatwasloanedtotheborrower.Asinvestors,thesearetheprimaryelementsthatneedtobeunderstoodwhenanalyzingabank’sfinancialstatement.3.MediumscaleanalysisTheprimarybusinessofabankismanagingthespreadbetweendeposits.Basicallywhentheinterestthatabankearnsfromloansisgreaterthantheinterestitmustpayondeposits,itgeneratesapositiveinterestspreadornetinterestincome.Thesizeofthisspreadisamajordeterminantoftheprofitgeneratedbyabank.Thisinterestrateriskisprimarilydeterminedbytheshapeoftheyieldcurve.Asaresult,netinterestincomewillvary,duetodifferencesinthetimingofaccrualchangesandchangingrateandyieldcurverelationships.Changesinthegenerallevelofmarketinterestratesalsomaycausechangesinthevolumeandmixofabank’sbalancesheetproducts.Forexample,wheneconomicactivitycontinuestoexpandwhileinterestratesarerising,commercialloandemandmayincreasewhileresidentialmortgageloangrowthandprepaymentsslow.Banks,inthenormalcourseofbusiness,assumefinancialriskbymakingloansatinterestratesthatdifferfromratespaidondeposits.Depositsoftenhaveshortermaturitiesthanloans.Theresultisabalancesheetmismatchbetweenassets(loans)andliabilities(deposits).Anupwardslopingyieldcurveisfavorabletoabankasthebulkofitsdepositsareshorttermandtheirloansarelongerterm.Thismismatchofmaturitiesgeneratesthenetinterestrevenuebanksenjoy.Whentheyieldcurveflattens,thismismatchcausesnetinterestrevenuetodiminish.4.EveninabusinessusingSixSigma?methodology.an“optimal”levelofworkingcapitalmanagementneedstobeidentified.Thetablebelowtiestogetherthebank’sbalancesheetwiththeincomestatementanddisplaystheyieldgeneratedfromearningassetsandinterestbearingdeposits.Mostbanksprovidethistypeoftableintheirannualreports.Thefollowingtablerepresentsthesamebankasinthepreviousexamples:Firstofall,thebalancesheetisanaveragebalanceforthelineitem,ratherthanthebalanceattheendoftheperiod.Averagebalancesprovideabetteranalyticalframeworktohelpunderstandthebank’sfinancialperformance.Noticethatforeachaveragebalanceitemthereisacorrespondinginterest-relatedincome,orexpenseitem,andtheaverageyieldforthetimeperiod.Italsodemonstratestheimpactaflatteningyieldcurvecanhaveonabank’snetinterestincome.Thebestplacetostartiswiththenetinterestincomelineitem.Thebankexperiencedlowernetinterestincomeeventhoughithadgrownaveragebalances.Tohelpunderstandhowthisoccurred,lookattheyieldachievedontotalearningassets.Forthecurrentperiod,itisactuallyhigherthanthepriorperiod.Thenexaminetheyieldontheinterest-bearingassets.Itissubstantiallyhigherinthecurrentperiod,causinghigherinterest-generatingexpenses.Thisdiscrepancyintheperformanceofthebankisduetotheflatteningoftheyieldcurve.Astheyieldcurveflattens,theinterestratethebankpaysonshortertermdepositstendstoincreasefasterthantheratesitcanearnfromitsloans.Thiscausesthenetinterestincomelinetonarrow,asshownabove.Onewaybankstryoovercometheimpactoftheflatteningoftheyieldcurveistoincreasethefeestheychargeforservices.Asthesefeesbecomealargerportionofthebank’sincome,itbecomeslessdependentonnetinterestincometodriveearnings.Changesinthegenerallevelofinterestratesmayaffectthevolumeofcertaintypesofbankingactivitiesthatgeneratefee-relatedincome.Forexample,thevolumeofresidentialmortgageloanoriginationstypicallydeclinesasinterestratesrise,resultinginloweroriginatingfees.Incontrast,mortgageservicingpoolsoftenfaceslowerprepaymentswhenratesarerising,sinceborrowersarelesslikelytorefinance.Adaresult,feeincomeandassociatedeconomicvaluearisingfrommortgageservicing-relatedbusinessesmayincreaseorremainstableinperiodsofmoderatelyrisinginterestrates.Whenanalyzingabankyoushouldalsoconsiderhowinterestrateriskmayactjointlywithotherrisksfacingthebank.Forexample,inarisingrateenvironment,loancustomersmaynotbeabletomeetinterestpaymentsbecauseoftheincreaseinthesizeofthepaymentorreductioninearnings.Theresultwillbeahigherlevelofproblemloans.Anincreaseininterestrateisexposesabankwithasignificantconcentrationinadjustablerateloanstocreditrisk.Forabankthatispredominatelyfundedwithshort-termliabilities,ariseinratesmaydecreasenetinterestincomeatthesametimecreditqualityproblemsareontheincrease.5.RelatedLiteratureTheimportanceofworkingcapitalmanagementisnotnewtothefinanceliterature.Overtwentyyearsago.LargayandStickney(1980)reportedthatthethen-recentbankruptcyofW.T.Grant.anationwidechainofdepartmentstores.shouldhavebeenanticipatedbecausethecorporationhadbeenrunningadeficitcashflowfromoperationsforeightofthelasttenyearsofitscorporatelife.AspartofastudyoftheFortune500’sfinancialmanagementpractices.GilbertandReichert(1995)findthataccountsreceivablemanagementmodelsareusedin59percentofthesefirmstoimproveworkingcapitalprojects.whileinventorymanagementmodelswereusedin60percentofthecompanies.Morerecently.Farragher.KleimanandSahu(1999)findthat55percentoffirmsintheS&PIndustrialindexcompletesomeformofacashflowassessment.butdidnotpresentinsightsregardingaccountsreceivableandinventorymanagement.orthevariationsofanycurrentassetaccountsorliabilityaccountsacrossindustries.Thus.mixedevidenceexistsconcerningtheuseofworkingcapitalmanagementtechniques.Theoreticaldeterminationofoptimaltradecreditlimitsarethesubjectofmanyarticlesovertheyears(e.g..Schwartz1974;Scherr1996).withscantattentionpaidtoactualaccountsreceivablemanagement.Acrossalimitedsample.WeinraubandVisscher(1998)observeatendencyoffirmswithlowlevelsofcurrentratiostoalsohavelowlevelsofcurrentliabilities.Simultaneouslyinvestigatingaccountsreceivableandpayableissues.Hill.Sartoris.andFerguson(1984)finddifferencesinthewaypaymentdatesaredefined.Payeesdefinethedateofpaymentasthedatepaymentisreceived.whilepayorsviewpaymentasthepostmarkdate.AdditionalWCMinsightacrossfirms.industries.andtimecanaddtothisbodyofresearch.ManessandZietlow(.51.496)presentstwomodelsofvaluecreationthatincorporateeffectiveshort-termfinancialmanagementactivities.However.thesemodelsaregenericmodelsanddonotconsideruniquefirmorindustryinfluences.ManessandZietlowdiscussindustryinfluencesinashortparagraphthatincludestheobservationthat.“Anindustryacompanyislocatedinmayhavemoreinfluenceonthatcompany’sfortunesthanoverallGNP”(.507).Infact.acarefulreviewofthis627textbookfindsonlysporadicinformationonactualfirmlevelsofWCMdimensions.virtuallynothingonindustryfactorsexceptforsomeboxeditemswithtitlessuchas.“ShouldaRetailerOfferanIn-HouseCreditCard”(128)andnothingonWCMstabilityovertime.Thisresearchwillattempttofillthisvoidbyinvestigatingpatternsrelatedtoworkingcapitalmeasureswithinindustriesandillustratedifferencesbetweenindustriesacrosstime.AnextensivesurveyoflibraryandInternetresourcesprovidedveryfewrecentreportsaboutworkingcapitalmanagement.ThemostrelevantsetofarticleswasWeiselandBradley’s()articleoncashflowmanagementandoneofinventorycontrolasaresultofeffectivesupplychainmanagementbyHadley().6.ResearchMethodTheCFORankingsThefirstannualCFOWorkingCapitalSurvey.ajointprojectwithRELConsultancyGroup.waspublishedintheJune1997issueofCFO(MintzandLezere1997).RELisaLondon.England-basedmanagementconsultingfirmspecializinginworkingcapitalissuesforitsgloballistofclients.Theoriginalsurveyreportsseveralworkingcapitalbenchmarksforpubliccompaniesusingdatafor1996.Eachcompanyisrankedagainstitspeersandalsoagainsttheentirefieldof1.000companies.RELcontinuestoupdatetheoriginalinformationonanannualbasis.RELusesthe“cashflowfromoperations”valuelocatedonfirmcashflowstatementstoestimatecashconversionefficiency(CCE).Thisvalueindicateshowwellacompanytransformsrevenuesintocashflow.A“daysofworkingcapital”(DWC)valueisbasedonthedollaramountineachoftheaggregate.equally-weightedreceivables.inventory.andpayablesaccounts.The“daysofworkingcapital”(DNC)representsthetimeperiodbetweenpurchaseofinventoryonacccountfromvendoruntilthesaletothecustomer.thecollectionofthereceivables.andpaymentreceipt.Thus.itreflectsthecompany’sabilitytofinanceitscoreoperationswithvendorcredit.AdetailedinvestigationofWCMispossiblebecauseCFOalsoprovidesfirmandindustryvaluesfordayssalesoutstanding(A/R).inventoryturnover.anddayspayablesoutstanding(A/P).7.ResearchFindingsAverageandAnnualWorkingCapitalManagementPerformanceWorkingcapitalmanagementcomponentdefinitionsandaveragevaluesfortheentire1996–period.Acrossthenearly1.000firmsinthesurvey.cashflowfromoperations.definedascashflowfromoperationsdividedbysalesandreferredtoas“cashconversionefficiency”(CCE).averages9.0percent.Incorporatinga95percentconfidenceinterval.CCErangesfrom5.6percentto12.4percent.Thedaysworkingcapital(DWC).definedasthesumofreceivablesandinventorieslesspayablesdividedbydailysales.averages51.8daysandisverysimilartothedaysthatsalesareoutstanding(50.6).becausetheinventoryturnoverrate(onceevery32.0days)issimilartothenumberofdaysthatpayablesareoutstanding(32.4days).Inallinstances.thestandarddeviationisrelativelysmall.suggestingthattheseworkingcapitalmanagementvariablesareconsistentacrossCFOreports.8.IndustryRankingsonOverallWorkingCapitalManagementPerformanceCFOmagazineprovidesanoverallworkingcapitalrankingforfirmsinitssurvey.usingthefollowingequation:Industry-baseddifferencesinoverallworkingcapitalmanagementarepresentedforthetwenty-sixindustriesthathadatleasteightcompaniesincludedintherankingseachyear.Inthetypicalyear.CFOmagazineranks970companiesduringthisperiod.IndustriesarelistedinorderofthemeanoverallCFOrankingofworkingcapitalperformance.Sincethebestaveragerankingpossibleforaneight-companyindustryis4.5(thisassumesthattheeightcompaniesarerankedonethrougheightfortheentiresurvey).itisquiteobviousthatallfirmsinthepetroleumindustrymusthavebeenreceivingveryhighoverallworkingcapitalmanagementrankings.Infact.thepetroleumindustryisrankedfirstinCCEandthirdinDWC(asillustratedinTable5anddiscussedlaterinthispaper).Furthermore.thepetroleumindustryhadtheloweststandarddeviationofworkingcapitalrankingsandrangeofworkingcapitalrankings.Theonlyotherindustrywithameanoverallrankinglessthan100wastheElectric&GasUtilityindustry.whichrankedsecondinCCEandfourthinDWC.ThetwoindustrieswiththeworstworkingcapitalrankingswereTextilesandApparel.Textilesranktwenty-secondinCCEandtwenty-sixthinDWC.Theapparelindustryrankstwenty-thirdandtwenty-fourthinthetwoworkingcapitalmeasures9.ResultsforBayerdataTheKramers–MoyalcoefficientswerecalculatedaccordingtoEqs.(5)and(6).Thetimescalewasdividedintohalf-openintervalsassumingthattheKramers–Moyalcoefficientsareconstantwithrespecttothetimescaleτineachofthesesubintervalsofthetimescale.Thesmallesttimescaleconsideredwas240sandalllargerscaleswerechosensuchthatτi＝0.9*τi+1.TheKramers–Moyalcoefficientsthemselveswereparameterisedinthefollowingform:Thisresultshowsthattherichandcomplexstructureoffinancialdata,expressedbymulti-scalestatistics,canbepinneddowntocoefficientswitharelativelysimplefunctionalform.10.DiscussionCreditriskismostsimplydefinedasthepotentialthatabankborrowerorcounter-partywillfailtomeetitsobligationsinaccordancewithagreedterms.Whenthishappens,thebankwillexperiencealossofsomeorallofthecredititprovidetoitscustomer.Toabsorbtheselosses,banksmaintainanallowanceforloanandleaselosses.Inessence,thisallowancecanbeviewedasapoolofcapitalspecificallysetasidetoabsorbestimatedloanlosses.Thisallowanceshouldbemaintainedatalevelthatisadequatetoabsorbtheestimatedamountofprobablelossesintheinstitution’sloanportfolio.Acarefulreviewofabank’sfinancialstatementscanhighlightthekeyfactorsthatshouldbeconsideredbecomesbeforemakingatradingorinvestingdecision.Investorsneedtohaveagoodunderstandingofthebusinesscycleandtheyieldcurve-bothhaveamajorimpactontheeconomicperformanceofbanks.Interestrateriskandcreditriskaretheprimaryfactorstoconsiderasabank’sfinancialperformancefollowstheyieldcurve.Whenitflattensorbecomesinvertedabank’snetinterestrevenueisputundergreaterpressure.Whentheyieldcurvereturnstoamoretraditionalshape,abank’snetinterestrevenueusuallyimproves.Creditriskcanbethelargestcontributortothenegativeperformanceofabank,evencausingittolosemoney.Inaddition,managementofcreditriskisasubjectiveprocessthatcanbemanipulatedintheshortterm.Investorsinbanksneedtobeawareofthesefactorsbeforetheycommittheircapital.銀行金融數據分析AndreasP.Nawroth,JoachimPeinke物理研究所，Carl-von-Ossietzky奧爾登堡大學，D-26111奧爾登伯格，德國摘要財務數據隨機分析已經被提出，尤其是我們探討怎樣統計在不一樣時間τ統計返回改變。財務數據時間規模依賴行為可分為兩個區域：第一個時間范圍是被描述為普遍特征小時間區域（范圍秒）。第二個時間范圍是增加了幾分鐘能夠被描述為隨機馬爾可夫規模級聯過程中期時間范圍。對應Fokker-Planck方程能夠從特定數據提取，并提供了一個非平衡熱力學描述復雜財務數據。關鍵詞：銀行；金融市場；隨機過程；Fokker-Planck方程1導言銀行財務報表分析不一樣于制造業和服務業企業。所以，一家銀行財務報表分析，需要用一個獨特方法來認識一家銀行有哪些獨特風險銀行需要對儲戶存款帳戶支付部分利息。他們經過對這些基金借款，接收貸款利息。他們利潤都起源于他們之間資金利率和借款利率。這能夠從許多不一樣借款借給許多起源能力，集中存款創造了資金在銀行體系固有流量。經過管理這種資金流動，銀行產生利潤，充當了中間人支付利息和利息接收和向客戶提供以信貸風險2小規模分析銀行業是一個高度杠桿業務，需要監管部門來支配最低資本水平，以確保各銀行和銀行系統償付能力。在美國，銀行主要監管機構可能是美國聯邦貯備委員會，對美國貨幣監理署，互助儲蓄銀行監管辦事處或任何一個50個州監管機構，依照銀行章程。在美國聯邦貯備委員會，有12個與12個不一樣管理人員群體地域。這些監管機構重視一定要求，限制及指導，意在堅持健全銀行系統完整性。作為世界上最嚴格監管銀行業產業之一，投資者有一定確保，保持在銀行體系穩健水平。所以，投資者能夠集中精力確定銀行將怎樣在不一樣經濟環境中推行自己大部分精力。下面是一個示例利潤表和一家大型銀行資產負債表。首先要注意是在報表行項目是不一樣經典制造或服務企業。相反，代表作品有利息或開支存款和貸款。

因為金融中介機構是銀行負擔風險兩個主要類型之一，因為他們管理資金經過其業務流程。利率風險是支付利息之間存款及貸款收到伴隨時間推移傳輸管理。信用風險是借款人可能性將拖欠貸款或租賃，造成銀行失去任何潛在利息是被租借給借款本金。作為投資者，這些都是需要了解在分析銀行財務報表主要原因。3中等規模分析某家銀行主要業務是管理存款之間傳輸。基本上當利息，銀行從貸款利息收入比它必須支付存款更大，它會產生一個主動息差或凈利息收入。這種傳輸大小是由銀行所產生利潤主要原因。這一利率風險主要取決于產量曲線形狀。所以，凈利息收入會有所不一樣，因為權責發生制改變和改變率和收益曲線關系時差。在市場利率水平改變也可能會造成在數量和銀行資產負債表產品組合改變。比如，當經濟活動繼續擴張，而利率上升，商業貸款需求可能增加，但住宅按揭貸款增加放緩銀行在正常業務過程中，負擔起在利率決議，從不一樣存款利率支付貸款金融風險。存款往往比貸款期限較短。其結果是不一樣資產（貸款）和負債（存款）資產負債表不匹配。一個向上傾斜收益率曲線，有利于銀行存款作為其大部分是短期和長久貸款。這種期限不匹配產生凈利息收入銀行享受。當收益曲線變得平坦，這不匹配造成凈利息收益降低。4.即使在一個業務中使用.六西格瑪方法論“最好”營運資金管理需要被確認下面表格聯絡在一起世行與損益表和顯示來自生息資產和計息存款產生收益率資產負債表。大部分銀行在其年度匯報中提供這種類型表。下表表示為在前面例子相同銀行：首先，資產負債表是一個行業項目平均余額，而不是在期末余額。平均余額提供一個愈加好分析框架，幫助了解銀行財務表現。注意，對于每個項目標平均余額有對應利益相關收入或支出項目，并為時間段內平均產量。這也顯示出一個扁平收益率曲線影響可能對銀行凈利息收入。最好地方是與凈利息收入線項目。經驗豐富銀行凈利息收入降低，即使它已發展平均余額。為了幫助了解這是怎樣發生，看時候總重視資產取得收益。對于現在時期，它實際上是比前期高。然后檢驗上生息資產收益率。這是在當期大幅高利率造成產生費用更高。這家銀行表現差異是因為收益曲線平坦。因為收益率曲線變平，利率銀行在短期存款支付往往增加速度比它貸款能夠賺快。這將造成該行凈利息收入縮小，如上所表示。?銀行嘗試一個方法克服了收益曲線平坦影響是增加費用，他們服務費。因為這些費用成為銀行收入較大部分，它變得越來越依賴于凈利息收入來帶動盈利在通常利率水平改變可能會影響到一些類型銀行活動產生費用關于收入額。比如，住宅按揭貸款發放量下降，通常伴隨利率上升，從而降低費用造成起源。與此相反，往往面臨抵押服務池慢預付款當利率在上升，因為借款人再融資可能性較小。廣告結果，收費收入和相關經濟價值抵押貸款服務關于業務可能會增加或保持適度穩定利率上升期間產生當你分析一個銀行也應考慮怎樣采取行動利率風險可能面臨風險與其余銀行聯合。比如，在一個上升利率環境下，貸款客戶可能無法滿足，因為在付款或收入降低大小增加利息支出。其結果將是一個問題貸款水平。在加息是一個公開可調整利率貸款信貸風險高度集中銀行。對于一個正在為主與短期負債資銀行，在利率上升可能會降低凈利息收入同時信貸質量問題在增加。5.相關文件營運資金管理主要性在于它并不是新金融文學。20多年前，斯蒂克尼（1980）匯報說。當初小波格蘭特全國連鎖百貨企業相繼破產，應該是因為企業經營了最終里經營里有8年經營赤字，這早就作為一個世界500強財務管理實踐研究一部分。吉爾伯特和銳徹(1995)發覺應收賬款管理模式在使用后，有百分之五十九企業提升營運資金項目，而庫存管理模型應用于百分之六十企業。最近，法瑞芬.克萊曼和薩胡（1999年）發覺百分之五十五企業中，標準普爾工業指數完成是某種形式現金流量評定，但并未提出關于應收賬款和存貨管理看法，或任何流動資產改變